From 5cc35d9ed9b3d58c8f34e9a7287765d82edde0b4 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 19 Apr 2022 15:55:04 +0200 Subject: [PATCH 01/56] rough implementation of semi Markov process implementation @BASF --- src/MultiStateSystems.jl | 3 +- src/core/types.jl | 1 + src/form/semi_markov_process.jl | 76 ++++++++++++++++++++++ test/elements/optical_monitoring_system.jl | 36 ++++++++++ test/elements/semi_analytical_example.jl | 34 ++++++++++ 5 files changed, 149 insertions(+), 1 deletion(-) create mode 100644 src/form/semi_markov_process.jl create mode 100644 test/elements/optical_monitoring_system.jl create mode 100644 test/elements/semi_analytical_example.jl diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index dd2bfff..c858674 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -36,6 +36,7 @@ const BASE_DIR = dirname(@__DIR__) include("core/types.jl") include("form/markov_process.jl") +include("form/semi_markov_process.jl") include("form/steady_state_process.jl") include("io/distributions.jl") @@ -50,7 +51,7 @@ include("prob/universal_generating_operator.jl") # export export BASE_DIR -export SteadyStateProcess, MarkovProcess +export SteadyStateProcess, MarkovProcess, SemiMarkovProcess export Cosine, 𝑪, Dirac, 𝑫, Exponential, 𝑬, Gamma, 𝑮, Uniform, 𝑼, Weibull, 𝑾 export Network, add_source!, add_sources!, add_user!, add_users!, add_component!, add_bidirectional_component!, add_components!, diff --git a/src/core/types.jl b/src/core/types.jl index 7d80f4e..f389be4 100644 --- a/src/core/types.jl +++ b/src/core/types.jl @@ -14,6 +14,7 @@ abstract type AbstractSTD{T} <: _LG.AbstractGraph{T} end abstract type AbstractNetwork{T} <: _LG.AbstractGraph{T} end abstract type AbstractStochasticProcess end abstract type AbstractMarkovProcess <: AbstractStochasticProcess end +abstract type AbstractSemiMarkovProcess <: AbstractStochasticProcess end # union types UIE = Union{Int,_LG.AbstractEdge} diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl new file mode 100644 index 0000000..bbac64a --- /dev/null +++ b/src/form/semi_markov_process.jl @@ -0,0 +1,76 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + + +# abstract types +mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end + +# properties +const semi_markov_process_props = [:renewal, :dynamic] + +# stochastic process +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) + t = zero(tsim):dt:tsim + Nt = length(t) + + # calculate H + A = zeros(ns(std) * Nt) + + for (ni,nt) in enumerate(t) + for tr in transitions(std) + id = ns(std) * (ni-1) + _LG.dst(tr) + # met wat moet hier vermeningvuldigd worden? + # - pure pdf + # - integral van de pdf over dt + # - cdf + A[id] = get_prop(std, _LG.src(tr), :init) * + pdf(get_prop(std, tr, :distr),0.0,nt) + end end + + U = zeros(ns(std) * Nt, ns(std) * Nt) + + for (ni,nt) in enumerate(t) + w = weights(ni) + # hier kan code optimalisatie gebeuren gegeven dat φ <<< t + φ = 0.0:dt:nt + for (nj,nφ) in enumerate(φ) + Ψ = zeros(ns(std), ns(std)) + for tr in transitions(std) + Ψ[_LG.dst(tr),_LG.src(tr)] = pdf(get_prop(std, tr, :distr),nφ,nt) + end + # ranges for time and sojourn time in U + rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) + rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) + if ni == nj + U[rT,rΦ] = Matrix(1.0I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ + else + U[rT,rΦ] = -dt .* w[nj] .* Ψ + end + end end + + H = U \ A + + Φ = zeros(Nt, ns(std)) + for st in states(std) + for (ni,nt) in t + w = weights(ni) + # hier kan code optimalisatie gebeuren gegeven dat φ <<< t + φ = 0.0:dt:nt + Φ[ni,st] += get_prop(std,st,:init) * ccdf(std,st,0.0,nt) + Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (ni-1) + st] * ccdf(std,st,nφ,nt) for (nj,nφ) in enumerate(φ)) + end end + + set_prop!(std, :cls, cls) + set_prop!(std, :time, t) + set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) +end + +# check whether sum of ccdf could be suffient +ccdf(std::AbstractSTD, ns::Int, φ::Real, t::Real) = + 1.0 - sum(cdf(get_prop(std,_LG.edge(ns,nx),:distr), φ, t) + for nx in _LG.outneighbors(G,ns)) \ No newline at end of file diff --git a/test/elements/optical_monitoring_system.jl b/test/elements/optical_monitoring_system.jl new file mode 100644 index 0000000..4e93179 --- /dev/null +++ b/test/elements/optical_monitoring_system.jl @@ -0,0 +1,36 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ +""" +Example considering a multi-state Markov model for a optical monitoring system +taken from: + +> A Multi-State Markov Model for a Short-Term Reliability Analysis of a Power + Generating Unit by A. Lisnianski, D. Elmakias, and H. Ben Haim (2012) + +""" + +# load pkgs +using Unitful +using MultiStateSystems + + + +# initialize the state-transition diagram +std = STD() + +# add the states to the std +add_states!(std, name = ["available", "unavailable"], + power = [1.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdᵃᵈ, rate = [0.0u"1/hr" 12.8928e-6u"1/hr" + 0.0833u"1/hr" 0.0u"1/hr"]) + +# return the std +return stdᵃᵈ \ No newline at end of file diff --git a/test/elements/semi_analytical_example.jl b/test/elements/semi_analytical_example.jl new file mode 100644 index 0000000..2c45b76 --- /dev/null +++ b/test/elements/semi_analytical_example.jl @@ -0,0 +1,34 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ +""" +Example considering a semi-analytical example of a multi-state semi-Markov model +taken from: + +> Mathematical formulation and numerical treatment based on transition frequency +densities and quadrature methods for non-homogeneous semi-Markov processes by +M. das Chagas Moura, and E. L. Droguett (2009) +""" + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram +std = STD() + +# add the states to the std +add_states!(std, name = ["operational", "non-critical degradation", "failed"], + init = [1.0, 0.0, 0.0]) + +# add the transitions to the std +add_transitions!(std, states = [(1,2),(2,3)], + distr = [Exponential(1000.0u"hr"), + Weibull(250.0u"hr",1.5)]) + +# return the std +return std \ No newline at end of file From 2ff856ddf2c0e848db00fcfbb012000077e263e5 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Wed, 20 Apr 2022 10:24:30 +0200 Subject: [PATCH 02/56] Exponential and Weibull distribution - added support for weights which are functions --- src/MultiStateSystems.jl | 3 +- src/core/types.jl | 2 +- src/io/distributions.jl | 420 ++++++++++----------------------------- 3 files changed, 107 insertions(+), 318 deletions(-) diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index c858674..6d643a4 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -52,7 +52,8 @@ include("prob/universal_generating_operator.jl") # export export BASE_DIR export SteadyStateProcess, MarkovProcess, SemiMarkovProcess -export Cosine, 𝑪, Dirac, 𝑫, Exponential, 𝑬, Gamma, 𝑮, Uniform, 𝑼, Weibull, 𝑾 +export Exponential, 𝑬, Weibull, 𝑾 +# export Cosine, 𝑪, Dirac, 𝑫, Exponential, 𝑬, Gamma, 𝑮, Uniform, 𝑼, Weibull, 𝑾 export Network, add_source!, add_sources!, add_user!, add_users!, add_component!, add_bidirectional_component!, add_components!, add_bidirectional_components! diff --git a/src/core/types.jl b/src/core/types.jl index f389be4..a533e14 100644 --- a/src/core/types.jl +++ b/src/core/types.jl @@ -9,7 +9,7 @@ # abstract types abstract type AbstractUGF end abstract type AbstractInfo end -abstract type AbstractDistribution{N,R} end +abstract type AbstractDistribution{X,Y,Z} end abstract type AbstractSTD{T} <: _LG.AbstractGraph{T} end abstract type AbstractNetwork{T} <: _LG.AbstractGraph{T} end abstract type AbstractStochasticProcess end diff --git a/src/io/distributions.jl b/src/io/distributions.jl index 5e800a6..8d6d40d 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -6,6 +6,10 @@ # See http://github.com/timmyfaraday/MultiStateSystems.jl # ################################################################################ +## eval +eval(ω::Number,t::Number) = ω +eval(ω::Function,t::Number) = ω(t) |> u"s/s" + ## quantile quantile_bisect(dst::AbstractDistribution, p::Real) = quantile_bisect(dst, p, minimum(dst), maximum(dst), 1.0e-12) @@ -24,9 +28,9 @@ function quantile_bisect(dst::AbstractDistribution, p::Real, lx::Real, rx::Real, return (lx + rx) / 2 end -## exponential +## exponential """ - Exponential + MultiStateSystems.Exponential The [*exponential distribution*](http://en.wikipedia.org/wiki/Exponential_distribution) with scale parameter `θ` and an optional weight `ω` has a probability density @@ -39,65 +43,77 @@ f(x; θ, ω) = \begin{cases} \end{cases} ``` """ -# struct -struct Exponential{N<:Number, R<:Real} <: AbstractDistribution{N,R} - θ::N # scale - ω::R # weight: 0.0 < ω <= 1.0 +# abstract type +abstract type AbstractExponential{X,Y,Z} <: AbstractDistribution{X,Y,Z} end + +# struct - θ::Number, ω::Real +struct ExponentialNR{X<:Number, Y<:Real, Z<:Function} <: AbstractExponential{X,Y,Z} + θ::X # scale + ω::Y # weight: 0.0 < ω <= 1.0 end +# constructors +Exponential() = ExponentialNR{Number,Real,Function}(1.0, 1.0) +Exponential(θ::Number) = ExponentialNR{Number,Real,Function}(θ, 1.0) +Exponential(θ::Number, ω::Real) = ExponentialNR{Number,Real,Function}(θ, ω) +# struct - θ::Number, ω::Function +struct ExponentialNF{X<:Number, Y<:Real, Z<:Function} <: AbstractExponential{X,Y,Z} + θ::X # scale + ω::Z # weight: 0.0 < ω(t) <= 1.0 +end # constructors -Exponential() = Exponential(1.0, 1.0) -Exponential(θ::Number) = Exponential(θ, 1.0) +Exponential(θ::Number, ω::Function) = ExponentialNF{Number,Real,Function}(θ, ω) # shortened constructors 𝑬() = Exponential() 𝑬(θ::Number) = Exponential(θ) 𝑬(θ::Number, ω::Real) = Exponential(θ, ω) +𝑬(θ::Number, ω::Function) = Exponential(θ, ω) -# functions -scale(dst::Exponential) = dst.θ -weight(dst::Exponential) = dst.ω -params(dst::Exponential) = (dst.θ, dst.ω) +# general functions +scale(dst::AbstractExponential) = dst.θ +weight(dst::AbstractExponential) = dst.ω +params(dst::AbstractExponential) = (dst.θ, dst.ω) -rate(dst::Exponential) = 1.0 / dst.θ +rate(dst::AbstractExponential) = 1.0 / dst.θ -minimum(dst::Exponential) = zero(dst.θ) -maximum(dst::Exponential) = (Inf)unit(dst.θ) +minimum(dst::AbstractExponential) = zero(dst.θ) +maximum(dst::AbstractExponential) = (Inf)unit(dst.θ) -xv(dst::Exponential, z::Real) = z * dst.θ -quantile(dst::Exponential, p::Real) = -xv(dst, log1p(-p)) -cquantile(dst::Exponential, p::Real) = -xv(dst, log(p)) -sojourn(dst::Exponential,dφ::Number,tol::Real) = - 0.0unit(dφ):dφ:cquantile(dst,tol) +xv(dst::AbstractExponential, z::Real) = z * dst.θ +quantile(dst::AbstractExponential, p::Real) = -xv(dst, log1p(-p)) +cquantile(dst::AbstractExponential, p::Real) = -xv(dst, log(p)) +sojourn(dst::AbstractExponential,dφ::Number,tol::Real) = + zero(dφ):dφ:cquantile(dst,tol) -function pdf(dst::Exponential, x::Number) +function pdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) θ, ω = params(dst) - dimension(θ)==dimension(x) || return false - if x >= (0)unit(θ) - y = uconvert(unit(θ),x) - ω * (1/θ) * exp(-y/θ) + dimension(θ)==dimension(φ)==dimension(t) || return false + if φ >= zero(θ) + y = uconvert(unit(θ),φ) + eval(ω,t) * (1/θ) * exp(-y/θ) else - zero(R)unit(θ) + zero(1/θ) end end -function cdf(dst::Exponential, x::Number) +function cdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) θ, ω = params(dst) - dimension(θ)==dimension(x) || return false - if x >= (0)unit(θ) - y = uconvert(unit(θ),x) - ω * (1 - exp(-y/θ)) + dimension(θ)==dimension(φ)==dimension(t) || return false + if φ >= zero(θ) + y = uconvert(unit(θ),φ) + eval(ω,t) * (1 - exp(-y/θ)) else - zero(R) + zero(Number) end end -function ccdf(dst::Exponential, x::Number) +function ccdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) θ, ω = params(dst) - dimension(θ)==dimension(x) || return false - if x >= (0)unit(θ) - y = uconvert(unit(θ),x) - ω * exp(-y/θ) + dimension(θ)==dimension(φ)==dimension(t) || return false + if φ >= zero(θ) + y = uconvert(unit(θ),φ) + eval(ω,t) * exp(-y/θ) else - ω + eval(ω,t) end end @@ -130,307 +146,79 @@ julia> 𝑾(5.0u"yr",4.0) # Weibull distr. with θ = 5.0 yr, α = 4.0 and ω julia> 𝑾(10.0,0.5,0.2) # scaled Weibull distr. with θ = 10.0, α = 0.5 and ω = 0.2 ``` """ -# struct -struct Weibull{N<:Number, R<:Real} <: AbstractDistribution{N,R} - θ::N # scale - α::R # shape - ω::R # weight: 0.0 < ω <= 1.0 +# abstract type +abstract type AbstractWeibull{X,Y,Z} <: AbstractDistribution{X,Y,Z} end + +# struct - θ::Number, α::Real, ω::Real +struct WeibullNRR{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} + θ::X # scale + α::Y # shape + ω::Y # weight: 0.0 < ω <= 1.0 end +# constructors +Weibull() = WeibullNRR{Number,Real,Function}(1.0, 1.0, 1.0) +Weibull(θ::Number) = WeibullNRR{Number,Real,Function}(θ, 1.0, 1.0) +Weibull(θ::Number, α::Real) = WeibullNRR{Number,Real,Function}(θ, α, 1.0) +Weibull(θ::Number, α::Real, ω::Real) = WeibullNRR{Number,Real,Function}(θ, α, ω) +# struct - θ::Number, α::Real, ω::Function +struct WeibullNRF{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} + θ::X # scale + α::Y # shape + ω::Z # weight: 0.0 < ω(t) <= 1.0 +end # constructors -Weibull() = Weibull(1.0, 1.0, 1.0) -Weibull(θ::Number) = Weibull(θ, 1.0, 1.0) -Weibull(θ::Number, α::Real) = Weibull(θ, α, 1.0) +Weibull(θ::Number, α::Real, ω::Function) = WeibullNRF{Number,Real,Function}(θ, α, ω) # shortened constructors 𝑾() = Weibull() 𝑾(θ::Number) = Weibull(θ) 𝑾(θ::Number, α::Real) = Weibull(θ, α) 𝑾(θ::Number, α::Real, ω::Real) = Weibull(θ, α, ω) +𝑾(θ::Number, α::Real, ω::Function) = Weibull(θ, α, ω) # functions -scale(dst::Weibull) = dst.θ -shape(dst::Weibull) = dst.α -weight(dst::Weibull) = dst.ω -params(dst::Weibull) = (dst.θ, dst.α, dst.ω) +scale(dst::AbstractWeibull) = dst.θ +shape(dst::AbstractWeibull) = dst.α +weight(dst::AbstractWeibull) = dst.ω +params(dst::AbstractWeibull) = (dst.θ, dst.α, dst.ω) -minimum(dst::Weibull) = zero(dst.θ) -maximum(dst::Weibull) = (Inf)unit(dst.θ) +minimum(dst::AbstractWeibull) = zero(dst.θ) +maximum(dst::AbstractWeibull) = (Inf)unit(dst.θ) -xv(dst::Weibull, z::Real) = dst.θ * z ^ (1 / dst.α) -quantile(dst::Weibull, p::Real) = xv(dst, -log1p(-p)) -cquantile(dst::Weibull, p::Real) = xv(dst, -log(p)) -sojourn(dst::Weibull,dφ::Number,tol::Real) = 0.0unit(dφ):dφ:cquantile(dst,tol) +xv(dst::AbstractWeibull, z::Real) = dst.θ * z ^ (1 / dst.α) +quantile(dst::AbstractWeibull, p::Real) = xv(dst, -log1p(-p)) +cquantile(dst::AbstractWeibull, p::Real) = xv(dst, -log(p)) +sojourn(dst::AbstractWeibull,dφ::Number,tol::Real) = + zero(dφ):dφ:cquantile(dst,tol) -function pdf(dst::Weibull, x::Number) +function pdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) θ, α, ω = params(dst) - dimension(θ)==dimension(x) || return false - if x >= (0)unit(θ) - y = (uconvert(unit(θ),x) + 1e-10unit(θ)) / θ - ω * (α / θ) * y^(α - 1) * exp(-y^α) + dimension(θ)==dimension(φ)==dimension(t) || return false + if φ >= zero(θ) + y = (uconvert(unit(θ),φ) + eps(θ)) / θ + eval(ω,t) * (α / θ) * y^(α - 1) * exp(-y^α) else - zero(R)unit(θ) + zero(1/θ) end end -function cdf(dst::Weibull, x::Number) +function cdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) θ, α, ω = params(dst) - dimension(θ)==dimension(x) || return false - if x >= (0)unit(θ) - y = uconvert(unit(θ),x) / θ - ustrip(ω * (1 - exp(-y^α))) + dimension(θ)==dimension(φ)==dimension(t) || return false + if φ >= zero(θ) + y = uconvert(unit(θ),φ) / θ + ustrip(eval(ω,t) * (1 - exp(-y^α))) else - zero(R) + zero(Number) end end -function ccdf(dst::Weibull, x::Number) +function ccdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) θ, α, ω = params(dst) - dimension(θ)==dimension(x) || return false - if x >= (0)unit(θ) - y = uconvert(unit(θ),x) / θ - ω * exp(-y^α) - else - ω - end -end - -## raised cosine -# struct -""" - Cosine - -The [**raised cosine distribution**](https://en.wikipedia.org/wiki/Raised_cosine_distribution) -with mean `μ` [`Number`], maximal deviation `s` [`Number`] and optional weight -`ω` [`Real`] has a probability density function -```math -f(x, μ, σ, ω) = \\begin{cases} - 0 &\\text{if:}~x < μ-s, \\\\ - \\frac{ω}{2s} \\big(1 + π \\cos\\big(\\frac{x - μ}{s}\\big)\big) &\\text{if:}~μ-s ≤ x ≤ μ+s, \\\\ - 0 &\\text{if:}~x > μ+s. - \\end{cases} -``` -# Constructors -| Full | Abbr. | Description | -| :---------------- | :------------ | :-------------------------------------------------------- | -| `Cosine(μ,s,ω)` | `𝑪(μ,s,ω)` | full constructor | -| `Cosine(μ,s)` | `𝑪(μ,s)` | constructor which defaults to `Cosine(μ,s,1.0)` | -| `Cosine(μ)` | `𝑪(μ)` | constructor which defaults to `Cosine(μ,1.0,1.0)` | -| `Cosine()` | `𝑪()` | empty constructor which defaults to `Cosine(1.0,1.0,1.0)` | -# Examples -```julia-repl -julia> Cosine() # default Raised Cosine distr. with μ = 1.0, s = 1.0 and ω = 1.0 -julia> 𝑪(3.0u"minute") # Raised Cosine distr. with μ = 3.0 min, s = 1.0 min and ω = 1.0 -julia> 𝑪(5.0u"yr",4.0u"d") # Raised Cosine distr. with μ = 5.0 yr, s = 4.0 d and ω = 1.0 -julia> 𝑪(10.0,0.5,0.2) # scaled Raised Cosine distr. with μ = 10.0, σ = 0.5 and ω = 0.2 -``` -""" -struct Cosine{N<:Number, R<:Real} <: AbstractDistribution{N,R} - μ::N # mean - s::N # maximal deviation - ω::R # weight -end - -# constructors -Cosine() = Cosine(1.0, 1.0, 1.0) -Cosine(μ::Number) = Cosine(μ, oneunit(μ), 1.0) -Cosine(μ::Number, s::Number) = Cosine(μ, uconvert(unit(μ), s), 1.0) - -# shortened constructors -𝑪() = Cosine() -𝑪(μ::Number) = Cosine(μ) -𝑪(μ::Number, s::Number) = Cosine(μ, uconvert(unit(μ),s)) -𝑪(μ::Number, s::Number, ω::Real) = Cosine(μ, uconvert(unit(μ), s), ω) - -# functions -mean(dst::Cosine) = dst.μ -dev(dst::Cosine) = dst.s -weight(dst::Cosine) = dst.ω -params(dst::Cosine) = (dst.μ, dst.s, dst.ω) - -minimum(dst::Cosine) = dst.μ-dst.s -maximum(dst::Cosine) = dst.μ+dst.s - -quantile(dst::Cosine, p::Real) = quantile_bisect(dst, p) -cquantile(dst::Cosine, p::Real) = quantile(dst, 1-p) -sojourn(dst::Cosine, dφ::Number, tol::Real) = - dst.μ-dst.s:dφ:dst.μ+dst.s+dφ - -function pdf(dst::Cosine, x::Number) - μ, s, ω = params(dst) - dimension(μ)==dimension(σ)==dimension(x) || return false - if μ-s <= x <= μ+s - y = (uconvert(unit(μ),x) - μ) / (2 * s) - ω / (2 * s) * (1 + cospi(y)) - else - zero(Real)/oneunit(μ) - end -end -function cdf(dst::Cosine, x::Number) - μ, s, ω = params(dst) - dimension(μ)==dimension(σ)==dimension(x) || return false - if μ-s > x - zero(Real) - elseif μ-s <= x <= μ+s - y = (uconvert(unit(μ),x) - μ) / s - ω / 2 * (1 + y + sinpi(y) / π) - elseif x > μ+s - ω - end -end -function ccdf(dst::Cosine, x::Number) - μ, s, ω = params(dst) - dimension(μ)==dimension(σ)==dimension(x) || return false - if μ-s > x - ω - elseif μ-s <= x <= μ+s - y = (μ - uconvert(unit(μ), x)) / s - ω / 2 * (1 + y + sinpi(y) / π) - elseif x > μ+s - zero(Real) - end -end - -## dirac -""" - Dirac - -The [*Dirac distribution*](https://en.wikipedia.org/wiki/Dirac_delta_function) -with offset `o` and optional weight `ω` has a probability density function - -```math -f(x; o, ω) = \begin{cases} - ω & x = 0, \\ - 0 & x ≠ 0. - \end{cases} -``` -""" -# struct -struct Dirac{N<:Number, R<:Real} <: AbstractDistribution{N,R} - o::N # offset - ω::R # weight: 0.0 < ω <= 1.0 -end - -# constructors -Dirac() = Dirac(0.0, 1.0) -Dirac(o::Number) = Dirac(o, 1.0) - -# shortened constructors -𝑫() = Dirac() -𝑫(o::Number) = Dirac(o) -𝑫(o::Number, ω::Real) = Dirac(o, ω) - -# functions -offset(dst::Dirac) = dst.o -weight(dst::Dirac) = dst.ω -params(dst::Dirac) = (dst.o, dst.ω) - -minimum(dst::Dirac) = dst.o -maximum(dst::Dirac) = dst.o - -quantile(dst::Dirac, p::Real) = dst.o -cquantile(dst::Dirac, p::Real) = dst.o - -function pdf(dst::Dirac, x::Number) - o, ω = params(dst) - dimension(o)==dimension(x) || return false - if x == o - ω - else - zero(R) - end -end -function cdf(dst::Dirac, x::Number) - o, ω = params(dst) - dimension(o)==dimension(x) || return false - if x > o - ω - else - zero(R) - end -end -function ccdf(dst::Dirac, x::Number) - o, ω = params(dst) - dimension(o)==dimension(x) || return false - if x > o - zero(R) - else - ω - end -end - -## uniform -""" - Uniform - -The [*continuous uniform distribution*](http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)) -over an interval `[a, b]` and with optional weight `ω` has a probability density -function - -```math -f(x; a, b, ω) = \begin{cases} - ω/(b - a) & a ≤ x ≤ b, \\ - 0 & a > x || x > b. - \end{cases} -``` -""" -# struct -struct Uniform{N<:Number, R<:Real} <: AbstractDistribution{N,R} - a::N # start - b::N # end - ω::R # weight: 0.0 < ω <= 1.0 -end - -# constructors -Uniform() = Uniform(0.0, 1.0, 1.0) -Uniform(a::Number, b::Number) = Uniform(a, b, 1.0) - -# shortened constructors -𝑼() = Uniform() -𝑼(a::Number, b::Number) = Uniform(a, b) -𝑼(a::Number, b::Number, ω::Real) = Uniform(a, b, ω) - -# functions -fr(dst::Uniform) = dst.a -to(dst::Uniform) = dst.b -weight(dst::Uniform) = dst.ω -params(dst::Uniform) = (dst.a, dst.b, dst.ω) - -minimum(dst::Uniform) = dst.a -maximum(dst::Uniform) = dst.b - -quantile(dst::Uniform, p::Real) = dst.a + p * (dst.b - dst.a) -cquantile(dst::Uniform, p::Real) = dst.b + p * (dst.a - dst.b) -sojourn(dst::Uniform,dφ::Number,tol::Real) = 0.0unit(dφ):dφ:cquantile(dst,tol) - -function pdf(dst::Uniform, x::Number) - a, b, ω = params(dst) - dimension(a)==dimension(b)==dimension(x) || return false - if a <= x <= b - ω / (b - a) - else - zero(R)unit(a) - end -end -function cdf(dst::Uniform, x::Number) - a, b, ω = params(dst) - dimension(a)==dimension(b)==dimension(x) || return false - if a > x - zero(R) - elseif a <= x <= b - y = uconvert(unit(a),x) - ω + ω * (y - b) / (b - a) - else - ω - end -end -function ccdf(dst::Uniform, x::Number) - a, b, ω = params(dst) - dimension(a)==dimension(b)==dimension(x) || return false - if a > x - ω - elseif a <= x <= b - y = uconvert(unit(μ),x) - ω * (b - y) / (b - a) + dimension(θ)==dimension(φ)==dimension(t) || return false + if φ >= zero(θ) + y = uconvert(unit(θ),φ) / θ + eval(ω,t) * exp(-y^α) else - zero(R) + eval(ω,t) end end \ No newline at end of file From ea43723bb43b4f8b2b06a8a0059cdcf3ee0e3241 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Wed, 20 Apr 2022 21:10:31 +0200 Subject: [PATCH 03/56] LogNormal distribution --- Project.toml | 4 +- src/MultiStateSystems.jl | 2 + src/io/distributions.jl | 114 ++++++++++++++++++++++++++++++++++++++- 3 files changed, 117 insertions(+), 3 deletions(-) diff --git a/Project.toml b/Project.toml index 72ba95e..99a7706 100644 --- a/Project.toml +++ b/Project.toml @@ -10,16 +10,18 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7" Multigraphs = "7ebac608-6c66-46e6-9856-b5f43e107bac" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" +SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" [compat] -julia = "1" AdditionalUnits = "0.1.2" LightGraphs = "1.3.5" Measurements = "2.6.0" Multigraphs = "0.2.2" OrdinaryDiffEq = "5.59.4" Unitful = "1.8.0" +SpecialFunctions = "2.1.4" +julia = "1" [extras] Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index 6d643a4..1ebb91a 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -16,6 +16,7 @@ import LinearAlgebra import Multigraphs import OrdinaryDiffEq import Measurements +import SpecialFunctions # using Pkgs using Unitful @@ -28,6 +29,7 @@ const _MG = Multigraphs const _ODE = OrdinaryDiffEq const _UF = Unitful const _MSM = Measurements +const _SF = SpecialFunctions # paths const BASE_DIR = dirname(@__DIR__) diff --git a/src/io/distributions.jl b/src/io/distributions.jl index 8d6d40d..9de69ae 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -119,7 +119,7 @@ end ## weibull """ - Weibull + MultiStateSystems.Weibull The [*Weibull distribution*](http://en.wikipedia.org/wiki/Weibull_distribution) with scale parameter `θ`, shape parameter `α` and optional weight `ω` has a @@ -168,7 +168,8 @@ struct WeibullNRF{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} ω::Z # weight: 0.0 < ω(t) <= 1.0 end # constructors -Weibull(θ::Number, α::Real, ω::Function) = WeibullNRF{Number,Real,Function}(θ, α, ω) +Weibull(θ::Number, α::Real, ω::Function) = + WeibullNRF{Number,Real,Function}(θ, α, ω) # shortened constructors 𝑾() = Weibull() @@ -221,4 +222,113 @@ function ccdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) else eval(ω,t) end +end + +## log-normal +""" + MultiStateSystems.LogNormal + +The [*Log-normal distribution*](https://en.wikipedia.org/wiki/Log-normal_distribution) +with expected value `μ` and standard deviation `σ` of the corresponding normal +distribution and optional weight `ω` has a probability density function + +```math +f(x, μ, σ, ω) = \\begin{cases} + \\frac{ω}{\\sqrt{2π} x σ} \\cdot \\cdot e^{-\\big(\\frac{(\\ln{x}-μ)^{2}}{2 σ^{2}}\\big)} &\\text{if:}~x ≥ 0, \\\\ + 0 &\\text{if:}~x < 0. + \\end{cases} +``` +# Constructors +| Full | Abbr. | Description | +| :----------------- | :------------ | :----------------------------------------------------------- | +| `LogNormal(μ,σ,ω)` | `𝑳(μ,σ,ω)` | full constructor | +| `LogNormal(μ,σ)` | `𝑳(μ,σ)` | constructor which defaults to `LogNormal(μ,σ,1.0)` | +| `LogNormal(μ)` | `𝑳(μ)` | constructor which defaults to `LogNormal(μ,1.0,1.0)` | +| `LogNormal()` | `𝑳()` | empty constructor which defaults to `LogNormal(1.0,1.0,1.0)` | +# Examples +```julia-repl +julia> LogNormal() # default Log-normal distr. with μ = 1.0, σ = 1.0 and ω = 1.0 +julia> 𝑳(3.0u"minute") # Log-normal distr. with μ = 3.0 min, σ = 1.0 min and ω = 1.0 +julia> 𝑳(5.0u"yr",4.0u"d") # Log-normal distr. with μ = 5.0 yr, σ = 4.0 d and ω = 1.0 +julia> 𝑳(10.0,0.5,0.2) # scaled Log-normal distr. with μ = 10.0, σ = 0.5 and ω = 0.2 +``` +""" +# abstract type +abstract type AbstractLogNormal{X,Y,Z} <: AbstractDistribution{X,Y,Z} end + +# struct - μ::Number, σ::Number, ω::Real +struct LogNormalNNR{X<:Number, Y<:Real, Z<:Function} <: AbstractLogNormal{X,Y,Z} + μ::X # mean of the corresponding normal distribution + σ::X # shape of the corresponding normal distribution + ω::Y # weight: 0.0 < ω <= 1.0 +end +# constructors +LogNormal() = LogNormalNNR{Number,Real,Function}(1.0, 1.0, 1.0) +LogNormal(μ::Number) = LogNormalNNR{Number,Real,Function}(μ, 1.0unit(μ), 1.0) +LogNormal(μ::Number, σ::Number) = + LogNormalNNR{Number,Real,Function}(μ, uconvert(unit(μ),σ), 1.0) +LogNormal(μ::Number, σ::Number, ω::Real) = + LogNormalNNR{Number,Real,Function}(μ, uconvert(unit(μ),σ), ω) + +# struct - μ::Number, σ::Number, ω::Function +struct LogNormalNNF{X<:Number, Y<:Real, Z<:Function} <: AbstractLogNormal{X,Y,Z} + μ::X # mean of the corresponding normal distribution + σ::X # shape of the corresponding normal distribution + ω::Z # weight: 0.0 < ω(t) <= 1.0 +end +# constructors +LogNormal(μ::Number, σ::Number, ω::Function) = + LogNormalNNF{Number,Real,Function}(μ, uconvert(unit(μ),σ), ω) + +# shortened constructors +𝑳() = LogNormal() +𝑳(μ::Number) = LogNormal(μ) +𝑳(μ::Number, σ::Number) = LogNormal(μ, σ) +𝑳(μ::Number, σ::Number, ω::Real) = LogNormal(μ, σ, ω) +𝑳(μ::Number, σ::Number, ω::Function) = LogNormal(μ, σ, ω) + +# functions +weight(dst::AbstractLogNormal) = dst.ω +params(dst::AbstractLogNormal) = (dst.μ, dst.σ, dst.ω) + +minimum(dst::AbstractLogNormal) = zero(dst.μ) +maximum(dst::AbstractLogNormal) = (Inf)unit(dst.μ) + +quantile(dst::AbstractLogNormal, p::Real) = + exp(dst.μ + sqrt(2) * dst.σ * _SF.erfinv(2.0 * p - 1.0)) +cquantile(dst::AbstractLogNormal, p::Real) = + exp(dst.μ + sqrt(2) * dst.σ * _SF.erfinv(2.0 * (1.0 - p) - 1.0)) +sojourn(dst::AbstractLogNormal,dφ::Number,tol::Real) = + zero(dst.μ):uconvert(dst.μ,dφ):cquantile(dst,tol) + +function pdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) + μ, σ, ω = params(dst) + dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false + if φ >= zero(μ) + x = ustrip(unit(φ), σ) + y = uconvert(unit(φ/φ),(log(φ) - μ)^2 / (2 * σ^2)) + eval(ω,t) / (sqrt(2 * pi) * x * φ) * exp(-y) + else + zero(1/φ) + end +end +function cdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) + μ, σ, ω = params(dst) + dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false + if φ >= zero(μ) + y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) + eval(ω,t) / 2 * _SF.erfc(-y) + else + zero(Number) + end +end +function ccdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) + μ, σ, ω = params(dst) + dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false + if φ >= zero(μ) + y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) + eval(ω,t) * (1 - _SF.erfc(-y) / 2) + else + eval(ω,t) + end end \ No newline at end of file From 3f4c799937c84bf22ad213fb3ebf1df7efab5260 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Wed, 20 Apr 2022 21:16:10 +0200 Subject: [PATCH 04/56] Update MultiStateSystems.jl --- src/MultiStateSystems.jl | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index 1ebb91a..cae96f1 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -54,8 +54,7 @@ include("prob/universal_generating_operator.jl") # export export BASE_DIR export SteadyStateProcess, MarkovProcess, SemiMarkovProcess -export Exponential, 𝑬, Weibull, 𝑾 -# export Cosine, 𝑪, Dirac, 𝑫, Exponential, 𝑬, Gamma, 𝑮, Uniform, 𝑼, Weibull, 𝑾 +export Exponential, 𝑬, LogNormal, 𝑳, Weibull, 𝑾 export Network, add_source!, add_sources!, add_user!, add_users!, add_component!, add_bidirectional_component!, add_components!, add_bidirectional_components! From 25b99ff7708b40857de08ee5c11eb85026388b6a Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Mon, 25 Apr 2022 09:24:12 +0200 Subject: [PATCH 05/56] added tests for distributions.jl --- Project.toml | 2 +- docs/src/distribution.md | 39 +++++--------- src/io/distributions.jl | 2 + test/distributions.jl | 112 +++++++++++++++++++++++++++++++++++++++ test/runtests.jl | 1 + 5 files changed, 128 insertions(+), 28 deletions(-) create mode 100644 test/distributions.jl diff --git a/Project.toml b/Project.toml index 99a7706..bbf8146 100644 --- a/Project.toml +++ b/Project.toml @@ -20,7 +20,7 @@ Measurements = "2.6.0" Multigraphs = "0.2.2" OrdinaryDiffEq = "5.59.4" Unitful = "1.8.0" -SpecialFunctions = "2.1.4" +SpecialFunctions = "1.8.4" julia = "1" [extras] diff --git a/docs/src/distribution.md b/docs/src/distribution.md index fc3bd86..0142e81 100644 --- a/docs/src/distribution.md +++ b/docs/src/distribution.md @@ -11,55 +11,40 @@ it to allow for weighted distributions as well as the ## Distributions Each distribution has a number of constructors, both based on its full name and -abbreviation, e.g., `Weibull()` is equivalent to `𝑾()`. Furthermore, -additional constructors are included for limited input, where all remaining -parameters are set to their default, e.g., `Weibull(10.0u"hr")` is equivalent -to `Weibull(10.0u"hr",1.0,1.0)`. +abbreviation, e.g., `Weibull()` is equivalent to `𝑾()`. The abbreviation +constructor is the first letter of the distribution in the `\bi` font. +Furthermore, additional constructors are included for limited input, where all +remaining parameters are set to their default, e.g., `Weibull(10.0u"hr")` is +equivalent to `Weibull(10.0u"hr",1.0,1.0)`. -All input parameters are either of the type `Number` or its subtype `Real`: +All input parameters are either of the type `Number`, its subtype `Real` or a +`Function`: ``` Number |- Unitful.Quantity, e.g., 10.0u"hr" |- Real |- AbstractFloat, e.g., 10.0 |- Integer, e.g., 10 +Function ``` All distributions may be scaled using a weight parameter `ω`, where -`0.0 < ω ≤ 1.0`. - -### Dirac Distribution - -```@docs -Dirac -``` - -## Uniform Distribution - -```@docs -Uniform -``` +`0.0 < ω::Real ≤ 1.0` or `0.0 < ω(t)::Fuction ≤ 1.0`. ## Exponential Distribution ```@docs -Exponential +MultiStateSystems.Exponential ``` ## Weibull Distribution ```@docs -Weibull -``` - -## Raised Cosine Distribution - -```@docs -Cosine +MultiStateSystems.Weibull ``` ## LogNormal Distribution ```@docs -LogNormal +MultiStateSystems.LogNormal ``` diff --git a/src/io/distributions.jl b/src/io/distributions.jl index 9de69ae..ac35031 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -80,12 +80,14 @@ rate(dst::AbstractExponential) = 1.0 / dst.θ minimum(dst::AbstractExponential) = zero(dst.θ) maximum(dst::AbstractExponential) = (Inf)unit(dst.θ) +# quantile xv(dst::AbstractExponential, z::Real) = z * dst.θ quantile(dst::AbstractExponential, p::Real) = -xv(dst, log1p(-p)) cquantile(dst::AbstractExponential, p::Real) = -xv(dst, log(p)) sojourn(dst::AbstractExponential,dφ::Number,tol::Real) = zero(dφ):dφ:cquantile(dst,tol) +# density functions function pdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) θ, ω = params(dst) dimension(θ)==dimension(φ)==dimension(t) || return false diff --git a/test/distributions.jl b/test/distributions.jl new file mode 100644 index 0000000..847e5b6 --- /dev/null +++ b/test/distributions.jl @@ -0,0 +1,112 @@ +################################################################################ +# Copyright 2022, Tom Van Acker # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +@testset "Distributions" begin + Ω(t) = max(0.0,min(1.0,0.01u"1/hr" * t)) + + @testset "Exponential" begin + # input + θ, ω, φ = 10.0u"hr", 0.8, 3.0u"hr" + + # constructors + @test 𝑬() == Exponential() == Exponential(1.0,1.0) + @test 𝑬(θ) == Exponential(θ) == Exponential(θ,1.0) + @test 𝑬(θ,ω) == Exponential(θ,ω) + @test 𝑬(θ,Ω) == Exponential(θ,Ω) + + # general functions + dst = Exponential(θ,ω) + + @test _MSS.scale(dst) == θ + @test _MSS.weight(dst) == ω + @test _MSS.params(dst) == (θ, ω) + + @test _MSS.rate(dst) == 1 / θ + + @test _MSS.minimum(dst) == zero(θ) + @test _MSS.maximum(dst) == (Inf)unit(θ) + + # quantile functions + # https://keisan.casio.com/menu/system/000000000540 + @test isapprox(_MSS.quantile(dst,0.4),5.1082562376u"hr",atol=1e-10u"hr") + @test _MSS.quantile(dst,0.8) == _MSS.cquantile(dst,0.2) + + # density functions + # https://keisan.casio.com/menu/system/000000000540 + @test isapprox(_MSS.pdf(dst,φ),ω * 0.0740818220u"1/hr",atol=1e-10u"1/hr") + @test isapprox(_MSS.cdf(dst,φ),ω * 0.2591817793,atol=1e-10) + @test _MSS.cdf(dst,φ) == ω - _MSS.ccdf(dst,φ) + end + + @testset "Weibull" begin + # dummy input + θ, α, ω, φ = 10.0u"hr", 1.3, 0.8, 3.0u"hr" + + # constructors + @test 𝑾() == Weibull() == Weibull(1.0,1.0,1.0) + @test 𝑾(θ) == Weibull(θ) == Weibull(θ,1.0,1.0) + @test 𝑾(θ,α) == Weibull(θ,α) == Weibull(θ,α,1.0) + @test 𝑾(θ,α,ω) == Weibull(θ,α,ω) + @test 𝑾(θ,α,Ω) == Weibull(θ,α,Ω) + + # general functions + dst = Weibull(θ,α,ω) + + @test _MSS.scale(dst) == θ + @test _MSS.shape(dst) == α + @test _MSS.weight(dst) == ω + @test _MSS.params(dst) == (θ, α, ω) + + @test _MSS.minimum(dst) == zero(θ) + @test _MSS.maximum(dst) == (Inf)unit(θ) + + # quantile functions + # https://keisan.casio.com/menu/system/000000000540 + @test isapprox(_MSS.quantile(dst,0.4),5.9647790998u"hr",atol=1e-10u"hr") + @test _MSS.quantile(dst,0.8) == _MSS.cquantile(dst,0.2) + + # density functions + # https://keisan.casio.com/menu/system/000000000540 + @test isapprox(_MSS.pdf(dst,φ),ω * 0.0735002655u"1/hr",atol=1e-10u"1/hr") + @test isapprox(_MSS.cdf(dst,φ),ω * 0.1886482463,atol=1e-10) + @test _MSS.cdf(dst,φ) == ω - _MSS.ccdf(dst,φ) + end + + @testset "LogNormal" begin + # dummy input + μ, σ, ω, φ = 1.0u"hr", 0.25u"hr", 0.8, 3.0u"hr" + + # constructors + @test 𝑳() == LogNormal() == LogNormal(1.0,1.0,1.0) + @test 𝑳(μ) == LogNormal(μ) == LogNormal(μ,oneunit(μ),1.0) + @test 𝑳(μ,σ) == LogNormal(μ,σ) == LogNormal(μ,σ,1.0) + @test 𝑳(μ,σ,ω) == LogNormal(μ,σ,ω) + @test 𝑳(μ,σ,Ω) == LogNormal(μ,σ,Ω) + + # general functions + dst = LogNormal(μ,σ,ω) + + @test _MSS.weight(dst) == ω + @test _MSS.params(dst) == (μ, σ, ω) + + @test _MSS.minimum(dst) == zero(μ) + @test _MSS.maximum(dst) == (Inf)unit(μ) + + # quantile functions + # https://keisan.casio.com/menu/system/000000000540 + @test isapprox(_MSS.quantile(dst,0.4),2.5514535699u"hr",atol=1e-10u"hr") + @test _MSS.quantile(dst,0.8) == _MSS.cquantile(dst,0.2) + + # density functions + # https://keisan.casio.com/menu/system/000000000540 + @test isapprox(_MSS.pdf(dst,φ),ω * 0.4921107291u"1/hr",atol=1e-10u"1/hr") + @test isapprox(_MSS.cdf(dst,φ),ω * 0.6533752704,atol=1e-10) + @test _MSS.cdf(dst,φ) == ω - _MSS.ccdf(dst,φ) + end + +end \ No newline at end of file diff --git a/test/runtests.jl b/test/runtests.jl index 5059f5d..77a08df 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -23,6 +23,7 @@ const _MSS = MultiStateSystems include("markov_process.jl") # io + include("distributions.jl") include("indices.jl") include("universal_generating_function.jl") From 4f07fcb3b3a4bbc923485186eb70a1936e4f57ae Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Mon, 25 Apr 2022 13:19:15 +0200 Subject: [PATCH 06/56] update markov_process.jl Solving the Markov Process results in probabilities for a fixed time range: 0.0:dt:tsim --- docs/src/processes.md | 6 +++--- src/form/markov_process.jl | 10 ++++++---- src/form/semi_markov_process.jl | 2 +- src/io/distributions.jl | 8 ++++++-- 4 files changed, 16 insertions(+), 10 deletions(-) diff --git a/docs/src/processes.md b/docs/src/processes.md index b811e83..9cff738 100644 --- a/docs/src/processes.md +++ b/docs/src/processes.md @@ -6,9 +6,9 @@ A number of stochastic processes are available to determine the state probabilities of an `std`: * Steady state process `SteadyStateProcess <: AbstractMarkovProcess` -* Markov chain `:markov_process` -* Markov process `:markov_process` -* Semi-Markov process `:semimarkov_process` +* Markov chain `MarkovChain <: AbstractMarkovProcess` +* Markov process `MarkovProcess <: AbstractMarkovProcess` +* Semi-Markov process `SemiMarkovProcess <: AbstractSemiMarkovProcess` * Van Acker process `:vanacker_process` Solving a stochastic process may be accomplished through: diff --git a/src/form/markov_process.jl b/src/form/markov_process.jl index 1760e7f..6b4d50d 100644 --- a/src/form/markov_process.jl +++ b/src/form/markov_process.jl @@ -50,11 +50,13 @@ function inhomogeneous_markov_process(du, u, p, t) if ns ≠ nt) end end end -function solve!(std::AbstractSTD, cls::AbstractMarkovProcess; tsim::Number=1.0u"yr", tol::Real=1e-8) +function solve!(std::AbstractSTD, cls::MarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) set_parameters!(std, cls) + + t = zero(dt):dt:tsim p = [std.graph,get_tprop(std,:rate),get_sprop(std,:info)] u₀ = get_sprop(std,:init) - ts = (0.0_UF.unit(tsim),tsim) + ts = (zero(tsim),tsim) if get_info(std,:time_homogeneous) prob = _ODE.ODEProblem(homogeneous_markov_process, u₀, ts, p) @@ -64,8 +66,8 @@ function solve!(std::AbstractSTD, cls::AbstractMarkovProcess; tsim::Number=1.0u" sol = _ODE.solve(prob, _ODE.Tsit5(), reltol = tol, abstol = tol) set_prop!(std, :cls, cls) - set_prop!(std, :time, sol.t) - set_prop!(std, states(std), :prob, [sol[ns,:] for ns in states(std)]) + set_prop!(std, :time, t) + set_prop!(std, states(std), :prob, [sol(t,idxs=ns) for ns in states(std)]) set_info!(std, :solved, true) end \ No newline at end of file diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index bbac64a..a4c30fb 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -15,7 +15,7 @@ const semi_markov_process_props = [:renewal, :dynamic] # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) - t = zero(tsim):dt:tsim + t = zero(dt):dt:tsim Nt = length(t) # calculate H diff --git a/src/io/distributions.jl b/src/io/distributions.jl index ac35031..0b9a1be 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -180,7 +180,7 @@ Weibull(θ::Number, α::Real, ω::Function) = 𝑾(θ::Number, α::Real, ω::Real) = Weibull(θ, α, ω) 𝑾(θ::Number, α::Real, ω::Function) = Weibull(θ, α, ω) -# functions +# general functions scale(dst::AbstractWeibull) = dst.θ shape(dst::AbstractWeibull) = dst.α weight(dst::AbstractWeibull) = dst.ω @@ -189,12 +189,14 @@ params(dst::AbstractWeibull) = (dst.θ, dst.α, dst.ω) minimum(dst::AbstractWeibull) = zero(dst.θ) maximum(dst::AbstractWeibull) = (Inf)unit(dst.θ) +# quantile functions xv(dst::AbstractWeibull, z::Real) = dst.θ * z ^ (1 / dst.α) quantile(dst::AbstractWeibull, p::Real) = xv(dst, -log1p(-p)) cquantile(dst::AbstractWeibull, p::Real) = xv(dst, -log(p)) sojourn(dst::AbstractWeibull,dφ::Number,tol::Real) = zero(dφ):dφ:cquantile(dst,tol) +# density functions function pdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) θ, α, ω = params(dst) dimension(θ)==dimension(φ)==dimension(t) || return false @@ -289,13 +291,14 @@ LogNormal(μ::Number, σ::Number, ω::Function) = 𝑳(μ::Number, σ::Number, ω::Real) = LogNormal(μ, σ, ω) 𝑳(μ::Number, σ::Number, ω::Function) = LogNormal(μ, σ, ω) -# functions +# general functions weight(dst::AbstractLogNormal) = dst.ω params(dst::AbstractLogNormal) = (dst.μ, dst.σ, dst.ω) minimum(dst::AbstractLogNormal) = zero(dst.μ) maximum(dst::AbstractLogNormal) = (Inf)unit(dst.μ) +# quantile functions quantile(dst::AbstractLogNormal, p::Real) = exp(dst.μ + sqrt(2) * dst.σ * _SF.erfinv(2.0 * p - 1.0)) cquantile(dst::AbstractLogNormal, p::Real) = @@ -303,6 +306,7 @@ cquantile(dst::AbstractLogNormal, p::Real) = sojourn(dst::AbstractLogNormal,dφ::Number,tol::Real) = zero(dst.μ):uconvert(dst.μ,dφ):cquantile(dst,tol) +# density functions function pdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) μ, σ, ω = params(dst) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false From 7111b0ab9bf98acb93dbbe4299aa3fe26babdb7e Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Mon, 25 Apr 2022 13:50:35 +0200 Subject: [PATCH 07/56] Added weighting function Weighting function following the suggested Simpson method. --- src/form/semi_markov_process.jl | 25 +++++++++++++++++++++++-- 1 file changed, 23 insertions(+), 2 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index bbac64a..9dae32e 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -14,7 +14,8 @@ mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end const semi_markov_process_props = [:renewal, :dynamic] # stochastic process -function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) +#function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=4500u"hr", dt::Number=1.0u"hr", tol::Real=1e-8) t = zero(tsim):dt:tsim Nt = length(t) @@ -70,7 +71,27 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1 set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) end +#determine integration weights based on extended Simpson's rule. w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. +function weights(x) + w = zeros(x) + for i in 1:x + if i % 2 == 0 + w[i] = 4/3 + else + w[i] = 2/3 + end end + w[1] = 1/3 + w[end] = 1/3 + + return w +end + # check whether sum of ccdf could be suffient ccdf(std::AbstractSTD, ns::Int, φ::Real, t::Real) = 1.0 - sum(cdf(get_prop(std,_LG.edge(ns,nx),:distr), φ, t) - for nx in _LG.outneighbors(G,ns)) \ No newline at end of file + for nx in _LG.outneighbors(G,ns)) + + + + + From b877a365ebe2750305c55f7f43a76a02835acaec Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Mon, 25 Apr 2022 13:50:54 +0200 Subject: [PATCH 08/56] Create semi-analytical.jl --- examples/semi-markov/semi-analytical.jl | 30 +++++++++++++++++++++++++ 1 file changed, 30 insertions(+) create mode 100644 examples/semi-markov/semi-analytical.jl diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl new file mode 100644 index 0000000..7958db6 --- /dev/null +++ b/examples/semi-markov/semi-analytical.jl @@ -0,0 +1,30 @@ +################################################################################ +# Copyright 2020, Tom Van Acker # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SemiMarkovProcess() + +std = STD() +add_states!(std, name = ["normal operation state","degradation state","failed state"], + power = [1.0u"MW", 1.0u"MW", 0.0u"MW"], + init = [1.0,0.0,0.0]) + +add_transitions!(std, distr = [Exponential(1000u"hr"), Weibull(250u"hr", 1.5)], + states = [(1,2),(2,3)]) + +# solve the network +solve!(std, cls) + +println("test") \ No newline at end of file From e35afd7c876a4a9b85c153816ddcd02c2c90fd36 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Tue, 26 Apr 2022 08:58:57 +0200 Subject: [PATCH 09/56] Update semi_markov_process.jl Temporary fix of unit compatibility problem line 46 --- src/form/semi_markov_process.jl | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 07f03d3..5b6f9ee 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -15,7 +15,8 @@ const semi_markov_process_props = [:renewal, :dynamic] # stochastic process -function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) +#function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=9u"hr", dt::Number=1.0u"hr", tol::Real=1e-8) t = zero(dt):dt:tsim Nt = length(t) @@ -38,9 +39,9 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1 for (ni,nt) in enumerate(t) w = weights(ni) # hier kan code optimalisatie gebeuren gegeven dat φ <<< t - φ = 0.0:dt:nt + φ = zero(dt):dt:nt for (nj,nφ) in enumerate(φ) - Ψ = zeros(ns(std), ns(std)) + Ψ = zeros(ns(std), ns(std))u"hr^-1" for tr in transitions(std) Ψ[_LG.dst(tr),_LG.src(tr)] = pdf(get_prop(std, tr, :distr),nφ,nt) end @@ -48,7 +49,7 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1 rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) if ni == nj - U[rT,rΦ] = Matrix(1.0I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ + U[rT,rΦ] = Matrix(1.0_LA.I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ else U[rT,rΦ] = -dt .* w[nj] .* Ψ end @@ -58,11 +59,11 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1 Φ = zeros(Nt, ns(std)) for st in states(std) - for (ni,nt) in t + for (ni,nt) in enumerate(t) w = weights(ni) # hier kan code optimalisatie gebeuren gegeven dat φ <<< t - φ = 0.0:dt:nt - Φ[ni,st] += get_prop(std,st,:init) * ccdf(std,st,0.0,nt) + φ = zero(dt):dt:nt + Φ[ni,st] += get_prop(std,st,:init) * ccdf(get_prop(std, tr, :distr),0.0,nt) Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (ni-1) + st] * ccdf(std,st,nφ,nt) for (nj,nφ) in enumerate(φ)) end end From ca6996ada5efbe6f19aaee36cd6b350286ea1a99 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 26 Apr 2022 14:22:26 +0200 Subject: [PATCH 10/56] small changes --- docs/src/processes.md | 27 +++++++++++++++++++++------ src/core/types.jl | 5 +++++ src/form/markov_process.jl | 17 +++++++++++++++-- src/form/semi_markov_process.jl | 12 ++++++++++-- src/form/steady_state_process.jl | 31 +++++++++++++++++-------------- 5 files changed, 68 insertions(+), 24 deletions(-) diff --git a/docs/src/processes.md b/docs/src/processes.md index 9cff738..b7df910 100644 --- a/docs/src/processes.md +++ b/docs/src/processes.md @@ -4,12 +4,14 @@ A number of stochastic processes are available to determine the state probabilities of an `std`: - -* Steady state process `SteadyStateProcess <: AbstractMarkovProcess` -* Markov chain `MarkovChain <: AbstractMarkovProcess` -* Markov process `MarkovProcess <: AbstractMarkovProcess` -* Semi-Markov process `SemiMarkovProcess <: AbstractSemiMarkovProcess` -* Van Acker process `:vanacker_process` +``` +AbstractStochasticProcess + |- AbstractMarkovProcess + |- SteadyStateProcess + |- MarkovProcess + |- AbstractSemiMarkovProcess + |- SemiMarkovProcess +``` Solving a stochastic process may be accomplished through: ```@docs @@ -60,6 +62,19 @@ probabilities, given transition rates ρ$_{ij}$(t) and initial values δ$_{i}$: dp_i(t)/dt = - ∑_j ρ_{ij}(t)p_i(t) + ∑_j ρ_{ji}(t)p_j(t), ∀ i ∈ 𝓢. ``` +## Semi-Markov Process + +| Spaces | | Properties | | +| :---------- | :-------------- | :---------- | :---------- | +| State-space | discrete | Renewal | ✅ | +| Time-space | continuous | Markov | ❎ | + +A semi-Markov process is described by a random variable $X_t$, where $t$ denotes +the calendar time. The possible values of $X_t$ are represented by the discrete +state-space 𝓢 of the state transition diagram `std`. + +A semi-Markov process... + ## Van Acker Process * `T. Van Acker, and D. Van Hertem (2018). Stochastic Process for the diff --git a/src/core/types.jl b/src/core/types.jl index a533e14..e7386e0 100644 --- a/src/core/types.jl +++ b/src/core/types.jl @@ -8,10 +8,15 @@ # abstract types abstract type AbstractUGF end + abstract type AbstractInfo end + abstract type AbstractDistribution{X,Y,Z} end + abstract type AbstractSTD{T} <: _LG.AbstractGraph{T} end + abstract type AbstractNetwork{T} <: _LG.AbstractGraph{T} end + abstract type AbstractStochasticProcess end abstract type AbstractMarkovProcess <: AbstractStochasticProcess end abstract type AbstractSemiMarkovProcess <: AbstractStochasticProcess end diff --git a/src/form/markov_process.jl b/src/form/markov_process.jl index 6b4d50d..b1620ca 100644 --- a/src/form/markov_process.jl +++ b/src/form/markov_process.jl @@ -13,7 +13,14 @@ mutable struct MarkovProcess <: AbstractMarkovProcess end const markov_process_props = [:renewal, :markovian, :dynamic] # parameters -function set_parameters!(std::AbstractSTD, cls::AbstractMarkovProcess) +function set_rates!(std::AbstractSTD, cls::AbstractMarkovProcess) + for nt in transitions(std) + if !has_prop(std, nt, :rate) && has_prop(std, nt, :distr) + if get_prop(std, nt, :distr) isa Exponential + set_prop!(std, nt, :rate, rate(get_prop(std, nt, :distr))) + end end end +end +function set_parameters!(std::AbstractSTD, cls::MarkovProcess) set_rates!(std, cls) end @@ -50,14 +57,18 @@ function inhomogeneous_markov_process(du, u, p, t) if ns ≠ nt) end end end -function solve!(std::AbstractSTD, cls::MarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) +function solve!(std::AbstractSTD, cls::MarkovProcess; + tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) + # set the input set_parameters!(std, cls) + # get the input t = zero(dt):dt:tsim p = [std.graph,get_tprop(std,:rate),get_sprop(std,:info)] u₀ = get_sprop(std,:init) ts = (zero(tsim),tsim) + # solve the problem if get_info(std,:time_homogeneous) prob = _ODE.ODEProblem(homogeneous_markov_process, u₀, ts, p) else @@ -65,9 +76,11 @@ function solve!(std::AbstractSTD, cls::MarkovProcess; tsim::Number=1.0u"yr", dt: end sol = _ODE.solve(prob, _ODE.Tsit5(), reltol = tol, abstol = tol) + # set the output set_prop!(std, :cls, cls) set_prop!(std, :time, t) set_prop!(std, states(std), :prob, [sol(t,idxs=ns) for ns in states(std)]) + # set the solved status set_info!(std, :solved, true) end \ No newline at end of file diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 5b6f9ee..dbfd351 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -14,12 +14,16 @@ mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end const semi_markov_process_props = [:renewal, :dynamic] # stochastic process +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; + tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) + # set the input + set_parameters!(std,cls) -#function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) -function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=9u"hr", dt::Number=1.0u"hr", tol::Real=1e-8) + # get the input t = zero(dt):dt:tsim Nt = length(t) + # solve the problem # calculate H A = zeros(ns(std) * Nt) @@ -67,9 +71,13 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=9 Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (ni-1) + st] * ccdf(std,st,nφ,nt) for (nj,nφ) in enumerate(φ)) end end + # set the output set_prop!(std, :cls, cls) set_prop!(std, :time, t) set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) + + # set the solved status + set_info!(std, :solved, true) end #determine integration weights based on extended Simpson's rule. w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. diff --git a/src/form/steady_state_process.jl b/src/form/steady_state_process.jl index 310adb6..f03c13a 100644 --- a/src/form/steady_state_process.jl +++ b/src/form/steady_state_process.jl @@ -13,13 +13,6 @@ mutable struct SteadyStateProcess <: AbstractMarkovProcess end const steady_state_process_props = [:renewal, :markovian, :steady_state] # parameters -function set_rates!(std::AbstractSTD, cls::AbstractMarkovProcess) - for nt in transitions(std) - if !has_prop(std, nt, :rate) && has_prop(std, nt, :distr) - if get_prop(std, nt, :distr) isa Exponential - set_prop!(std, nt, :rate, rate(get_prop(std, nt, :distr))) - end end end -end function set_markov_chain_matrix!(std::AbstractSTD, cls::SteadyStateProcess) P = zeros(_MSM.Measurement, ns(std), ns(std)) for nt in transitions(std) @@ -40,14 +33,24 @@ function set_parameters!(std::AbstractSTD, cls::SteadyStateProcess) end # stochastic process -solve_steady_state(std) = - hcat(get_prop(std, :P) .- _LA.I(ns(std)),ones(ns(std)))' \ [zeros(ns(std))..., 1.0] -function solve!(std::AbstractSTD, cls::SteadyStateProcess) +function solve!(std::AbstractSTD, cls::SteadyStateProcess; + tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) + # set the input set_parameters!(std, cls) - + + # get the input + t = [Inf] + P = get_prop(std, :P) + Ns = ns(std) + + # solve the problem + sol = hcat(P .- _LA.I(Ns),ones(Ns))' \ [zeros(Ns)..., 1.0] + + # set the output set_prop!(std, :cls, cls) - set_prop!(std, :time, [Inf]) - set_prop!(std, states(std), :prob, solve_steady_state(std)) - + set_prop!(std, :time, t) + set_prop!(std, states(std), :prob, sol) + + # set the solved status set_info!(std, :solved, true) end \ No newline at end of file From bec900077e67d67f9025299fc81601c60c8c42f6 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 26 Apr 2022 14:27:15 +0200 Subject: [PATCH 11/56] Update semi_markov_process.jl --- src/form/semi_markov_process.jl | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index dbfd351..02c96bb 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -13,6 +13,11 @@ mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end # properties const semi_markov_process_props = [:renewal, :dynamic] +# parameters +function set_parameters!(std::AbstractSTD, cls::MarkovProcess) + +end + # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) From 5c7ad67dbfd2a781cc5fe54fb255d3bb7e5b1672 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 26 Apr 2022 14:40:33 +0200 Subject: [PATCH 12/56] update solvedSTD allow for prob::Vector{Vector}, i.e., for p(t) rather than only p(Inf). --- src/form/semi_markov_process.jl | 2 +- src/io/state_transition_diagram.jl | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 02c96bb..1451bb3 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -14,7 +14,7 @@ mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end const semi_markov_process_props = [:renewal, :dynamic] # parameters -function set_parameters!(std::AbstractSTD, cls::MarkovProcess) +function set_parameters!(std::AbstractSTD, cls::SemiMarkovProcess) end diff --git a/src/io/state_transition_diagram.jl b/src/io/state_transition_diagram.jl index 18e027f..787505c 100644 --- a/src/io/state_transition_diagram.jl +++ b/src/io/state_transition_diagram.jl @@ -63,7 +63,7 @@ julia> stdᵍᵉⁿ = solvedSTD(prob = [0.1,0.2,0.7], ``` """ function solvedSTD(;prob::Vector, kwargs...) - isapprox(1.0, sum(prob), rtol=1e-6) || return false + all(isapprox.(1.0, sum(prob), rtol=1e-6)) || return false std = STD(length(prob)) set_info!(std,:solved,true) From 0431e045810bde994818977dcbe096cf35a33784 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 26 Apr 2022 15:48:06 +0200 Subject: [PATCH 13/56] UGO for time dependent probabilities --- src/io/state_transition_diagram.jl | 4 +++- src/prob/universal_generating_operator.jl | 2 +- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/src/io/state_transition_diagram.jl b/src/io/state_transition_diagram.jl index 787505c..c3cdec2 100644 --- a/src/io/state_transition_diagram.jl +++ b/src/io/state_transition_diagram.jl @@ -62,10 +62,12 @@ julia> stdᵍᵉⁿ = solvedSTD(prob = [0.1,0.2,0.7], power = [0.0u"MW",0.0u"MW",2.0u"MW"]) ``` """ -function solvedSTD(;prob::Vector, kwargs...) +function solvedSTD(;prob::Vector, time::Vector=[(Inf)u"yr"], kwargs...) + length(first(prob)) == length(time) || return false all(isapprox.(1.0, sum(prob), rtol=1e-6)) || return false std = STD(length(prob)) + set_prop!(std,:time,time) set_info!(std,:solved,true) set_prop!(std,:msr,collect(intersect(MsrSet,keys(kwargs)))[1]) set_prop!(std,states(std),:prob,prob) diff --git a/src/prob/universal_generating_operator.jl b/src/prob/universal_generating_operator.jl index ba40ac9..ff299f0 100644 --- a/src/prob/universal_generating_operator.jl +++ b/src/prob/universal_generating_operator.jl @@ -40,7 +40,7 @@ end ## Probability Function probability_function(pr::Vector) = - vec([prod(np) for np in Iterators.product(pr...)]) + vec([.*(np...) for np in Iterators.product(pr...)]) ## Structure Function function user_structure_function(ntw::AbstractNetwork, u_node::Int) From 0300203068bc6c8932f95544f428d66f60900c80 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Thu, 28 Apr 2022 09:59:14 +0200 Subject: [PATCH 14/56] Minor changes and fixes in semi_markov_process.jl --- examples/semi-markov/semi-analytical.jl | 6 +++--- src/form/semi_markov_process.jl | 11 ++++++----- 2 files changed, 9 insertions(+), 8 deletions(-) diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index 7958db6..4077950 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -21,10 +21,10 @@ add_states!(std, name = ["normal operation state","degradation state","failed s power = [1.0u"MW", 1.0u"MW", 0.0u"MW"], init = [1.0,0.0,0.0]) -add_transitions!(std, distr = [Exponential(1000u"hr"), Weibull(250u"hr", 1.5)], +add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5)], states = [(1,2),(2,3)]) # solve the network -solve!(std, cls) +solve!(std, cls , tsim = 9u"hr", dt = 3u"hr", tol = 1e-8) -println("test") \ No newline at end of file +Φ = get_prop(std, 3, :prob) \ No newline at end of file diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 1451bb3..ae10eeb 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -50,7 +50,7 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # hier kan code optimalisatie gebeuren gegeven dat φ <<< t φ = zero(dt):dt:nt for (nj,nφ) in enumerate(φ) - Ψ = zeros(ns(std), ns(std))u"hr^-1" + Ψ = zeros(ns(std), ns(std))unit(1/dt) for tr in transitions(std) Ψ[_LG.dst(tr),_LG.src(tr)] = pdf(get_prop(std, tr, :distr),nφ,nt) end @@ -72,8 +72,8 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; w = weights(ni) # hier kan code optimalisatie gebeuren gegeven dat φ <<< t φ = zero(dt):dt:nt - Φ[ni,st] += get_prop(std,st,:init) * ccdf(get_prop(std, tr, :distr),0.0,nt) - Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (ni-1) + st] * ccdf(std,st,nφ,nt) for (nj,nφ) in enumerate(φ)) + Φ[ni,st] += get_prop(std,st,:init) * ccdf(std, st, 0.0, nt) + Φ[ni,st] += sum(dt .* w[nj]unit(1/dt) .* H[ns(std) * (ni-1) + st] * ccdf(std, st, nφ, nt) for (nj,nφ) in enumerate(φ)) end end # set the output @@ -101,9 +101,10 @@ function weights(x) end # check whether sum of ccdf could be suffient -ccdf(std::AbstractSTD, ns::Int, φ::Real, t::Real) = +ccdf(std::AbstractSTD, ns::Int, φ::Real, t::Quantity) = 1.0 - sum(cdf(get_prop(std,_LG.edge(ns,nx),:distr), φ, t) - for nx in _LG.outneighbors(G,ns)) + for nx in _LG.outneighbors(std, ns)) + From 3ef1edb6bb7e0222cf930076bfc762528c9d51fb Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 6 May 2022 16:59:51 +0200 Subject: [PATCH 15/56] Implementation of optical monitoring example --- .../semi-markov/optical-monitoring-system.jl | 47 +++++++++++++++++++ 1 file changed, 47 insertions(+) create mode 100644 examples/semi-markov/optical-monitoring-system.jl diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl new file mode 100644 index 0000000..b64b9e5 --- /dev/null +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -0,0 +1,47 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SemiMarkovProcess() + +# Initializing the state transition diagram of the application example as can be +# found in "Mathematical formulation and numerical treatment based on transition +# frequency densities and quadrature methods for non-homogeneous semi-Markov processes" +# by Moura and Droguett. + +std = STD() +add_states!(std, name = ["normal operation state","reïnstallation state","restore state","halted state"], + power = [1.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW"], + init = [1.0,0.0,0.0,0.0]) + +add_transitions!(std, distr = [Exponential(10000.0u"hr", x -> -0.00004x + 0.6), Weibull(150.0u"hr", 1.36, x -> 0.00004x + 0.4), Exponential(20u"hr", 0.82), LogNormal(2.5u"hr", 0.25u"hr", 0.18), Exponential(20u"hr", 0.62), LogNormal(4.0u"hr", 0.4u"hr", 0.38)], + states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)]) + +# solve the network +solve!(std, cls , tsim = 8760u"hr", dt = 6u"hr", tol = 1e-8) + +Φ1 = _MSS.get_prop(std, 1, :prob) +Φ2 = _MSS.get_prop(std, 2, :prob) +Φ3 = _MSS.get_prop(std, 3, :prob) +Φ4 = _MSS.get_prop(std, 4, :prob) + +using Plots + +t = 0:6:8760 + +plot(t, Φ2) +plot(t, Φ3) +plot(t, Φ4) +plot(t, Φ1) From a086de56fa795c6496d4ad5b7dcc844a6d93a942 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 6 May 2022 17:00:15 +0200 Subject: [PATCH 16/56] Update semi-analytical.jl --- examples/semi-markov/semi-analytical.jl | 21 ++++++++++++++++++--- 1 file changed, 18 insertions(+), 3 deletions(-) diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index 4077950..a478cae 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -1,5 +1,5 @@ ################################################################################ -# Copyright 2020, Tom Van Acker # +# Copyright 2022, Tom Van Acker, Glenn Emmers # ################################################################################ # MultiStateSystems.jl # # A Julia package to solve multi-state system models. # @@ -16,6 +16,11 @@ const _MSS = MultiStateSystems # setting for a specific analysis cls = SemiMarkovProcess() +# Initializing the state transition diagram of the semi analytical example as can be +# found in "Mathematical formulation and numerical treatment based on transition +# frequency densities and quadrature methods for non-homogeneous semi-Markov processes" +# by Moura and Droguett. + std = STD() add_states!(std, name = ["normal operation state","degradation state","failed state"], power = [1.0u"MW", 1.0u"MW", 0.0u"MW"], @@ -25,6 +30,16 @@ add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5 states = [(1,2),(2,3)]) # solve the network -solve!(std, cls , tsim = 9u"hr", dt = 3u"hr", tol = 1e-8) +solve!(std, cls , tsim = 4500u"hr", dt = 3u"hr", tol = 1e-8) + +Φ1 = _MSS.get_prop(std, 1, :prob); +Φ2 = _MSS.get_prop(std, 2, :prob); +Φ = _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob); + +using Plots + +t = 0:3:4500 -Φ = get_prop(std, 3, :prob) \ No newline at end of file +plot(t, Φ1) +plot(t, Φ2) +plot(t, Φ) From e8a44aa6da1e051d4d59a72b707f326e69fe31b7 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 6 May 2022 17:01:17 +0200 Subject: [PATCH 17/56] Update semi_markov_process.jl Correct implementation of sojourn time and time in callbacks of pdf and cdf. Restructured file. --- src/form/semi_markov_process.jl | 130 +++++++++++++++++++++----------- 1 file changed, 88 insertions(+), 42 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index ae10eeb..88c69cd 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -18,31 +18,25 @@ function set_parameters!(std::AbstractSTD, cls::SemiMarkovProcess) end -# stochastic process -function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) - # set the input - set_parameters!(std,cls) +function set_A(std::AbstractSTD, t::StepRange, dt::Number, Nt::Int64) + "A indicates that state j can be reached if the process was initially + in state i and remains there until time t." - # get the input - t = zero(dt):dt:tsim - Nt = length(t) - - # solve the problem - # calculate H A = zeros(ns(std) * Nt) for (ni,nt) in enumerate(t) for tr in transitions(std) id = ns(std) * (ni-1) + _LG.dst(tr) - # met wat moet hier vermeningvuldigd worden? - # - pure pdf - # - integral van de pdf over dt - # - cdf - A[id] = get_prop(std, _LG.src(tr), :init) * - pdf(get_prop(std, tr, :distr),0.0,nt) + A[id] = A[id] + get_prop(std, _LG.src(tr), :init)unit(dt) * + pdf(get_prop(std, tr, :distr), nt - 0.0u"hr",0.0u"hr") end end - + replace_nan!(A) + return A +end + +function set_U(std::AbstractSTD, t::StepRange, dt::Number, Nt::Int64) + "U indicates that state j can be reached if the process enters state i + at time φ and remains there until time t" U = zeros(ns(std) * Nt, ns(std) * Nt) for (ni,nt) in enumerate(t) @@ -52,9 +46,10 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; for (nj,nφ) in enumerate(φ) Ψ = zeros(ns(std), ns(std))unit(1/dt) for tr in transitions(std) - Ψ[_LG.dst(tr),_LG.src(tr)] = pdf(get_prop(std, tr, :distr),nφ,nt) + Ψ[_LG.dst(tr),_LG.src(tr)] = pdf(get_prop(std, tr, :distr),nt-nφ,nφ) + # distr betreden op nϕ en blijven tot nt. Sojourn time = nt-nϕ end - # ranges for time and sojourn time in U + # ranges for time and state entrance time in U rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) if ni == nj @@ -64,7 +59,24 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; end end end - H = U \ A + replace_nan!(U) + return U +end + +# stochastic process +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; + tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) + # set the input + set_parameters!(std,cls) + + # get the input + t = zero(dt):dt:tsim + Nt = length(t) + + # solve the problem + # calculate H + + H = set_U(std, t, dt, Nt)\set_A(std, t, dt, Nt) Φ = zeros(Nt, ns(std)) for st in states(std) @@ -72,8 +84,8 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; w = weights(ni) # hier kan code optimalisatie gebeuren gegeven dat φ <<< t φ = zero(dt):dt:nt - Φ[ni,st] += get_prop(std,st,:init) * ccdf(std, st, 0.0, nt) - Φ[ni,st] += sum(dt .* w[nj]unit(1/dt) .* H[ns(std) * (ni-1) + st] * ccdf(std, st, nφ, nt) for (nj,nφ) in enumerate(φ)) + Φ[ni,st] += get_prop(std,st,:init) * ccdf(std, st, nt - 0.0u"hr",0.0u"hr") + Φ[ni,st] += sum(dt .* w[nj]unit(1/dt) .* H[ns(std) * (nj-1) + st] * ccdf(std, st, nt - nφ, nφ) for (nj,nφ) in enumerate(φ)) end end # set the output @@ -87,26 +99,60 @@ end #determine integration weights based on extended Simpson's rule. w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. function weights(x) - w = zeros(x) - for i in 1:x - if i % 2 == 0 - w[i] = 4/3 - else - w[i] = 2/3 - end end - w[1] = 1/3 - w[end] = 1/3 - - return w -end + # w = zeros(x) + # for i in 1:x + # if i % 2 == 0 + # w[i] = 4/3 + # else + # w[i] = 2/3 + # end end + # w[1] = 1/3 + # w[end] = 1/3 + + # return w + if x==1 + weights = [0] + elseif x==2 + weights = [1/2;1/2] + elseif x==3 + weights = [1/3;4/3;1/3] + elseif x==4 + weights = [3/8;9/8;9/8;3/8] + elseif x==5 + weights = (2/45).*[7;32;12;32;7] + elseif x==6 + weights = (5/288).*[19;75;50;50;75;19] + elseif x==7 + weights = (1/140).*[41;216;27;272;27;216;41] + elseif x==8 + weights = (7/17280).*[751;3577;1323;2989;2989;1323;3577;751] + else + weights = 48*ones(x) + weights[1:4] = [17;59;43;49] + weights[end-3:end] = [49;43;59;17] + weights = (1/48).*weights + end +end # check whether sum of ccdf could be suffient -ccdf(std::AbstractSTD, ns::Int, φ::Real, t::Quantity) = - 1.0 - sum(cdf(get_prop(std,_LG.edge(ns,nx),:distr), φ, t) - for nx in _LG.outneighbors(std, ns)) - - - - +ccdf(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) = + 1.0 - mysum(std, ns, φ, t) + + +function mysum(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) +# Summation function to overcome summation error over empty collection. + if _LG.outneighbors(std.graph, ns) != Int64[] + F = sum(cdf(get_prop(std,_LG.Edge(ns,nx),:distr), φ, t) + for nx in _LG.outneighbors(std.graph, ns)) + else + F = 0 +end end + +function replace_nan!(x) + for i = eachindex(x) + if isnan(x[i]) + x[i] = 0 + end end +end From 61b10876c8e047880df9f940511d4adc79dad2ed Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 6 May 2022 17:04:39 +0200 Subject: [PATCH 18/56] Stripped weight of unit in distributions.jl The evaluation of the probability function in the transition rates gave an error caused by the unit coupled to "t". This is resolved by stripping "t" of it's unit for the sole purpose of evaluating that function. Most likely there is a better solution to this problem. --- src/io/distributions.jl | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/src/io/distributions.jl b/src/io/distributions.jl index 0b9a1be..643e3a4 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -93,7 +93,7 @@ function pdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) - eval(ω,t) * (1/θ) * exp(-y/θ) + eval(ω,_UF.ustrip(t)) * (1/θ) * exp(-y/θ) else zero(1/θ) end @@ -103,7 +103,7 @@ function cdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) - eval(ω,t) * (1 - exp(-y/θ)) + eval(ω,_UF.ustrip(t)) * (1 - exp(-y/θ)) else zero(Number) end @@ -113,9 +113,9 @@ function ccdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) - eval(ω,t) * exp(-y/θ) + eval(ω,_UF.ustrip(t)) * exp(-y/θ) else - eval(ω,t) + eval(ω,_UF.ustrip(t)) end end @@ -202,7 +202,7 @@ function pdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = (uconvert(unit(θ),φ) + eps(θ)) / θ - eval(ω,t) * (α / θ) * y^(α - 1) * exp(-y^α) + eval(ω,_UF.ustrip(t)) * (α / θ) * y^(α - 1) * exp(-y^α) else zero(1/θ) end @@ -212,7 +212,7 @@ function cdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) / θ - ustrip(eval(ω,t) * (1 - exp(-y^α))) + ustrip(eval(ω,_UF.ustrip(t)) * (1 - exp(-y^α))) else zero(Number) end @@ -222,9 +222,9 @@ function ccdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) / θ - eval(ω,t) * exp(-y^α) + eval(ω,_UF.ustrip(t)) * exp(-y^α) else - eval(ω,t) + eval(ω,_UF.ustrip(t)) end end @@ -313,7 +313,7 @@ function pdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) if φ >= zero(μ) x = ustrip(unit(φ), σ) y = uconvert(unit(φ/φ),(log(φ) - μ)^2 / (2 * σ^2)) - eval(ω,t) / (sqrt(2 * pi) * x * φ) * exp(-y) + eval(ω,_UF.ustrip(t)) / (sqrt(2 * pi) * x * φ) * exp(-y) else zero(1/φ) end @@ -323,7 +323,7 @@ function cdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false if φ >= zero(μ) y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) - eval(ω,t) / 2 * _SF.erfc(-y) + eval(ω,_UF.ustrip(t)) / 2 * _SF.erfc(-y) else zero(Number) end @@ -333,8 +333,8 @@ function ccdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false if φ >= zero(μ) y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) - eval(ω,t) * (1 - _SF.erfc(-y) / 2) + eval(ω,_UF.ustrip(t)) * (1 - _SF.erfc(-y) / 2) else - eval(ω,t) + eval(ω,_UF.ustrip(t)) end end \ No newline at end of file From 04289b111e02852fbd6c40edd964833a786b653d Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Sat, 7 May 2022 14:35:40 +0200 Subject: [PATCH 19/56] small changes --- .../semi-markov/optical-monitoring-system.jl | 66 ++++++++++++------- examples/semi-markov/semi-analytical.jl | 56 ++++++++++------ src/io/distributions.jl | 24 +++---- 3 files changed, 89 insertions(+), 57 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index b64b9e5..20c2745 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -5,9 +5,24 @@ # A Julia package to solve multi-state system models. # # See http://github.com/timmyfaraday/MultiStateSystems.jl # ################################################################################ +""" +Example considering a semi-Markov model taken from: + +> Mathematical formulation and numerical treatment based on transition frequency + densities and quadrature methods for non-homogeneous semi-Markov processes by + Moura and Droguett (2009) + +States: +- 1 : normal operation state +- 2 : reinstallation state +- 3 : restoration state +- 4 : halted state +""" # load pkgs +using Plots using Unitful +using UnitfulRecipes using MultiStateSystems # pkg const @@ -16,32 +31,35 @@ const _MSS = MultiStateSystems # setting for a specific analysis cls = SemiMarkovProcess() -# Initializing the state transition diagram of the application example as can be -# found in "Mathematical formulation and numerical treatment based on transition -# frequency densities and quadrature methods for non-homogeneous semi-Markov processes" -# by Moura and Droguett. - +# initialize the state-transition diagram std = STD() -add_states!(std, name = ["normal operation state","reïnstallation state","restore state","halted state"], - power = [1.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW"], - init = [1.0,0.0,0.0,0.0]) -add_transitions!(std, distr = [Exponential(10000.0u"hr", x -> -0.00004x + 0.6), Weibull(150.0u"hr", 1.36, x -> 0.00004x + 0.4), Exponential(20u"hr", 0.82), LogNormal(2.5u"hr", 0.25u"hr", 0.18), Exponential(20u"hr", 0.62), LogNormal(4.0u"hr", 0.4u"hr", 0.38)], - states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)]) - -# solve the network -solve!(std, cls , tsim = 8760u"hr", dt = 6u"hr", tol = 1e-8) - -Φ1 = _MSS.get_prop(std, 1, :prob) -Φ2 = _MSS.get_prop(std, 2, :prob) -Φ3 = _MSS.get_prop(std, 3, :prob) -Φ4 = _MSS.get_prop(std, 4, :prob) +# add the states to the std +add_states!(std, name = ["normal operation state","reinstallation state","restore state","halted state"], + init = [1.0,0.0,0.0,0.0]) -using Plots +# add the transitions to the std +add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], + distr = [ Exponential(10000.0u"hr", t -> -0.00004u"1/hr" * t + 0.6), + Weibull(150.0u"hr", 1.36, t -> 0.00004u"1/hr" * t + 0.4), + Exponential(20.0u"hr", 0.82), + LogNormal(2.5u"hr", 0.25u"hr", 0.18), + Exponential(20.0u"hr", 0.62), + LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) + +# solve the std +solve!(std, cls, tsim = 8760.0u"hr", dt = 6.0u"hr") -t = 0:6:8760 +# plot the probabilities +plot(_MSS.get_prop(std, :time), + [_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)], + label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), + xlabel="time", + ylabel="probability") -plot(t, Φ2) -plot(t, Φ3) -plot(t, Φ4) -plot(t, Φ1) +# plot the reliability +plot(_MSS.get_prop(std, :time), + _MSS.get_prop(std, 1, :prob), + label="reliability", + xlabel="time", + ylabel="probability") \ No newline at end of file diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index a478cae..b6a1792 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -5,9 +5,23 @@ # A Julia package to solve multi-state system models. # # See http://github.com/timmyfaraday/MultiStateSystems.jl # ################################################################################ +""" +Example considering a semi-Markov model taken from: + +> Mathematical formulation and numerical treatment based on transition frequency + densities and quadrature methods for non-homogeneous semi-Markov processes by + Moura and Droguett (2009) + +States: +- 1 : normal operation state +- 2 : degradation state +- 3 : failed state +""" # load pkgs +using Plots using Unitful +using UnitfulRecipes using MultiStateSystems # pkg const @@ -16,30 +30,30 @@ const _MSS = MultiStateSystems # setting for a specific analysis cls = SemiMarkovProcess() -# Initializing the state transition diagram of the semi analytical example as can be -# found in "Mathematical formulation and numerical treatment based on transition -# frequency densities and quadrature methods for non-homogeneous semi-Markov processes" -# by Moura and Droguett. - +# initialize the state-transition diagram std = STD() + +# add the states to the std add_states!(std, name = ["normal operation state","degradation state","failed state"], - power = [1.0u"MW", 1.0u"MW", 0.0u"MW"], - init = [1.0,0.0,0.0]) + init = [1.0,0.0,0.0]) +# add the transitions to the std add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5)], states = [(1,2),(2,3)]) -# solve the network -solve!(std, cls , tsim = 4500u"hr", dt = 3u"hr", tol = 1e-8) - -Φ1 = _MSS.get_prop(std, 1, :prob); -Φ2 = _MSS.get_prop(std, 2, :prob); -Φ = _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob); - -using Plots - -t = 0:3:4500 - -plot(t, Φ1) -plot(t, Φ2) -plot(t, Φ) +# solve the std +solve!(std, cls, tsim = 4500u"hr", dt = 3u"hr") + +# plot all probabilities +plot(_MSS.get_prop(std, :time), + [_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)], + label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), + xlabel="time", + ylabel="probability") + +# plot the reliability +plot(_MSS.get_prop(std, :time), + _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob), + label="reliability", + xlabel="time", + ylabel="probability") \ No newline at end of file diff --git a/src/io/distributions.jl b/src/io/distributions.jl index 643e3a4..0b9a1be 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -93,7 +93,7 @@ function pdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) - eval(ω,_UF.ustrip(t)) * (1/θ) * exp(-y/θ) + eval(ω,t) * (1/θ) * exp(-y/θ) else zero(1/θ) end @@ -103,7 +103,7 @@ function cdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) - eval(ω,_UF.ustrip(t)) * (1 - exp(-y/θ)) + eval(ω,t) * (1 - exp(-y/θ)) else zero(Number) end @@ -113,9 +113,9 @@ function ccdf(dst::AbstractExponential, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) - eval(ω,_UF.ustrip(t)) * exp(-y/θ) + eval(ω,t) * exp(-y/θ) else - eval(ω,_UF.ustrip(t)) + eval(ω,t) end end @@ -202,7 +202,7 @@ function pdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = (uconvert(unit(θ),φ) + eps(θ)) / θ - eval(ω,_UF.ustrip(t)) * (α / θ) * y^(α - 1) * exp(-y^α) + eval(ω,t) * (α / θ) * y^(α - 1) * exp(-y^α) else zero(1/θ) end @@ -212,7 +212,7 @@ function cdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) / θ - ustrip(eval(ω,_UF.ustrip(t)) * (1 - exp(-y^α))) + ustrip(eval(ω,t) * (1 - exp(-y^α))) else zero(Number) end @@ -222,9 +222,9 @@ function ccdf(dst::AbstractWeibull, φ::Number, t::Number=zero(φ)) dimension(θ)==dimension(φ)==dimension(t) || return false if φ >= zero(θ) y = uconvert(unit(θ),φ) / θ - eval(ω,_UF.ustrip(t)) * exp(-y^α) + eval(ω,t) * exp(-y^α) else - eval(ω,_UF.ustrip(t)) + eval(ω,t) end end @@ -313,7 +313,7 @@ function pdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) if φ >= zero(μ) x = ustrip(unit(φ), σ) y = uconvert(unit(φ/φ),(log(φ) - μ)^2 / (2 * σ^2)) - eval(ω,_UF.ustrip(t)) / (sqrt(2 * pi) * x * φ) * exp(-y) + eval(ω,t) / (sqrt(2 * pi) * x * φ) * exp(-y) else zero(1/φ) end @@ -323,7 +323,7 @@ function cdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false if φ >= zero(μ) y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) - eval(ω,_UF.ustrip(t)) / 2 * _SF.erfc(-y) + eval(ω,t) / 2 * _SF.erfc(-y) else zero(Number) end @@ -333,8 +333,8 @@ function ccdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false if φ >= zero(μ) y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) - eval(ω,_UF.ustrip(t)) * (1 - _SF.erfc(-y) / 2) + eval(ω,t) * (1 - _SF.erfc(-y) / 2) else - eval(ω,_UF.ustrip(t)) + eval(ω,t) end end \ No newline at end of file From 6c03d0b0c5dc4894dbfe42a15289ca31b09f1d94 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Sun, 8 May 2022 19:52:18 +0200 Subject: [PATCH 20/56] Update semi-analytical.jl --- examples/semi-markov/semi-analytical.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index b6a1792..68e16d2 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -42,7 +42,7 @@ add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5 states = [(1,2),(2,3)]) # solve the std -solve!(std, cls, tsim = 4500u"hr", dt = 3u"hr") +solve!(std, cls, tsim = 4500.0u"hr", dt = 3.0u"hr") # plot all probabilities plot(_MSS.get_prop(std, :time), From 5fdc97f34c43967f041630d6010b5735b270ea4b Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 10 May 2022 14:07:42 +0200 Subject: [PATCH 21/56] Update semi_markov_process.jl --- src/form/semi_markov_process.jl | 178 +++++++++++++++++++------------- 1 file changed, 106 insertions(+), 72 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 88c69cd..efea31b 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -6,7 +6,6 @@ # See http://github.com/timmyfaraday/MultiStateSystems.jl # ################################################################################ - # abstract types mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end @@ -18,38 +17,74 @@ function set_parameters!(std::AbstractSTD, cls::SemiMarkovProcess) end -function set_A(std::AbstractSTD, t::StepRange, dt::Number, Nt::Int64) - "A indicates that state j can be reached if the process was initially - in state i and remains there until time t." +# UNITS +# cdf - [-] +# ccdf - [-] +# pdf - [unit(1/dt)] -> ∫ pdf dt = [-] +# Consequently: +# A - unit of the pdf [unit(1/dt)] + +""" + MultiStateSystems.set_A(std::MultiStateSystems.AbstractSTD, t::StepRangeLen) + +A indicates that state j can be reached if the process was initially in state i +and remains there until time t. + +The unit of A is [unit(1/t)] +""" +function set_A(std::AbstractSTD, t::StepRangeLen) + dt = step(t) + Nt = length(t) - A = zeros(ns(std) * Nt) + A = zeros(typeof(1/dt), ns(std) * Nt) for (ni,nt) in enumerate(t) for tr in transitions(std) id = ns(std) * (ni-1) + _LG.dst(tr) - A[id] = A[id] + get_prop(std, _LG.src(tr), :init)unit(dt) * - pdf(get_prop(std, tr, :distr), nt - 0.0u"hr",0.0u"hr") + # TOM: I removed the unit(dt), the initial probability has no unit, + # as probability has no unit. + # The pdf has a unit [1/unit(t)] as this has no meaning until you + # take the integral under the pdf, given that the x-axis is time, + # this integral would result in a unitless probability. + # TOM: I removed the - 0.0u"hr" in the second argument of the pdf + # function as this is pointless. + # TOM: I changed 0.0u"hr" in the third argument of the pdf function + # to zero(dt) to be agnostic + A[id] += get_prop(std, _LG.src(tr), :init) * + pdf(get_prop(std, tr, :distr), nt, zero(dt)) end end - replace_nan!(A) + # TOM: the replacement of NaN is easier done as follows + A[isnan.(A)] .= zero(1/dt) + return A end -function set_U(std::AbstractSTD, t::StepRange, dt::Number, Nt::Int64) - "U indicates that state j can be reached if the process enters state i - at time φ and remains there until time t" - U = zeros(ns(std) * Nt, ns(std) * Nt) +""" + MultiStateSystems.set_U(std::MultiStateSystems.AbstractSTD, t::StepRangeLen) + +U indicates that state j can be reached if the process enters state i at time φ +and remains there until time t + +The unit of U is [-] +""" +function set_U(std::AbstractSTD, t::StepRangeLen) + dt = step(t) + Nt = length(t) + + U = zeros(Float64, ns(std) * Nt, ns(std) * Nt) for (ni,nt) in enumerate(t) w = weights(ni) - # hier kan code optimalisatie gebeuren gegeven dat φ <<< t φ = zero(dt):dt:nt for (nj,nφ) in enumerate(φ) - Ψ = zeros(ns(std), ns(std))unit(1/dt) + # TOM: I internalized unit(1/dt) after the zeros function as + # typeof(1/dt) to be agnostic + Ψ = zeros(typeof(1/dt), ns(std), ns(std)) for tr in transitions(std) - Ψ[_LG.dst(tr),_LG.src(tr)] = pdf(get_prop(std, tr, :distr),nt-nφ,nφ) - # distr betreden op nϕ en blijven tot nt. Sojourn time = nt-nϕ + # GLENN: distr betreden op nϕ en blijven tot nt, φ = nt - nϕ + Ψ[_LG.dst(tr), _LG.src(tr)] = + pdf(get_prop(std, tr, :distr), nt - nφ, nφ) end - # ranges for time and state entrance time in U rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) if ni == nj @@ -58,8 +93,9 @@ function set_U(std::AbstractSTD, t::StepRange, dt::Number, Nt::Int64) U[rT,rΦ] = -dt .* w[nj] .* Ψ end end end + # TOM: the replacement of NaN is easier done as follows + U[isnan.(U)] .= 0.0 - replace_nan!(U) return U end @@ -70,22 +106,30 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; set_parameters!(std,cls) # get the input - t = zero(dt):dt:tsim - Nt = length(t) + t = zero(dt):dt:tsim + Nt = length(t) # solve the problem - # calculate H - - H = set_U(std, t, dt, Nt)\set_A(std, t, dt, Nt) - - Φ = zeros(Nt, ns(std)) + Φ = zeros(Nt, ns(std)) + # TOM: dt and Nt can easily be accessed from t, and are therefore removed as + # arguments for both functions set_U and set_A + H = set_U(std, t) \ set_A(std, t) for st in states(std) for (ni,nt) in enumerate(t) - w = weights(ni) - # hier kan code optimalisatie gebeuren gegeven dat φ <<< t - φ = zero(dt):dt:nt - Φ[ni,st] += get_prop(std,st,:init) * ccdf(std, st, nt - 0.0u"hr",0.0u"hr") - Φ[ni,st] += sum(dt .* w[nj]unit(1/dt) .* H[ns(std) * (nj-1) + st] * ccdf(std, st, nt - nφ, nφ) for (nj,nφ) in enumerate(φ)) + w = weights(ni) + φ = zero(dt):dt:nt + # TOM: I removed the - 0.0u"hr" in the second argument of the ccdf + # function as this is pointless. + # TOM: I changed 0.0u"hr" in the third argument of the ccdf function + # to zero(dt) to be agnostic + Φ[ni,st] += get_prop(std,st,:init) * ccdf(std, st, nt, zero(dt)) + # TOM: I removed the unit(1/dt) after the w[nj] as this does not + # make any sense. + # TOM: In order for this formula to make sense the unit of H needs + # to be unit(1/dt). Currently, it is the inverse, i.e., unit(dt). + Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj - 1) + st] .* + ccdf(std, st, nt - nφ, nφ) + for (nj,nφ) in enumerate(φ)) end end # set the output @@ -97,48 +141,39 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; set_info!(std, :solved, true) end -#determine integration weights based on extended Simpson's rule. w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. -function weights(x) - # w = zeros(x) - # for i in 1:x - # if i % 2 == 0 - # w[i] = 4/3 - # else - # w[i] = 2/3 - # end end - # w[1] = 1/3 - # w[end] = 1/3 - - # return w - if x==1 - weights = [0] - elseif x==2 - weights = [1/2;1/2] - elseif x==3 - weights = [1/3;4/3;1/3] - elseif x==4 - weights = [3/8;9/8;9/8;3/8] - elseif x==5 - weights = (2/45).*[7;32;12;32;7] - elseif x==6 - weights = (5/288).*[19;75;50;50;75;19] - elseif x==7 - weights = (1/140).*[41;216;27;272;27;216;41] - elseif x==8 - weights = (7/17280).*[751;3577;1323;2989;2989;1323;3577;751] - else - weights = 48*ones(x) - weights[1:4] = [17;59;43;49] - weights[end-3:end] = [49;43;59;17] - weights = (1/48).*weights - end +# TOM: rewrote the weights function for better readability. +""" + MultiStateSystems.weights(x::Int) + +Determine integration weights based on extended Simpson's rule. +w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. +""" +function weights(x::Int) + x==1 && return [0] + x==2 && return [1/2, 1/2] + x==3 && return [1/3, 4/3, 1/3] + x==4 && return [3/8, 9/8, 9/8, 3/8] + x==5 && return (2/45) .* [7, 32, 12, 32, 7] + x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] + x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] + x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] + + weights = 48 * ones(x) + weights[1:4] = [17, 59, 43, 49] + weights[end-3:end] = [49, 43, 59, 17] + return (1/48) .* weights end +# # TOM: Alternative formulation for the state ccdf, using the trapping info prop +# cdf(std::AbstractSTD, ns::Int, φ::Number, t::Number) = +# sum(cdf(get_prop(std, _LG.Edge(ns,nx), :distr), φ, t) for nx in _LG.outneighbors(std.graph, ns)) +# ccdf(std::AbstractSTD, ns::Int, φ::Number, t::Number) = +# ifelse(get_prop(std, ns, :trapping), 1.0, 1.0 - cdf(std, ns, φ, t)) + # check whether sum of ccdf could be suffient ccdf(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) = 1.0 - mysum(std, ns, φ, t) - function mysum(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) # Summation function to overcome summation error over empty collection. if _LG.outneighbors(std.graph, ns) != Int64[] @@ -148,11 +183,10 @@ function mysum(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) F = 0 end end -function replace_nan!(x) - for i = eachindex(x) - if isnan(x[i]) - x[i] = 0 - end end -end +# TOM: added functionality to enable \ with units. +elunit(A::Matrix{U}) where U = _UF.unit(U) +elunit(b::Vector{U}) where U = _UF.unit(U) +_LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = + (ustrip.(A) \ ustrip(b)) * (elunit(b) / elunit(A)) From 9cb524bc15910c1346b5a769e0939f21ef00e741 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 10 May 2022 14:34:36 +0200 Subject: [PATCH 22/56] Update semi_markov_process.jl --- src/form/semi_markov_process.jl | 52 +++++---------------------------- 1 file changed, 8 insertions(+), 44 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index efea31b..11ff864 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -12,18 +12,6 @@ mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end # properties const semi_markov_process_props = [:renewal, :dynamic] -# parameters -function set_parameters!(std::AbstractSTD, cls::SemiMarkovProcess) - -end - -# UNITS -# cdf - [-] -# ccdf - [-] -# pdf - [unit(1/dt)] -> ∫ pdf dt = [-] -# Consequently: -# A - unit of the pdf [unit(1/dt)] - """ MultiStateSystems.set_A(std::MultiStateSystems.AbstractSTD, t::StepRangeLen) @@ -41,19 +29,10 @@ function set_A(std::AbstractSTD, t::StepRangeLen) for (ni,nt) in enumerate(t) for tr in transitions(std) id = ns(std) * (ni-1) + _LG.dst(tr) - # TOM: I removed the unit(dt), the initial probability has no unit, - # as probability has no unit. - # The pdf has a unit [1/unit(t)] as this has no meaning until you - # take the integral under the pdf, given that the x-axis is time, - # this integral would result in a unitless probability. - # TOM: I removed the - 0.0u"hr" in the second argument of the pdf - # function as this is pointless. - # TOM: I changed 0.0u"hr" in the third argument of the pdf function - # to zero(dt) to be agnostic + # NB: GLENN same clarification A[id] += get_prop(std, _LG.src(tr), :init) * pdf(get_prop(std, tr, :distr), nt, zero(dt)) end end - # TOM: the replacement of NaN is easier done as follows A[isnan.(A)] .= zero(1/dt) return A @@ -77,11 +56,9 @@ function set_U(std::AbstractSTD, t::StepRangeLen) w = weights(ni) φ = zero(dt):dt:nt for (nj,nφ) in enumerate(φ) - # TOM: I internalized unit(1/dt) after the zeros function as - # typeof(1/dt) to be agnostic Ψ = zeros(typeof(1/dt), ns(std), ns(std)) for tr in transitions(std) - # GLENN: distr betreden op nϕ en blijven tot nt, φ = nt - nϕ + # NB: GLENN additional clarification distr betreden op nϕ en blijven tot nt, φ = nt - nϕ Ψ[_LG.dst(tr), _LG.src(tr)] = pdf(get_prop(std, tr, :distr), nt - nφ, nφ) end @@ -93,7 +70,6 @@ function set_U(std::AbstractSTD, t::StepRangeLen) U[rT,rΦ] = -dt .* w[nj] .* Ψ end end end - # TOM: the replacement of NaN is easier done as follows U[isnan.(U)] .= 0.0 return U @@ -101,34 +77,23 @@ end # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) - # set the input - set_parameters!(std,cls) - + tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) # get the input t = zero(dt):dt:tsim Nt = length(t) # solve the problem Φ = zeros(Nt, ns(std)) - # TOM: dt and Nt can easily be accessed from t, and are therefore removed as - # arguments for both functions set_U and set_A H = set_U(std, t) \ set_A(std, t) for st in states(std) for (ni,nt) in enumerate(t) w = weights(ni) + # TOM: φ <<< t φ = zero(dt):dt:nt - # TOM: I removed the - 0.0u"hr" in the second argument of the ccdf - # function as this is pointless. - # TOM: I changed 0.0u"hr" in the third argument of the ccdf function - # to zero(dt) to be agnostic - Φ[ni,st] += get_prop(std,st,:init) * ccdf(std, st, nt, zero(dt)) - # TOM: I removed the unit(1/dt) after the w[nj] as this does not - # make any sense. - # TOM: In order for this formula to make sense the unit of H needs - # to be unit(1/dt). Currently, it is the inverse, i.e., unit(dt). - Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj - 1) + st] .* - ccdf(std, st, nt - nφ, nφ) + # NB: ccdf(t-φ,φ) where φ = 0.0, GLENN, additional clarification + Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) + Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + ccdf(std, st, nt-nφ, nφ) for (nj,nφ) in enumerate(φ)) end end @@ -141,7 +106,6 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; set_info!(std, :solved, true) end -# TOM: rewrote the weights function for better readability. """ MultiStateSystems.weights(x::Int) From 122bfbf8ad140f2c89e5e795fec42d31d94448ee Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Tue, 10 May 2022 15:22:54 +0200 Subject: [PATCH 23/56] Create validation_test.jl --- examples/semi-markov/validation_test.jl | 60 +++++++++++++++++++++++++ 1 file changed, 60 insertions(+) create mode 100644 examples/semi-markov/validation_test.jl diff --git a/examples/semi-markov/validation_test.jl b/examples/semi-markov/validation_test.jl new file mode 100644 index 0000000..10eb866 --- /dev/null +++ b/examples/semi-markov/validation_test.jl @@ -0,0 +1,60 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SemiMarkovProcess() + +# Initializing the state transition diagram of a homogeneous semi markov process to test +# the model + +std = STD() +add_states!(std, name = ["normal operation state","fault operation state f1","Primary post-fault state f1","Secondary post-fault state f1", "Fault operation state for f1", "Primary post-fault state for f2", "secondary post-fault state for f2", "fault operation state for f3", "Primary post-fault state for f3", "secondary post-fault state for f3"], + power = [1.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW"], + init = [1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + +add_transitions!(std, distr = [Weibull(10000.0u"hr", 1.25, 0.33), LogNormal(10.0u"hr", 0.08u"hr", 0.8), LogNormal(13.0u"hr", 0.08u"hr", 0.2), LogNormal(100.0u"hr", 0.08u"hr"), Weibull(1000.0u"hr", 10), Weibull(8000.0u"hr", 1.5, 0.33), LogNormal(10.0u"hr", 0.08u"hr", 0.8), LogNormal(13.0u"hr", 0.08u"hr", 0.2), LogNormal(100u"hr", 0.08u"hr"), Weibull(1000.0u"hr", 10), Weibull(12500.0u"hr", 1.75, 0.33), LogNormal(10.0u"hr", 0.08u"hr", 0.8), LogNormal(13.0u"hr", 0.08u"hr", 0.2), LogNormal(100.0u"hr", 0.08u"hr"), Weibull(1000.0u"hr", 10.0)], + states = [(1,2),(2,3),(2,4),(4,3),(3,1),(1,5),(5,6),(5,7),(7,6),(6,1),(1,8),(8,9),(8,10),(10,9),(9,1)]) + +# solve the network +solve!(std, cls , tsim = 450000u"hr", dt = 300u"hr", tol = 1e-8) + +Φ1 = _MSS.get_prop(std, 1, :prob) +Φ2 = _MSS.get_prop(std, 2, :prob) +Φ3 = _MSS.get_prop(std, 3, :prob) +Φ4 = _MSS.get_prop(std, 4, :prob) +Φ5 = _MSS.get_prop(std, 5, :prob) +Φ6 = _MSS.get_prop(std, 6, :prob) +Φ7 = _MSS.get_prop(std, 7, :prob) +Φ8 = _MSS.get_prop(std, 8, :prob) +Φ9 = _MSS.get_prop(std, 9, :prob) +Φ10 = _MSS.get_prop(std, 10, :prob) + + +using Plots + +t = 0:300:450000 + +plot(t, Φ2) +plot(t, Φ3) +plot(t, Φ4) +plot(t, Φ5) +plot(t, Φ6) +plot(t, Φ7) +plot(t, Φ8) +plot(t, Φ9) +plot(t, Φ10) +plot(t, Φ1) +# +# \ No newline at end of file From 1a36464604da5b812bbb44b27c218b80f24fc959 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 10 May 2022 15:27:45 +0200 Subject: [PATCH 24/56] small updates --- .../semi-markov/optical-monitoring-system.jl | 4 ++-- src/form/semi_markov_process.jl | 18 +++++++++--------- 2 files changed, 11 insertions(+), 11 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 20c2745..1c37044 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -48,7 +48,7 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # solve the std -solve!(std, cls, tsim = 8760.0u"hr", dt = 6.0u"hr") +solve!(std, cls, tsim = 8760.0u"hr", dt = 5.84u"hr") # plot the probabilities plot(_MSS.get_prop(std, :time), @@ -58,7 +58,7 @@ plot(_MSS.get_prop(std, :time), ylabel="probability") # plot the reliability -plot(_MSS.get_prop(std, :time), +plot!(_MSS.get_prop(std, :time), _MSS.get_prop(std, 1, :prob), label="reliability", xlabel="time", diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 11ff864..01b8531 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -54,13 +54,13 @@ function set_U(std::AbstractSTD, t::StepRangeLen) for (ni,nt) in enumerate(t) w = weights(ni) - φ = zero(dt):dt:nt - for (nj,nφ) in enumerate(φ) + l = zero(dt):dt:nt + for (nj,nl) in enumerate(l) Ψ = zeros(typeof(1/dt), ns(std), ns(std)) for tr in transitions(std) - # NB: GLENN additional clarification distr betreden op nϕ en blijven tot nt, φ = nt - nϕ + # NB: GLENN additional clarification distr betreden op nϕ en blijven tot nt, φ = nt - nl Ψ[_LG.dst(tr), _LG.src(tr)] = - pdf(get_prop(std, tr, :distr), nt - nφ, nφ) + pdf(get_prop(std, tr, :distr), nt - nl, nl) end rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) @@ -88,13 +88,13 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; for st in states(std) for (ni,nt) in enumerate(t) w = weights(ni) - # TOM: φ <<< t - φ = zero(dt):dt:nt - # NB: ccdf(t-φ,φ) where φ = 0.0, GLENN, additional clarification + # TOM: φ <<< t, zero could be higher + l = zero(dt):dt:nt + # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* - ccdf(std, st, nt-nφ, nφ) - for (nj,nφ) in enumerate(φ)) + ccdf(std, st, nt-nl, nl) + for (nj,nl) in enumerate(l)) end end # set the output From 3512e6c6be2eaa13f8f07722f04ba5f192cfaafa Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Thu, 12 May 2022 18:00:59 +0200 Subject: [PATCH 25/56] Cleanup validation_test.jl --- examples/semi-markov/validation_test.jl | 66 +++++++++++++------------ 1 file changed, 34 insertions(+), 32 deletions(-) diff --git a/examples/semi-markov/validation_test.jl b/examples/semi-markov/validation_test.jl index 10eb866..af5e14b 100644 --- a/examples/semi-markov/validation_test.jl +++ b/examples/semi-markov/validation_test.jl @@ -7,7 +7,9 @@ ################################################################################ # load pkgs +using Plots using Unitful +using UnitfulRecipes using MultiStateSystems # pkg const @@ -24,37 +26,37 @@ add_states!(std, name = ["normal operation state","fault operation state f1","P power = [1.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW"], init = [1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) -add_transitions!(std, distr = [Weibull(10000.0u"hr", 1.25, 0.33), LogNormal(10.0u"hr", 0.08u"hr", 0.8), LogNormal(13.0u"hr", 0.08u"hr", 0.2), LogNormal(100.0u"hr", 0.08u"hr"), Weibull(1000.0u"hr", 10), Weibull(8000.0u"hr", 1.5, 0.33), LogNormal(10.0u"hr", 0.08u"hr", 0.8), LogNormal(13.0u"hr", 0.08u"hr", 0.2), LogNormal(100u"hr", 0.08u"hr"), Weibull(1000.0u"hr", 10), Weibull(12500.0u"hr", 1.75, 0.33), LogNormal(10.0u"hr", 0.08u"hr", 0.8), LogNormal(13.0u"hr", 0.08u"hr", 0.2), LogNormal(100.0u"hr", 0.08u"hr"), Weibull(1000.0u"hr", 10.0)], - states = [(1,2),(2,3),(2,4),(4,3),(3,1),(1,5),(5,6),(5,7),(7,6),(6,1),(1,8),(8,9),(8,10),(10,9),(9,1)]) +add_transitions!(std, states = [(1,2),(2,3),(2,4),(4,3),(3,1),(1,5),(5,6),(5,7),(7,6),(6,1),(1,8),(8,9),(8,10),(10,9),(9,1)], + distr = [Weibull(10000.0u"hr", 1.25, 0.33), + LogNormal(10.0u"hr", 0.08u"hr", 0.8), + LogNormal(13.0u"hr", 0.08u"hr", 0.2), + LogNormal(100.0u"hr", 0.08u"hr"), + Weibull(1000.0u"hr", 10), + Weibull(8000.0u"hr", 1.5, 0.33), + LogNormal(10.0u"hr", 0.08u"hr", 0.8), + LogNormal(13.0u"hr", 0.08u"hr", 0.2), + LogNormal(100u"hr", 0.08u"hr"), + Weibull(1000.0u"hr", 10), + Weibull(12500.0u"hr", 1.75, 0.33), + LogNormal(10.0u"hr", 0.08u"hr", 0.8), + LogNormal(13.0u"hr", 0.08u"hr", 0.2), + LogNormal(100.0u"hr", 0.08u"hr"), + Weibull(1000.0u"hr", 10.0)]) + # solve the network -solve!(std, cls , tsim = 450000u"hr", dt = 300u"hr", tol = 1e-8) - -Φ1 = _MSS.get_prop(std, 1, :prob) -Φ2 = _MSS.get_prop(std, 2, :prob) -Φ3 = _MSS.get_prop(std, 3, :prob) -Φ4 = _MSS.get_prop(std, 4, :prob) -Φ5 = _MSS.get_prop(std, 5, :prob) -Φ6 = _MSS.get_prop(std, 6, :prob) -Φ7 = _MSS.get_prop(std, 7, :prob) -Φ8 = _MSS.get_prop(std, 8, :prob) -Φ9 = _MSS.get_prop(std, 9, :prob) -Φ10 = _MSS.get_prop(std, 10, :prob) - - -using Plots - -t = 0:300:450000 - -plot(t, Φ2) -plot(t, Φ3) -plot(t, Φ4) -plot(t, Φ5) -plot(t, Φ6) -plot(t, Φ7) -plot(t, Φ8) -plot(t, Φ9) -plot(t, Φ10) -plot(t, Φ1) -# -# \ No newline at end of file +solve!(std, cls , tsim = 450000.0u"hr", dt = 600u"hr") + +# plot the probabilities +plot(_MSS.get_prop(std, :time), + [_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)], + label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), + xlabel="time", + ylabel="probability") + +# plot the reliability +plot!(_MSS.get_prop(std, :time), + _MSS.get_prop(std, 1, :prob), + label="reliability", + xlabel="time", + ylabel="probability") From ba892c03019ea831e4fed996a3fb9a67568451d7 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Fri, 13 May 2022 12:02:31 +0200 Subject: [PATCH 26/56] add QuadGK for integrals --- Project.toml | 4 +- examples/semi-markov/semi-analytical.jl | 79 +++++++++++++++++++++---- src/MultiStateSystems.jl | 2 + src/form/markov_process.jl | 10 +++- 4 files changed, 79 insertions(+), 16 deletions(-) diff --git a/Project.toml b/Project.toml index bbf8146..dd6ee2e 100644 --- a/Project.toml +++ b/Project.toml @@ -10,6 +10,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7" Multigraphs = "7ebac608-6c66-46e6-9856-b5f43e107bac" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" +QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" @@ -19,8 +20,9 @@ LightGraphs = "1.3.5" Measurements = "2.6.0" Multigraphs = "0.2.2" OrdinaryDiffEq = "5.59.4" -Unitful = "1.8.0" SpecialFunctions = "1.8.4" +Unitful = "1.8.0" +QuadGK = "2.4.2" julia = "1" [extras] diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index 68e16d2..a6426b9 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -23,12 +23,20 @@ using Plots using Unitful using UnitfulRecipes using MultiStateSystems +using LightGraphs +using QuadGK # pkg const const _MSS = MultiStateSystems +const _LG = LightGraphs + +# constants +dt = 3.0u"hr" +tsim = 4500.0u"hr" +t = zero(dt):dt:tsim # setting for a specific analysis -cls = SemiMarkovProcess() +cls = MarkovProcess() # initialize the state-transition diagram std = STD() @@ -40,20 +48,67 @@ add_states!(std, name = ["normal operation state","degradation state","failed s # add the transitions to the std add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5)], states = [(1,2),(2,3)]) - -# solve the std -solve!(std, cls, tsim = 4500.0u"hr", dt = 3.0u"hr") + +# trapping +_MSS.set_info!(std, 3, :trapping, true) + +# # solve the std - Markov +# solve!(std, cls, tsim = tsim, dt = dt) + +# # probabilities - Markov +# PM1 = _MSS.get_prop(std,1,:prob) +# PM2 = _MSS.get_prop(std,2,:prob) +# PM3 = _MSS.get_prop(std,3,:prob) + +# # plot all probabilities +# plot(_MSS.get_prop(std, :time), +# [PM1, PM2, PM3], +# label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), +# xlabel="time", +# ylabel="probability") + +# solve the std - Analytical +dτ = dt / 100 +dst1 = _MSS.get_prop(std,_LG.Edge(1,2),:distr) +dst2 = _MSS.get_prop(std,_LG.Edge(2,3),:distr) + +PA1 = 1.0 .- _MSS.cdf.(dst1,t,t) +PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,x) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] +PA3 = 1.0 .- (PA1 .+ PA2) # plot all probabilities -plot(_MSS.get_prop(std, :time), - [_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)], +plot(t, [PA1, PA2, PA3], label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), xlabel="time", ylabel="probability") -# plot the reliability -plot(_MSS.get_prop(std, :time), - _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob), - label="reliability", - xlabel="time", - ylabel="probability") \ No newline at end of file +# solve the std - Semi-Markov +# setting for a specific analysis +cls = SemiMarkovProcess() + +# solve the std - SEMIMarkov +solve!(std, cls, tsim = tsim, dt = dt) + +# probabilities - SEMIMarkov +PS1 = _MSS.get_prop(std,1,:prob) +PS2 = _MSS.get_prop(std,2,:prob) +PS3 = _MSS.get_prop(std,3,:prob) + +# plot all probabilities +plot!(t, [PS1, PS2, PS3], + label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), + xlabel="time", + ylabel="probability") + + + + + + + +# # plot the reliability +# plot(_MSS.get_prop(std, :time), +# _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob), +# label="reliability", +# xlabel="time", +# ylabel="probability") \ No newline at end of file diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index cae96f1..85f8ab9 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -17,6 +17,7 @@ import Multigraphs import OrdinaryDiffEq import Measurements import SpecialFunctions +import QuadGK # using Pkgs using Unitful @@ -30,6 +31,7 @@ const _ODE = OrdinaryDiffEq const _UF = Unitful const _MSM = Measurements const _SF = SpecialFunctions +const _QGK = QuadGK # paths const BASE_DIR = dirname(@__DIR__) diff --git a/src/form/markov_process.jl b/src/form/markov_process.jl index b1620ca..847b2f7 100644 --- a/src/form/markov_process.jl +++ b/src/form/markov_process.jl @@ -16,7 +16,7 @@ const markov_process_props = [:renewal, :markovian, :dynamic] function set_rates!(std::AbstractSTD, cls::AbstractMarkovProcess) for nt in transitions(std) if !has_prop(std, nt, :rate) && has_prop(std, nt, :distr) - if get_prop(std, nt, :distr) isa Exponential + if get_prop(std, nt, :distr) isa AbstractExponential set_prop!(std, nt, :rate, rate(get_prop(std, nt, :distr))) end end end end @@ -28,11 +28,15 @@ end function homogeneous_markov_process(du, u, p, t) G, ρ, info = p for ns in 1:_LG.nv(G) - if info[ns].trapping + if isempty(_LG.outneighbors(G,ns)) du[ns] = sum(ρ[_LG.Edge(nt,ns)]*u[nt] for nt in _LG.inneighbors(G,ns) if ns ≠ nt) - else + elseif isempty(_LG.inneighbors(G,ns)) + du[ns] = - sum(ρ[_LG.Edge(ns,nt)]*u[ns] + for nt in _LG.outneighbors(G,ns) + if ns ≠ nt) + else du[ns] = sum(ρ[_LG.Edge(nt,ns)]*u[nt] for nt in _LG.inneighbors(G,ns) if ns ≠ nt) - From 3a7298617c1fb8766f88451f6866a57b83fa7084 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Tue, 17 May 2022 11:46:48 +0200 Subject: [PATCH 27/56] Merge branch 'semi-markov' of https://github.com/timmyfaraday/MultiStateSystems.jl into semi-markov --- examples/lvdc/elements/ac.jl | 6 ++-- examples/lvdc/elements/acdc.jl | 2 +- examples/lvdc/elements/battery.jl | 6 ++-- examples/lvdc/elements/dcdc.jl | 4 +-- examples/lvdc/elements/fe.jl | 27 +++++++++++++++ examples/lvdc/elements/inv.jl | 27 +++++++++++++++ examples/lvdc/elements/switch.jl | 27 +++++++++++++++ examples/lvdc/elements/transfo.jl | 27 +++++++++++++++ examples/lvdc/networks/AC_case_1.jl | 43 ++++++++++++++++++++++++ examples/lvdc/networks/AC_case_2.jl | 44 ++++++++++++++++++++++++ examples/lvdc/networks/AC_case_4.jl | 52 +++++++++++++++++++++++++++++ 11 files changed, 256 insertions(+), 9 deletions(-) create mode 100644 examples/lvdc/elements/fe.jl create mode 100644 examples/lvdc/elements/inv.jl create mode 100644 examples/lvdc/elements/switch.jl create mode 100644 examples/lvdc/elements/transfo.jl create mode 100644 examples/lvdc/networks/AC_case_1.jl create mode 100644 examples/lvdc/networks/AC_case_2.jl create mode 100644 examples/lvdc/networks/AC_case_4.jl diff --git a/examples/lvdc/elements/ac.jl b/examples/lvdc/elements/ac.jl index 682025b..578b665 100644 --- a/examples/lvdc/elements/ac.jl +++ b/examples/lvdc/elements/ac.jl @@ -1,5 +1,5 @@ ################################################################################ -# Copyright 2020, Tom Van Acker # +# Copyright 2022, Tom Van Acker, Glenn Emmers # ################################################################################ # MultiStateSystems.jl # # A Julia package to solve multi-state system models. # @@ -20,8 +20,8 @@ add_states!(stdᵃᶜ, name = ["available", "unavailable"], init = [1.0, 0.0]) # add the transitions to the std -add_transitions!(stdᵃᶜ, rate = [0.0u"1/hr" 1.14e-4u"1/hr" - 12.0u"1/hr" 0.0u"1/hr"]) +add_transitions!(stdᵃᶜ, rate = [0.0u"1/hr" 3.142e-4u"1/hr" + 0.8058u"1/hr" 0.0u"1/hr"]) # return the std return stdᵃᶜ \ No newline at end of file diff --git a/examples/lvdc/elements/acdc.jl b/examples/lvdc/elements/acdc.jl index c67cc38..32ebc52 100644 --- a/examples/lvdc/elements/acdc.jl +++ b/examples/lvdc/elements/acdc.jl @@ -1,5 +1,5 @@ ################################################################################ -# Copyright 2020, Tom Van Acker # +# Copyright 2022, Tom Van Acker, Glenn Emmers # ################################################################################ # MultiStateSystems.jl # # A Julia package to solve multi-state system models. # diff --git a/examples/lvdc/elements/battery.jl b/examples/lvdc/elements/battery.jl index b9ab52e..666b545 100644 --- a/examples/lvdc/elements/battery.jl +++ b/examples/lvdc/elements/battery.jl @@ -1,5 +1,5 @@ ################################################################################ -# Copyright 2020, Tom Van Acker # +# Copyright 2022, Tom Van Acke, Glenn Emmers # ################################################################################ # MultiStateSystems.jl # # A Julia package to solve multi-state system models. # @@ -20,8 +20,8 @@ add_states!(stdᵇ, name = ["available", "unavailable"], init = [1.0, 0.0]) # add the transitions to the std -add_transitions!(stdᵇ, rate = [0.0u"1/hr" 13.0e-6u"1/hr" - 0.006u"1/hr" 0.0u"1/hr"]) +add_transitions!(stdᵇ, rate = [0.0u"1/hr" 2.07222222e-6u"1/hr" + 0.0658u"1/hr" 0.0u"1/hr"]) # return the std return stdᵇ \ No newline at end of file diff --git a/examples/lvdc/elements/dcdc.jl b/examples/lvdc/elements/dcdc.jl index 2e75c6b..6c03bf8 100644 --- a/examples/lvdc/elements/dcdc.jl +++ b/examples/lvdc/elements/dcdc.jl @@ -1,5 +1,5 @@ ################################################################################ -# Copyright 2020, Tom Van Acker # +# Copyright 2022, Tom Van Acker, Glenn Emmers # ################################################################################ # MultiStateSystems.jl # # A Julia package to solve multi-state system models. # @@ -20,7 +20,7 @@ add_states!(stdᵈᵈ, name = ["available", "unavailable"], init = [1.0, 0.0]) # add the transitions to the std -add_transitions!(stdᵈᵈ, rate = [0.0u"1/hr" 8.06e-6u"1/hr" +add_transitions!(stdᵈᵈ, rate = [0.0u"1/hr" 8.058e-6u"1/hr" 0.125u"1/hr" 0.0u"1/hr"]) # return the std diff --git a/examples/lvdc/elements/fe.jl b/examples/lvdc/elements/fe.jl new file mode 100644 index 0000000..1330807 --- /dev/null +++ b/examples/lvdc/elements/fe.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc +# converter +stdᶠᵉ = STD() + +# add the states to the std +add_states!(stdᶠᵉ, name = ["available", "unavailable"], + power = [1.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdᶠᵉ, rate = [0.0u"1/hr" 2.9666667e-6u"1/hr" + 0.1400u"1/hr" 0.0u"1/hr"]) + +# return the std +return stdᶠᵉ \ No newline at end of file diff --git a/examples/lvdc/elements/inv.jl b/examples/lvdc/elements/inv.jl new file mode 100644 index 0000000..6bee49f --- /dev/null +++ b/examples/lvdc/elements/inv.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc +# converter +stdⁱⁿᵛ = STD() + +# add the states to the std +add_states!(stdⁱⁿᵛ, name = ["available", "unavailable"], + power = [1.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdⁱⁿᵛ, rate = [0.0u"1/hr" 2.3305555e-6u"1/hr" + 0.0936u"1/hr" 0.0u"1/hr"]) + +# return the std +return stdⁱⁿᵛ \ No newline at end of file diff --git a/examples/lvdc/elements/switch.jl b/examples/lvdc/elements/switch.jl new file mode 100644 index 0000000..0d095c2 --- /dev/null +++ b/examples/lvdc/elements/switch.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc +# converter +stdˢʷ = STD() + +# add the states to the std +add_states!(stdˢʷ, name = ["available", "unavailable"], + power = [1.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdˢʷ, rate = [0.0u"1/hr" 4.21667e-6u"1/hr" + 0.4269u"1/hr" 0.0u"1/hr"]) + +# return the std +return stdˢʷ \ No newline at end of file diff --git a/examples/lvdc/elements/transfo.jl b/examples/lvdc/elements/transfo.jl new file mode 100644 index 0000000..f914ae1 --- /dev/null +++ b/examples/lvdc/elements/transfo.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc +# converter +stdᵗᶠ = STD() + +# add the states to the std +add_states!(stdᵗᶠ, name = ["available", "unavailable"], + power = [1.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdᵗᶠ, rate = [0.0u"1/hr" 8.5777e-6u"1/hr" + 0.9552u"1/hr" 0.0u"1/hr"]) + +# return the std +return stdᵗᶠ \ No newline at end of file diff --git a/examples/lvdc/networks/AC_case_1.jl b/examples/lvdc/networks/AC_case_1.jl new file mode 100644 index 0000000..914fdbb --- /dev/null +++ b/examples/lvdc/networks/AC_case_1.jl @@ -0,0 +1,43 @@ +################################################################################ +# Copyright 2020, Tom Van Acker # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SteadyStateProcess() + +# include the stochastic models for the elements +stdᵃᶜ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/ac.jl")) +stdᵗᶠ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/transfo.jl")) +stdⁱⁿᵛ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/inv.jl")) + +# solve the state-transitions diagrams +solve!(stdᵃᵈ, cls) +solve!(stdᵗᶠ, cls) +solve!(stdⁱⁿᵛ, cls) + +# initialize the network corresponding to the low voltage dc system +ntwˡᵛ = Network() + +add_users!(ntwˡᵛ, node = [3,4]) +add_sources!(ntwˡᵛ, node = [1], + name = ["ac grid"], + std = [stdᵃᶜ]) +add_components!(ntwˡᵛ, edge = [(1,2),(2,3),(3,4)], + name = ["transfo", "ac/dc","dc/ac"], + std = [stdᵗᶠ, stdⁱⁿᵛ, stdⁱⁿᵛ]) + +solve!(ntwˡᵛ) + +ntwˡᵛ.usr[1][:ugf] +ntwˡᵛ.usr[2][:ugf] \ No newline at end of file diff --git a/examples/lvdc/networks/AC_case_2.jl b/examples/lvdc/networks/AC_case_2.jl new file mode 100644 index 0000000..fa1581d --- /dev/null +++ b/examples/lvdc/networks/AC_case_2.jl @@ -0,0 +1,44 @@ +################################################################################ +# Copyright 2020, Tom Van Acker # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SteadyStateProcess() + +# include the stochastic models for the elements +stdᵃᶜ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/ac.jl")) +stdᵗᶠ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/transfo.jl")) +stdⁱⁿᵛ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/inv.jl")) + + +# solve the state-transitions diagrams +solve!(stdᵃᶜ, cls) +solve!(stdᵗᶠ, cls) +solve!(stdⁱⁿᵛ, cls) + +# initialize the network corresponding to the low voltage dc system +ntwˡᵛ = Network() + +add_users!(ntwˡᵛ, node = [2,4]) +add_sources!(ntwˡᵛ, node = [1], + name = ["ac grid"], + std = [stdᵃᶜ]) +add_components!(ntwˡᵛ, edge = [(1,2),(2,3),(3,4)], + name = ["transfo", "ac/dc","dc/ac"], + std = [stdᵗᶠ, stdⁱⁿᵛ, stdⁱⁿᵛ]) + +solve!(ntwˡᵛ) + +ntwˡᵛ.usr[1][:ugf] +ntwˡᵛ.usr[2][:ugf] \ No newline at end of file diff --git a/examples/lvdc/networks/AC_case_4.jl b/examples/lvdc/networks/AC_case_4.jl new file mode 100644 index 0000000..fd5ea22 --- /dev/null +++ b/examples/lvdc/networks/AC_case_4.jl @@ -0,0 +1,52 @@ +################################################################################ +# Copyright 2020, Tom Van Acker # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SteadyStateProcess() + +# include the stochastic models for the elements +stdᵃᵈ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/acdc.jl")) +stdᵃᶜ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/ac.jl")) +stdᵈᵈ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/dcdc.jl")) +stdᵇ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/battery.jl")) +stdˢʷ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/switch.jl")) +stdᶜ = include(joinpath(_MSS.BASE_DIR,"examples/lvdc/elements/switch.jl")) +# solve the state-transitions diagrams +solve!(stdᵃᵈ, cls) +solve!(stdᵃᶜ, cls) +solve!(stdᵈᵈ, cls) +solve!(stdᵇ, cls) +solve!(stdˢʷ, cls) +solve!(stdᶜ,cls) + +# initialize the network corresponding to the low voltage dc system + +ntwˡᵛ = Network() + + +add_users!(ntwˡᵛ, node = [5]) +add_sources!(ntwˡᵛ, node = [1,2], + name = ["ac grid","ac grid"], + std = [stdᵃᶜ, stdᵃᶜ]) +add_components!(ntwˡᵛ, edge = [(1,3),(1,4),(2,3),(2,4),(3,5), (4,5)], + name = ["cable", "cable", "cable", "cable", "cable", "cable"], + std = [stdᶜ, stdᶜ, stdᶜ, stdᶜ, stdᶜ, stdᶜ]) +add_bidirectional_component((ntwˡᵛ, edge = (3,4), std = stdᶜ)) + + +solve!(ntwˡᵛ) + +ntwˡᵛ.usr[1][:ugf] +ntwˡᵛ.usr[2][:ugf] \ No newline at end of file From c61d2404f8a87191ded83ec629ce2ddb80315a33 Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Tue, 17 May 2022 14:04:14 +0200 Subject: [PATCH 28/56] Update Project.toml --- Project.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Project.toml b/Project.toml index dd6ee2e..4779863 100644 --- a/Project.toml +++ b/Project.toml @@ -20,9 +20,9 @@ LightGraphs = "1.3.5" Measurements = "2.6.0" Multigraphs = "0.2.2" OrdinaryDiffEq = "5.59.4" +QuadGK = "2.4.2" SpecialFunctions = "1.8.4" Unitful = "1.8.0" -QuadGK = "2.4.2" julia = "1" [extras] From e62140c0c701542a20e5a6fcdb6b38beba58ec40 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Tue, 17 May 2022 16:26:33 +0200 Subject: [PATCH 29/56] *Update universal_generating_operator.jl *needs to be improved, once it occurs twice it should be a nogo_seq Co-Authored-By: Tom Van Acker --- src/prob/universal_generating_operator.jl | 1 + 1 file changed, 1 insertion(+) diff --git a/src/prob/universal_generating_operator.jl b/src/prob/universal_generating_operator.jl index ff299f0..564692c 100644 --- a/src/prob/universal_generating_operator.jl +++ b/src/prob/universal_generating_operator.jl @@ -99,6 +99,7 @@ function unique_sequence(npaths::Vector{<:Vector}) for ni in 1:length(npath)-3+1 seq = npath[ni:ni+3-1] push!(all_seqs, seq) + if all(x -> has_subvector(x,seq), npaths) push!(nogo_seqs, seq) end ### needs to be improved, once it occurs twice it should be a nogo_seq for xpath in npaths if check_sequence(seq, xpath) push!(nogo_seqs, seq) end end From 3773a85af6a2247ed9c853afa178d7b4b6d79dc5 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Mon, 23 May 2022 11:54:13 +0200 Subject: [PATCH 30/56] Small adjustments for debugging --- examples/semi-markov/semi-analytical.jl | 29 +++++++++-- src/MultiStateSystems.jl | 2 + src/form/semi_markov_process.jl | 64 ++++++++++++++++++------- 3 files changed, 75 insertions(+), 20 deletions(-) diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index a6426b9..2bc2781 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -68,12 +68,13 @@ _MSS.set_info!(std, 3, :trapping, true) # ylabel="probability") # solve the std - Analytical -dτ = dt / 100 +dτ = dt / 1 dst1 = _MSS.get_prop(std,_LG.Edge(1,2),:distr) dst2 = _MSS.get_prop(std,_LG.Edge(2,3),:distr) -PA1 = 1.0 .- _MSS.cdf.(dst1,t,t) -PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,x) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] +PA1 = 1.0 .- _MSS.cdf.(dst1,t,zero(dt)) +PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] +PA22= [sum(dτ * _MSS.weights(length(zero(nt):dτ:nt))[ni] * _MSS.pdf.(dst1,nl,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-nl,nt)) for (ni,nl) in enumerate(zero(nt):dτ:nt)) for nt in t] PA3 = 1.0 .- (PA1 .+ PA2) # plot all probabilities @@ -87,23 +88,43 @@ plot(t, [PA1, PA2, PA3], cls = SemiMarkovProcess() # solve the std - SEMIMarkov -solve!(std, cls, tsim = tsim, dt = dt) +h3 = solve!(std, cls, tsim = tsim, dt = dt) # probabilities - SEMIMarkov PS1 = _MSS.get_prop(std,1,:prob) PS2 = _MSS.get_prop(std,2,:prob) PS3 = _MSS.get_prop(std,3,:prob) + # plot all probabilities plot!(t, [PS1, PS2, PS3], label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), xlabel="time", ylabel="probability") + + +plot(t, [PA1-PS1, diff[:,1]], + label="State 1", + xlabel="time", + ylabel="probability difference") +plot(t, PS2-PA2, + label=["State 2" "diff"], + xlabel="time", + ylabel="probability difference") +plot(t, PS3-PA3, + label=["State 3" "diff"], + xlabel="time", + ylabel="probability difference") + +plot(t, h4[2](ustrip(t))-h3[2](ustrip(t)), + label=["H array diff for State 2"], + xlabel="time", + ylabel="rate (1/t)") # # plot the reliability diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index 85f8ab9..276bbd2 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -18,6 +18,7 @@ import OrdinaryDiffEq import Measurements import SpecialFunctions import QuadGK +import Interpolations # using Pkgs using Unitful @@ -32,6 +33,7 @@ const _UF = Unitful const _MSM = Measurements const _SF = SpecialFunctions const _QGK = QuadGK +const _INT = Interpolations # paths const BASE_DIR = dirname(@__DIR__) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 01b8531..26e6a98 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -84,7 +84,15 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # solve the problem Φ = zeros(Nt, ns(std)) - H = set_U(std, t) \ set_A(std, t) + diff = zeros(Nt, ns(std)) + H =set_U(std, t) \ set_A(std, t) + + unit_h = unit(H[1]) + + H = ustrip(H) + + h = [_INT.LinearInterpolation(ustrip(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; + for st in states(std) for (ni,nt) in enumerate(t) w = weights(ni) @@ -92,11 +100,14 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; l = zero(dt):dt:nt # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + # Φ[ni,st] += _QGK.quadgk(x -> unit_h * h[st](ustrip(x)) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] + + Φ[ni,st] += sum(dt .* w[nj] .* unit_h * H[ns(std) * (nj-1) + st] .* ccdf(std, st, nt-nl, nl) for (nj,nl) in enumerate(l)) end end + # set the output set_prop!(std, :cls, cls) set_prop!(std, :time, t) @@ -104,6 +115,7 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) + return h end """ @@ -112,21 +124,41 @@ end Determine integration weights based on extended Simpson's rule. w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. """ -function weights(x::Int) - x==1 && return [0] - x==2 && return [1/2, 1/2] - x==3 && return [1/3, 4/3, 1/3] - x==4 && return [3/8, 9/8, 9/8, 3/8] - x==5 && return (2/45) .* [7, 32, 12, 32, 7] - x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] - x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] - x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] +# function weights(x::Int) +# x==1 && return [0] +# x==2 && return [1/2, 1/2] +# x==3 && return [1/3, 4/3, 1/3] +# x==4 && return [3/8, 9/8, 9/8, 3/8] +# x==5 && return (2/45) .* [7, 32, 12, 32, 7] +# x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] +# x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] +# x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] - weights = 48 * ones(x) - weights[1:4] = [17, 59, 43, 49] - weights[end-3:end] = [49, 43, 59, 17] - return (1/48) .* weights -end +# weights = 48 * ones(x) +# weights[1:4] = [17, 59, 43, 49] +# weights[end-3:end] = [49, 43, 59, 17] +# return (1/48) .* weights +# end + +function weights(x::Int) + w = zeros(x) + for i in 1:length(w) + if i % 2 == 0 + w[i] = 4/3 + else + w[i] = 2/3 + end end + w[1] = 1/3 + w[end] = 1/3 + + return w +end + +# function weights(x::Int) +# w = ones(x) +# return w +# end + # # TOM: Alternative formulation for the state ccdf, using the trapping info prop # cdf(std::AbstractSTD, ns::Int, φ::Number, t::Number) = From d1779d73271777fd55dab170eea4863d83f9c080 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Mon, 30 May 2022 12:49:55 +0200 Subject: [PATCH 31/56] set_U functional with sparse matrix, SparseArrays added to MSS --- src/MultiStateSystems.jl | 2 + src/form/semi_markov_process.jl | 109 +++++++++++++++++++++----------- 2 files changed, 74 insertions(+), 37 deletions(-) diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index 276bbd2..3687c8c 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -19,6 +19,7 @@ import Measurements import SpecialFunctions import QuadGK import Interpolations +import SparseArrays # using Pkgs using Unitful @@ -34,6 +35,7 @@ const _MSM = Measurements const _SF = SpecialFunctions const _QGK = QuadGK const _INT = Interpolations +const _SA = SparseArrays # paths const BASE_DIR = dirname(@__DIR__) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 26e6a98..6374293 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -59,6 +59,7 @@ function set_U(std::AbstractSTD, t::StepRangeLen) Ψ = zeros(typeof(1/dt), ns(std), ns(std)) for tr in transitions(std) # NB: GLENN additional clarification distr betreden op nϕ en blijven tot nt, φ = nt - nl + # pdf Ψ[_LG.dst(tr), _LG.src(tr)] = pdf(get_prop(std, tr, :distr), nt - nl, nl) end @@ -75,9 +76,39 @@ function set_U(std::AbstractSTD, t::StepRangeLen) return U end +function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) + dt = step(t) + Nt = length(t) + Ns = ns(std) + + # initialize three vectors I,J,V respectively row, column and value indices + I,J,V = Int[],Int[],Number[] + + push!(I, 1:Ns*Nt...) + push!(J, 1:Ns*Nt...) + push!(V, ones(Number,Ns*Nt)...) + + for tr in transitions(std) + # dummy value not necessary, since every diagonal entry requires a one to be added to it. + # Sparse Arrays allow to add values to the same location twice and add those + # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. + dst = get_prop(std, tr, :distr) + lb = floor(cquantile(dst, tol) / dt) * dt + for (ni,nt) in enumerate(t) + Φ = min(zero(dt),lb):dt:nt + NΦ = length(Φ) + + push!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)...) + push!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]...) + push!(V, .- dt .* weights(ni)[1:NΦ] .* pdf.(dst, nt.-Φ, Φ)...) + end end + + return _SA.sparse(I, J, V) +end + # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) + tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real) # Default value of tol taken away for now to compare results # get the input t = zero(dt):dt:tsim Nt = length(t) @@ -85,13 +116,14 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # solve the problem Φ = zeros(Nt, ns(std)) diff = zeros(Nt, ns(std)) - H =set_U(std, t) \ set_A(std, t) - unit_h = unit(H[1]) + # @time U = set_U(std,t,tol) + @time U = set_U(std,t) + A = ustrip(set_A(std,t)) - H = ustrip(H) + H=U\A*unit(1/dt) - h = [_INT.LinearInterpolation(ustrip(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; + h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end for st in states(std) for (ni,nt) in enumerate(t) @@ -99,12 +131,13 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # TOM: φ <<< t, zero could be higher l = zero(dt):dt:nt # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification + # Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - # Φ[ni,st] += _QGK.quadgk(x -> unit_h * h[st](ustrip(x)) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] + Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] - Φ[ni,st] += sum(dt .* w[nj] .* unit_h * H[ns(std) * (nj-1) + st] .* - ccdf(std, st, nt-nl, nl) - for (nj,nl) in enumerate(l)) + # Φ[ni,st] += sum(dt .* w[nj] .* unit_h * H[ns(std) * (nj-1) + st] .* + # ccdf(std, st, nt-nl, nl) + # for (nj,nl) in enumerate(l)) end end @@ -115,7 +148,10 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) - return h + + # h = [h[st](t) for st in states(std)]; + + return end """ @@ -124,35 +160,35 @@ end Determine integration weights based on extended Simpson's rule. w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. """ -# function weights(x::Int) -# x==1 && return [0] -# x==2 && return [1/2, 1/2] -# x==3 && return [1/3, 4/3, 1/3] -# x==4 && return [3/8, 9/8, 9/8, 3/8] -# x==5 && return (2/45) .* [7, 32, 12, 32, 7] -# x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] -# x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] -# x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] +function weights(x::Int) + x==1 && return [0] + x==2 && return [1/2, 1/2] + x==3 && return [1/3, 4/3, 1/3] + x==4 && return [3/8, 9/8, 9/8, 3/8] + x==5 && return (2/45) .* [7, 32, 12, 32, 7] + x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] + x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] + x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] -# weights = 48 * ones(x) -# weights[1:4] = [17, 59, 43, 49] -# weights[end-3:end] = [49, 43, 59, 17] -# return (1/48) .* weights -# end + weights = 48 * ones(x) + weights[1:4] = [17, 59, 43, 49] + weights[end-3:end] = [49, 43, 59, 17] + return (1/48) .* weights +end -function weights(x::Int) - w = zeros(x) - for i in 1:length(w) - if i % 2 == 0 - w[i] = 4/3 - else - w[i] = 2/3 - end end - w[1] = 1/3 - w[end] = 1/3 +# function weights(x::Int) +# w = zeros(x) +# for i in 1:length(w) +# if i % 2 == 0 +# w[i] = 4/3 +# else +# w[i] = 2/3 +# end end +# w[1] = 1/3 +# w[end] = 1/3 - return w -end +# return w +# end # function weights(x::Int) # w = ones(x) @@ -185,4 +221,3 @@ elunit(b::Vector{U}) where U = _UF.unit(U) _LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = (ustrip.(A) \ ustrip(b)) * (elunit(b) / elunit(A)) - From 30876a6da5cd866bd188502e0417668060c1474b Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Wed, 1 Jun 2022 10:08:00 +0200 Subject: [PATCH 32/56] Minor changes semi_markov_process.jl --- examples/semi-markov/semi-analytical.jl | 62 ++++++++++++++----------- src/form/semi_markov_process.jl | 11 ++--- 2 files changed, 39 insertions(+), 34 deletions(-) diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index 2bc2781..1300153 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -36,7 +36,7 @@ tsim = 4500.0u"hr" t = zero(dt):dt:tsim # setting for a specific analysis -cls = MarkovProcess() +cls = SemiMarkovProcess() # initialize the state-transition diagram std = STD() @@ -50,7 +50,7 @@ add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5 states = [(1,2),(2,3)]) # trapping -_MSS.set_info!(std, 3, :trapping, true) +# _MSS.set_info!(std, 3, :trapping, true) # # solve the std - Markov # solve!(std, cls, tsim = tsim, dt = dt) @@ -67,21 +67,17 @@ _MSS.set_info!(std, 3, :trapping, true) # xlabel="time", # ylabel="probability") -# solve the std - Analytical -dτ = dt / 1 -dst1 = _MSS.get_prop(std,_LG.Edge(1,2),:distr) -dst2 = _MSS.get_prop(std,_LG.Edge(2,3),:distr) +# # solve the std - Analytical +# dτ = dt / 1 +# dst1 = _MSS.get_prop(std,_LG.Edge(1,2),:distr) +# dst2 = _MSS.get_prop(std,_LG.Edge(2,3),:distr) + +# PA1 = 1.0 .- _MSS.cdf.(dst1,t,zero(dt)) +# PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] +# PA22= [sum(dτ * _MSS.weights(length(zero(nt):dτ:nt))[ni] * _MSS.pdf.(dst1,nl,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-nl,nt)) for (ni,nl) in enumerate(zero(nt):dτ:nt)) for nt in t] +# PA3 = 1.0 .- (PA1 .+ PA2) -PA1 = 1.0 .- _MSS.cdf.(dst1,t,zero(dt)) -PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] -PA22= [sum(dτ * _MSS.weights(length(zero(nt):dτ:nt))[ni] * _MSS.pdf.(dst1,nl,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-nl,nt)) for (ni,nl) in enumerate(zero(nt):dτ:nt)) for nt in t] -PA3 = 1.0 .- (PA1 .+ PA2) -# plot all probabilities -plot(t, [PA1, PA2, PA3], - label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), - xlabel="time", - ylabel="probability") # solve the std - Semi-Markov # setting for a specific analysis @@ -96,31 +92,41 @@ PS2 = _MSS.get_prop(std,2,:prob) PS3 = _MSS.get_prop(std,3,:prob) -# plot all probabilities -plot!(t, [PS1, PS2, PS3], - label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), - xlabel="time", - ylabel="probability") - - + +ϵ = 1e-16; -plot(t, [PA1-PS1, diff[:,1]], - label="State 1", +plot(t, [PA1.-PS1.+ϵ, PA2.-PS2.+ϵ, PA3.-PS3.+ ϵ], + label=["State 1" "State 2" "State 3"], xlabel="time", + yscale = :log, ylabel="probability difference") -plot(t, PS2-PA2, - label=["State 2" "diff"], +plot!(t, PA2.-PS2.+ϵ, + label="State 2", xlabel="time", + yscale = :log, ylabel="probability difference") -plot(t, PS3-PA3, - label=["State 3" "diff"], +plot!(t, PA3.-PS3.+ ϵ, + label="State 3", xlabel="time", + yscale = :log, ylabel="probability difference") + # plot all probabilities +plot(t, [PA1, PA2, PA3], + label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), + xlabel="time", + ylabel="probability") + + # plot all probabilities +plot!(t, [PS1, PS2, PS3], + label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), + xlabel="time", + ylabel="probability") + plot(t, h4[2](ustrip(t))-h3[2](ustrip(t)), label=["H array diff for State 2"], xlabel="time", diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 6374293..8b5a64f 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -94,7 +94,7 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. dst = get_prop(std, tr, :distr) lb = floor(cquantile(dst, tol) / dt) * dt - for (ni,nt) in enumerate(t) + @time for (ni,nt) in enumerate(t) Φ = min(zero(dt),lb):dt:nt NΦ = length(Φ) @@ -102,13 +102,13 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) push!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]...) push!(V, .- dt .* weights(ni)[1:NΦ] .* pdf.(dst, nt.-Φ, Φ)...) end end - + V[isnan.(V)] .= 0.0 return _SA.sparse(I, J, V) end # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real) # Default value of tol taken away for now to compare results + tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) # get the input t = zero(dt):dt:tsim Nt = length(t) @@ -117,13 +117,12 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; Φ = zeros(Nt, ns(std)) diff = zeros(Nt, ns(std)) - # @time U = set_U(std,t,tol) - @time U = set_U(std,t) + U = set_U(std,t,tol) A = ustrip(set_A(std,t)) H=U\A*unit(1/dt) - h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end for st in states(std) for (ni,nt) in enumerate(t) From 0378582defd03a2623ad42c9cfa6238749273bab Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Wed, 1 Jun 2022 10:25:03 +0200 Subject: [PATCH 33/56] Update semi-analytical.jl --- examples/semi-markov/semi-analytical.jl | 100 ++++++++++++------------ 1 file changed, 50 insertions(+), 50 deletions(-) diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index 1300153..3b2934b 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -79,63 +79,63 @@ add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5 -# solve the std - Semi-Markov -# setting for a specific analysis -cls = SemiMarkovProcess() +# # solve the std - Semi-Markov +# # setting for a specific analysis +# cls = SemiMarkovProcess() # solve the std - SEMIMarkov -h3 = solve!(std, cls, tsim = tsim, dt = dt) +solve!(std, cls, tsim = tsim, dt = dt) -# probabilities - SEMIMarkov -PS1 = _MSS.get_prop(std,1,:prob) -PS2 = _MSS.get_prop(std,2,:prob) -PS3 = _MSS.get_prop(std,3,:prob) +# # probabilities - SEMIMarkov +# PS1 = _MSS.get_prop(std,1,:prob) +# PS2 = _MSS.get_prop(std,2,:prob) +# PS3 = _MSS.get_prop(std,3,:prob) -ϵ = 1e-16; - -plot(t, [PA1.-PS1.+ϵ, PA2.-PS2.+ϵ, PA3.-PS3.+ ϵ], - label=["State 1" "State 2" "State 3"], - xlabel="time", - yscale = :log, - ylabel="probability difference") - -plot!(t, PA2.-PS2.+ϵ, - label="State 2", - xlabel="time", - yscale = :log, - ylabel="probability difference") - -plot!(t, PA3.-PS3.+ ϵ, - label="State 3", - xlabel="time", - yscale = :log, - ylabel="probability difference") - - # plot all probabilities -plot(t, [PA1, PA2, PA3], - label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), - xlabel="time", - ylabel="probability") +# ϵ = 1e-16; + +# plot(t, [PA1.-PS1.+ϵ, PA2.-PS2.+ϵ, PA3.-PS3.+ ϵ], +# label=["State 1" "State 2" "State 3"], +# xlabel="time", +# yscale = :log, +# ylabel="probability difference") + +# plot!(t, PA2.-PS2.+ϵ, +# label="State 2", +# xlabel="time", +# yscale = :log, +# ylabel="probability difference") + +# plot!(t, PA3.-PS3.+ ϵ, +# label="State 3", +# xlabel="time", +# yscale = :log, +# ylabel="probability difference") + +# # plot all probabilities +# plot(t, [PA1, PA2, PA3], +# label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), +# xlabel="time", +# ylabel="probability") - # plot all probabilities -plot!(t, [PS1, PS2, PS3], - label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), - xlabel="time", - ylabel="probability") - -plot(t, h4[2](ustrip(t))-h3[2](ustrip(t)), - label=["H array diff for State 2"], - xlabel="time", - ylabel="rate (1/t)") - - -# # plot the reliability -# plot(_MSS.get_prop(std, :time), -# _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob), -# label="reliability", +# # plot all probabilities +# plot!(t, [PS1, PS2, PS3], +# label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), # xlabel="time", -# ylabel="probability") \ No newline at end of file +# ylabel="probability") + +# plot(t, h4[2](ustrip(t))-h3[2](ustrip(t)), +# label=["H array diff for State 2"], +# xlabel="time", +# ylabel="rate (1/t)") + + +# # # plot the reliability +# # plot(_MSS.get_prop(std, :time), +# # _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob), +# # label="reliability", +# # xlabel="time", +# # ylabel="probability") \ No newline at end of file From c799bdf9cf8fa743c338f45e8b2c674869ff00c0 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Tue, 7 Jun 2022 10:22:39 +0200 Subject: [PATCH 34/56] Optimization of Semi_markov_process.jl --- .../semi-markov/optical-monitoring-system.jl | 6 +- src/form/semi_markov_process.jl | 74 +++++++++++-------- test/semi_markov_process.jl | 26 +++++++ 3 files changed, 74 insertions(+), 32 deletions(-) create mode 100644 test/semi_markov_process.jl diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 1c37044..43d25c3 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -25,6 +25,8 @@ using Unitful using UnitfulRecipes using MultiStateSystems + + # pkg const const _MSS = MultiStateSystems @@ -48,7 +50,7 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # solve the std -solve!(std, cls, tsim = 8760.0u"hr", dt = 5.84u"hr") +solve!(std, cls, tsim = 8760.0u"hr", dt = 5.84u"hr", tol=1e-8) # plot the probabilities plot(_MSS.get_prop(std, :time), @@ -58,7 +60,7 @@ plot(_MSS.get_prop(std, :time), ylabel="probability") # plot the reliability -plot!(_MSS.get_prop(std, :time), +plot(_MSS.get_prop(std, :time), _MSS.get_prop(std, 1, :prob), label="reliability", xlabel="time", diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 8b5a64f..e2fc7c4 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -54,7 +54,8 @@ function set_U(std::AbstractSTD, t::StepRangeLen) for (ni,nt) in enumerate(t) w = weights(ni) - l = zero(dt):dt:nt + # l = zero(dt):dt:nt + l = t[1]:dt:nt for (nj,nl) in enumerate(l) Ψ = zeros(typeof(1/dt), ns(std), ns(std)) for tr in transitions(std) @@ -84,9 +85,9 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) # initialize three vectors I,J,V respectively row, column and value indices I,J,V = Int[],Int[],Number[] - push!(I, 1:Ns*Nt...) - push!(J, 1:Ns*Nt...) - push!(V, ones(Number,Ns*Nt)...) + append!(I, 1:Ns*Nt) + append!(J, 1:Ns*Nt) + append!(V, ones(Number,Ns*Nt)) for tr in transitions(std) # dummy value not necessary, since every diagonal entry requires a one to be added to it. @@ -95,12 +96,13 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) dst = get_prop(std, tr, :distr) lb = floor(cquantile(dst, tol) / dt) * dt @time for (ni,nt) in enumerate(t) - Φ = min(zero(dt),lb):dt:nt + Φ = t[1]:dt:nt + # Φ = min(zero(dt),lb):dt:nt NΦ = length(Φ) - push!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)...) - push!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]...) - push!(V, .- dt .* weights(ni)[1:NΦ] .* pdf.(dst, nt.-Φ, Φ)...) + append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) + append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) + append!(V, .- dt .* weights(ni)[1:NΦ] .* pdf.(dst, nt.-Φ, Φ)) end end V[isnan.(V)] .= 0.0 return _SA.sparse(I, J, V) @@ -108,10 +110,11 @@ end # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1.0u"d", tol::Real=1e-8) + t::StepRangeLen, tol::Real=1e-8) # get the input - t = zero(dt):dt:tsim Nt = length(t) + t = t + dt = step(t) # solve the problem Φ = zeros(Nt, ns(std)) @@ -125,14 +128,16 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end for st in states(std) - for (ni,nt) in enumerate(t) + @time for (ni,nt) in enumerate(t) w = weights(ni) # TOM: φ <<< t, zero could be higher - l = zero(dt):dt:nt + # l = zero(dt):dt:nt + l = t[1]:dt:nt # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification # Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] + # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] + Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-8)[1] # Φ[ni,st] += sum(dt .* w[nj] .* unit_h * H[ns(std) * (nj-1) + st] .* # ccdf(std, st, nt-nl, nl) @@ -148,9 +153,7 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) - # h = [h[st](t) for st in states(std)]; - - return + return [h[st](t) for st in states(std)] end """ @@ -159,21 +162,21 @@ end Determine integration weights based on extended Simpson's rule. w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. """ -function weights(x::Int) - x==1 && return [0] - x==2 && return [1/2, 1/2] - x==3 && return [1/3, 4/3, 1/3] - x==4 && return [3/8, 9/8, 9/8, 3/8] - x==5 && return (2/45) .* [7, 32, 12, 32, 7] - x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] - x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] - x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] +# function weights(x::Int) +# x==1 && return [0] +# x==2 && return [1/2, 1/2] +# x==3 && return [1/3, 4/3, 1/3] +# x==4 && return [3/8, 9/8, 9/8, 3/8] +# x==5 && return (2/45) .* [7, 32, 12, 32, 7] +# x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] +# x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] +# x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] - weights = 48 * ones(x) - weights[1:4] = [17, 59, 43, 49] - weights[end-3:end] = [49, 43, 59, 17] - return (1/48) .* weights -end +# weights = 48 * ones(x) +# weights[1:4] = [17, 59, 43, 49] +# weights[end-3:end] = [49, 43, 59, 17] +# return (1/48) .* weights +# end # function weights(x::Int) # w = zeros(x) @@ -189,6 +192,17 @@ end # return w # end +function weights(x::Int) + if x==1 + w = [0] + else + w = ones(x) + w[1] = 1/2 + w[end] = 1/2 + end + return w +end + # function weights(x::Int) # w = ones(x) # return w diff --git a/test/semi_markov_process.jl b/test/semi_markov_process.jl new file mode 100644 index 0000000..e2df044 --- /dev/null +++ b/test/semi_markov_process.jl @@ -0,0 +1,26 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +@testset "Semi Markov Process" begin + + @testset "Coal Fired Power Generating Unit" begin + # Example from: A Multi-State Markov Model for a Short-Term Reliability + # Analysis of a Power Generating Unit (p. 4) + stdᶜᶠ = include(joinpath(_MSS.BASE_DIR,"test/elements/coal_fired_power_generating_unit.jl")) + + solve!(stdᶜᶠ, MarkovProcess(), tsim = 1.0u"yr") + prb_m = [np[end] for np in _MSS.get_sprop(stdᶜᶠ, :prob)] + + solve!(stdᶜᶠ, SteadyStateProcess()) + prb_s = [np[end] for np in _MSS.get_sprop(stdᶜᶠ, :prob)] + + @test isapprox(sum(prb_m), 1.0, rtol=1e-6) + @test all(isapprox.(prb_m, prb_s, rtol=1e-6)) + end + +end \ No newline at end of file From a906b167da62d12b75b0dd3b226dae6755a6b33a Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Wed, 30 Nov 2022 17:07:11 +0100 Subject: [PATCH 35/56] Unitful compatibility adjustment Adjustments made to improve compatibility with unitful and guarantee results from the pdf's --- .../semi-markov/optical-monitoring-system.jl | 4 +- src/form/semi_markov_process.jl | 42 +++++++++++-------- 2 files changed, 27 insertions(+), 19 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 43d25c3..c5b78c8 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -50,7 +50,7 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # solve the std -solve!(std, cls, tsim = 8760.0u"hr", dt = 5.84u"hr", tol=1e-8) +solve!(std, cls, tsim = 8760.0u"hr", dt = 2u"hr", tol=1e-8) # plot the probabilities plot(_MSS.get_prop(std, :time), @@ -60,7 +60,7 @@ plot(_MSS.get_prop(std, :time), ylabel="probability") # plot the reliability -plot(_MSS.get_prop(std, :time), +plot!(_MSS.get_prop(std, :time), _MSS.get_prop(std, 1, :prob), label="reliability", xlabel="time", diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index e2fc7c4..9cacf60 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -62,7 +62,7 @@ function set_U(std::AbstractSTD, t::StepRangeLen) # NB: GLENN additional clarification distr betreden op nϕ en blijven tot nt, φ = nt - nl # pdf Ψ[_LG.dst(tr), _LG.src(tr)] = - pdf(get_prop(std, tr, :distr), nt - nl, nl) + pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 end rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) @@ -96,13 +96,15 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) dst = get_prop(std, tr, :distr) lb = floor(cquantile(dst, tol) / dt) * dt @time for (ni,nt) in enumerate(t) - Φ = t[1]:dt:nt + Φ = nt:-dt:t[1] + lt = t[1]:dt:nt # Φ = min(zero(dt),lb):dt:nt NΦ = length(Φ) append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) - append!(V, .- dt .* weights(ni)[1:NΦ] .* pdf.(dst, nt.-Φ, Φ)) + # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) + append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) end end V[isnan.(V)] .= 0.0 return _SA.sparse(I, J, V) @@ -110,38 +112,43 @@ end # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - t::StepRangeLen, tol::Real=1e-8) + tsim::Number=1.0u"yr", dt::Number=1u"hr", tol::Real=1e-8) + # get the input + dt = dt |> unit(tsim) + t = zero(dt):dt:tsim Nt = length(t) - t = t - dt = step(t) + println(t) + # solve the problem Φ = zeros(Nt, ns(std)) diff = zeros(Nt, ns(std)) U = set_U(std,t,tol) + # U = set_U(std,t) A = ustrip(set_A(std,t)) + println("time to calculate H") + @time H=U\A*unit(1/t[1]) + - H=U\A*unit(1/dt) - - h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + # h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end for st in states(std) @time for (ni,nt) in enumerate(t) w = weights(ni) # TOM: φ <<< t, zero could be higher # l = zero(dt):dt:nt - l = t[1]:dt:nt + l = t[1]:dt:nt .|> unit(tsim) # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification # Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] - Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-8)[1] + # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-8)[1] - # Φ[ni,st] += sum(dt .* w[nj] .* unit_h * H[ns(std) * (nj-1) + st] .* - # ccdf(std, st, nt-nl, nl) - # for (nj,nl) in enumerate(l)) + Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + ccdf(std, st, nt-nl, nl) + for (nj,nl) in enumerate(l)) end end @@ -153,7 +160,8 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) - return [h[st](t) for st in states(std)] + # return [h[st](t) for st in states(std)] + return U end """ @@ -182,9 +190,9 @@ w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. # w = zeros(x) # for i in 1:length(w) # if i % 2 == 0 -# w[i] = 4/3 +# w[i] = 2/3 # else -# w[i] = 2/3 +# w[i] = 4/3 # end end # w[1] = 1/3 # w[end] = 1/3 From 69ed3c8618fa7e79971c1ff3611fafeb8550996a Mon Sep 17 00:00:00 2001 From: Tom Van Acker Date: Wed, 30 Nov 2022 22:14:13 +0100 Subject: [PATCH 36/56] update the log-normal MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Given the ln-function, all unitful quantities are expressed in terms of the unit of μ for the pdf, cdf and ccdf. --- Project.toml | 2 ++ src/io/distributions.jl | 16 +++++++++++----- 2 files changed, 13 insertions(+), 5 deletions(-) diff --git a/Project.toml b/Project.toml index 4779863..4f6089e 100644 --- a/Project.toml +++ b/Project.toml @@ -5,12 +5,14 @@ version = "0.1.2" [deps] AdditionalUnits = "02d9b4f0-7821-44c6-acbd-01a1ab91b72e" +Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59" LightGraphs = "093fc24a-ae57-5d10-9952-331d41423f4d" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7" Multigraphs = "7ebac608-6c66-46e6-9856-b5f43e107bac" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" +SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" diff --git a/src/io/distributions.jl b/src/io/distributions.jl index 0b9a1be..a36a335 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -242,6 +242,9 @@ f(x, μ, σ, ω) = \\begin{cases} 0 &\\text{if:}~x < 0. \\end{cases} ``` + +Given the ln-function, all Unitful values are converted to correspond with the unit of `μ`. + # Constructors | Full | Abbr. | Description | | :----------------- | :------------ | :----------------------------------------------------------- | @@ -311,9 +314,10 @@ function pdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) μ, σ, ω = params(dst) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false if φ >= zero(μ) - x = ustrip(unit(φ), σ) - y = uconvert(unit(φ/φ),(log(φ) - μ)^2 / (2 * σ^2)) - eval(ω,t) / (sqrt(2 * pi) * x * φ) * exp(-y) + x = ustrip(unit(μ), σ) + y = uconvert(unit(μ), φ) + z = uconvert(unit(μ/μ),(log(y) - μ)^2 / (2 * σ^2)) + eval(ω,t) / (sqrt(2 * pi) * x * y) * exp(-z) else zero(1/φ) end @@ -322,7 +326,8 @@ function cdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) μ, σ, ω = params(dst) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false if φ >= zero(μ) - y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) + x = uconvert(unit(μ), φ) + y = uconvert(unit(μ/μ),(log(x) - μ) / (sqrt(2) * σ)) eval(ω,t) / 2 * _SF.erfc(-y) else zero(Number) @@ -332,7 +337,8 @@ function ccdf(dst::AbstractLogNormal, φ::Number, t::Number=zero(φ)) μ, σ, ω = params(dst) dimension(μ)==dimension(σ)==dimension(φ)==dimension(t) || return false if φ >= zero(μ) - y = uconvert(unit(φ/φ),(log(φ) - μ) / (sqrt(2) * σ)) + x = uconvert(unit(μ), φ) + y = uconvert(unit(μ/μ),(log(x) - μ) / (sqrt(2) * σ)) eval(ω,t) * (1 - _SF.erfc(-y) / 2) else eval(ω,t) From 88b75ff95db9b1260fdc3ece09f6a026a186a1dc Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Wed, 14 Jun 2023 21:17:48 +0200 Subject: [PATCH 37/56] Final version of SMP --- .../semi-markov/optical-monitoring-system.jl | 2 +- examples/semi-markov/semi-analytical.jl | 57 +++++++++++-------- src/form/semi_markov_process.jl | 46 +++++++++------ 3 files changed, 63 insertions(+), 42 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index c5b78c8..d0c0eac 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -50,7 +50,7 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # solve the std -solve!(std, cls, tsim = 8760.0u"hr", dt = 2u"hr", tol=1e-8) +solve!(std, cls, tsim = 8760.0u"hr", dt = 5.84u"hr", tol=1e-8) # plot the probabilities plot(_MSS.get_prop(std, :time), diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index 3b2934b..168148a 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -31,7 +31,7 @@ const _MSS = MultiStateSystems const _LG = LightGraphs # constants -dt = 3.0u"hr" +dt = 0.1u"hr" tsim = 4500.0u"hr" t = zero(dt):dt:tsim @@ -50,7 +50,7 @@ add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5 states = [(1,2),(2,3)]) # trapping -# _MSS.set_info!(std, 3, :trapping, true) +_MSS.set_info!(std, 3, :trapping, true) # # solve the std - Markov # solve!(std, cls, tsim = tsim, dt = dt) @@ -68,14 +68,14 @@ add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5 # ylabel="probability") # # solve the std - Analytical -# dτ = dt / 1 -# dst1 = _MSS.get_prop(std,_LG.Edge(1,2),:distr) -# dst2 = _MSS.get_prop(std,_LG.Edge(2,3),:distr) +dτ = dt / 10 +dst1 = _MSS.get_prop(std,_LG.Edge(1,2),:distr) +dst2 = _MSS.get_prop(std,_LG.Edge(2,3),:distr) -# PA1 = 1.0 .- _MSS.cdf.(dst1,t,zero(dt)) -# PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] -# PA22= [sum(dτ * _MSS.weights(length(zero(nt):dτ:nt))[ni] * _MSS.pdf.(dst1,nl,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-nl,nt)) for (ni,nl) in enumerate(zero(nt):dτ:nt)) for nt in t] -# PA3 = 1.0 .- (PA1 .+ PA2) +PA1 = 1.0 .- _MSS.cdf.(dst1,t,zero(dt)) +PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] +PA22= [sum(dτ * _MSS.weights(length(zero(nt):dτ:nt))[ni] * _MSS.pdf.(dst1,nl,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-nl,nt)) for (ni,nl) in enumerate(zero(nt):dτ:nt)) for nt in t] +PA3 = 1.0 .- (PA1 .+ PA2) @@ -87,21 +87,28 @@ add_transitions!(std, distr = [Exponential(1000.0u"hr"), Weibull(250.0u"hr", 1.5 solve!(std, cls, tsim = tsim, dt = dt) # # probabilities - SEMIMarkov -# PS1 = _MSS.get_prop(std,1,:prob) -# PS2 = _MSS.get_prop(std,2,:prob) -# PS3 = _MSS.get_prop(std,3,:prob) - +PS1 = _MSS.get_prop(std,1,:prob) +PS2 = _MSS.get_prop(std,2,:prob) +PS3 = _MSS.get_prop(std,3,:prob) +plot(t, [PS1, PS2, PS3], + label=["State 1" "State 2" "State 3"], + xlabel="time", + ylabel="probability") +plot(t, PA1.+PA2, + label="State 1+ State 2", + xlabel="time", + ylabel="probability") -# ϵ = 1e-16; +ϵ = 1e-16; -# plot(t, [PA1.-PS1.+ϵ, PA2.-PS2.+ϵ, PA3.-PS3.+ ϵ], -# label=["State 1" "State 2" "State 3"], -# xlabel="time", -# yscale = :log, -# ylabel="probability difference") +plot(t, [PA1.-PS1.+ϵ, PA2.-PS2.+ϵ, PA3.-PS3.+ ϵ], + label=["State 1" "State 2" "State 3"], + xlabel="time", + yscale = :log, + ylabel="probability difference") # plot!(t, PA2.-PS2.+ϵ, # label="State 2", @@ -133,9 +140,9 @@ solve!(std, cls, tsim = tsim, dt = dt) # ylabel="rate (1/t)") -# # # plot the reliability -# # plot(_MSS.get_prop(std, :time), -# # _MSS.get_prop(std, 1, :prob) + _MSS.get_prop(std, 2, :prob), -# # label="reliability", -# # xlabel="time", -# # ylabel="probability") \ No newline at end of file +# plot the reliability + plot(_MSS.get_prop(std,:time), + _MSS.get_prop(std,1,:prob), + label="reliability", + xlabel="time", + ylabel="probability") \ No newline at end of file diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 9cacf60..892cf1c 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -29,7 +29,10 @@ function set_A(std::AbstractSTD, t::StepRangeLen) for (ni,nt) in enumerate(t) for tr in transitions(std) id = ns(std) * (ni-1) + _LG.dst(tr) - # NB: GLENN same clarification + # The content of the A-vector is the probability of initially being + # in state (_LG.src(tr)) times the probability of transitioning out + # of that state entered at sojourn time zero and evaluated at + # time t = (nt) A[id] += get_prop(std, _LG.src(tr), :init) * pdf(get_prop(std, tr, :distr), nt, zero(dt)) end end @@ -60,6 +63,7 @@ function set_U(std::AbstractSTD, t::StepRangeLen) Ψ = zeros(typeof(1/dt), ns(std), ns(std)) for tr in transitions(std) # NB: GLENN additional clarification distr betreden op nϕ en blijven tot nt, φ = nt - nl + # Comment # pdf Ψ[_LG.dst(tr), _LG.src(tr)] = pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 @@ -118,37 +122,33 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; dt = dt |> unit(tsim) t = zero(dt):dt:tsim Nt = length(t) - println(t) - # solve the problem Φ = zeros(Nt, ns(std)) - diff = zeros(Nt, ns(std)) U = set_U(std,t,tol) # U = set_U(std,t) A = ustrip(set_A(std,t)) - println("time to calculate H") - @time H=U\A*unit(1/t[1]) + H=U\A*unit(1/t[1]) - # h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end for st in states(std) - @time for (ni,nt) in enumerate(t) + for (ni,nt) in enumerate(t) w = weights(ni) # TOM: φ <<< t, zero could be higher # l = zero(dt):dt:nt l = t[1]:dt:nt .|> unit(tsim) # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification - # + # Comment Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] - # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-8)[1] + Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-8)[1] - Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* - ccdf(std, st, nt-nl, nl) - for (nj,nl) in enumerate(l)) + # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + # ccdf(std, st, nt-nl, nl) + # for (nj,nl) in enumerate(l)) end end @@ -159,9 +159,6 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) - - # return [h[st](t) for st in states(std)] - return U end """ @@ -242,3 +239,20 @@ elunit(b::Vector{U}) where U = _UF.unit(U) _LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = (ustrip.(A) \ ustrip(b)) * (elunit(b) / elunit(A)) +function battery_system_availability(i, T, ntw_av, μ, σ) + # Calculate the probability that the battery does not run out of charge before + # the power sources are repaired at time t. With a lognormal distribution for + # the repair time with mean μ and standard deviation σ. + p_failure = 1 - ntw_av[i] + p_repair_time_ge_T = ccdf(LogNormal(μ, σ),T) + return 1-p_failure*p_repair_time_ge_T +end + +function battery_system_availability(i, T, ntw_av, θ) + # Calculate the probability that the battery does not run out of charge before + # the power sources are repaired at time t. With a lognormal distribution for + # the repair time with mean μ and standard deviation σ. + p_failure = 1 - ntw_av[i] + p_repair_time_ge_T = ccdf(Exponential(θ),T) + return 1-p_failure*p_repair_time_ge_T +end \ No newline at end of file From b9e73d77e0c7a755c539174a9f72717f5b434672 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 14 Jul 2023 11:40:45 +0200 Subject: [PATCH 38/56] Adding final comments and examples --- .../semi-markov/optical-monitoring-system.jl | 16 +++-- examples/semi-markov/single-feeder.jl | 65 +++++++++++++++++++ examples/semi-markov/validation_test.jl | 10 ++- src/form/semi_markov_process.jl | 29 +++++---- 4 files changed, 104 insertions(+), 16 deletions(-) create mode 100644 examples/semi-markov/single-feeder.jl diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index d0c0eac..05510ed 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -24,6 +24,7 @@ using Plots using Unitful using UnitfulRecipes using MultiStateSystems +using Revise @@ -50,7 +51,14 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # solve the std -solve!(std, cls, tsim = 8760.0u"hr", dt = 5.84u"hr", tol=1e-8) +@time solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol=1e-8) + +#To do: Testen of de resultaten van mijn eigen analyse goed uitkomen op 1, toch uitzoeken waar effect van weighting precies vandaan komt, wat doet die numerieke backslash operator precies? + +# 1. Set U with sparse matrix and H integrated numerically with simpson rule: 49.679 seconds; 1.00001173 +# 2. Set U with sparse matrix and H integrated with quadgk: 133.125 seconds; 0.999999001 +# 3. Set U with standard method and H integrated numerically with simpson rule; 40.318 seconds; 1.00001173 +# 4. Set U with standard method and H integrated with quadgk: 123.198 seconds; 0.999999001 # plot the probabilities plot(_MSS.get_prop(std, :time), @@ -60,8 +68,8 @@ plot(_MSS.get_prop(std, :time), ylabel="probability") # plot the reliability -plot!(_MSS.get_prop(std, :time), - _MSS.get_prop(std, 1, :prob), - label="reliability", +plot(_MSS.get_prop(std, :time), + _MSS.get_prop(std, 1, :prob)+_MSS.get_prop(std, 2, :prob)+_MSS.get_prop(std, 3, :prob)+_MSS.get_prop(std, 4, :prob), + label="reliability weight trap", xlabel="time", ylabel="probability") \ No newline at end of file diff --git a/examples/semi-markov/single-feeder.jl b/examples/semi-markov/single-feeder.jl new file mode 100644 index 0000000..9188c4c --- /dev/null +++ b/examples/semi-markov/single-feeder.jl @@ -0,0 +1,65 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Plots +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SemiMarkovProcess() + +# Initializing the state transition diagram of a homogeneous semi markov process to test +# the model + +std = STD() +add_states!(std, name = ["normal operation state","fault operation state f1","Primary post-fault state","Secondary post-fault state", "Fault operation state for f2", "Fault operation state for f3"], + power = [1.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW"], + init = [1.0,0.0,0.0,0.0,0.0,0.0]) + +add_transitions!(std, states = [(1,2),(1,5),(1,6),(2,3),(5,3),(6,3),(2,4),(5,4),(6,4),(3,4),(4,1)], + distr = [Exponential(4000.0u"hr", 0.3), + Exponential(10000.0u"hr", 0.4), + Exponential(25000.0u"hr", 0.3), + LogNormal(10.0u"hr", 0.08u"hr", 0.8), + LogNormal(10.0u"hr", 0.08u"hr", 0.8), + LogNormal(10.0u"hr", 0.08u"hr", 0.8), + LogNormal(10.0u"hr", 0.08u"hr", 0.2), + LogNormal(10.0u"hr", 0.08u"hr", 0.2), + LogNormal(10.0u"hr", 0.08u"hr", 0.2), + LogNormal(100u"hr", 0.08u"hr"), + Weibull(1000.0u"hr", 10)]) + + +# solve the network +solve!(std, cls , tsim = 10000.0u"hr", dt = 10u"hr") + +# plot the probabilities +plot(_MSS.get_prop(std, :time), + [_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)], + label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), + xlabel="time", + ylabel="probability") + +# plot the reliability +plot(_MSS.get_prop(std, :time), + _MSS.get_prop(std, 1, :prob), + label="semi-Markov", + xlabel="time", + ylabel="Availability") + + +tot_prob = [] +ns = 11 +tot_prob .+= _MSS.get_prop(std, ns, :prob) +for ns in _MSS.states(std) + tot_prob .+= _MSS.get_prop(std, ns, :prob) +end diff --git a/examples/semi-markov/validation_test.jl b/examples/semi-markov/validation_test.jl index af5e14b..6064f86 100644 --- a/examples/semi-markov/validation_test.jl +++ b/examples/semi-markov/validation_test.jl @@ -45,7 +45,7 @@ add_transitions!(std, states = [(1,2),(2,3),(2,4),(4,3),(3,1),(1,5),(5,6),(5,7), # solve the network -solve!(std, cls , tsim = 450000.0u"hr", dt = 600u"hr") +solve!(std, cls , tsim = 4500.0u"hr", dt = 1800u"s") # plot the probabilities plot(_MSS.get_prop(std, :time), @@ -60,3 +60,11 @@ plot!(_MSS.get_prop(std, :time), label="reliability", xlabel="time", ylabel="probability") + + +tot_prob = [] +ns = 10 +tot_prob .+= _MSS.get_prop(std, ns, :prob) +for ns in _MSS.states(std) + tot_prob .+= _MSS.get_prop(std, ns, :prob) +end diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 892cf1c..f9f88ee 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -50,6 +50,7 @@ and remains there until time t The unit of U is [-] """ function set_U(std::AbstractSTD, t::StepRangeLen) + # dt = step(t) Nt = length(t) @@ -62,9 +63,9 @@ function set_U(std::AbstractSTD, t::StepRangeLen) for (nj,nl) in enumerate(l) Ψ = zeros(typeof(1/dt), ns(std), ns(std)) for tr in transitions(std) - # NB: GLENN additional clarification distr betreden op nϕ en blijven tot nt, φ = nt - nl - # Comment - # pdf + # The results of the pdf depends on two factors: + # - How long has the system been in this particular state = sojourn time (nt - nl) with nt the index of the current time t and nl the index of entrance time. + # - The time at which the system entered a certain state, with nl the index of this entrance time. This determines weight attributed to this particular transition. Ψ[_LG.dst(tr), _LG.src(tr)] = pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 end @@ -99,10 +100,10 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. dst = get_prop(std, tr, :distr) lb = floor(cquantile(dst, tol) / dt) * dt - @time for (ni,nt) in enumerate(t) + for (ni,nt) in enumerate(t) Φ = nt:-dt:t[1] + # Φ represents the sojourn time, ranging from lt = t[1]:dt:nt - # Φ = min(zero(dt),lb):dt:nt NΦ = length(Φ) append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) @@ -141,14 +142,20 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # l = zero(dt):dt:nt l = t[1]:dt:nt .|> unit(tsim) # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification - # Comment + # The probability of being in a state st at time nt depends on two things: + # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. + # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time + # of entering the state (0) to determine the weight and the sojourn time (nt-0). + # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). + # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. + # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at + # The last transition time x and the sojourn time nt-x. Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), zero(dt),nt,rtol=1e-8)[1] - Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-8)[1] + # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] - # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* - # ccdf(std, st, nt-nl, nl) - # for (nj,nl) in enumerate(l)) + Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + ccdf(std, st, nt-nl, nl) + for (nj,nl) in enumerate(l)) end end From ae5383d703d40fabc932e0c35c2500c6775e107b Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Mon, 24 Jul 2023 11:33:27 +0200 Subject: [PATCH 39/56] First version of more detailed numerical inrush calculation method --- .../semi-markov/optical-monitoring-system.jl | 63 +++++- examples/semi-markov/single-feeder.jl | 10 +- examples/semi-markov/validation_test.jl | 4 +- src/form/semi_markov_process.jl | 187 +++++++++++++++++- 4 files changed, 251 insertions(+), 13 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 05510ed..a7f51ed 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -22,10 +22,10 @@ States: # load pkgs using Plots using Unitful -using UnitfulRecipes using MultiStateSystems using Revise - +using CSV +using DataFrames # pkg const @@ -51,7 +51,17 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # solve the std -@time solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol=1e-8) +@time H1, H1c, H = solve!(std, cls, tsim = 8760.0u"hr"; dt = 4u"hr", acc = 10, steps = 150, tol=1e-8) + # h = solve!(std, cls, tsim = 596.0u"hr", dt = 4u"hr", tol=1e-8) +steps = 150; +acc = 10; +dt = 4u"hr"; +tsim = 8760.0u"hr"; +dt_n = dt/acc |> unit(tsim); +t_n = zero(dt_n):dt_n:dt_n*(steps)*acc +time = zero(dt):dt:149.0*dt; + +length(t_n) #To do: Testen of de resultaten van mijn eigen analyse goed uitkomen op 1, toch uitzoeken waar effect van weighting precies vandaan komt, wat doet die numerieke backslash operator precies? @@ -72,4 +82,49 @@ plot(_MSS.get_prop(std, :time), _MSS.get_prop(std, 1, :prob)+_MSS.get_prop(std, 2, :prob)+_MSS.get_prop(std, 3, :prob)+_MSS.get_prop(std, 4, :prob), label="reliability weight trap", xlabel="time", - ylabel="probability") \ No newline at end of file + ylabel="probability") + +plot(_MSS.get_prop(std, :time), + _MSS.get_prop(std, 1, :prob), + label="State 1", + xlabel="time", + ylabel="State Probability") + +plot(_MSS.get_prop(std, :time), + ustrip(h[1]), + label="h[1]", + xlabel="time", + ylabel="State Probability") + +plot!(t_n[1:end-4], + ustrip(H1[4]), + label="H1[1]", + xlabel="time", + ylabel="Transition frequency density function") + +time = _MSS.get_prop(std, :time); +state1 = _MSS.get_prop(std, 1, :prob); +state2 = _MSS.get_prop(std, 2, :prob); +state3 = _MSS.get_prop(std, 3, :prob); +state4 = _MSS.get_prop(std, 4, :prob); +stfd1 = ustrip(H[1]); +stfd2 = ustrip(H[2]); +stfd3 = ustrip(H[3]); +stfd4 = ustrip(H[4]); + +ut = Array{String}(undef,length(time)) +for i in 1:1:length(time) + ut[i] = string(unit(time[1])) +end + +results = DataFrames.DataFrame(time = ustrip(time), unit = ut, + state1 = state1, + state2 = state2, + state3 = state3, + state4 = state4, + H1 = stfd1, + H2 = stfd2, + H3 = stfd3, + H4 = stfd4); + +CSV.write("C:/Users/gemmers/Documents/GitHub/MSS/Results/Journal_Semi_Markov/OMS_results.csv", results) \ No newline at end of file diff --git a/examples/semi-markov/single-feeder.jl b/examples/semi-markov/single-feeder.jl index 9188c4c..fbb571a 100644 --- a/examples/semi-markov/single-feeder.jl +++ b/examples/semi-markov/single-feeder.jl @@ -36,7 +36,7 @@ add_transitions!(std, states = [(1,2),(1,5),(1,6),(2,3),(5,3),(6,3),(2,4),(5,4), LogNormal(10.0u"hr", 0.08u"hr", 0.2), LogNormal(10.0u"hr", 0.08u"hr", 0.2), LogNormal(100u"hr", 0.08u"hr"), - Weibull(1000.0u"hr", 10)]) + Weibull(100.0u"hr", 10)]) # solve the network @@ -56,10 +56,14 @@ plot(_MSS.get_prop(std, :time), xlabel="time", ylabel="Availability") +plot(_MSS.get_prop(std, :time), + sum(_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)), + label="semi-Markov", + xlabel="time", + ylabel="Availability") + sum.(_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)) tot_prob = [] -ns = 11 -tot_prob .+= _MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std) tot_prob .+= _MSS.get_prop(std, ns, :prob) end diff --git a/examples/semi-markov/validation_test.jl b/examples/semi-markov/validation_test.jl index 6064f86..f8b7825 100644 --- a/examples/semi-markov/validation_test.jl +++ b/examples/semi-markov/validation_test.jl @@ -45,7 +45,7 @@ add_transitions!(std, states = [(1,2),(2,3),(2,4),(4,3),(3,1),(1,5),(5,6),(5,7), # solve the network -solve!(std, cls , tsim = 4500.0u"hr", dt = 1800u"s") +solve!(std, cls , tsim = 10000.0u"hr", dt = 10u"hr") # plot the probabilities plot(_MSS.get_prop(std, :time), @@ -55,7 +55,7 @@ plot(_MSS.get_prop(std, :time), ylabel="probability") # plot the reliability -plot!(_MSS.get_prop(std, :time), +plot(_MSS.get_prop(std, :time), _MSS.get_prop(std, 1, :prob), label="reliability", xlabel="time", diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index f9f88ee..ab2dd3c 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -41,6 +41,31 @@ function set_A(std::AbstractSTD, t::StepRangeLen) return A end +function set_A(std::AbstractSTD, t::StepRangeLen, H::Vector, steps::Number) + dt = step(t) + Nt = length(t) + Ns = ns(std) + + A = zeros(typeof(1/dt), ns(std) * Nt) + + A[1:length(H)] = H + + for (ni,nt) in enumerate(t) + if ni > steps + for tr in transitions(std) + id = ns(std) * (ni-1) + _LG.dst(tr) + # The content of the A-vector is the probability of initially being + # in state (_LG.src(tr)) times the probability of transitioning out + # of that state entered at sojourn time zero and evaluated at + # time t = (nt) + A[id] += get_prop(std, _LG.src(tr), :init) * + pdf(get_prop(std, tr, :distr), nt, zero(dt)) + end end end + A[isnan.(A)] .= zero(1/dt) + + return A +end + """ MultiStateSystems.set_U(std::MultiStateSystems.AbstractSTD, t::StepRangeLen) @@ -115,10 +140,45 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) return _SA.sparse(I, J, V) end +function set_U(std::AbstractSTD, t::StepRangeLen, steps::Number, tol::Real) + dt = step(t) + Nt = length(t) + Ns = ns(std) + + # initialize three vectors I,J,V respectively row, column and value indices + I,J,V = Int[],Int[],Number[] + + append!(I, 1:Ns*Nt) + append!(J, 1:Ns*Nt) + append!(V, ones(Number,Ns*Nt)) + + for tr in transitions(std) + # dummy value not necessary, since every diagonal entry requires a one to be added to it. + # Sparse Arrays allow to add values to the same location twice and add those + # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. + dst = get_prop(std, tr, :distr) + lb = floor(cquantile(dst, tol) / dt) * dt + for (ni,nt) in enumerate(t) + if ni > steps + Φ = nt:-dt:t[1] + # Φ represents the sojourn time, ranging from + lt = t[1]:dt:nt + NΦ = length(Φ) + + append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) + append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) + # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) + append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) + end + end end + V[isnan.(V)] .= 0.0 + return _SA.sparse(I, J, V) +end + # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1u"hr", tol::Real=1e-8) - + tsim::Number=1.0u"yr", dt::Number=1u"hr") + tol = 1e-8; # get the input dt = dt |> unit(tsim) t = zero(dt):dt:tsim @@ -133,7 +193,8 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; H=U\A*unit(1/t[1]) - h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + # h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + h = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; for st in states(std) for (ni,nt) in enumerate(t) @@ -166,8 +227,91 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) + return h +end + +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; + tsim::Number=1.0u"yr", dt::Number=1u"hr", acc::Int64=10, steps::Number=100.0, tol::Real=1e-8) + + # Get the input for solving numerical inrush phase + dt_n = dt/acc |> unit(tsim); + t_n = zero(dt_n):dt_n:dt_n*(steps)*acc; + + U = set_U(std,t_n[1:end-1],tol) + A = ustrip(set_A(std,t_n[1:end-1])) + H1 = U\A*unit(1/t_n[1]) + + H_c = compress(H1, acc, std) + + H1o = [ map(x->H1[ns(std) * (x-1) + st], 1:length(t_n)-ns(std)) for st in states(std)]; + H1co = [ map(x->H_c[ns(std) * (x-1) + st], 1:Int(length(H_c)/ns(std))) for st in states(std)]; + + # get the input for final problem solution + dt = dt |> unit(tsim) + t = zero(dt):dt:tsim + Nt = length(t) + + # solve the problem + Φ = zeros(Nt, ns(std)) + + U = set_U(std,t,steps,tol) + A = ustrip(set_A(std,t,H_c,steps)) + H=U\A*unit(1/t[1]) + + Ho = [ map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; + + for st in states(std) + for (ni,nt) in enumerate(t) + w = weights(ni) + # TOM: φ <<< t, zero could be higher + # l = zero(dt):dt:nt + l = t_n[1]:dt:nt .|> unit(tsim) + # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification + # The probability of being in a state st at time nt depends on two things: + # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. + # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time + # of entering the state (0) to determine the weight and the sojourn time (nt-0). + # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). + # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. + # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at + # The last transition time x and the sojourn time nt-x. + Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) + # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] + + Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + ccdf(std, st, nt-nl, nl) + for (nj,nl) in enumerate(l)) + end end + + # set the output + set_prop!(std, :cls, cls) + set_prop!(std, :time, t) + set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) + + # set the solved status + set_info!(std, :solved, true) + + return H1o, H1co, Ho +end + +function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) + Ns = ns(std) + + for st in states(std) + init = get_prop(std, _LG.src(tr), :init) + + if init > 0.0 + p = init .* ccdf.(std, st, t, zero(dt)) + + integral(std, st, t, H[st:Ns:end], tol) + else + p = integral(std, st, t, H[st:Ns:end], tol) + end + set_prop!(std, st, :prob, p) + end end + + """ MultiStateSystems.weights(x::Int) @@ -262,4 +406,39 @@ function battery_system_availability(i, T, ntw_av, θ) p_failure = 1 - ntw_av[i] p_repair_time_ge_T = ccdf(Exponential(θ),T) return 1-p_failure*p_repair_time_ge_T -end \ No newline at end of file +end + +function integral(std::AbstractSTD, st::Int, t::StepRangeLen, h::Vector, tol::Real) + # controleer voor schaalfactor + d2h = abs.(diff(diff(h))) + id = 1 + idx = [1] + + while true + next_id = findfirst(x -> x > tol, cumsum(d2h[id:end])) + next_id == nothing ? break : ~ ; + + global id += next_id + push!(idx,id) + end + push!(idx,length(d2h)) + τ = t[idx] + + γ = _INT.LinearInterpolation(collect(t), h) + + ϕ = [_QGK.quadgk(x -> h(x) * ccdf.(std, st, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] + # niet gelijk gespacete interpolatie + p = _INT.LinearInterpolation(τ, ϕ)(t) +end + +function compress(v::Vector, y::Int, std::AbstractSTD) + n = length(v) + Ns = ns(std) + compressed_v = zeros(Int(n ÷ y))*unit(v[1]) + for st in 1:Ns + for i in 1:Int(n/Ns ÷ y) + compressed_v[Ns*(i-1)+st] = v[y*Ns*(i-1)+st]; + end + end + return compressed_v + end \ No newline at end of file From 8792e241afd6b17be82726d3293caf7307ca8bf7 Mon Sep 17 00:00:00 2001 From: Glenn Emmers Date: Fri, 28 Jul 2023 13:05:20 +0200 Subject: [PATCH 40/56] Addition of tests, working set_P --- .../semi-markov/optical-monitoring-system.jl | 51 ++++-- src/core/types.jl | 1 + src/form/semi_markov_process.jl | 151 +++++++++++------- src/io/state_transition_diagram.jl | 4 + test/elements/CAP_ac.jl | 30 ++++ test/elements/optical_monitoring_system.jl | 24 +-- test/semi_markov_process.jl | 30 ++-- 7 files changed, 193 insertions(+), 98 deletions(-) create mode 100644 test/elements/CAP_ac.jl diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index a7f51ed..ce0e285 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -51,15 +51,24 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # solve the std -@time H1, H1c, H = solve!(std, cls, tsim = 8760.0u"hr"; dt = 4u"hr", acc = 10, steps = 150, tol=1e-8) - # h = solve!(std, cls, tsim = 596.0u"hr", dt = 4u"hr", tol=1e-8) +# @time H1_20, H1c_20, H_accurate_20 = _MSS.solved!(std, cls, tsim = 8760.0u"hr", dt = 10u"hr", acc = 20, steps = 50, tol=1e-8) +# @time H1_40, H1c_40, H_accurate_40 = _MSS.solved!(std, cls, tsim = 200.0u"hr", dt = 4u"hr", acc = 10, steps = 40, tol=1e-8) +h_base = solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol=1e-7); +_MSS.solveP!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8); + +h_base_select=h_base[1][1:10:end] + +plot([h_base_select.-H_accurate_20[1],h_base_select.-H_accurate_40[1]]) + +dH = abs.(diff(H_accurate_20[1])) +append!(dH,zero(H[1][1])) steps = 150; acc = 10; dt = 4u"hr"; tsim = 8760.0u"hr"; dt_n = dt/acc |> unit(tsim); t_n = zero(dt_n):dt_n:dt_n*(steps)*acc -time = zero(dt):dt:149.0*dt; +time_c = zero(dt):dt:149.0*dt; length(t_n) @@ -90,14 +99,14 @@ plot(_MSS.get_prop(std, :time), xlabel="time", ylabel="State Probability") -plot(_MSS.get_prop(std, :time), - ustrip(h[1]), - label="h[1]", +plot(_MSS.get_prop(std, :time)[1:length(dh)], + ustrip(h), + label="diff H", xlabel="time", ylabel="State Probability") -plot!(t_n[1:end-4], - ustrip(H1[4]), +plot(_MSS.get_prop(std, :time)[1:length(H[1])], + ustrip(H[1]), label="H1[1]", xlabel="time", ylabel="Transition frequency density function") @@ -108,9 +117,12 @@ state2 = _MSS.get_prop(std, 2, :prob); state3 = _MSS.get_prop(std, 3, :prob); state4 = _MSS.get_prop(std, 4, :prob); stfd1 = ustrip(H[1]); -stfd2 = ustrip(H[2]); -stfd3 = ustrip(H[3]); -stfd4 = ustrip(H[4]); +diffstfd1 = ustrip(dh); +stfd1d = ustrip(H1[1]); + +time2 = time_c; +stfd3 = ustrip(h[3]); +stfd4 = ustrip(h[4]); ut = Array{String}(undef,length(time)) for i in 1:1:length(time) @@ -122,9 +134,16 @@ results = DataFrames.DataFrame(time = ustrip(time), unit = ut, state2 = state2, state3 = state3, state4 = state4, - H1 = stfd1, - H2 = stfd2, - H3 = stfd3, - H4 = stfd4); + h1 = stfd1, + h2 = stfd2, + h3 = stfd3, + h4 = stfd4); + +results = DataFrames.DataFrame(time = ustrip(time), unit = ut, + h1 = stfd1, + H1 = stfd1d, + dh = diffstfd1); + + -CSV.write("C:/Users/gemmers/Documents/GitHub/MSS/Results/Journal_Semi_Markov/OMS_results.csv", results) \ No newline at end of file +CSV.write("C:/Users/gemmers/Documents/GitHub/MSS/Results/Journal_Semi_Markov/diffH_results.csv", results) \ No newline at end of file diff --git a/src/core/types.jl b/src/core/types.jl index e7386e0..d05e6c1 100644 --- a/src/core/types.jl +++ b/src/core/types.jl @@ -31,3 +31,4 @@ PropDict = Dict{Symbol,Any} # broadcastable Broadcast.broadcastable(dst::AbstractDistribution) = Ref(dst) +Broadcast.broadcastable(std::AbstractSTD) = Ref(std) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index ab2dd3c..675a7eb 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -51,7 +51,7 @@ function set_A(std::AbstractSTD, t::StepRangeLen, H::Vector, steps::Number) A[1:length(H)] = H for (ni,nt) in enumerate(t) - if ni > steps + if ni > steps + 1 for tr in transitions(std) id = ns(std) * (ni-1) + _LG.dst(tr) # The content of the A-vector is the probability of initially being @@ -159,7 +159,7 @@ function set_U(std::AbstractSTD, t::StepRangeLen, steps::Number, tol::Real) dst = get_prop(std, tr, :distr) lb = floor(cquantile(dst, tol) / dt) * dt for (ni,nt) in enumerate(t) - if ni > steps + if ni > steps + 1 Φ = nt:-dt:t[1] # Φ represents the sojourn time, ranging from lt = t[1]:dt:nt @@ -177,8 +177,7 @@ end # stochastic process function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1u"hr") - tol = 1e-8; + tsim::Number=1.0u"yr", dt::Number=1u"d", tol::Real=1e-8) # get the input dt = dt |> unit(tsim) t = zero(dt):dt:tsim @@ -187,36 +186,40 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # solve the problem Φ = zeros(Nt, ns(std)) - U = set_U(std,t,tol) - # U = set_U(std,t) - A = ustrip(set_A(std,t)) + println("set_U") + @time U = set_U(std,t,tol) + println("set_A") + @time A = ustrip(set_A(std,t)) H=U\A*unit(1/t[1]) - - # h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end - h = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; - - for st in states(std) + # println("set_P") + # @time set_P(std, t, H, tol) + println("Linear interpolation of H") + @time h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + h_sol = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; + + println("Integration of H to Φ") + @time for st in states(std) for (ni,nt) in enumerate(t) w = weights(ni) # TOM: φ <<< t, zero could be higher # l = zero(dt):dt:nt l = t[1]:dt:nt .|> unit(tsim) - # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification - # The probability of being in a state st at time nt depends on two things: - # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. - # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time - # of entering the state (0) to determine the weight and the sojourn time (nt-0). - # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). - # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. - # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at - # The last transition time x and the sojourn time nt-x. + # # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification + # # The probability of being in a state st at time nt depends on two things: + # # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. + # # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time + # # of entering the state (0) to determine the weight and the sojourn time (nt-0). + # # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). + # # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. + # # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at + # # The last transition time x and the sojourn time nt-x. Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] + Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] - Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* - ccdf(std, st, nt-nl, nl) - for (nj,nl) in enumerate(l)) + # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + # ccdf(std, st, nt-nl, nl) + # for (nj,nl) in enumerate(l)) end end @@ -227,21 +230,48 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) - return h + return h_sol end -function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; +function solveP!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; + tsim::Number=1.0u"yr", dt::Number=1u"hr", tol::Real=1e-8) + # get the input + dt = dt |> unit(tsim) + t = zero(dt):dt:tsim + Nt = length(t) + + # solve the problem + Φ = zeros(Nt, ns(std)) + + println("set_U") + @time U = set_U(std,t,tol) + println("set_A") + @time A = ustrip(set_A(std,t)) + H=U\A*unit(1/t[1]) + + println("set_P") + @time set_P(std, t, H, tol) + + # set the output + set_prop!(std, :cls, cls) + set_prop!(std, :time, t) + + # set the solved status + set_info!(std, :solved, true) +end + +function solved!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1u"hr", acc::Int64=10, steps::Number=100.0, tol::Real=1e-8) # Get the input for solving numerical inrush phase dt_n = dt/acc |> unit(tsim); t_n = zero(dt_n):dt_n:dt_n*(steps)*acc; - U = set_U(std,t_n[1:end-1],tol) - A = ustrip(set_A(std,t_n[1:end-1])) + U = set_U(std,t_n[1:end],tol) + A = ustrip(set_A(std,t_n[1:end])) H1 = U\A*unit(1/t_n[1]) - H_c = compress(H1, acc, std) + H_c = compress(H1, steps, std) H1o = [ map(x->H1[ns(std) * (x-1) + st], 1:length(t_n)-ns(std)) for st in states(std)]; H1co = [ map(x->H_c[ns(std) * (x-1) + st], 1:Int(length(H_c)/ns(std))) for st in states(std)]; @@ -260,12 +290,15 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; Ho = [ map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; + # set_P(std, t, H, tol) + h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + for st in states(std) for (ni,nt) in enumerate(t) w = weights(ni) # TOM: φ <<< t, zero could be higher # l = zero(dt):dt:nt - l = t_n[1]:dt:nt .|> unit(tsim) + l = t[1]:dt:nt .|> unit(tsim) # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification # The probability of being in a state st at time nt depends on two things: # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. @@ -276,13 +309,14 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at # The last transition time x and the sojourn time nt-x. Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - # Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] + Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] - Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* - ccdf(std, st, nt-nl, nl) - for (nj,nl) in enumerate(l)) + # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* + # ccdf(std, st, nt-nl, nl) + # for (nj,nl) in enumerate(l)) end end + # set the output set_prop!(std, :cls, cls) set_prop!(std, :time, t) @@ -296,15 +330,17 @@ end function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) Ns = ns(std) + Nt = length(t) - for st in states(std) - init = get_prop(std, _LG.src(tr), :init) + idx_s = + for st in states(std) + init = get_prop(std, st, :init) + h = map(x->H[ns(std) * (x-1) + st], 1:Nt) if init > 0.0 - p = init .* ccdf.(std, st, t, zero(dt)) - + integral(std, st, t, H[st:Ns:end], tol) + p = init .* ccdf.(std, st, t, zero(t[1])) .+ integral(std, st, t, h, tol) else - p = integral(std, st, t, H[st:Ns:end], tol) + p = integral(std, st, t, h, tol) end set_prop!(std, st, :prob, p) end @@ -371,18 +407,6 @@ end # ccdf(std::AbstractSTD, ns::Int, φ::Number, t::Number) = # ifelse(get_prop(std, ns, :trapping), 1.0, 1.0 - cdf(std, ns, φ, t)) -# check whether sum of ccdf could be suffient -ccdf(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) = - 1.0 - mysum(std, ns, φ, t) - -function mysum(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) -# Summation function to overcome summation error over empty collection. - if _LG.outneighbors(std.graph, ns) != Int64[] - F = sum(cdf(get_prop(std,_LG.Edge(ns,nx),:distr), φ, t) - for nx in _LG.outneighbors(std.graph, ns)) - else - F = 0 -end end # TOM: added functionality to enable \ with units. elunit(A::Matrix{U}) where U = _UF.unit(U) @@ -410,8 +434,8 @@ end function integral(std::AbstractSTD, st::Int, t::StepRangeLen, h::Vector, tol::Real) # controleer voor schaalfactor - d2h = abs.(diff(diff(h))) - id = 1 + d2h = abs.(diff(diff(ustrip(h)))) + global id = 1 idx = [1] while true @@ -421,24 +445,27 @@ function integral(std::AbstractSTD, st::Int, t::StepRangeLen, h::Vector, tol::Re global id += next_id push!(idx,id) end - push!(idx,length(d2h)) + push!(idx,length(d2h)+2) τ = t[idx] + γ = _INT.interpolate((τ,), h[idx], _INT.Gridded(_INT.Linear())) - γ = _INT.LinearInterpolation(collect(t), h) - - ϕ = [_QGK.quadgk(x -> h(x) * ccdf.(std, st, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] + ϕ = [_QGK.quadgk(x -> γ(x) * ccdf.(std, st, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] # niet gelijk gespacete interpolatie + # Y = interpolate((x,), y, Gridded(Linear())) p = _INT.LinearInterpolation(τ, ϕ)(t) + println(size(idx)) + return p end -function compress(v::Vector, y::Int, std::AbstractSTD) +function compress(v::Vector, steps::Int, std::AbstractSTD) n = length(v) Ns = ns(std) - compressed_v = zeros(Int(n ÷ y))*unit(v[1]) + y = Int((n-Ns)/(Ns*steps)) + compressed_v = zeros((steps+1)*Ns)*unit(v[1]) for st in 1:Ns - for i in 1:Int(n/Ns ÷ y) + for i in 1:steps+1 compressed_v[Ns*(i-1)+st] = v[y*Ns*(i-1)+st]; end end return compressed_v - end \ No newline at end of file +end \ No newline at end of file diff --git a/src/io/state_transition_diagram.jl b/src/io/state_transition_diagram.jl index c3cdec2..28080ed 100644 --- a/src/io/state_transition_diagram.jl +++ b/src/io/state_transition_diagram.jl @@ -117,6 +117,10 @@ set_prop!(std::AbstractSTD, prop::Symbol, value) = set_props!(std, Dict(prop => value)) set_props!(std::AbstractSTD, dict::Dict) = merge!(std.props, dict) +ccdf(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) = + 1.0 - sum(cdf(get_prop(std, _LG.Edge(ns,nx),:distr), φ, t) + for nx in _LG.outneighbors(std.graph, ns); init = 0.0) + ## Info # structs mutable struct STDInfo{B<:Bool} <: AbstractInfo diff --git a/test/elements/CAP_ac.jl b/test/elements/CAP_ac.jl new file mode 100644 index 0000000..e1590b3 --- /dev/null +++ b/test/elements/CAP_ac.jl @@ -0,0 +1,30 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc capacitance +stdᶜᵃᵖᵃᶜ = STD() + +# add the states to the std +add_states!(stdᶜᵃᵖᵃᶜ, name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + + +# add the transitions to the std +add_transitions!(stdᶜᵃᵖᵃᶜ, states = [(1,2),(2,1)], + distr = [ Exponential(5.0u"yr"), + Exponential(48.0u"d")]) + + # LogNormal(3.0u"yr", 1.0u"yr") + +# solve the std +return stdᶜᵃᵖᵃᶜ \ No newline at end of file diff --git a/test/elements/optical_monitoring_system.jl b/test/elements/optical_monitoring_system.jl index 4e93179..d36af33 100644 --- a/test/elements/optical_monitoring_system.jl +++ b/test/elements/optical_monitoring_system.jl @@ -6,7 +6,7 @@ # See http://github.com/timmyfaraday/MultiStateSystems.jl # ################################################################################ """ -Example considering a multi-state Markov model for a optical monitoring system +Example considering a multi-state Markov model for an optical monitoring system taken from: > A Multi-State Markov Model for a Short-Term Reliability Analysis of a Power @@ -18,19 +18,21 @@ taken from: using Unitful using MultiStateSystems - - # initialize the state-transition diagram std = STD() -# add the states to the std -add_states!(std, name = ["available", "unavailable"], - power = [1.0u"MW", 0.0u"MW"], - init = [1.0, 0.0]) +# add the states to the std +add_states!(std, name = ["normal operation state","reinstallation state","restore state","halted state"], + init = [1.0,0.0,0.0,0.0]) -# add the transitions to the std -add_transitions!(stdᵃᵈ, rate = [0.0u"1/hr" 12.8928e-6u"1/hr" - 0.0833u"1/hr" 0.0u"1/hr"]) +# add the transitions to the std +add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], + distr = [ Exponential(10000.0u"hr", t -> -0.00004u"1/hr" * t + 0.6), + Weibull(150.0u"hr", 1.36, t -> 0.00004u"1/hr" * t + 0.4), + Exponential(20.0u"hr", 0.82), + LogNormal(2.5u"hr", 0.25u"hr", 0.18), + Exponential(20.0u"hr", 0.62), + LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) # return the std -return stdᵃᵈ \ No newline at end of file +return std \ No newline at end of file diff --git a/test/semi_markov_process.jl b/test/semi_markov_process.jl index e2df044..a704e94 100644 --- a/test/semi_markov_process.jl +++ b/test/semi_markov_process.jl @@ -8,19 +8,31 @@ @testset "Semi Markov Process" begin - @testset "Coal Fired Power Generating Unit" begin - # Example from: A Multi-State Markov Model for a Short-Term Reliability - # Analysis of a Power Generating Unit (p. 4) - stdᶜᶠ = include(joinpath(_MSS.BASE_DIR,"test/elements/coal_fired_power_generating_unit.jl")) + @testset "AC/DC converter capacitance" begin + # Example from: A semi-Markovian approach to evaluate the availability + # of LVDC systems with integrated battery storage + stdᶜᵃᵖ = include(joinpath(_MSS.BASE_DIR,"test/elements/CAP_ac.jl")) - solve!(stdᶜᶠ, MarkovProcess(), tsim = 1.0u"yr") - prb_m = [np[end] for np in _MSS.get_sprop(stdᶜᶠ, :prob)] + solve!(stdᶜᵃᵖ, MarkovProcess(), tsim = 1.0u"yr") + prb_m = [np[end] for np in _MSS.get_sprop(stdᶜᵃᵖ, :prob)] - solve!(stdᶜᶠ, SteadyStateProcess()) - prb_s = [np[end] for np in _MSS.get_sprop(stdᶜᶠ, :prob)] + solve!(stdᶜᵃᵖ, SemiMarkovProcess(), tsim = 1.0u"yr") + prb_s = [np[end] for np in _MSS.get_sprop(stdᶜᵃᵖ, :prob)] @test isapprox(sum(prb_m), 1.0, rtol=1e-6) @test all(isapprox.(prb_m, prb_s, rtol=1e-6)) end -end \ No newline at end of file + @testset "Optical Monitoring System" begin + # Example considering a multi-state Markov model for an optical monitoring system + # taken from: + # > A Multi-State Markov Model for a Short-Term Reliability Analysis of a Power + # Generating Unit by A. Lisnianski, D. Elmakias, and H. Ben Haim (2012) + + stdᵒᵐˢ = include(joinpath(_MSS.BASE_DIR,"test/elements/optical_monitoring_system.jl")) + solve!(stdᵒᵐˢ, SemiMarkovProcess(), tsim = 1.0u"yr", dt = 4.01u"hr") + prb_oms = [np[end] for np in _MSS.get_sprop(stdᵒᵐˢ, :prob)] + @test isapprox(sum(prb_oms), 1.0, rtol=1e-6) + end + +end From 8e4d67b78901de9735e079a043356eb4c6670b91 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Sun, 30 Jul 2023 22:09:31 +0200 Subject: [PATCH 41/56] Significant performance improvement of Set_U --- .../semi-markov/optical-monitoring-system.jl | 11 +- src/MultiStateSystems.jl | 3 + src/form/semi_markov_process.jl | 489 ++++++++++-------- src/io/distributions.jl | 14 +- test/elements/CAP_ac.jl | 17 + 5 files changed, 318 insertions(+), 216 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index ce0e285..6a74452 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -52,15 +52,20 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], # solve the std # @time H1_20, H1c_20, H_accurate_20 = _MSS.solved!(std, cls, tsim = 8760.0u"hr", dt = 10u"hr", acc = 20, steps = 50, tol=1e-8) -# @time H1_40, H1c_40, H_accurate_40 = _MSS.solved!(std, cls, tsim = 200.0u"hr", dt = 4u"hr", acc = 10, steps = 40, tol=1e-8) -h_base = solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol=1e-7); +# @time H1_40, H1c_40, H_accurate_40 = _MSS.solved!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", acc = 10, steps = 40, tol=1e-8); +# h_base = solve!(std, cls, tsim =400.0u"hr", dt = 4u"hr", tol=1e-7); _MSS.solveP!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8); +dt = 4u"hr" +t = 0u"hr":dt:400.0u"hr"; + +@time U = set_U(std, t, 1e-8) + h_base_select=h_base[1][1:10:end] plot([h_base_select.-H_accurate_20[1],h_base_select.-H_accurate_40[1]]) -dH = abs.(diff(H_accurate_20[1])) +dH = abs.(diff(H_accurate_40[1])) append!(dH,zero(H[1][1])) steps = 150; acc = 10; diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index 3687c8c..ddd3af4 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -68,5 +68,8 @@ export STD, solvedSTD, add_state!, add_states!, add_transition!, add_transition export UGF export solve! export solve_network! +export set_U +export set_A +export set_P end diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 675a7eb..a27b7db 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -74,164 +74,244 @@ and remains there until time t The unit of U is [-] """ -function set_U(std::AbstractSTD, t::StepRangeLen) - # - dt = step(t) - Nt = length(t) +# function set_U(std::AbstractSTD, t::StepRangeLen) +# # +# dt = step(t) +# Nt = length(t) + +# U = zeros(Float64, ns(std) * Nt, ns(std) * Nt) + +# for (ni,nt) in enumerate(t) +# w = weights(ni) +# # l = zero(dt):dt:nt +# l = t[1]:dt:nt +# for (nj,nl) in enumerate(l) +# Ψ = zeros(typeof(1/dt), ns(std), ns(std)) +# for tr in transitions(std) +# # The results of the pdf depends on two factors: +# # - How long has the system been in this particular state = sojourn time (nt - nl) with nt the index of the current time t and nl the index of entrance time. +# # - The time at which the system entered a certain state, with nl the index of this entrance time. This determines weight attributed to this particular transition. +# Ψ[_LG.dst(tr), _LG.src(tr)] = +# pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 +# end +# rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) +# rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) +# if ni == nj +# U[rT,rΦ] = Matrix(1.0_LA.I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ +# else +# U[rT,rΦ] = -dt .* w[nj] .* Ψ +# end +# end end +# U[isnan.(U)] .= 0.0 - U = zeros(Float64, ns(std) * Nt, ns(std) * Nt) +# return U +# end +# function set_U(std::AbstractSTD, t::StepRangeLen) +# # +# dt = step(t) +# Nt = length(t) + +# I,J,V = Int[],Int[],Number[] + +# append!(I, 1:Ns*Nt) +# append!(J, 1:Ns*Nt) +# append!(V, ones(Number,Ns*Nt)) + +# for (ni,nt) in enumerate(t) +# w = weights(ni) +# # l = zero(dt):dt:nt +# l = t[1]:dt:nt +# for (nj,nl) in enumerate(l) +# Ψ = zeros(typeof(1/dt), ns(std), ns(std)) +# for tr in transitions(std) +# # The results of the pdf depends on two factors: +# # - How long has the system been in this particular state = sojourn time (nt - nl) with nt the index of the current time t and nl the index of entrance time. +# # - The time at which the system entered a certain state, with nl the index of this entrance time. This determines weight attributed to this particular transition. +# Ψ[_LG.dst(tr), _LG.src(tr)] = +# pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 +# end +# append!(I,(ns(std) * (ni - 1) + 1):(ns(std) * ni)) +# append!(J,(ns(std) * (nj - 1) + 1):(ns(std) * nj)) +# if ni == nj +# U[rT,rΦ] = Matrix(1.0_LA.I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ +# else +# U[rT,rΦ] = -dt .* w[nj] .* Ψ +# end +# end end +# U[isnan.(U)] .= 0.0 - for (ni,nt) in enumerate(t) - w = weights(ni) - # l = zero(dt):dt:nt - l = t[1]:dt:nt - for (nj,nl) in enumerate(l) - Ψ = zeros(typeof(1/dt), ns(std), ns(std)) - for tr in transitions(std) - # The results of the pdf depends on two factors: - # - How long has the system been in this particular state = sojourn time (nt - nl) with nt the index of the current time t and nl the index of entrance time. - # - The time at which the system entered a certain state, with nl the index of this entrance time. This determines weight attributed to this particular transition. - Ψ[_LG.dst(tr), _LG.src(tr)] = - pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 - end - rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) - rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) - if ni == nj - U[rT,rΦ] = Matrix(1.0_LA.I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ - else - U[rT,rΦ] = -dt .* w[nj] .* Ψ - end - end end - U[isnan.(U)] .= 0.0 +# return U +# end - return U -end +# function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) +# dt = step(t) +# Nt = length(t) +# Ns = ns(std) -function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) - dt = step(t) - Nt = length(t) - Ns = ns(std) +# # initialize three vectors I,J,V respectively row, column and value indices +# I,J,V = Int[],Int[],Number[] - # initialize three vectors I,J,V respectively row, column and value indices - I,J,V = Int[],Int[],Number[] - - append!(I, 1:Ns*Nt) - append!(J, 1:Ns*Nt) - append!(V, ones(Number,Ns*Nt)) +# append!(I, 1:Ns*Nt) +# append!(J, 1:Ns*Nt) +# append!(V, ones(Number,Ns*Nt)) - for tr in transitions(std) - # dummy value not necessary, since every diagonal entry requires a one to be added to it. - # Sparse Arrays allow to add values to the same location twice and add those - # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. - dst = get_prop(std, tr, :distr) - lb = floor(cquantile(dst, tol) / dt) * dt - for (ni,nt) in enumerate(t) - Φ = nt:-dt:t[1] - # Φ represents the sojourn time, ranging from - lt = t[1]:dt:nt - NΦ = length(Φ) +# for tr in transitions(std) +# # dummy value not necessary, since every diagonal entry requires a one to be added to it. +# # Sparse Arrays allow to add values to the same location twice and add those +# # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. +# dst = get_prop(std, tr, :distr) +# lb = floor(cquantile(dst, tol) / dt) * dt +# for (ni,nt) in enumerate(t) +# Φ = nt:-dt:t[1] +# # Φ represents the sojourn time, ranging from +# lt = t[1]:dt:nt +# NΦ = length(Φ) - append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) - append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) - # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) - append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) - end end - V[isnan.(V)] .= 0.0 - return _SA.sparse(I, J, V) -end +# append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) +# append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) +# # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) +# append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) +# end end +# V[isnan.(V)] .= 0.0 +# return _SA.sparse(I, J, V) +# end + -function set_U(std::AbstractSTD, t::StepRangeLen, steps::Number, tol::Real) +function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) dt = step(t) Nt = length(t) Ns = ns(std) - # initialize three vectors I,J,V respectively row, column and value indices - I,J,V = Int[],Int[],Number[] + I,J,V = Int[],Int[],Float64[] append!(I, 1:Ns*Nt) append!(J, 1:Ns*Nt) - append!(V, ones(Number,Ns*Nt)) + append!(V, ones(Float64,Ns*Nt)) for tr in transitions(std) # dummy value not necessary, since every diagonal entry requires a one to be added to it. # Sparse Arrays allow to add values to the same location twice and add those # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. - dst = get_prop(std, tr, :distr) - lb = floor(cquantile(dst, tol) / dt) * dt - for (ni,nt) in enumerate(t) - if ni > steps + 1 - Φ = nt:-dt:t[1] - # Φ represents the sojourn time, ranging from - lt = t[1]:dt:nt - NΦ = length(Φ) - - append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) - append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) - # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) - append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) - end - end end - V[isnan.(V)] .= 0.0 + dst = get_prop(std, tr, :distr) + _fill_U!(tr, dt, t, Ns, dst, I, J, V, tol) + end return _SA.sparse(I, J, V) end -# stochastic process -function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1u"d", tol::Real=1e-8) - # get the input - dt = dt |> unit(tsim) - t = zero(dt):dt:tsim - Nt = length(t) - - # solve the problem - Φ = zeros(Nt, ns(std)) +function _fill_U!(tr, dt, t, Ns, dst, I, J, V, tol) + # lb = floor(cquantile(dst, tol) / dt) * dt + for (ni,nt) in enumerate(t) + Φ = nt:-dt:t[1] + # Φ represents the sojourn time, ranging from + lt = t[1]:dt:nt + NΦ = length(Φ) + for nj in 1:NΦ + push!(I, Ns * (ni-1) + _LG.dst(tr)) + push!(J, Ns * (nj-1) + _LG.src(tr)) + push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) + if isnan(V[end]) + V[end] = 0.0 + end + end + # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) + # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) + end +end + +# function set_U(std::AbstractSTD, t::StepRangeLen, steps::Number, tol::Real) +# dt = step(t) +# Nt = length(t) +# Ns = ns(std) + +# # initialize three vectors I,J,V respectively row, column and value indices +# I,J,V = Int[],Int[],Number[] + +# append!(I, 1:Ns*Nt) +# append!(J, 1:Ns*Nt) +# append!(V, ones(Number,Ns*Nt)) + +# for tr in transitions(std) +# # dummy value not necessary, since every diagonal entry requires a one to be added to it. +# # Sparse Arrays allow to add values to the same location twice and add those +# # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. +# dst = get_prop(std, tr, :distr) +# lb = floor(cquantile(dst, tol) / dt) * dt +# for (ni,nt) in enumerate(t) +# if ni > steps + 1 +# Φ = nt:-dt:t[1] +# # Φ represents the sojourn time, ranging from +# lt = t[1]:dt:nt +# NΦ = length(Φ) + +# append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) +# append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) +# # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) +# append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) +# end +# end end +# V[isnan.(V)] .= 0.0 +# return _SA.sparse(I, J, V) +# end - println("set_U") - @time U = set_U(std,t,tol) - println("set_A") - @time A = ustrip(set_A(std,t)) - H=U\A*unit(1/t[1]) +# stochastic process +# function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; +# tsim::Number=1.0u"yr", dt::Number=1u"d", tol::Real=1e-8) +# # get the input +# dt = dt |> unit(tsim) +# t = zero(dt):dt:tsim +# Nt = length(t) + +# # solve the problem +# Φ = zeros(Nt, ns(std)) +# QTI = Quantity{Float64, 𝐓 ^-1, Unitful.FreeUnits{(unit(1/dt)), 𝐓 ^-1, nothing}}[] + + +# println("set_U") +# @time U = set_U(std,t,tol) +# println("set_A") +# @time A = ustrip(set_A(std,t)) +# H=U\A*unit(1/t[1]) - # println("set_P") - # @time set_P(std, t, H, tol) - println("Linear interpolation of H") - @time h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end - h_sol = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; - - println("Integration of H to Φ") - @time for st in states(std) - for (ni,nt) in enumerate(t) - w = weights(ni) - # TOM: φ <<< t, zero could be higher - # l = zero(dt):dt:nt - l = t[1]:dt:nt .|> unit(tsim) - # # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification - # # The probability of being in a state st at time nt depends on two things: - # # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. - # # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time - # # of entering the state (0) to determine the weight and the sojourn time (nt-0). - # # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). - # # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. - # # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at - # # The last transition time x and the sojourn time nt-x. - Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] +# # println("set_P") +# # @time set_P(std, t, H, tol) +# println("Linear interpolation of H") +# @time h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end +# h_sol = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; + +# println("Integration of H to Φ") +# @time for st in states(std) +# for (ni,nt) in enumerate(t) +# w = weights(ni) +# # TOM: φ <<< t, zero could be higher +# # l = zero(dt):dt:nt +# l = t[1]:dt:nt .|> unit(tsim) +# # # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification +# # # The probability of being in a state st at time nt depends on two things: +# # # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. +# # # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time +# # # of entering the state (0) to determine the weight and the sojourn time (nt-0). +# # # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). +# # # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. +# # # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at +# # # The last transition time x and the sojourn time nt-x. +# Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) +# Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] - # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* - # ccdf(std, st, nt-nl, nl) - # for (nj,nl) in enumerate(l)) - end end +# # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* +# # ccdf(std, st, nt-nl, nl) +# # for (nj,nl) in enumerate(l)) +# end end - # set the output - set_prop!(std, :cls, cls) - set_prop!(std, :time, t) - set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) - - # set the solved status - set_info!(std, :solved, true) - return h_sol -end +# # set the output +# set_prop!(std, :cls, cls) +# set_prop!(std, :time, t) +# set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) + +# # set the solved status +# set_info!(std, :solved, true) +# return h_sol +# end function solveP!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=1u"hr", tol::Real=1e-8) @@ -248,7 +328,7 @@ function solveP!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; println("set_A") @time A = ustrip(set_A(std,t)) H=U\A*unit(1/t[1]) - + println("set_P") @time set_P(std, t, H, tol) @@ -260,87 +340,86 @@ function solveP!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; set_info!(std, :solved, true) end -function solved!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1u"hr", acc::Int64=10, steps::Number=100.0, tol::Real=1e-8) +# function solved!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; +# tsim::Number=1.0u"yr", dt::Number=1u"hr", acc::Int64=10, steps::Number=100.0, tol::Real=1e-8) - # Get the input for solving numerical inrush phase - dt_n = dt/acc |> unit(tsim); - t_n = zero(dt_n):dt_n:dt_n*(steps)*acc; +# # Get the input for solving numerical inrush phase +# dt_n = dt/acc |> unit(tsim); +# t_n = zero(dt_n):dt_n:dt_n*(steps)*acc; - U = set_U(std,t_n[1:end],tol) - A = ustrip(set_A(std,t_n[1:end])) - H1 = U\A*unit(1/t_n[1]) +# U = set_U(std,t_n[1:end],tol) +# A = ustrip(set_A(std,t_n[1:end])) +# H1 = U\A*unit(1/t_n[1]) - H_c = compress(H1, steps, std) - - H1o = [ map(x->H1[ns(std) * (x-1) + st], 1:length(t_n)-ns(std)) for st in states(std)]; - H1co = [ map(x->H_c[ns(std) * (x-1) + st], 1:Int(length(H_c)/ns(std))) for st in states(std)]; - - # get the input for final problem solution - dt = dt |> unit(tsim) - t = zero(dt):dt:tsim - Nt = length(t) - - # solve the problem - Φ = zeros(Nt, ns(std)) - - U = set_U(std,t,steps,tol) - A = ustrip(set_A(std,t,H_c,steps)) - H=U\A*unit(1/t[1]) - - Ho = [ map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; - - # set_P(std, t, H, tol) - h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end - - for st in states(std) - for (ni,nt) in enumerate(t) - w = weights(ni) - # TOM: φ <<< t, zero could be higher - # l = zero(dt):dt:nt - l = t[1]:dt:nt .|> unit(tsim) - # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification - # The probability of being in a state st at time nt depends on two things: - # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. - # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time - # of entering the state (0) to determine the weight and the sojourn time (nt-0). - # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). - # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. - # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at - # The last transition time x and the sojourn time nt-x. - Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) - Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] +# H_c = compress(H1, steps, std) + +# H1o = [ map(x->H1[ns(std) * (x-1) + st], 1:length(t_n)-ns(std)) for st in states(std)]; +# H1co = [ map(x->H_c[ns(std) * (x-1) + st], 1:Int(length(H_c)/ns(std))) for st in states(std)]; + +# # get the input for final problem solution +# dt = dt |> unit(tsim) +# t = zero(dt):dt:tsim +# Nt = length(t) + +# # solve the problem +# Φ = zeros(Nt, ns(std)) + +# U = set_U(std,t,steps,tol) +# A = ustrip(set_A(std,t,H_c,steps)) +# H=U\A*unit(1/t[1]) + +# Ho = [ map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; + +# # set_P(std, t, H, tol) +# h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end + +# for st in states(std) +# for (ni,nt) in enumerate(t) +# w = weights(ni) +# # TOM: φ <<< t, zero could be higher +# # l = zero(dt):dt:nt +# l = t[1]:dt:nt .|> unit(tsim) +# # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification +# # The probability of being in a state st at time nt depends on two things: +# # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. +# # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time +# # of entering the state (0) to determine the weight and the sojourn time (nt-0). +# # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). +# # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. +# # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at +# # The last transition time x and the sojourn time nt-x. +# Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) +# Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] - # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* - # ccdf(std, st, nt-nl, nl) - # for (nj,nl) in enumerate(l)) - end end +# # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* +# # ccdf(std, st, nt-nl, nl) +# # for (nj,nl) in enumerate(l)) +# end end - # set the output - set_prop!(std, :cls, cls) - set_prop!(std, :time, t) - set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) +# # set the output +# set_prop!(std, :cls, cls) +# set_prop!(std, :time, t) +# set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) - # set the solved status - set_info!(std, :solved, true) +# # set the solved status +# set_info!(std, :solved, true) - return H1o, H1co, Ho -end +# return H1o, H1co, Ho +# end function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) Ns = ns(std) Nt = length(t) - idx_s = - for st in states(std) + dst_v = [get_prop(std, _LG.Edge(st,nx),:distr) for nx in _LG.outneighbors(std.graph, st)] init = get_prop(std, st, :init) h = map(x->H[ns(std) * (x-1) + st], 1:Nt) if init > 0.0 - p = init .* ccdf.(std, st, t, zero(t[1])) .+ integral(std, st, t, h, tol) + p = init .* 1-sum(cdf(dstr, 0, zero(t[1])) for dstr in dst_v) .+ integral(dst_v, t, h, tol) else - p = integral(std, st, t, h, tol) + p = integral(dst_v, t, h, tol) end set_prop!(std, st, :prob, p) end @@ -384,15 +463,14 @@ w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. # return w # end -function weights(x::Int) - if x==1 - w = [0] +function weights(N::Int, p::Int) + if N==1 + return 0.0 + elseif p == 1 || p == N + return 0.5 else - w = ones(x) - w[1] = 1/2 - w[end] = 1/2 + return 1.0 end - return w end # function weights(x::Int) @@ -432,24 +510,23 @@ function battery_system_availability(i, T, ntw_av, θ) return 1-p_failure*p_repair_time_ge_T end -function integral(std::AbstractSTD, st::Int, t::StepRangeLen, h::Vector, tol::Real) +function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) # controleer voor schaalfactor d2h = abs.(diff(diff(ustrip(h)))) - global id = 1 + id = 1 idx = [1] while true next_id = findfirst(x -> x > tol, cumsum(d2h[id:end])) next_id == nothing ? break : ~ ; - global id += next_id + id += next_id push!(idx,id) end push!(idx,length(d2h)+2) τ = t[idx] γ = _INT.interpolate((τ,), h[idx], _INT.Gridded(_INT.Linear())) - - ϕ = [_QGK.quadgk(x -> γ(x) * ccdf.(std, st, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] + ϕ = [_QGK.quadgk(x -> γ(x) * (1-sum(cdf(dstr, nτ-x, x) for dstr in dst_v)), t[1], nτ, rtol=tol)[1] for nτ in τ] # niet gelijk gespacete interpolatie # Y = interpolate((x,), y, Gridded(Linear())) p = _INT.LinearInterpolation(τ, ϕ)(t) diff --git a/src/io/distributions.jl b/src/io/distributions.jl index a36a335..f2c2c57 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -47,23 +47,23 @@ f(x; θ, ω) = \begin{cases} abstract type AbstractExponential{X,Y,Z} <: AbstractDistribution{X,Y,Z} end # struct - θ::Number, ω::Real -struct ExponentialNR{X<:Number, Y<:Real, Z<:Function} <: AbstractExponential{X,Y,Z} +struct ExponentialNR{X<:Number, Y<:Real} <: AbstractExponential{X,Y,Function} θ::X # scale ω::Y # weight: 0.0 < ω <= 1.0 end # constructors -Exponential() = ExponentialNR{Number,Real,Function}(1.0, 1.0) -Exponential(θ::Number) = ExponentialNR{Number,Real,Function}(θ, 1.0) -Exponential(θ::Number, ω::Real) = ExponentialNR{Number,Real,Function}(θ, ω) +Exponential() = ExponentialNR(1.0, 1.0) +Exponential(θ::X) where {X<:Number}= ExponentialNR(θ, 1.0) +Exponential(θ::X, ω::Y) where {X<:Number,Y<:Real}= ExponentialNR(θ, ω) # struct - θ::Number, ω::Function -struct ExponentialNF{X<:Number, Y<:Real, Z<:Function} <: AbstractExponential{X,Y,Z} +struct ExponentialNF{X<:Number, Z<:Function} <: AbstractExponential{X,Real,Z} θ::X # scale ω::Z # weight: 0.0 < ω(t) <= 1.0 end # constructors -Exponential(θ::Number, ω::Function) = ExponentialNF{Number,Real,Function}(θ, ω) - +Exponential(θ::X, ω::Z) where {X<:Number,Z<:Function}= ExponentialNF(θ, ω) +#Exponential(θ::Number, ω::Function) = ExponentialNF{Number,Real,Function}(θ, ω) # shortened constructors 𝑬() = Exponential() 𝑬(θ::Number) = Exponential(θ) diff --git a/test/elements/CAP_ac.jl b/test/elements/CAP_ac.jl index e1590b3..7755e9a 100644 --- a/test/elements/CAP_ac.jl +++ b/test/elements/CAP_ac.jl @@ -9,6 +9,12 @@ # load pkgs using Unitful using MultiStateSystems +using Revise + +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SemiMarkovProcess() # initialize the state-transition diagram corresponding to the front-end ac/dc capacitance stdᶜᵃᵖᵃᶜ = STD() @@ -26,5 +32,16 @@ add_transitions!(stdᶜᵃᵖᵃᶜ, states = [(1,2),(2,1)], # LogNormal(3.0u"yr", 1.0u"yr") +# dt = 4u"hr" +# t = 0u"hr":dt:8760.0u"hr"; + +# @time U = set_U(stdᶜᵃᵖᵃᶜ, t, 1e-8) + +_MSS.solveP!(stdᶜᵃᵖᵃᶜ, cls, tsim = 20.0u"hr", dt = 4u"hr", tol = 1e-9); + +t = 0.0u"hr":4u"hr":1.0u"yr"; + + + # solve the std return stdᶜᵃᵖᵃᶜ \ No newline at end of file From 7914ebd814dd997d11069b9948b78ac91092f3db Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Tue, 1 Aug 2023 10:38:16 +0200 Subject: [PATCH 42/56] Improvements of distributions.jl Clear allocation of type to distribution constructors. --- src/MultiStateSystems.jl | 4 +--- src/io/distributions.jl | 38 +++++++++++++++++++------------------- 2 files changed, 20 insertions(+), 22 deletions(-) diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index ddd3af4..e6d21bf 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -68,8 +68,6 @@ export STD, solvedSTD, add_state!, add_states!, add_transition!, add_transition export UGF export solve! export solve_network! -export set_U -export set_A -export set_P + end diff --git a/src/io/distributions.jl b/src/io/distributions.jl index f2c2c57..35ef75c 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -158,10 +158,10 @@ struct WeibullNRR{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} ω::Y # weight: 0.0 < ω <= 1.0 end # constructors -Weibull() = WeibullNRR{Number,Real,Function}(1.0, 1.0, 1.0) -Weibull(θ::Number) = WeibullNRR{Number,Real,Function}(θ, 1.0, 1.0) -Weibull(θ::Number, α::Real) = WeibullNRR{Number,Real,Function}(θ, α, 1.0) -Weibull(θ::Number, α::Real, ω::Real) = WeibullNRR{Number,Real,Function}(θ, α, ω) +Weibull() = WeibullNRR(1.0, 1.0, 1.0) +Weibull(θ::X) where {X<:Number} = WeibullNRR(θ, 1.0, 1.0) +Weibull(θ::X, α::Y) where{X<:Number, Y<:Real}= WeibullNRR(θ, α, 1.0) +Weibull(θ::X, α::Y, ω::Z) where{X<:Number, Y<:Real, Z<:Real}= WeibullNRR(θ, α, ω) # struct - θ::Number, α::Real, ω::Function struct WeibullNRF{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} @@ -170,8 +170,8 @@ struct WeibullNRF{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} ω::Z # weight: 0.0 < ω(t) <= 1.0 end # constructors -Weibull(θ::Number, α::Real, ω::Function) = - WeibullNRF{Number,Real,Function}(θ, α, ω) +Weibull(θ::X, α::Y, ω::Z) where{X<:Number, Y<:Real, Z<:Function}= + WeibullNRF(θ, α, ω) # shortened constructors 𝑾() = Weibull() @@ -264,28 +264,28 @@ julia> 𝑳(10.0,0.5,0.2) # scaled Log-normal distr. with μ = 10.0, σ = 0 abstract type AbstractLogNormal{X,Y,Z} <: AbstractDistribution{X,Y,Z} end # struct - μ::Number, σ::Number, ω::Real -struct LogNormalNNR{X<:Number, Y<:Real, Z<:Function} <: AbstractLogNormal{X,Y,Z} +struct LogNormalNNR{X<:Number, Y<:Number, Z<:Real} <: AbstractLogNormal{X,Y,Z} μ::X # mean of the corresponding normal distribution - σ::X # shape of the corresponding normal distribution - ω::Y # weight: 0.0 < ω <= 1.0 + σ::Y # shape of the corresponding normal distribution + ω::Z # weight: 0.0 < ω <= 1.0 end # constructors -LogNormal() = LogNormalNNR{Number,Real,Function}(1.0, 1.0, 1.0) -LogNormal(μ::Number) = LogNormalNNR{Number,Real,Function}(μ, 1.0unit(μ), 1.0) -LogNormal(μ::Number, σ::Number) = - LogNormalNNR{Number,Real,Function}(μ, uconvert(unit(μ),σ), 1.0) -LogNormal(μ::Number, σ::Number, ω::Real) = - LogNormalNNR{Number,Real,Function}(μ, uconvert(unit(μ),σ), ω) +LogNormal() = LogNormalNNR(1.0, 1.0, 1.0) +LogNormal(μ::X) where {X<:Number} = LogNormalNNR(μ, 1.0unit(μ), 1.0) +LogNormal(μ::X, σ::Y) where {X<:Number, Y<:Number} = + LogNormalNNR(μ, uconvert(unit(μ),σ), 1.0) +LogNormal(μ::X, σ::Y, ω::Z) where {X<:Number, Y<:Number, Z<:Real} = + LogNormalNNR(μ, uconvert(unit(μ),σ), ω) # struct - μ::Number, σ::Number, ω::Function -struct LogNormalNNF{X<:Number, Y<:Real, Z<:Function} <: AbstractLogNormal{X,Y,Z} +struct LogNormalNNF{X<:Number, Y<:Number, Z<:Function} <: AbstractLogNormal{X,Y,Z} μ::X # mean of the corresponding normal distribution - σ::X # shape of the corresponding normal distribution + σ::Y # shape of the corresponding normal distribution ω::Z # weight: 0.0 < ω(t) <= 1.0 end # constructors -LogNormal(μ::Number, σ::Number, ω::Function) = - LogNormalNNF{Number,Real,Function}(μ, uconvert(unit(μ),σ), ω) +LogNormal(μ::X, σ::Y, ω::Z) where {X<:Number, Y<:Number, Z<:Function}= + LogNormalNNF(μ, uconvert(unit(μ),σ), ω) # shortened constructors 𝑳() = LogNormal() From 74d3a1920dfa7129c083667d9b7f41466d6ed2b9 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Thu, 3 Aug 2023 18:39:37 +0200 Subject: [PATCH 43/56] Optimized Set_U, Set_A and Set_P, including passing tests --- .../semi-markov/optical-monitoring-system.jl | 6 +- src/form/semi_markov_process.jl | 195 +++++++++++++----- src/io/state_transition_diagram.jl | 4 +- test/elements/CAP_ac.jl | 13 -- test/semi_markov_process.jl | 2 +- 5 files changed, 150 insertions(+), 70 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 6a74452..d376898 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -54,7 +54,7 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], # @time H1_20, H1c_20, H_accurate_20 = _MSS.solved!(std, cls, tsim = 8760.0u"hr", dt = 10u"hr", acc = 20, steps = 50, tol=1e-8) # @time H1_40, H1c_40, H_accurate_40 = _MSS.solved!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", acc = 10, steps = 40, tol=1e-8); # h_base = solve!(std, cls, tsim =400.0u"hr", dt = 4u"hr", tol=1e-7); -_MSS.solveP!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8); +@time solve!(std, cls, tsim = 1.0u"yr", dt = 4u"hr", tol = 1e-8); dt = 4u"hr" t = 0u"hr":dt:400.0u"hr"; @@ -104,8 +104,8 @@ plot(_MSS.get_prop(std, :time), xlabel="time", ylabel="State Probability") -plot(_MSS.get_prop(std, :time)[1:length(dh)], - ustrip(h), +plot(_MSS.get_prop(std, :time), + ustrip(h[1]), label="diff H", xlabel="time", ylabel="State Probability") diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index a27b7db..66b4365 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -20,25 +20,37 @@ and remains there until time t. The unit of A is [unit(1/t)] """ -function set_A(std::AbstractSTD, t::StepRangeLen) +function set_A(std::AbstractSTD, t::StepRangeLen, tol::Real) dt = step(t) Nt = length(t) A = zeros(typeof(1/dt), ns(std) * Nt) + for tr in transitions(std) + init = get_prop(std, _LG.src(tr), :init) + if init > 0.0 + dst = get_prop(std, tr, :distr) + idx = _LG.dst(tr) + lb = floor(cquantile(dst, tol) / dt) * dt + _fill_A!(std, t, A, idx, dst, init, lb) + end + end + return A +end + +function _fill_A!(std, t, A, idx, dst, init, lb) for (ni,nt) in enumerate(t) - for tr in transitions(std) - id = ns(std) * (ni-1) + _LG.dst(tr) + # if nt <= lb + id = ns(std) * (ni-1) + idx # The content of the A-vector is the probability of initially being # in state (_LG.src(tr)) times the probability of transitioning out # of that state entered at sojourn time zero and evaluated at # time t = (nt) - A[id] += get_prop(std, _LG.src(tr), :init) * - pdf(get_prop(std, tr, :distr), nt, zero(dt)) - end end - A[isnan.(A)] .= zero(1/dt) - - return A + A[id] += init * pdf(dst, nt, zero(t[1])) + if isnan(A[id]) + A[id] = zero(1/t[1]) + end + end end function set_A(std::AbstractSTD, t::StepRangeLen, H::Vector, steps::Number) @@ -198,21 +210,36 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) return _SA.sparse(I, J, V) end -function _fill_U!(tr, dt, t, Ns, dst, I, J, V, tol) - # lb = floor(cquantile(dst, tol) / dt) * dt +function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t::StepRangeLen, Ns::Int, dst::AbstractDistribution, I::Vector, J::Vector, V::Vector, tol::Real) + # lb = floor(cquantile(dst, tol/1000) / dt) * dt for (ni,nt) in enumerate(t) - Φ = nt:-dt:t[1] - # Φ represents the sojourn time, ranging from - lt = t[1]:dt:nt - NΦ = length(Φ) - for nj in 1:NΦ - push!(I, Ns * (ni-1) + _LG.dst(tr)) - push!(J, Ns * (nj-1) + _LG.src(tr)) - push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) - if isnan(V[end]) - V[end] = 0.0 - end - end + # if nt <= lb + Φ = nt:-dt:t[1] + # Φ represents the sojourn time, ranging from + lt = t[1]:dt:nt + NΦ = length(Φ) + for nj in 1:NΦ + push!(I, Ns * (ni-1) + _LG.dst(tr)) + push!(J, Ns * (nj-1) + _LG.src(tr)) + push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) + if isnan(V[end]) + V[end] = 0.0 + end + end + # else + # Φ = lb:-dt:t[1] + # # Φ represents the sojourn time, ranging from + # lt = t[1]:dt:nt + # NΦ = length(Φ) + # for nj in 1:NΦ + # push!(I, Ns * (ni-1) + _LG.dst(tr)) + # push!(J, Ns * (nj-1) + _LG.src(tr)) + # push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) + # if isnan(V[end]) + # V[end] = 0.0 + # end + # end + # end # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) end @@ -263,25 +290,24 @@ end # # solve the problem # Φ = zeros(Nt, ns(std)) -# QTI = Quantity{Float64, 𝐓 ^-1, Unitful.FreeUnits{(unit(1/dt)), 𝐓 ^-1, nothing}}[] # println("set_U") -# @time U = set_U(std,t,tol) +# U = set_U(std,t,tol) # println("set_A") -# @time A = ustrip(set_A(std,t)) +# A = ustrip(set_A(std,t,tol)) # H=U\A*unit(1/t[1]) # # println("set_P") # # @time set_P(std, t, H, tol) # println("Linear interpolation of H") -# @time h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end +# h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end # h_sol = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; # println("Integration of H to Φ") -# @time for st in states(std) +# for st in states(std) # for (ni,nt) in enumerate(t) -# w = weights(ni) +# # w = weights(ni) # # TOM: φ <<< t, zero could be higher # # l = zero(dt):dt:nt # l = t[1]:dt:nt .|> unit(tsim) @@ -313,24 +339,24 @@ end # return h_sol # end -function solveP!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=1u"hr", tol::Real=1e-8) +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; + tsim::Number=1.0u"yr", dt::Number=4u"hr", tol::Real=1e-8) # get the input dt = dt |> unit(tsim) t = zero(dt):dt:tsim - Nt = length(t) - # solve the problem - Φ = zeros(Nt, ns(std)) + # solve the problem println("set_U") - @time U = set_U(std,t,tol) + U = set_U(std,t,tol) println("set_A") - @time A = ustrip(set_A(std,t)) + A = ustrip(set_A(std,t,tol)) H=U\A*unit(1/t[1]) + # h = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)] + println("set_P") - @time set_P(std, t, H, tol) + set_P(std, t, H, tol) # set the output set_prop!(std, :cls, cls) @@ -338,6 +364,7 @@ function solveP!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) + # return h end # function solved!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; @@ -409,22 +436,38 @@ end # end function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) - Ns = ns(std) Nt = length(t) for st in states(std) dst_v = [get_prop(std, _LG.Edge(st,nx),:distr) for nx in _LG.outneighbors(std.graph, st)] init = get_prop(std, st, :init) - h = map(x->H[ns(std) * (x-1) + st], 1:Nt) - if init > 0.0 - p = init .* 1-sum(cdf(dstr, 0, zero(t[1])) for dstr in dst_v) .+ integral(dst_v, t, h, tol) - else - p = integral(dst_v, t, h, tol) - end + h = map(x->H[ns(std) * (x-1) + st], 1:Nt) + p = set_int(dst_v, t, h, init, tol) set_prop!(std, st, :prob, p) - end + end end +# function set_int(dst_v, t, h, init, tol) +# if init > 0.0 +# p = init .* [ccdf(dst_v, φ, zero(t[1])) for φ in t] .+ integral(dst_v, t, h, tol) +# else +# p = integral(dst_v, t, h, tol) +# end +# return p +# end + +function set_int(dst_v, t, h, init, tol) + if init > 0.0 + CDF = zeros(Float64, length(t)) + for dst in dst_v + CDF = cdf!(dst, t, CDF) + end + p = init .* (1 .- CDF) .+ integral(dst_v, t, h, tol) + else + p = integral(dst_v, t, h, tol) + end + return p +end """ @@ -464,15 +507,35 @@ w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. # end function weights(N::Int, p::Int) - if N==1 - return 0.0 - elseif p == 1 || p == N + if p == 1 || p == N return 0.5 else return 1.0 end end +# function weights(N::Int, p::Int) +# if N==1 +# return 0.0 +# elseif p == 1 || p == N +# return 0.5 +# else +# return 1.0 +# end +# end + +# function weights(N::Int, p::Int) +# if N==1 +# return 0.0 +# elseif p == 1 || p == N +# return 1/3 +# elseif p % 2 == 0 +# return 2/3 +# else +# return 4/3 +# end +# end + # function weights(x::Int) # w = ones(x) # return w @@ -514,10 +577,12 @@ function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) # controleer voor schaalfactor d2h = abs.(diff(diff(ustrip(h)))) id = 1 - idx = [1] + idx = Int[1] + reltol = maximum(ustrip(h))*tol + # reltol = (maximum(d2h)-Base.minimum(d2h))*tol while true - next_id = findfirst(x -> x > tol, cumsum(d2h[id:end])) + next_id = findfirst(x -> x > reltol, cumsum(d2h[id:end])) next_id == nothing ? break : ~ ; id += next_id @@ -526,14 +591,19 @@ function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) push!(idx,length(d2h)+2) τ = t[idx] γ = _INT.interpolate((τ,), h[idx], _INT.Gridded(_INT.Linear())) - ϕ = [_QGK.quadgk(x -> γ(x) * (1-sum(cdf(dstr, nτ-x, x) for dstr in dst_v)), t[1], nτ, rtol=tol)[1] for nτ in τ] + if isempty(dst_v) + ϕ = [_QGK.quadgk(x -> γ(x), t[1], nτ, rtol=tol)[1] for nτ in τ] + else + ϕ = [_QGK.quadgk(x -> γ(x) * ccdf(dst_v, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] + end # niet gelijk gespacete interpolatie # Y = interpolate((x,), y, Gridded(Linear())) p = _INT.LinearInterpolation(τ, ϕ)(t) - println(size(idx)) return p end + + function compress(v::Vector, steps::Int, std::AbstractSTD) n = length(v) Ns = ns(std) @@ -545,4 +615,25 @@ function compress(v::Vector, steps::Int, std::AbstractSTD) end end return compressed_v +end + +ccdf(dst_v::Vector, φ::Quantity, t::Quantity) = + 1.0 - cdfsum(dst_v, φ, t) + +function cdfsum(dst_v::Vector, φ::Quantity, t::Quantity) + val = zero(Float64) + for dst in dst_v + val::Float64 = cdf!(dst, φ, t, val) + end + return val +end + +function cdf!(dst::AbstractDistribution, t::StepRangeLen, C::Vector) + C += cdf.(dst, t, zero(t[1])) + return C +end + +function cdf!(dst::AbstractDistribution, φ::Quantity, t::Quantity, c::Float64) + c += cdf(dst, φ, t) + return c end \ No newline at end of file diff --git a/src/io/state_transition_diagram.jl b/src/io/state_transition_diagram.jl index 28080ed..f0de51b 100644 --- a/src/io/state_transition_diagram.jl +++ b/src/io/state_transition_diagram.jl @@ -120,7 +120,9 @@ set_props!(std::AbstractSTD, dict::Dict) = merge!(std.props, dict) ccdf(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) = 1.0 - sum(cdf(get_prop(std, _LG.Edge(ns,nx),:distr), φ, t) for nx in _LG.outneighbors(std.graph, ns); init = 0.0) - + +# ccdf(dst_v::Vector, φ::Quantity, t::Quantity) = +# 1.0 - sum(cdf(dst, φ, t) for dst in dst_v; init = 0.0) ## Info # structs mutable struct STDInfo{B<:Bool} <: AbstractInfo diff --git a/test/elements/CAP_ac.jl b/test/elements/CAP_ac.jl index 7755e9a..e0bd8d6 100644 --- a/test/elements/CAP_ac.jl +++ b/test/elements/CAP_ac.jl @@ -29,19 +29,6 @@ add_states!(stdᶜᵃᵖᵃᶜ, name = ["available", "unavailable"], add_transitions!(stdᶜᵃᵖᵃᶜ, states = [(1,2),(2,1)], distr = [ Exponential(5.0u"yr"), Exponential(48.0u"d")]) - - # LogNormal(3.0u"yr", 1.0u"yr") - -# dt = 4u"hr" -# t = 0u"hr":dt:8760.0u"hr"; - -# @time U = set_U(stdᶜᵃᵖᵃᶜ, t, 1e-8) - -_MSS.solveP!(stdᶜᵃᵖᵃᶜ, cls, tsim = 20.0u"hr", dt = 4u"hr", tol = 1e-9); - -t = 0.0u"hr":4u"hr":1.0u"yr"; - - # solve the std return stdᶜᵃᵖᵃᶜ \ No newline at end of file diff --git a/test/semi_markov_process.jl b/test/semi_markov_process.jl index a704e94..6ab3aeb 100644 --- a/test/semi_markov_process.jl +++ b/test/semi_markov_process.jl @@ -30,7 +30,7 @@ # Generating Unit by A. Lisnianski, D. Elmakias, and H. Ben Haim (2012) stdᵒᵐˢ = include(joinpath(_MSS.BASE_DIR,"test/elements/optical_monitoring_system.jl")) - solve!(stdᵒᵐˢ, SemiMarkovProcess(), tsim = 1.0u"yr", dt = 4.01u"hr") + solve!(stdᵒᵐˢ, SemiMarkovProcess(), tsim = 1.0u"yr") prb_oms = [np[end] for np in _MSS.get_sprop(stdᵒᵐˢ, :prob)] @test isapprox(sum(prb_oms), 1.0, rtol=1e-6) end From f34a3ea01d983a0f402604feb57de0bf8e2d1f14 Mon Sep 17 00:00:00 2001 From: Glenn Emmers Date: Fri, 4 Aug 2023 15:30:22 +0200 Subject: [PATCH 44/56] Added lower bound implementation to both set_A and set_U, cleaned up code, added tests. --- .../semi-markov/optical-monitoring-system.jl | 108 +--- src/form/semi_markov_process.jl | 482 +++--------------- test/semi_markov_process.jl | 6 +- 3 files changed, 87 insertions(+), 509 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index d376898..5ae88fe 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -20,13 +20,8 @@ States: """ # load pkgs -using Plots using Unitful using MultiStateSystems -using Revise -using CSV -using DataFrames - # pkg const const _MSS = MultiStateSystems @@ -50,105 +45,4 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], Exponential(20.0u"hr", 0.62), LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) -# solve the std -# @time H1_20, H1c_20, H_accurate_20 = _MSS.solved!(std, cls, tsim = 8760.0u"hr", dt = 10u"hr", acc = 20, steps = 50, tol=1e-8) -# @time H1_40, H1c_40, H_accurate_40 = _MSS.solved!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", acc = 10, steps = 40, tol=1e-8); -# h_base = solve!(std, cls, tsim =400.0u"hr", dt = 4u"hr", tol=1e-7); -@time solve!(std, cls, tsim = 1.0u"yr", dt = 4u"hr", tol = 1e-8); - -dt = 4u"hr" -t = 0u"hr":dt:400.0u"hr"; - -@time U = set_U(std, t, 1e-8) - -h_base_select=h_base[1][1:10:end] - -plot([h_base_select.-H_accurate_20[1],h_base_select.-H_accurate_40[1]]) - -dH = abs.(diff(H_accurate_40[1])) -append!(dH,zero(H[1][1])) -steps = 150; -acc = 10; -dt = 4u"hr"; -tsim = 8760.0u"hr"; -dt_n = dt/acc |> unit(tsim); -t_n = zero(dt_n):dt_n:dt_n*(steps)*acc -time_c = zero(dt):dt:149.0*dt; - -length(t_n) - -#To do: Testen of de resultaten van mijn eigen analyse goed uitkomen op 1, toch uitzoeken waar effect van weighting precies vandaan komt, wat doet die numerieke backslash operator precies? - -# 1. Set U with sparse matrix and H integrated numerically with simpson rule: 49.679 seconds; 1.00001173 -# 2. Set U with sparse matrix and H integrated with quadgk: 133.125 seconds; 0.999999001 -# 3. Set U with standard method and H integrated numerically with simpson rule; 40.318 seconds; 1.00001173 -# 4. Set U with standard method and H integrated with quadgk: 123.198 seconds; 0.999999001 - -# plot the probabilities -plot(_MSS.get_prop(std, :time), - [_MSS.get_prop(std, ns, :prob) for ns in _MSS.states(std)], - label=reshape([_MSS.get_prop(std, ns, :name) for ns in _MSS.states(std)],1,:), - xlabel="time", - ylabel="probability") - -# plot the reliability -plot(_MSS.get_prop(std, :time), - _MSS.get_prop(std, 1, :prob)+_MSS.get_prop(std, 2, :prob)+_MSS.get_prop(std, 3, :prob)+_MSS.get_prop(std, 4, :prob), - label="reliability weight trap", - xlabel="time", - ylabel="probability") - -plot(_MSS.get_prop(std, :time), - _MSS.get_prop(std, 1, :prob), - label="State 1", - xlabel="time", - ylabel="State Probability") - -plot(_MSS.get_prop(std, :time), - ustrip(h[1]), - label="diff H", - xlabel="time", - ylabel="State Probability") - -plot(_MSS.get_prop(std, :time)[1:length(H[1])], - ustrip(H[1]), - label="H1[1]", - xlabel="time", - ylabel="Transition frequency density function") - -time = _MSS.get_prop(std, :time); -state1 = _MSS.get_prop(std, 1, :prob); -state2 = _MSS.get_prop(std, 2, :prob); -state3 = _MSS.get_prop(std, 3, :prob); -state4 = _MSS.get_prop(std, 4, :prob); -stfd1 = ustrip(H[1]); -diffstfd1 = ustrip(dh); -stfd1d = ustrip(H1[1]); - -time2 = time_c; -stfd3 = ustrip(h[3]); -stfd4 = ustrip(h[4]); - -ut = Array{String}(undef,length(time)) -for i in 1:1:length(time) - ut[i] = string(unit(time[1])) -end - -results = DataFrames.DataFrame(time = ustrip(time), unit = ut, - state1 = state1, - state2 = state2, - state3 = state3, - state4 = state4, - h1 = stfd1, - h2 = stfd2, - h3 = stfd3, - h4 = stfd4); - -results = DataFrames.DataFrame(time = ustrip(time), unit = ut, - h1 = stfd1, - H1 = stfd1d, - dh = diffstfd1); - - - -CSV.write("C:/Users/gemmers/Documents/GitHub/MSS/Results/Journal_Semi_Markov/diffH_results.csv", results) \ No newline at end of file +solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8) \ No newline at end of file diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 66b4365..b4ddd12 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -31,7 +31,7 @@ function set_A(std::AbstractSTD, t::StepRangeLen, tol::Real) if init > 0.0 dst = get_prop(std, tr, :distr) idx = _LG.dst(tr) - lb = floor(cquantile(dst, tol) / dt) * dt + lb = floor(cquantile(dst, tol*1e-3) / dt) * dt _fill_A!(std, t, A, idx, dst, init, lb) end end @@ -40,7 +40,7 @@ end function _fill_A!(std, t, A, idx, dst, init, lb) for (ni,nt) in enumerate(t) - # if nt <= lb + if nt <= lb id = ns(std) * (ni-1) + idx # The content of the A-vector is the probability of initially being # in state (_LG.src(tr)) times the probability of transitioning out @@ -50,33 +50,9 @@ function _fill_A!(std, t, A, idx, dst, init, lb) if isnan(A[id]) A[id] = zero(1/t[1]) end - end + end end end -function set_A(std::AbstractSTD, t::StepRangeLen, H::Vector, steps::Number) - dt = step(t) - Nt = length(t) - Ns = ns(std) - - A = zeros(typeof(1/dt), ns(std) * Nt) - - A[1:length(H)] = H - - for (ni,nt) in enumerate(t) - if ni > steps + 1 - for tr in transitions(std) - id = ns(std) * (ni-1) + _LG.dst(tr) - # The content of the A-vector is the probability of initially being - # in state (_LG.src(tr)) times the probability of transitioning out - # of that state entered at sojourn time zero and evaluated at - # time t = (nt) - A[id] += get_prop(std, _LG.src(tr), :init) * - pdf(get_prop(std, tr, :distr), nt, zero(dt)) - end end end - A[isnan.(A)] .= zero(1/dt) - - return A -end """ MultiStateSystems.set_U(std::MultiStateSystems.AbstractSTD, t::StepRangeLen) @@ -86,108 +62,6 @@ and remains there until time t The unit of U is [-] """ -# function set_U(std::AbstractSTD, t::StepRangeLen) -# # -# dt = step(t) -# Nt = length(t) - -# U = zeros(Float64, ns(std) * Nt, ns(std) * Nt) - -# for (ni,nt) in enumerate(t) -# w = weights(ni) -# # l = zero(dt):dt:nt -# l = t[1]:dt:nt -# for (nj,nl) in enumerate(l) -# Ψ = zeros(typeof(1/dt), ns(std), ns(std)) -# for tr in transitions(std) -# # The results of the pdf depends on two factors: -# # - How long has the system been in this particular state = sojourn time (nt - nl) with nt the index of the current time t and nl the index of entrance time. -# # - The time at which the system entered a certain state, with nl the index of this entrance time. This determines weight attributed to this particular transition. -# Ψ[_LG.dst(tr), _LG.src(tr)] = -# pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 -# end -# rT = (ns(std) * (ni - 1) + 1):(ns(std) * ni) -# rΦ = (ns(std) * (nj - 1) + 1):(ns(std) * nj) -# if ni == nj -# U[rT,rΦ] = Matrix(1.0_LA.I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ -# else -# U[rT,rΦ] = -dt .* w[nj] .* Ψ -# end -# end end -# U[isnan.(U)] .= 0.0 - -# return U -# end -# function set_U(std::AbstractSTD, t::StepRangeLen) -# # -# dt = step(t) -# Nt = length(t) - -# I,J,V = Int[],Int[],Number[] - -# append!(I, 1:Ns*Nt) -# append!(J, 1:Ns*Nt) -# append!(V, ones(Number,Ns*Nt)) - -# for (ni,nt) in enumerate(t) -# w = weights(ni) -# # l = zero(dt):dt:nt -# l = t[1]:dt:nt -# for (nj,nl) in enumerate(l) -# Ψ = zeros(typeof(1/dt), ns(std), ns(std)) -# for tr in transitions(std) -# # The results of the pdf depends on two factors: -# # - How long has the system been in this particular state = sojourn time (nt - nl) with nt the index of the current time t and nl the index of entrance time. -# # - The time at which the system entered a certain state, with nl the index of this entrance time. This determines weight attributed to this particular transition. -# Ψ[_LG.dst(tr), _LG.src(tr)] = -# pdf(get_prop(std, tr, :distr), nt - nl, nl) |> unit(dt)^-1 -# end -# append!(I,(ns(std) * (ni - 1) + 1):(ns(std) * ni)) -# append!(J,(ns(std) * (nj - 1) + 1):(ns(std) * nj)) -# if ni == nj -# U[rT,rΦ] = Matrix(1.0_LA.I, ns(std), ns(std)) .- dt .* w[nj] .* Ψ -# else -# U[rT,rΦ] = -dt .* w[nj] .* Ψ -# end -# end end -# U[isnan.(U)] .= 0.0 - -# return U -# end - -# function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) -# dt = step(t) -# Nt = length(t) -# Ns = ns(std) - -# # initialize three vectors I,J,V respectively row, column and value indices -# I,J,V = Int[],Int[],Number[] - -# append!(I, 1:Ns*Nt) -# append!(J, 1:Ns*Nt) -# append!(V, ones(Number,Ns*Nt)) - -# for tr in transitions(std) -# # dummy value not necessary, since every diagonal entry requires a one to be added to it. -# # Sparse Arrays allow to add values to the same location twice and add those -# # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. -# dst = get_prop(std, tr, :distr) -# lb = floor(cquantile(dst, tol) / dt) * dt -# for (ni,nt) in enumerate(t) -# Φ = nt:-dt:t[1] -# # Φ represents the sojourn time, ranging from -# lt = t[1]:dt:nt -# NΦ = length(Φ) - -# append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) -# append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) -# # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) -# append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) -# end end -# V[isnan.(V)] .= 0.0 -# return _SA.sparse(I, J, V) -# end - function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) dt = step(t) @@ -211,9 +85,9 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) end function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t::StepRangeLen, Ns::Int, dst::AbstractDistribution, I::Vector, J::Vector, V::Vector, tol::Real) - # lb = floor(cquantile(dst, tol/1000) / dt) * dt + lb = Int(floor(cquantile(dst, tol*1e-3) / dt)) for (ni,nt) in enumerate(t) - # if nt <= lb + if ni <= lb Φ = nt:-dt:t[1] # Φ represents the sojourn time, ranging from lt = t[1]:dt:nt @@ -226,118 +100,24 @@ function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t: V[end] = 0.0 end end - # else - # Φ = lb:-dt:t[1] - # # Φ represents the sojourn time, ranging from - # lt = t[1]:dt:nt - # NΦ = length(Φ) - # for nj in 1:NΦ - # push!(I, Ns * (ni-1) + _LG.dst(tr)) - # push!(J, Ns * (nj-1) + _LG.src(tr)) - # push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) - # if isnan(V[end]) - # V[end] = 0.0 - # end - # end - # end + else + Φ = nt:-dt:t[1] + # Φ represents the sojourn time, ranging from + lt = t[1]:dt:nt + NΦ = length(lt) + for nj in NΦ:-1:NΦ-lb + push!(I, Ns * (ni-1) + _LG.dst(tr)) + push!(J, Ns * (nj-1) + _LG.src(tr)) + push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) + if isnan(V[end]) + V[end] = 0.0 + end + end + end # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) end end - -# function set_U(std::AbstractSTD, t::StepRangeLen, steps::Number, tol::Real) -# dt = step(t) -# Nt = length(t) -# Ns = ns(std) - -# # initialize three vectors I,J,V respectively row, column and value indices -# I,J,V = Int[],Int[],Number[] - -# append!(I, 1:Ns*Nt) -# append!(J, 1:Ns*Nt) -# append!(V, ones(Number,Ns*Nt)) - -# for tr in transitions(std) -# # dummy value not necessary, since every diagonal entry requires a one to be added to it. -# # Sparse Arrays allow to add values to the same location twice and add those -# # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. -# dst = get_prop(std, tr, :distr) -# lb = floor(cquantile(dst, tol) / dt) * dt -# for (ni,nt) in enumerate(t) -# if ni > steps + 1 -# Φ = nt:-dt:t[1] -# # Φ represents the sojourn time, ranging from -# lt = t[1]:dt:nt -# NΦ = length(Φ) - -# append!(I, (Ns * (ni-1) + _LG.dst(tr)).*ones(Int,NΦ)) -# append!(J, [Ns * (nj-1) + _LG.src(tr) for nj in 1:NΦ]) -# # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) -# append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) -# end -# end end -# V[isnan.(V)] .= 0.0 -# return _SA.sparse(I, J, V) -# end - -# stochastic process -# function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; -# tsim::Number=1.0u"yr", dt::Number=1u"d", tol::Real=1e-8) -# # get the input -# dt = dt |> unit(tsim) -# t = zero(dt):dt:tsim -# Nt = length(t) - -# # solve the problem -# Φ = zeros(Nt, ns(std)) - - -# println("set_U") -# U = set_U(std,t,tol) -# println("set_A") -# A = ustrip(set_A(std,t,tol)) -# H=U\A*unit(1/t[1]) - -# # println("set_P") -# # @time set_P(std, t, H, tol) -# println("Linear interpolation of H") -# h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end -# h_sol = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; - -# println("Integration of H to Φ") -# for st in states(std) -# for (ni,nt) in enumerate(t) -# # w = weights(ni) -# # TOM: φ <<< t, zero could be higher -# # l = zero(dt):dt:nt -# l = t[1]:dt:nt .|> unit(tsim) -# # # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification -# # # The probability of being in a state st at time nt depends on two things: -# # # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. -# # # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time -# # # of entering the state (0) to determine the weight and the sojourn time (nt-0). -# # # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). -# # # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. -# # # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at -# # # The last transition time x and the sojourn time nt-x. -# Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) -# Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] - -# # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* -# # ccdf(std, st, nt-nl, nl) -# # for (nj,nl) in enumerate(l)) -# end end - - -# # set the output -# set_prop!(std, :cls, cls) -# set_prop!(std, :time, t) -# set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) - -# # set the solved status -# set_info!(std, :solved, true) -# return h_sol -# end function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; tsim::Number=1.0u"yr", dt::Number=4u"hr", tol::Real=1e-8) @@ -347,15 +127,10 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # solve the problem - println("set_U") U = set_U(std,t,tol) - println("set_A") A = ustrip(set_A(std,t,tol)) H=U\A*unit(1/t[1]) - # h = [map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)] - - println("set_P") set_P(std, t, H, tol) # set the output @@ -367,73 +142,6 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # return h end -# function solved!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; -# tsim::Number=1.0u"yr", dt::Number=1u"hr", acc::Int64=10, steps::Number=100.0, tol::Real=1e-8) - -# # Get the input for solving numerical inrush phase -# dt_n = dt/acc |> unit(tsim); -# t_n = zero(dt_n):dt_n:dt_n*(steps)*acc; - -# U = set_U(std,t_n[1:end],tol) -# A = ustrip(set_A(std,t_n[1:end])) -# H1 = U\A*unit(1/t_n[1]) - -# H_c = compress(H1, steps, std) - -# H1o = [ map(x->H1[ns(std) * (x-1) + st], 1:length(t_n)-ns(std)) for st in states(std)]; -# H1co = [ map(x->H_c[ns(std) * (x-1) + st], 1:Int(length(H_c)/ns(std))) for st in states(std)]; - -# # get the input for final problem solution -# dt = dt |> unit(tsim) -# t = zero(dt):dt:tsim -# Nt = length(t) - -# # solve the problem -# Φ = zeros(Nt, ns(std)) - -# U = set_U(std,t,steps,tol) -# A = ustrip(set_A(std,t,H_c,steps)) -# H=U\A*unit(1/t[1]) - -# Ho = [ map(x->H[ns(std) * (x-1) + st], 1:Nt) for st in states(std)]; - -# # set_P(std, t, H, tol) -# h = [_INT.LinearInterpolation(collect(t), map(x->H[ns(std) * (x-1) + st], 1:Nt)) for st in states(std)]; # splice id H = st:NS:end - -# for st in states(std) -# for (ni,nt) in enumerate(t) -# w = weights(ni) -# # TOM: φ <<< t, zero could be higher -# # l = zero(dt):dt:nt -# l = t[1]:dt:nt .|> unit(tsim) -# # NB: ccdf(t-l,φ) where φ = 0.0, GLENN, additional clarification -# # The probability of being in a state st at time nt depends on two things: -# # First, the probability of being in that state initially, times the probability of not having transitioned out of that state until time nt. -# # The probability of not having transitioned until time nt is characterized by the complementary cumulative density function evaluated at the time -# # of entering the state (0) to determine the weight and the sojourn time (nt-0). -# # Second, on the probability of having transitioned to state st at time x and the probability of not having transitioned out of that state during the sojourn time (nt-x). -# # The probability of having transitioned to state st at time x is characterized by the integral of the transition frequency density h of state st. -# # The probability of not having transitioned out of that state during the sojourn time (nt-x) is characterized by the complementary cumulative density function evaluated at -# # The last transition time x and the sojourn time nt-x. -# Φ[ni,st] += get_prop(std, st, :init) * ccdf(std, st, nt, zero(dt)) -# Φ[ni,st] += _QGK.quadgk(x -> h[st](x) * ccdf(std, st, nt-x, x), t[1],nt,rtol=1e-7)[1] - -# # Φ[ni,st] += sum(dt .* w[nj] .* H[ns(std) * (nj-1) + st] .* -# # ccdf(std, st, nt-nl, nl) -# # for (nj,nl) in enumerate(l)) -# end end - - -# # set the output -# set_prop!(std, :cls, cls) -# set_prop!(std, :time, t) -# set_prop!(std, states(std), :prob, [Φ[:,ns] for ns in states(std)]) - -# # set the solved status -# set_info!(std, :solved, true) - -# return H1o, H1co, Ho -# end function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) Nt = length(t) @@ -447,15 +155,6 @@ function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) end end -# function set_int(dst_v, t, h, init, tol) -# if init > 0.0 -# p = init .* [ccdf(dst_v, φ, zero(t[1])) for φ in t] .+ integral(dst_v, t, h, tol) -# else -# p = integral(dst_v, t, h, tol) -# end -# return p -# end - function set_int(dst_v, t, h, init, tol) if init > 0.0 CDF = zeros(Float64, length(t)) @@ -473,38 +172,9 @@ end """ MultiStateSystems.weights(x::Int) -Determine integration weights based on extended Simpson's rule. -w[1] and w[end] = 1/3, even weights = 4/3 and uneven weights = 2/3. +Determine integration weights based on Simpson's rule. +w[1] and w[end] = 1/2, other weights = 1. """ -# function weights(x::Int) -# x==1 && return [0] -# x==2 && return [1/2, 1/2] -# x==3 && return [1/3, 4/3, 1/3] -# x==4 && return [3/8, 9/8, 9/8, 3/8] -# x==5 && return (2/45) .* [7, 32, 12, 32, 7] -# x==6 && return (5/288) .* [19, 75, 50, 50, 75, 19] -# x==7 && return (1/140) .* [41, 216, 27, 272, 27, 216, 41] -# x==8 && return (7/17280) .* [751, 3577, 1323, 2989, 2989, 1323, 3577, 751] - -# weights = 48 * ones(x) -# weights[1:4] = [17, 59, 43, 49] -# weights[end-3:end] = [49, 43, 59, 17] -# return (1/48) .* weights -# end - -# function weights(x::Int) -# w = zeros(x) -# for i in 1:length(w) -# if i % 2 == 0 -# w[i] = 2/3 -# else -# w[i] = 4/3 -# end end -# w[1] = 1/3 -# w[end] = 1/3 - -# return w -# end function weights(N::Int, p::Int) if p == 1 || p == N @@ -514,34 +184,6 @@ function weights(N::Int, p::Int) end end -# function weights(N::Int, p::Int) -# if N==1 -# return 0.0 -# elseif p == 1 || p == N -# return 0.5 -# else -# return 1.0 -# end -# end - -# function weights(N::Int, p::Int) -# if N==1 -# return 0.0 -# elseif p == 1 || p == N -# return 1/3 -# elseif p % 2 == 0 -# return 2/3 -# else -# return 4/3 -# end -# end - -# function weights(x::Int) -# w = ones(x) -# return w -# end - - # # TOM: Alternative formulation for the state ccdf, using the trapping info prop # cdf(std::AbstractSTD, ns::Int, φ::Number, t::Number) = # sum(cdf(get_prop(std, _LG.Edge(ns,nx), :distr), φ, t) for nx in _LG.outneighbors(std.graph, ns)) @@ -555,23 +197,6 @@ elunit(b::Vector{U}) where U = _UF.unit(U) _LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = (ustrip.(A) \ ustrip(b)) * (elunit(b) / elunit(A)) -function battery_system_availability(i, T, ntw_av, μ, σ) - # Calculate the probability that the battery does not run out of charge before - # the power sources are repaired at time t. With a lognormal distribution for - # the repair time with mean μ and standard deviation σ. - p_failure = 1 - ntw_av[i] - p_repair_time_ge_T = ccdf(LogNormal(μ, σ),T) - return 1-p_failure*p_repair_time_ge_T -end - -function battery_system_availability(i, T, ntw_av, θ) - # Calculate the probability that the battery does not run out of charge before - # the power sources are repaired at time t. With a lognormal distribution for - # the repair time with mean μ and standard deviation σ. - p_failure = 1 - ntw_av[i] - p_repair_time_ge_T = ccdf(Exponential(θ),T) - return 1-p_failure*p_repair_time_ge_T -end function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) # controleer voor schaalfactor @@ -628,12 +253,71 @@ function cdfsum(dst_v::Vector, φ::Quantity, t::Quantity) return val end -function cdf!(dst::AbstractDistribution, t::StepRangeLen, C::Vector) - C += cdf.(dst, t, zero(t[1])) + +function cdf!(dst::AbstractDistribution, t::StepRangeLen, C::Vector)::Vector + C .+= cdf.(dst, t, zero(t[1])) return C end -function cdf!(dst::AbstractDistribution, φ::Quantity, t::Quantity, c::Float64) + +function cdf!(dst::AbstractDistribution, φ::Quantity, t::Quantity, c::Float64)::Float64 c += cdf(dst, φ, t) return c +end + +# function cdfsum(dst_v::Vector{T}, φ::Quantity, t::Quantity) where T<:AbstractDistribution +# val::Float64 = 0.0 +# for dst in dst_v +# val = cdfsum_inner(dst, φ, t, val) +# end +# return val +# end + +# function cdfsum_inner(dst::AbstractExponential, φ::Quantity, t::Quantity, c::Float64)::Float64 +# c += cdf(dst, φ, t) +# return c +# end + +# # cdfsum_inner for the specific AbstractExponential types +# function cdfsum_inner(dst::AbstractWeibull, φ::Quantity, t::Quantity, c::Float64)::Float64 +# c += cdf(dst, φ, t) +# return c +# end + +# function cdfsum_inner(dst::AbstractLogNormal, φ::Quantity, t::Quantity, c::Float64)::Float64 +# c += cdf(dst, φ, t) +# return c +# end + +# function cdf!(dst::AbstractExponential, t::StepRangeLen, C::Vector)::Vector +# C .+= cdf.(dst, t, zero(t[1])) +# return C +# end + +# function cdf!(dst::AbstractWeibull, t::StepRangeLen, C::Vector)::Vector +# C .+= cdf.(dst, t, zero(t[1])) +# return C +# end + +# function cdf!(dst::AbstractLogNormal, t::StepRangeLen, C::Vector)::Vector +# C .+= cdf.(dst, t, zero(t[1])) +# return C +# end + +function battery_system_availability(i, T, ntw_av, μ, σ) + # Calculate the probability that the battery does not run out of charge before + # the power sources are repaired at time t. With a lognormal distribution for + # the repair time with mean μ and standard deviation σ. + p_failure = 1 - ntw_av[i] + p_repair_time_ge_T = ccdf(LogNormal(μ, σ),T) + return 1-p_failure*p_repair_time_ge_T +end + +function battery_system_availability(i, T, ntw_av, θ) + # Calculate the probability that the battery does not run out of charge before + # the power sources are repaired at time t. With an exponential distribution for + # the repair time with mean μ and standard deviation σ. + p_failure = 1 - ntw_av[i] + p_repair_time_ge_T = ccdf(Exponential(θ),T) + return 1-p_failure*p_repair_time_ge_T end \ No newline at end of file diff --git a/test/semi_markov_process.jl b/test/semi_markov_process.jl index 6ab3aeb..9632cbd 100644 --- a/test/semi_markov_process.jl +++ b/test/semi_markov_process.jl @@ -13,13 +13,13 @@ # of LVDC systems with integrated battery storage stdᶜᵃᵖ = include(joinpath(_MSS.BASE_DIR,"test/elements/CAP_ac.jl")) - solve!(stdᶜᵃᵖ, MarkovProcess(), tsim = 1.0u"yr") + solve!(stdᶜᵃᵖ, MarkovProcess(), tsim = 2.0u"yr") prb_m = [np[end] for np in _MSS.get_sprop(stdᶜᵃᵖ, :prob)] - solve!(stdᶜᵃᵖ, SemiMarkovProcess(), tsim = 1.0u"yr") + solve!(stdᶜᵃᵖ, SemiMarkovProcess(), tsim = 2.0u"yr") prb_s = [np[end] for np in _MSS.get_sprop(stdᶜᵃᵖ, :prob)] - @test isapprox(sum(prb_m), 1.0, rtol=1e-6) + @test isapprox(sum(prb_s), 1.0, rtol=1e-6) @test all(isapprox.(prb_m, prb_s, rtol=1e-6)) end From 274b36e1ee526bbe66f7cd4844ee5d67d6bc4338 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Mon, 7 Aug 2023 18:04:57 +0200 Subject: [PATCH 45/56] Small adjustment to distributions.jl --- src/io/distributions.jl | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/io/distributions.jl b/src/io/distributions.jl index 35ef75c..51229d2 100644 --- a/src/io/distributions.jl +++ b/src/io/distributions.jl @@ -152,16 +152,16 @@ julia> 𝑾(10.0,0.5,0.2) # scaled Weibull distr. with θ = 10.0, α = 0.5 a abstract type AbstractWeibull{X,Y,Z} <: AbstractDistribution{X,Y,Z} end # struct - θ::Number, α::Real, ω::Real -struct WeibullNRR{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} +struct WeibullNRR{X<:Number, Y<:Real, Z<:Real} <: AbstractWeibull{X,Y,Z} θ::X # scale α::Y # shape - ω::Y # weight: 0.0 < ω <= 1.0 + ω::Z # weight: 0.0 < ω <= 1.0 end # constructors Weibull() = WeibullNRR(1.0, 1.0, 1.0) Weibull(θ::X) where {X<:Number} = WeibullNRR(θ, 1.0, 1.0) -Weibull(θ::X, α::Y) where{X<:Number, Y<:Real}= WeibullNRR(θ, α, 1.0) -Weibull(θ::X, α::Y, ω::Z) where{X<:Number, Y<:Real, Z<:Real}= WeibullNRR(θ, α, ω) +Weibull(θ::X, α::Y) where {X<:Number, Y<:Real} = WeibullNRR(θ, α, 1.0) +Weibull(θ::X, α::Y, ω::Z) where {X<:Number, Y<:Real, Z<:Real} = WeibullNRR(θ, α, ω) # struct - θ::Number, α::Real, ω::Function struct WeibullNRF{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} @@ -170,7 +170,7 @@ struct WeibullNRF{X<:Number, Y<:Real, Z<:Function} <: AbstractWeibull{X,Y,Z} ω::Z # weight: 0.0 < ω(t) <= 1.0 end # constructors -Weibull(θ::X, α::Y, ω::Z) where{X<:Number, Y<:Real, Z<:Function}= +Weibull(θ::X, α::Y, ω::Z) where {X<:Number, Y<:Real, Z<:Function} = WeibullNRF(θ, α, ω) # shortened constructors From 08a2aa514d3c3d5693d688f7c5ca753355de875b Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 11 Aug 2023 08:58:13 +0200 Subject: [PATCH 46/56] Update semi_markov_process.jl --- src/form/semi_markov_process.jl | 22 ++++------------------ 1 file changed, 4 insertions(+), 18 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index b4ddd12..ef989ce 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -75,9 +75,6 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) append!(V, ones(Float64,Ns*Nt)) for tr in transitions(std) - # dummy value not necessary, since every diagonal entry requires a one to be added to it. - # Sparse Arrays allow to add values to the same location twice and add those - # dummy_value = ifelse(_LG.src(tr) == _LG.dst(tr),zero(1/dt),oneunit(1/dt)) # dummy_value voegt nu een 1 toe wanneer dest and source gelijk zijn, maar dit moet enkel in geval ni en nj ook nog gelijk zijn. Extra controle in de tijdslus. dst = get_prop(std, tr, :distr) _fill_U!(tr, dt, t, Ns, dst, I, J, V, tol) end @@ -89,8 +86,9 @@ function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t: for (ni,nt) in enumerate(t) if ni <= lb Φ = nt:-dt:t[1] - # Φ represents the sojourn time, ranging from + # Φ represents the sojourn time lt = t[1]:dt:nt + # lt is the last transition time NΦ = length(Φ) for nj in 1:NΦ push!(I, Ns * (ni-1) + _LG.dst(tr)) @@ -102,8 +100,9 @@ function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t: end else Φ = nt:-dt:t[1] - # Φ represents the sojourn time, ranging from + # Φ represents the sojourn time lt = t[1]:dt:nt + # lt is the last transition time NΦ = length(lt) for nj in NΦ:-1:NΦ-lb push!(I, Ns * (ni-1) + _LG.dst(tr)) @@ -114,8 +113,6 @@ function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t: end end end - # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, nt.-Φ, Φ) .|> unit(dt)^-1)) - # append!(V, .- dt .* weights(ni)[1:NΦ] .* (pdf.(dst, Φ, lt) .|> unit(dt)^-1)) end end @@ -139,7 +136,6 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # set the solved status set_info!(std, :solved, true) - # return h end @@ -184,13 +180,6 @@ function weights(N::Int, p::Int) end end -# # TOM: Alternative formulation for the state ccdf, using the trapping info prop -# cdf(std::AbstractSTD, ns::Int, φ::Number, t::Number) = -# sum(cdf(get_prop(std, _LG.Edge(ns,nx), :distr), φ, t) for nx in _LG.outneighbors(std.graph, ns)) -# ccdf(std::AbstractSTD, ns::Int, φ::Number, t::Number) = -# ifelse(get_prop(std, ns, :trapping), 1.0, 1.0 - cdf(std, ns, φ, t)) - - # TOM: added functionality to enable \ with units. elunit(A::Matrix{U}) where U = _UF.unit(U) elunit(b::Vector{U}) where U = _UF.unit(U) @@ -199,7 +188,6 @@ _LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) - # controleer voor schaalfactor d2h = abs.(diff(diff(ustrip(h)))) id = 1 idx = Int[1] @@ -221,8 +209,6 @@ function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) else ϕ = [_QGK.quadgk(x -> γ(x) * ccdf(dst_v, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] end - # niet gelijk gespacete interpolatie - # Y = interpolate((x,), y, Gridded(Linear())) p = _INT.LinearInterpolation(τ, ϕ)(t) return p end From 2f87978494836ec80a9b2aa77e57c7d55423272f Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 11 Aug 2023 12:15:07 +0200 Subject: [PATCH 47/56] Adjustments made to set_P --- .../semi-markov/optical-monitoring-system.jl | 10 +- src/form/semi_markov_process.jl | 134 ++++-------------- src/io/state_transition_diagram.jl | 4 +- test/runtests.jl | 1 + 4 files changed, 38 insertions(+), 111 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 5ae88fe..18b87d1 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -22,6 +22,8 @@ States: # load pkgs using Unitful using MultiStateSystems +using Revise +using Plots # pkg const const _MSS = MultiStateSystems @@ -45,4 +47,10 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], Exponential(20.0u"hr", 0.62), LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) -solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8) \ No newline at end of file +U = solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8) + +plot(_MSS.get_prop(std, :time), + _MSS.get_prop(std, 1, :prob), + label="reliability", + xlabel="time", + ylabel="probability") diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index ef989ce..3d5616d 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -82,6 +82,21 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) end function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t::StepRangeLen, Ns::Int, dst::AbstractDistribution, I::Vector, J::Vector, V::Vector, tol::Real) + # id_lb, id_ub = Int(ceil(quantile(dst, tol*1e-3) / dt)), Int(floor(cquantile(dst, tol*1e-3) / dt)) + # lb, ub = id_lb * dt - dt, id_ub * dt + # for (ni,nt) in enumerate(t) + # φ = min(nt,ub):-dt:lb + # lt = reverse(φ) + # idx = min(ni,id_ub):-1:id_lb + # for (nj,id) in enumerate(idx) + # push!(I, Ns * (ni-1) + _LG.dst(tr)) + # push!(J, Ns * (id-1) + _LG.src(tr)) + # push!(V,- dt * weights(ni, id) * (pdf(dst, φ[nj], lt[nj]) |> unit(dt)^-1)) + # if isnan(V[end]) + # V[end] = 0.0 + # end + # end + # end lb = Int(floor(cquantile(dst, tol*1e-3) / dt)) for (ni,nt) in enumerate(t) if ni <= lb @@ -124,11 +139,12 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # solve the problem - U = set_U(std,t,tol) - A = ustrip(set_A(std,t,tol)) - H=U\A*unit(1/t[1]) + @time U = set_U(std,t,tol) + @time A = ustrip(set_A(std,t,tol)) + @time H=U\A*unit(1/t[1]) - set_P(std, t, H, tol) + println("set_P") + @time set_P(std, t, H, tol) # set the output set_prop!(std, :cls, cls) @@ -146,18 +162,14 @@ function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) dst_v = [get_prop(std, _LG.Edge(st,nx),:distr) for nx in _LG.outneighbors(std.graph, st)] init = get_prop(std, st, :init) h = map(x->H[ns(std) * (x-1) + st], 1:Nt) - p = set_int(dst_v, t, h, init, tol) + p = set_int(std, st, dst_v, t, h, init, tol) set_prop!(std, st, :prob, p) end end -function set_int(dst_v, t, h, init, tol) +function set_int(std, st, dst_v, t, h, init, tol) if init > 0.0 - CDF = zeros(Float64, length(t)) - for dst in dst_v - CDF = cdf!(dst, t, CDF) - end - p = init .* (1 .- CDF) .+ integral(dst_v, t, h, tol) + p = init .* ccdf.(std, st, t, zero(t[1])) .+ integral(dst_v, t, h, tol) else p = integral(dst_v, t, h, tol) end @@ -205,105 +217,11 @@ function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) τ = t[idx] γ = _INT.interpolate((τ,), h[idx], _INT.Gridded(_INT.Linear())) if isempty(dst_v) - ϕ = [_QGK.quadgk(x -> γ(x), t[1], nτ, rtol=tol)[1] for nτ in τ] + ϕ = [_QGK.quadgk(x -> γ(x), t[1], nτ, rtol=tol)[1] for nτ in τ] else - ϕ = [_QGK.quadgk(x -> γ(x) * ccdf(dst_v, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] + ϕ = [_QGK.quadgk(x -> γ(x), t[1], nτ, rtol = tol)[1] for nτ in τ] .- + sum([_QGK.quadgk(x -> γ(x) * cdf(dst, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] for dst in dst_v) end p = _INT.LinearInterpolation(τ, ϕ)(t) return p end - - - -function compress(v::Vector, steps::Int, std::AbstractSTD) - n = length(v) - Ns = ns(std) - y = Int((n-Ns)/(Ns*steps)) - compressed_v = zeros((steps+1)*Ns)*unit(v[1]) - for st in 1:Ns - for i in 1:steps+1 - compressed_v[Ns*(i-1)+st] = v[y*Ns*(i-1)+st]; - end - end - return compressed_v -end - -ccdf(dst_v::Vector, φ::Quantity, t::Quantity) = - 1.0 - cdfsum(dst_v, φ, t) - -function cdfsum(dst_v::Vector, φ::Quantity, t::Quantity) - val = zero(Float64) - for dst in dst_v - val::Float64 = cdf!(dst, φ, t, val) - end - return val -end - - -function cdf!(dst::AbstractDistribution, t::StepRangeLen, C::Vector)::Vector - C .+= cdf.(dst, t, zero(t[1])) - return C -end - - -function cdf!(dst::AbstractDistribution, φ::Quantity, t::Quantity, c::Float64)::Float64 - c += cdf(dst, φ, t) - return c -end - -# function cdfsum(dst_v::Vector{T}, φ::Quantity, t::Quantity) where T<:AbstractDistribution -# val::Float64 = 0.0 -# for dst in dst_v -# val = cdfsum_inner(dst, φ, t, val) -# end -# return val -# end - -# function cdfsum_inner(dst::AbstractExponential, φ::Quantity, t::Quantity, c::Float64)::Float64 -# c += cdf(dst, φ, t) -# return c -# end - -# # cdfsum_inner for the specific AbstractExponential types -# function cdfsum_inner(dst::AbstractWeibull, φ::Quantity, t::Quantity, c::Float64)::Float64 -# c += cdf(dst, φ, t) -# return c -# end - -# function cdfsum_inner(dst::AbstractLogNormal, φ::Quantity, t::Quantity, c::Float64)::Float64 -# c += cdf(dst, φ, t) -# return c -# end - -# function cdf!(dst::AbstractExponential, t::StepRangeLen, C::Vector)::Vector -# C .+= cdf.(dst, t, zero(t[1])) -# return C -# end - -# function cdf!(dst::AbstractWeibull, t::StepRangeLen, C::Vector)::Vector -# C .+= cdf.(dst, t, zero(t[1])) -# return C -# end - -# function cdf!(dst::AbstractLogNormal, t::StepRangeLen, C::Vector)::Vector -# C .+= cdf.(dst, t, zero(t[1])) -# return C -# end - -function battery_system_availability(i, T, ntw_av, μ, σ) - # Calculate the probability that the battery does not run out of charge before - # the power sources are repaired at time t. With a lognormal distribution for - # the repair time with mean μ and standard deviation σ. - p_failure = 1 - ntw_av[i] - p_repair_time_ge_T = ccdf(LogNormal(μ, σ),T) - return 1-p_failure*p_repair_time_ge_T -end - -function battery_system_availability(i, T, ntw_av, θ) - # Calculate the probability that the battery does not run out of charge before - # the power sources are repaired at time t. With an exponential distribution for - # the repair time with mean μ and standard deviation σ. - p_failure = 1 - ntw_av[i] - p_repair_time_ge_T = ccdf(Exponential(θ),T) - return 1-p_failure*p_repair_time_ge_T -end \ No newline at end of file diff --git a/src/io/state_transition_diagram.jl b/src/io/state_transition_diagram.jl index f0de51b..077711e 100644 --- a/src/io/state_transition_diagram.jl +++ b/src/io/state_transition_diagram.jl @@ -121,8 +121,8 @@ ccdf(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) = 1.0 - sum(cdf(get_prop(std, _LG.Edge(ns,nx),:distr), φ, t) for nx in _LG.outneighbors(std.graph, ns); init = 0.0) -# ccdf(dst_v::Vector, φ::Quantity, t::Quantity) = -# 1.0 - sum(cdf(dst, φ, t) for dst in dst_v; init = 0.0) +ccdf(dst_v::Vector, φ::Quantity, t::Quantity) = + 1.0 - sum(cdf(dst, φ, t) for dst in dst_v; init = 0.0) ## Info # structs mutable struct STDInfo{B<:Bool} <: AbstractInfo diff --git a/test/runtests.jl b/test/runtests.jl index 77a08df..e147a08 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -21,6 +21,7 @@ const _MSS = MultiStateSystems # form include("steady_state_process.jl") include("markov_process.jl") + include("semi_markov_process.jl") # io include("distributions.jl") From a555e69c149533fff881a8655ff8c1946ac83538 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 11 Aug 2023 13:00:37 +0200 Subject: [PATCH 48/56] Adjustment of set_U to include upper and lower bound value limits --- .../semi-markov/optical-monitoring-system.jl | 8 +- src/form/semi_markov_process.jl | 98 +++++++++---------- 2 files changed, 49 insertions(+), 57 deletions(-) diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 18b87d1..952ffbf 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -47,10 +47,4 @@ add_transitions!(std, states = [(1,1),(1,2),(2,1),(2,3),(3,1),(3,4)], Exponential(20.0u"hr", 0.62), LogNormal(4.0u"hr", 0.4u"hr", 0.38)]) -U = solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8) - -plot(_MSS.get_prop(std, :time), - _MSS.get_prop(std, 1, :prob), - label="reliability", - xlabel="time", - ylabel="probability") +solve!(std, cls, tsim = 8760.0u"hr", dt = 4u"hr", tol = 1e-8) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 3d5616d..e45aea1 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -82,53 +82,52 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) end function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t::StepRangeLen, Ns::Int, dst::AbstractDistribution, I::Vector, J::Vector, V::Vector, tol::Real) - # id_lb, id_ub = Int(ceil(quantile(dst, tol*1e-3) / dt)), Int(floor(cquantile(dst, tol*1e-3) / dt)) - # lb, ub = id_lb * dt - dt, id_ub * dt - # for (ni,nt) in enumerate(t) - # φ = min(nt,ub):-dt:lb - # lt = reverse(φ) - # idx = min(ni,id_ub):-1:id_lb - # for (nj,id) in enumerate(idx) - # push!(I, Ns * (ni-1) + _LG.dst(tr)) - # push!(J, Ns * (id-1) + _LG.src(tr)) - # push!(V,- dt * weights(ni, id) * (pdf(dst, φ[nj], lt[nj]) |> unit(dt)^-1)) - # if isnan(V[end]) - # V[end] = 0.0 - # end - # end - # end - lb = Int(floor(cquantile(dst, tol*1e-3) / dt)) + id_lb, id_ub = Int(ceil(quantile(dst, tol*1e-3) / dt)), Int(floor(cquantile(dst, tol*1e-3) / dt)) for (ni,nt) in enumerate(t) - if ni <= lb - Φ = nt:-dt:t[1] - # Φ represents the sojourn time - lt = t[1]:dt:nt - # lt is the last transition time - NΦ = length(Φ) - for nj in 1:NΦ - push!(I, Ns * (ni-1) + _LG.dst(tr)) - push!(J, Ns * (nj-1) + _LG.src(tr)) - push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) - if isnan(V[end]) - V[end] = 0.0 - end - end - else - Φ = nt:-dt:t[1] - # Φ represents the sojourn time - lt = t[1]:dt:nt - # lt is the last transition time - NΦ = length(lt) - for nj in NΦ:-1:NΦ-lb - push!(I, Ns * (ni-1) + _LG.dst(tr)) - push!(J, Ns * (nj-1) + _LG.src(tr)) - push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) - if isnan(V[end]) - V[end] = 0.0 - end - end + φ = nt:-dt:t[1] + lt = reverse(φ) + idx = ni-id_lb+1:-1:max(1,ni-id_ub) + for id in idx + push!(I, Ns * (ni-1) + _LG.dst(tr)) + push!(J, Ns * (id-1) + _LG.src(tr)) + push!(V,- dt * weights(ni, id) * (pdf(dst, φ[id], lt[id]) |> unit(dt)^-1)) + if isnan(V[end]) + V[end] = 0.0 + end end - end + end + # lb = Int(floor(cquantile(dst, tol*1e-3) / dt)) + # for (ni,nt) in enumerate(t) + # if ni <= lb + # Φ = nt:-dt:t[1] + # # Φ represents the sojourn time + # lt = t[1]:dt:nt + # # lt is the last transition time + # NΦ = length(Φ) + # for nj in 1:NΦ + # push!(I, Ns * (ni-1) + _LG.dst(tr)) + # push!(J, Ns * (nj-1) + _LG.src(tr)) + # push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) + # if isnan(V[end]) + # V[end] = 0.0 + # end + # end + # else + # Φ = nt:-dt:t[1] + # # Φ represents the sojourn time + # lt = t[1]:dt:nt + # # lt is the last transition time + # NΦ = length(lt) + # for nj in NΦ:-1:NΦ-lb + # push!(I, Ns * (ni-1) + _LG.dst(tr)) + # push!(J, Ns * (nj-1) + _LG.src(tr)) + # push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) + # if isnan(V[end]) + # V[end] = 0.0 + # end + # end + # end + # end end function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; @@ -139,12 +138,11 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; # solve the problem - @time U = set_U(std,t,tol) - @time A = ustrip(set_A(std,t,tol)) - @time H=U\A*unit(1/t[1]) + U = set_U(std,t,tol) + A = ustrip(set_A(std,t,tol)) + H=U\A*unit(1/t[1]) - println("set_P") - @time set_P(std, t, H, tol) + set_P(std, t, H, tol) # set the output set_prop!(std, :cls, cls) From 4fb3cdad1d0c43c2c04e680801d316d2b850b944 Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Wed, 30 Aug 2023 13:41:02 +0200 Subject: [PATCH 49/56] Adjustment to integration of probability function, added tests --- src/form/semi_markov_process.jl | 108 +++++++++++++------------------- test/runtests.jl | 1 + test/semi_markov_process.jl | 43 ++++++++++--- 3 files changed, 79 insertions(+), 73 deletions(-) diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index e45aea1..c27b529 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -96,38 +96,6 @@ function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t: end end end - # lb = Int(floor(cquantile(dst, tol*1e-3) / dt)) - # for (ni,nt) in enumerate(t) - # if ni <= lb - # Φ = nt:-dt:t[1] - # # Φ represents the sojourn time - # lt = t[1]:dt:nt - # # lt is the last transition time - # NΦ = length(Φ) - # for nj in 1:NΦ - # push!(I, Ns * (ni-1) + _LG.dst(tr)) - # push!(J, Ns * (nj-1) + _LG.src(tr)) - # push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) - # if isnan(V[end]) - # V[end] = 0.0 - # end - # end - # else - # Φ = nt:-dt:t[1] - # # Φ represents the sojourn time - # lt = t[1]:dt:nt - # # lt is the last transition time - # NΦ = length(lt) - # for nj in NΦ:-1:NΦ-lb - # push!(I, Ns * (ni-1) + _LG.dst(tr)) - # push!(J, Ns * (nj-1) + _LG.src(tr)) - # push!(V,- dt * weights(NΦ, nj) * (pdf(dst, Φ[nj], lt[nj]) |> unit(dt)^-1)) - # if isnan(V[end]) - # V[end] = 0.0 - # end - # end - # end - # end end function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; @@ -136,7 +104,6 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; dt = dt |> unit(tsim) t = zero(dt):dt:tsim - # solve the problem U = set_U(std,t,tol) A = ustrip(set_A(std,t,tol)) @@ -153,16 +120,55 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; end +# function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) +# Nt = length(t) + +# for st in states(std) +# dst_v = [get_prop(std, _LG.Edge(st,nx),:distr) for nx in _LG.outneighbors(std.graph, st)] +# init = get_prop(std, st, :init) +# h = map(x->H[ns(std) * (x-1) + st], 1:Nt) +# p = set_int(std, st, dst_v, t, h, init, tol) +# set_prop!(std, st, :prob, p) +# end +# end + function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) + dt = step(t) Nt = length(t) - for st in states(std) dst_v = [get_prop(std, _LG.Edge(st,nx),:distr) for nx in _LG.outneighbors(std.graph, st)] init = get_prop(std, st, :init) - h = map(x->H[ns(std) * (x-1) + st], 1:Nt) - p = set_int(std, st, dst_v, t, h, init, tol) + + if init > 0.0 + p = init .* ccdf.(std, st, t, zero(t[1])) .+ num_integral(std, dst_v, t, dt, st, H, tol) + else + p = num_integral(std, dst_v, t, dt, st, H, tol) + end set_prop!(std, st, :prob, p) - end + end +end + +function num_integral(std::AbstractSTD, dst_v::Vector, t::StepRangeLen, dt::Quantity, st::Int, H::Vector, tol::Real) + Φ = Float64[] + if isempty(dst_v) + for (ni,nt) in enumerate(t) + l = t[1]:dt:nt + push!(Φ, sum(dt .* weights(ni, nj) .* H[ns(std) * (nj-1) + st] + for (nj,nl) in enumerate(l))) + end + else + for (ni,nt) in enumerate(t) + l = t[1]:dt:nt + push!(Φ, sum(dt .* weights(ni, nj) .* H[ns(std) * (nj-1) + st] + for (nj,nl) in enumerate(l))) + for dst in dst_v + Φ[ni] -= sum(dt .* weights(ni, nj) .* H[ns(std) * (nj-1) + st] .* + cdf(dst, nt-nl, nl) + for (nj,nl) in enumerate(l)) + end + end + end + return Φ end function set_int(std, st, dst_v, t, h, init, tol) @@ -195,31 +201,3 @@ elunit(A::Matrix{U}) where U = _UF.unit(U) elunit(b::Vector{U}) where U = _UF.unit(U) _LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = (ustrip.(A) \ ustrip(b)) * (elunit(b) / elunit(A)) - - -function integral(dst_v::Vector, t::StepRangeLen, h::Vector, tol::Real) - d2h = abs.(diff(diff(ustrip(h)))) - id = 1 - idx = Int[1] - reltol = maximum(ustrip(h))*tol - # reltol = (maximum(d2h)-Base.minimum(d2h))*tol - - while true - next_id = findfirst(x -> x > reltol, cumsum(d2h[id:end])) - next_id == nothing ? break : ~ ; - - id += next_id - push!(idx,id) - end - push!(idx,length(d2h)+2) - τ = t[idx] - γ = _INT.interpolate((τ,), h[idx], _INT.Gridded(_INT.Linear())) - if isempty(dst_v) - ϕ = [_QGK.quadgk(x -> γ(x), t[1], nτ, rtol=tol)[1] for nτ in τ] - else - ϕ = [_QGK.quadgk(x -> γ(x), t[1], nτ, rtol = tol)[1] for nτ in τ] .- - sum([_QGK.quadgk(x -> γ(x) * cdf(dst, nτ-x, x), t[1], nτ, rtol=tol)[1] for nτ in τ] for dst in dst_v) - end - p = _INT.LinearInterpolation(τ, ϕ)(t) - return p -end diff --git a/test/runtests.jl b/test/runtests.jl index e147a08..d7580af 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -11,6 +11,7 @@ using Test using Unitful using Measurements using AdditionalUnits +using QuadGK using MultiStateSystems # pkg const diff --git a/test/semi_markov_process.jl b/test/semi_markov_process.jl index 9632cbd..d266ee1 100644 --- a/test/semi_markov_process.jl +++ b/test/semi_markov_process.jl @@ -13,26 +13,53 @@ # of LVDC systems with integrated battery storage stdᶜᵃᵖ = include(joinpath(_MSS.BASE_DIR,"test/elements/CAP_ac.jl")) - solve!(stdᶜᵃᵖ, MarkovProcess(), tsim = 2.0u"yr") + solve!(stdᶜᵃᵖ, MarkovProcess(), tsim = 1.0u"yr") prb_m = [np[end] for np in _MSS.get_sprop(stdᶜᵃᵖ, :prob)] - solve!(stdᶜᵃᵖ, SemiMarkovProcess(), tsim = 2.0u"yr") + solve!(stdᶜᵃᵖ, SemiMarkovProcess(), tsim = 1.0u"yr") prb_s = [np[end] for np in _MSS.get_sprop(stdᶜᵃᵖ, :prob)] - @test isapprox(sum(prb_s), 1.0, rtol=1e-6) - @test all(isapprox.(prb_m, prb_s, rtol=1e-6)) + @test isapprox(sum(prb_s), 1.0, rtol=1e-5) + @test all(isapprox.(prb_m, prb_s, rtol=1e-5)) end @testset "Optical Monitoring System" begin # Example considering a multi-state Markov model for an optical monitoring system # taken from: - # > A Multi-State Markov Model for a Short-Term Reliability Analysis of a Power - # Generating Unit by A. Lisnianski, D. Elmakias, and H. Ben Haim (2012) + # > Mathematical formulation and numerical treatment based on transition frequency + # densities and quadrature methods for non-homogeneous semi-Markov processes by + # M. das Chagas Moura, and E. L. Droguett (2009) stdᵒᵐˢ = include(joinpath(_MSS.BASE_DIR,"test/elements/optical_monitoring_system.jl")) - solve!(stdᵒᵐˢ, SemiMarkovProcess(), tsim = 1.0u"yr") + solve!(stdᵒᵐˢ, SemiMarkovProcess(), tsim = 8760.0u"hr") prb_oms = [np[end] for np in _MSS.get_sprop(stdᵒᵐˢ, :prob)] - @test isapprox(sum(prb_oms), 1.0, rtol=1e-6) + @test isapprox(sum(prb_oms), 1.0, rtol=1e-4) + @test isapprox(prb_oms[1], 0.8846075098143418, rtol = 1e-5) + @test isapprox(prb_oms[2], 0.003709508099739578, rtol = 1e-5) + @test isapprox(prb_oms[3], 0.001238170881240272, rtol = 1e-5) + @test isapprox(prb_oms[4], 0.11045656347369365, rtol = 1e-5) end + @testset "Semi-Analytical Example" begin + # A semi-analytical example example of a multi-state semi-Markov model + # taken from: + # > Mathematical formulation and numerical treatment based on transition frequency + # densities and quadrature methods for non-homogeneous semi-Markov processes by + # M. das Chagas Moura, and E. L. Droguett (2009) + stdˢᵃ = include(joinpath(_MSS.BASE_DIR,"test/elements/semi_analytical_example.jl")) + solve!(stdˢᵃ, SemiMarkovProcess(), tsim = 4500.0u"hr", dt = 1.0u"hr") + prb_sa = [np[end] for np in _MSS.get_sprop(stdˢᵃ, :prob)] + + # analytical solution + dt = 3.0u"hr" + tsim = 4500.0u"hr" + t = 0u"hr":dt:tsim + dst1 = _MSS.Exponential(1000.0u"hr") + dst2 = _MSS.Weibull(250.0u"hr", 1.5) + PA1 = 1.0 .- _MSS.cdf.(dst1,t,t) + PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,x) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] + + @test isapprox(sum(prb_sa), 1.0, rtol=1e-4) + @test isapprox(prb_sa[1]+prb_sa[2], PA1[end]+PA2[end], rtol = 1e-5) + end end From ffd87a8ac6626d675080f7ea9b1c7e5f6ba9f71a Mon Sep 17 00:00:00 2001 From: timmyfaraday Date: Thu, 14 Sep 2023 14:01:39 +0200 Subject: [PATCH 50/56] update of the pkg environment --- Project.toml | 19 +++---- .../semi-markov/optical-monitoring-system.jl | 1 - examples/semi-markov/semi-analytical.jl | 8 +-- src/MultiStateSystems.jl | 3 +- src/core/types.jl | 6 +-- src/form/markov_process.jl | 36 ++++++------- src/form/semi_markov_process.jl | 16 +++--- src/form/steady_state_process.jl | 2 +- src/io/network.jl | 8 +-- src/io/state_transition_diagram.jl | 50 +++++++++---------- test/elements/CAP_ac.jl | 1 - 11 files changed, 74 insertions(+), 76 deletions(-) diff --git a/Project.toml b/Project.toml index 4f6089e..d259bc6 100644 --- a/Project.toml +++ b/Project.toml @@ -5,8 +5,8 @@ version = "0.1.2" [deps] AdditionalUnits = "02d9b4f0-7821-44c6-acbd-01a1ab91b72e" +Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6" Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59" -LightGraphs = "093fc24a-ae57-5d10-9952-331d41423f4d" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7" Multigraphs = "7ebac608-6c66-46e6-9856-b5f43e107bac" @@ -17,14 +17,15 @@ SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" [compat] -AdditionalUnits = "0.1.2" -LightGraphs = "1.3.5" -Measurements = "2.6.0" -Multigraphs = "0.2.2" -OrdinaryDiffEq = "5.59.4" -QuadGK = "2.4.2" -SpecialFunctions = "1.8.4" -Unitful = "1.8.0" +AdditionalUnits = "0.1.4" +Graphs = "1.8.0" +Interpolations = "0.14.7" +Measurements = "2.9.0" +Multigraphs = "0.3.0" +OrdinaryDiffEq = "6.55.0" +QuadGK = "2.8.2" +SpecialFunctions = "2.3.1" +Unitful = "1.17.0" julia = "1" [extras] diff --git a/examples/semi-markov/optical-monitoring-system.jl b/examples/semi-markov/optical-monitoring-system.jl index 952ffbf..a6fd981 100644 --- a/examples/semi-markov/optical-monitoring-system.jl +++ b/examples/semi-markov/optical-monitoring-system.jl @@ -22,7 +22,6 @@ States: # load pkgs using Unitful using MultiStateSystems -using Revise using Plots # pkg const diff --git a/examples/semi-markov/semi-analytical.jl b/examples/semi-markov/semi-analytical.jl index 168148a..d2f0d69 100644 --- a/examples/semi-markov/semi-analytical.jl +++ b/examples/semi-markov/semi-analytical.jl @@ -23,12 +23,12 @@ using Plots using Unitful using UnitfulRecipes using MultiStateSystems -using LightGraphs +using Graphs using QuadGK # pkg const const _MSS = MultiStateSystems -const _LG = LightGraphs +const Graphs = Graphs # constants dt = 0.1u"hr" @@ -69,8 +69,8 @@ _MSS.set_info!(std, 3, :trapping, true) # # solve the std - Analytical dτ = dt / 10 -dst1 = _MSS.get_prop(std,_LG.Edge(1,2),:distr) -dst2 = _MSS.get_prop(std,_LG.Edge(2,3),:distr) +dst1 = _MSS.get_prop(std,Graphs.Edge(1,2),:distr) +dst2 = _MSS.get_prop(std,Graphs.Edge(2,3),:distr) PA1 = 1.0 .- _MSS.cdf.(dst1,t,zero(dt)) PA2 = [quadgk(x -> _MSS.pdf.(dst1,x,zero(nt)) * (1.0 - _MSS.cdf(dst2,nt.-x,nt)),zero(nt),nt,rtol=1e-8)[1] for nt in t] diff --git a/src/MultiStateSystems.jl b/src/MultiStateSystems.jl index e6d21bf..ccf92f6 100644 --- a/src/MultiStateSystems.jl +++ b/src/MultiStateSystems.jl @@ -11,7 +11,7 @@ module MultiStateSystems # import pkgs import Base: maximum -import LightGraphs +import Graphs import LinearAlgebra import Multigraphs import OrdinaryDiffEq @@ -27,7 +27,6 @@ using AdditionalUnits # pkg const const _LA = LinearAlgebra -const _LG = LightGraphs const _MG = Multigraphs const _ODE = OrdinaryDiffEq const _UF = Unitful diff --git a/src/core/types.jl b/src/core/types.jl index d05e6c1..1a1e35c 100644 --- a/src/core/types.jl +++ b/src/core/types.jl @@ -13,16 +13,16 @@ abstract type AbstractInfo end abstract type AbstractDistribution{X,Y,Z} end -abstract type AbstractSTD{T} <: _LG.AbstractGraph{T} end +abstract type AbstractSTD{T} <: Graphs.AbstractGraph{T} end -abstract type AbstractNetwork{T} <: _LG.AbstractGraph{T} end +abstract type AbstractNetwork{T} <: Graphs.AbstractGraph{T} end abstract type AbstractStochasticProcess end abstract type AbstractMarkovProcess <: AbstractStochasticProcess end abstract type AbstractSemiMarkovProcess <: AbstractStochasticProcess end # union types -UIE = Union{Int,_LG.AbstractEdge} +UIE = Union{Int,Graphs.AbstractEdge} Single = Union{Bool,Number,String,Symbol,AbstractSTD,Tuple} # dict types diff --git a/src/form/markov_process.jl b/src/form/markov_process.jl index 847b2f7..ed799e1 100644 --- a/src/form/markov_process.jl +++ b/src/form/markov_process.jl @@ -27,37 +27,37 @@ end # stochastic process function homogeneous_markov_process(du, u, p, t) G, ρ, info = p - for ns in 1:_LG.nv(G) - if isempty(_LG.outneighbors(G,ns)) - du[ns] = sum(ρ[_LG.Edge(nt,ns)]*u[nt] - for nt in _LG.inneighbors(G,ns) + for ns in 1:Graphs.nv(G) + if isempty(Graphs.outneighbors(G,ns)) + du[ns] = sum(ρ[Graphs.Edge(nt,ns)]*u[nt] + for nt in Graphs.inneighbors(G,ns) if ns ≠ nt) - elseif isempty(_LG.inneighbors(G,ns)) - du[ns] = - sum(ρ[_LG.Edge(ns,nt)]*u[ns] - for nt in _LG.outneighbors(G,ns) + elseif isempty(Graphs.inneighbors(G,ns)) + du[ns] = - sum(ρ[Graphs.Edge(ns,nt)]*u[ns] + for nt in Graphs.outneighbors(G,ns) if ns ≠ nt) else - du[ns] = sum(ρ[_LG.Edge(nt,ns)]*u[nt] - for nt in _LG.inneighbors(G,ns) + du[ns] = sum(ρ[Graphs.Edge(nt,ns)]*u[nt] + for nt in Graphs.inneighbors(G,ns) if ns ≠ nt) - - sum(ρ[_LG.Edge(ns,nt)]*u[ns] - for nt in _LG.outneighbors(G,ns) + sum(ρ[Graphs.Edge(ns,nt)]*u[ns] + for nt in Graphs.outneighbors(G,ns) if ns ≠ nt) end end end function inhomogeneous_markov_process(du, u, p, t) G, ρ, info = p - for ns in 1:_LG.nv(G) + for ns in 1:Graphs.nv(G) if info[ns].trapping - du[ns] = sum(ρ[_LG.Edge(nt,ns)](t)*u[nt] - for nt in _LG.inneighbors(G,ns) + du[ns] = sum(ρ[Graphs.Edge(nt,ns)](t)*u[nt] + for nt in Graphs.inneighbors(G,ns) if ns ≠ nt) else - du[ns] = sum(ρ[_LG.Edge(nt,ns)](t)*u[nt] - for nt in _LG.inneighbors(G,ns) + du[ns] = sum(ρ[Graphs.Edge(nt,ns)](t)*u[nt] + for nt in Graphs.inneighbors(G,ns) if ns ≠ nt) - - sum(ρ[_LG.Edge(ns,nt)](t)*u[ns] - for nt in _LG.outneighbors(G,ns) + sum(ρ[Graphs.Edge(ns,nt)](t)*u[ns] + for nt in Graphs.outneighbors(G,ns) if ns ≠ nt) end end end diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index c27b529..25db535 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -27,10 +27,10 @@ function set_A(std::AbstractSTD, t::StepRangeLen, tol::Real) A = zeros(typeof(1/dt), ns(std) * Nt) for tr in transitions(std) - init = get_prop(std, _LG.src(tr), :init) + init = get_prop(std, Graphs.src(tr), :init) if init > 0.0 dst = get_prop(std, tr, :distr) - idx = _LG.dst(tr) + idx = Graphs.dst(tr) lb = floor(cquantile(dst, tol*1e-3) / dt) * dt _fill_A!(std, t, A, idx, dst, init, lb) end @@ -43,7 +43,7 @@ function _fill_A!(std, t, A, idx, dst, init, lb) if nt <= lb id = ns(std) * (ni-1) + idx # The content of the A-vector is the probability of initially being - # in state (_LG.src(tr)) times the probability of transitioning out + # in state (Graphs.src(tr)) times the probability of transitioning out # of that state entered at sojourn time zero and evaluated at # time t = (nt) A[id] += init * pdf(dst, nt, zero(t[1])) @@ -81,15 +81,15 @@ function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) return _SA.sparse(I, J, V) end -function _fill_U!(tr::LightGraphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t::StepRangeLen, Ns::Int, dst::AbstractDistribution, I::Vector, J::Vector, V::Vector, tol::Real) +function _fill_U!(tr::Graphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t::StepRangeLen, Ns::Int, dst::AbstractDistribution, I::Vector, J::Vector, V::Vector, tol::Real) id_lb, id_ub = Int(ceil(quantile(dst, tol*1e-3) / dt)), Int(floor(cquantile(dst, tol*1e-3) / dt)) for (ni,nt) in enumerate(t) φ = nt:-dt:t[1] lt = reverse(φ) idx = ni-id_lb+1:-1:max(1,ni-id_ub) for id in idx - push!(I, Ns * (ni-1) + _LG.dst(tr)) - push!(J, Ns * (id-1) + _LG.src(tr)) + push!(I, Ns * (ni-1) + Graphs.dst(tr)) + push!(J, Ns * (id-1) + Graphs.src(tr)) push!(V,- dt * weights(ni, id) * (pdf(dst, φ[id], lt[id]) |> unit(dt)^-1)) if isnan(V[end]) V[end] = 0.0 @@ -124,7 +124,7 @@ end # Nt = length(t) # for st in states(std) -# dst_v = [get_prop(std, _LG.Edge(st,nx),:distr) for nx in _LG.outneighbors(std.graph, st)] +# dst_v = [get_prop(std, Graphs.Edge(st,nx),:distr) for nx in Graphs.outneighbors(std.graph, st)] # init = get_prop(std, st, :init) # h = map(x->H[ns(std) * (x-1) + st], 1:Nt) # p = set_int(std, st, dst_v, t, h, init, tol) @@ -136,7 +136,7 @@ function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) dt = step(t) Nt = length(t) for st in states(std) - dst_v = [get_prop(std, _LG.Edge(st,nx),:distr) for nx in _LG.outneighbors(std.graph, st)] + dst_v = [get_prop(std, Graphs.Edge(st,nx),:distr) for nx in Graphs.outneighbors(std.graph, st)] init = get_prop(std, st, :init) if init > 0.0 diff --git a/src/form/steady_state_process.jl b/src/form/steady_state_process.jl index f03c13a..fbb739c 100644 --- a/src/form/steady_state_process.jl +++ b/src/form/steady_state_process.jl @@ -17,7 +17,7 @@ function set_markov_chain_matrix!(std::AbstractSTD, cls::SteadyStateProcess) P = zeros(_MSM.Measurement, ns(std), ns(std)) for nt in transitions(std) rate = get_prop(std, nt, :rate) - P[_LG.src(nt),_LG.dst(nt)] = + P[Graphs.src(nt),Graphs.dst(nt)] = ifelse(_UF.unit(rate)==_UF.NoUnits, rate, rate * 1.0u"s" |> u"s/s") end for ns in 1:ns(std) diff --git a/src/io/network.jl b/src/io/network.jl index b0eb3bb..0bfc65d 100644 --- a/src/io/network.jl +++ b/src/io/network.jl @@ -80,14 +80,14 @@ update_lib!(type::Symbol,array::Array,lib::Dict) = haskey(lib,array[end][type]) ? push!(lib[array[end][type]],length(array)) : lib[array[end][type]] = [length(array)] ; -weights(ntw::AbstractNetwork) = _LG.weights(ntw.graph) +weights(ntw::AbstractNetwork) = Graphs.weights(ntw.graph) has_path(ntw::AbstractNetwork, s_node::Int, u_node::Int) = - _LG.has_path(ntw.graph, s_node, u_node) + Graphs.has_path(ntw.graph, s_node, u_node) max_paths(graph::_MG.DiMultigraph) = _MG.nv(graph) + _MG.ne(graph, count_mul = true) nodal_paths(graph::_MG.DiMultigraph, s_node::Int, u_node::Int) = - sort(_LG.yen_k_shortest_paths(graph, s_node, u_node, - _LG.weights(graph), max_paths(graph)).paths) + sort(Graphs.yen_k_shortest_paths(graph, s_node, u_node, + Graphs.weights(graph), max_paths(graph)).paths) mul_path(graph::_MG.DiMultigraph, npath::Array{Int,1}) = [1:mul_edge(graph,(npath[ni],npath[ni+1])) for ni in 1:length(npath)-1] diff --git a/src/io/state_transition_diagram.jl b/src/io/state_transition_diagram.jl index 077711e..e64e672 100644 --- a/src/io/state_transition_diagram.jl +++ b/src/io/state_transition_diagram.jl @@ -9,20 +9,20 @@ ## State-Transition Diagram # structs struct STD{I<:Int} <: AbstractSTD{I} - graph::_LG.DiGraph{I} + graph::Graphs.DiGraph{I} props::PropDict sprops::Dict{I,PropDict} - tprops::Dict{_LG.Edge{I},PropDict} + tprops::Dict{Graphs.Edge{I},PropDict} end # constructors function STD(Ns::Int) - graph = _LG.DiGraph(Ns) + graph = Graphs.DiGraph(Ns) props = PropDict(:info => STDInfo()) sprops = Dict{Int,PropDict}(ns => PropDict() for ns in 1:Ns) - tprops = Dict{_LG.Edge{Int},PropDict}() + tprops = Dict{Graphs.Edge{Int},PropDict}() return STD(graph, props, sprops, tprops) end @@ -92,11 +92,11 @@ julia> stdᵍᵉⁿ = STD() ``` """ function STD() - graph = _LG.DiGraph() + graph = Graphs.DiGraph() props = PropDict(:info => STDInfo()) sprops = Dict{Int,PropDict}() - tprops = Dict{_LG.Edge{Int},PropDict}() + tprops = Dict{Graphs.Edge{Int},PropDict}() return STD(graph, props, sprops, tprops) end @@ -108,7 +108,7 @@ is_directed(std::STD) = true props(std::AbstractSTD) = std.props props(std::AbstractSTD, s::Int) = get(std.sprops, s, PropDict()) -props(std::AbstractSTD, t::_LG.Edge) = get(std.tprops, t, PropDict()) +props(std::AbstractSTD, t::Graphs.Edge) = get(std.tprops, t, PropDict()) get_prop(std::AbstractSTD, prop::Symbol) = haskey(props(std), prop) ? props(std)[prop] : ~ ; @@ -118,8 +118,8 @@ set_prop!(std::AbstractSTD, prop::Symbol, value) = set_props!(std::AbstractSTD, dict::Dict) = merge!(std.props, dict) ccdf(std::AbstractSTD, ns::Int, φ::Quantity, t::Quantity) = - 1.0 - sum(cdf(get_prop(std, _LG.Edge(ns,nx),:distr), φ, t) - for nx in _LG.outneighbors(std.graph, ns); init = 0.0) + 1.0 - sum(cdf(get_prop(std, Graphs.Edge(ns,nx),:distr), φ, t) + for nx in Graphs.outneighbors(std.graph, ns); init = 0.0) ccdf(dst_v::Vector, φ::Quantity, t::Quantity) = 1.0 - sum(cdf(dst, φ, t) for dst in dst_v; init = 0.0) @@ -158,17 +158,17 @@ get_info(std::AbstractSTD, ns::Int, info::Symbol) = getproperty(std.sprops[ns][:info],info) set_info!(std::AbstractSTD, ns::Int, info::Symbol, value::Bool) = setproperty!(std.sprops[ns][:info],info,value) -get_info(std::AbstractSTD, nt::_LG.Edge, info::Symbol) = +get_info(std::AbstractSTD, nt::Graphs.Edge, info::Symbol) = getproperty(std.tprops[nt][:info],info) -set_info!(std::AbstractSTD, nt::_LG.Edge, info::Symbol, value::Bool) = +set_info!(std::AbstractSTD, nt::Graphs.Edge, info::Symbol, value::Bool) = setproperty!(std.tprops[nt][:info],info,value) ## State # functions -ns(std::AbstractSTD) = _LG.nv(std.graph) -states(std::AbstractSTD) = _LG.vertices(std.graph) -add_vertex!(std::AbstractSTD) = _LG.add_vertex!(std.graph) -has_vertex(std::AbstractSTD, x...) = _LG.has_vertex(std.graph, x...) +ns(std::AbstractSTD) = Graphs.nv(std.graph) +states(std::AbstractSTD) = Graphs.vertices(std.graph) +add_vertex!(std::AbstractSTD) = Graphs.add_vertex!(std.graph) +has_vertex(std::AbstractSTD, x...) = Graphs.has_vertex(std.graph, x...) get_sprop(std::AbstractSTD, prop::Symbol) = [get_prop(std, ns, prop) for ns in states(std)] @@ -236,19 +236,19 @@ end ## Transition # functions -nt(std::AbstractSTD) = _LG.ne(std.graph) -transitions(std::AbstractSTD) = _LG.edges(std.graph) -has_edge(std::AbstractSTD, x...) = _LG.has_edge(std.graph, x...) -add_edge!(std::AbstractSTD, x...) = _LG.add_edge!(std.graph, x...) +nt(std::AbstractSTD) = Graphs.ne(std.graph) +transitions(std::AbstractSTD) = Graphs.edges(std.graph) +has_edge(std::AbstractSTD, x...) = Graphs.has_edge(std.graph, x...) +add_edge!(std::AbstractSTD, x...) = Graphs.add_edge!(std.graph, x...) get_tprop(std::AbstractSTD, prop::Symbol) = Dict(nt => get_prop(std,nt,prop) for nt in transitions(std)) -get_prop(std::AbstractSTD, nt::_LG.Edge, prop::Symbol) = props(std,nt)[prop] -has_prop(std::AbstractSTD, nt::_LG.Edge, prop::Symbol) = +get_prop(std::AbstractSTD, nt::Graphs.Edge, prop::Symbol) = props(std,nt)[prop] +has_prop(std::AbstractSTD, nt::Graphs.Edge, prop::Symbol) = haskey(props(std,nt), prop) -set_prop!(std::AbstractSTD, nt::_LG.Edge, prop::Symbol, value::Any) = +set_prop!(std::AbstractSTD, nt::Graphs.Edge, prop::Symbol, value::Any) = set_props!(std,nt,Dict{Symbol,Any}(prop => value)) -set_props!(std::AbstractSTD, nt::_LG.Edge, prop_dict::Dict) = +set_props!(std::AbstractSTD, nt::Graphs.Edge, prop_dict::Dict) = haskey(std.tprops,nt) ? merge!(std.tprops[nt],prop_dict) : std.tprops[nt] = prop_dict ; @@ -273,14 +273,14 @@ julia> add_transition!(stdᵍᵉⁿ, rate = 0.001u"1/hr", function add_transition!(std::AbstractSTD; kwargs...) test(kwargs) || return false haskey(kwargs,:states) || return false - edge = _LG.Edge(kwargs[:states]) + edge = Graphs.Edge(kwargs[:states]) add_edge!(std, edge) || return false set_prop!(std, edge, :info, TransInfo()) # TODO auto capture info prop set_props!(std, edge, Dict(kwargs...)) return true end function add_transition!(std::AbstractSTD, crd::Tuple{Int,Int}, prop_dict::Dict) - edge = _LG.Edge(crd) + edge = Graphs.Edge(crd) add_edge!(std, edge) || return false set_prop!(std, edge, :info, TransInfo()) # TODO auto capture info prop set_props!(std, edge, prop_dict) diff --git a/test/elements/CAP_ac.jl b/test/elements/CAP_ac.jl index e0bd8d6..b9fa80f 100644 --- a/test/elements/CAP_ac.jl +++ b/test/elements/CAP_ac.jl @@ -9,7 +9,6 @@ # load pkgs using Unitful using MultiStateSystems -using Revise const _MSS = MultiStateSystems From 35fdab0784d166d9c4e568639fc273a63c422275 Mon Sep 17 00:00:00 2001 From: timmyfaraday Date: Wed, 27 Sep 2023 18:08:55 +0200 Subject: [PATCH 51/56] rewrite of semi-markov model --- .vscode/settings.json | 1 + src/form/semi_markov_process.jl | 248 +++++++++++++------------------- src/io/utils.jl | 11 +- 3 files changed, 109 insertions(+), 151 deletions(-) create mode 100644 .vscode/settings.json diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..9e26dfe --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1 @@ +{} \ No newline at end of file diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 25db535..2c2f5d3 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -12,192 +12,140 @@ mutable struct SemiMarkovProcess <: AbstractSemiMarkovProcess end # properties const semi_markov_process_props = [:renewal, :dynamic] -""" - MultiStateSystems.set_A(std::MultiStateSystems.AbstractSTD, t::StepRangeLen) - -A indicates that state j can be reached if the process was initially in state i -and remains there until time t. - -The unit of A is [unit(1/t)] -""" -function set_A(std::AbstractSTD, t::StepRangeLen, tol::Real) +# stochastic process +# A indicates that state j can be reached if the process was initially in +# state i and remains there until time t. The unit of A is [unit(1/t)] +function get_A(std::AbstractSTD, t::StepRangeLen, tol::Real) dt = step(t) + Ns = ns(std) Nt = length(t) - A = zeros(typeof(1/dt), ns(std) * Nt) + A = zeros(typeof(1/dt), Ns*Nt) for tr in transitions(std) - init = get_prop(std, Graphs.src(tr), :init) - if init > 0.0 - dst = get_prop(std, tr, :distr) - idx = Graphs.dst(tr) - lb = floor(cquantile(dst, tol*1e-3) / dt) * dt - _fill_A!(std, t, A, idx, dst, init, lb) - end + dst = get_prop(std, tr, :distr) + fr, to = Graphs.src(tr), Graphs.dst(tr) + init = get_prop(std, fr, :init) + + init > 0.0 ? _fill_A!(to, init, Ns, tol, dst, t, A) : ~ ; end + return A end +function _fill_A!(to::Int, init::Real, Ns::Int, tol::Real, + dst::AbstractDistribution, t::StepRangeLen, A::Vector) + dt = step(t) + lb, ub = quantile(dst, tol) - dt, cquantile(dst, tol) + dt + + for (ni,nt) in enumerate(t) if lb <= nt <= ub + id = Ns * (ni-1) + to -function _fill_A!(std, t, A, idx, dst, init, lb) - for (ni,nt) in enumerate(t) - if nt <= lb - id = ns(std) * (ni-1) + idx - # The content of the A-vector is the probability of initially being - # in state (Graphs.src(tr)) times the probability of transitioning out - # of that state entered at sojourn time zero and evaluated at - # time t = (nt) - A[id] += init * pdf(dst, nt, zero(t[1])) - if isnan(A[id]) - A[id] = zero(1/t[1]) - end + A[id] += init * pdf(dst, nt, zero(dt)) + isnan(A[id]) ? A[id] = zero(1/dt) : ~ ; end end end - - -""" - MultiStateSystems.set_U(std::MultiStateSystems.AbstractSTD, t::StepRangeLen) - -U indicates that state j can be reached if the process enters state i at time φ -and remains there until time t - -The unit of U is [-] -""" - -function set_U(std::AbstractSTD, t::StepRangeLen, tol::Real) - dt = step(t) - Nt = length(t) +# U indicates that state j can be reached if the process enters state i at +# sojourn time φ and remains there until calendar time t. The unit of U is [-] +function get_U(std::AbstractSTD, t::StepRangeLen, tol::Real) Ns = ns(std) - # initialize three vectors I,J,V respectively row, column and value indices - I,J,V = Int[],Int[],Float64[] + Nt = length(t) - append!(I, 1:Ns*Nt) - append!(J, 1:Ns*Nt) - append!(V, ones(Float64,Ns*Nt)) + I, J, V = Int[1:Ns*Nt;], Int[1:Ns*Nt;], ones(Float64,Ns*Nt) for tr in transitions(std) - dst = get_prop(std, tr, :distr) - _fill_U!(tr, dt, t, Ns, dst, I, J, V, tol) + dst = get_prop(std, tr, :distr) + fr, to = Graphs.src(tr), Graphs.dst(tr) + + _fill_U!(fr, to, Ns, tol, dst, t, I, J, V) end + return _SA.sparse(I, J, V) end +function _fill_U!(fr::Int, to::Int, Ns::Int, tol::Real, dst::AbstractDistribution, + t::StepRangeLen, I::Vector, J::Vector, V::Vector) + dt = step(t) + lb, ub = quantile(dst, tol) - dt, cquantile(dst, tol) + dt -function _fill_U!(tr::Graphs.SimpleGraphs.SimpleEdge{Int64}, dt::Number, t::StepRangeLen, Ns::Int, dst::AbstractDistribution, I::Vector, J::Vector, V::Vector, tol::Real) - id_lb, id_ub = Int(ceil(quantile(dst, tol*1e-3) / dt)), Int(floor(cquantile(dst, tol*1e-3) / dt)) for (ni,nt) in enumerate(t) - φ = nt:-dt:t[1] - lt = reverse(φ) - idx = ni-id_lb+1:-1:max(1,ni-id_ub) - for id in idx - push!(I, Ns * (ni-1) + Graphs.dst(tr)) - push!(J, Ns * (id-1) + Graphs.src(tr)) - push!(V,- dt * weights(ni, id) * (pdf(dst, φ[id], lt[id]) |> unit(dt)^-1)) - if isnan(V[end]) - V[end] = 0.0 - end - end + φ = nt:-dt:t[1] + τ = reverse(φ) + + for (nj,nφ) in enumerate(φ) if lb <= nφ <= ub + push!(I, Ns * (ni-1) + to) + push!(J, Ns * (nj-1) + fr) + push!(V, -dt * weights(ni,nj) * (pdf(dst, nφ, τ[nj]) |> unit(1/dt))) + isnan(V[end]) ? V[end] = 0.0 : ~ ; + end end end end +# p indicates the probability of being in a state i at calendar time t. The unit +# of p is [-]. +function set_p!(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) + Ns = ns(std) + Nt = length(t) -function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; - tsim::Number=1.0u"yr", dt::Number=4u"hr", tol::Real=1e-8) - # get the input - dt = dt |> unit(tsim) - t = zero(dt):dt:tsim - - # solve the problem - U = set_U(std,t,tol) - A = ustrip(set_A(std,t,tol)) - H=U\A*unit(1/t[1]) - - set_P(std, t, H, tol) - - # set the output - set_prop!(std, :cls, cls) - set_prop!(std, :time, t) + for st in states(std) + h = map(x -> H[Ns * (x-1) + st], 1:Nt) + init = get_prop(std, st, :init) + DST = [get_prop(std, Graphs.Edge(st,nx), :distr) + for nx in Graphs.outneighbors(std.graph, st)] - # set the solved status - set_info!(std, :solved, true) + _set_p!(std, st, init, tol, DST, t, h) + end end - - -# function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) -# Nt = length(t) - -# for st in states(std) -# dst_v = [get_prop(std, Graphs.Edge(st,nx),:distr) for nx in Graphs.outneighbors(std.graph, st)] -# init = get_prop(std, st, :init) -# h = map(x->H[ns(std) * (x-1) + st], 1:Nt) -# p = set_int(std, st, dst_v, t, h, init, tol) -# set_prop!(std, st, :prob, p) -# end -# end - -function set_P(std::AbstractSTD, t::StepRangeLen, H::Vector, tol::Real) +# p = init ⋅ ccdf(st) + ∫ h dt - ∑ᵢ ∫ h ⋅ cdf(dstᵢ) dt +# p = init - ∑ᵢ init * cdf(dstᵢ) + ∫ h dt - ∑ᵢ ∫ h ⋅ cdf(dstᵢ) dt +# p = init + ∫ h dt - ∑ᵢ init ⋅ cdf(dstᵢ) + ∫ h ⋅ cdf(dstᵢ) dt +function _set_p!(std::AbstractSTD, st::Int, init::Real, tol::Real, DST::Vector, + t::StepRangeLen, h::Vector) dt = step(t) - Nt = length(t) - for st in states(std) - dst_v = [get_prop(std, Graphs.Edge(st,nx),:distr) for nx in Graphs.outneighbors(std.graph, st)] - init = get_prop(std, st, :init) - - if init > 0.0 - p = init .* ccdf.(std, st, t, zero(t[1])) .+ num_integral(std, dst_v, t, dt, st, H, tol) - else - p = num_integral(std, dst_v, t, dt, st, H, tol) - end - set_prop!(std, st, :prob, p) + + p = init .+ [sum(dt * weights(ni,nj) * h[nj] for nj in 1:ni) + for (ni,nt) in enumerate(t)] + for dst in DST + _fill_p!(init, dst, t, h, p) end + + set_prop!(std, st, :prob, p) end +function _fill_p!(init::Real, dst::AbstractDistribution, t::StepRangeLen, + h::Vector, p::Vector) + dt = step(t) -function num_integral(std::AbstractSTD, dst_v::Vector, t::StepRangeLen, dt::Quantity, st::Int, H::Vector, tol::Real) - Φ = Float64[] - if isempty(dst_v) + if init > 0 for (ni,nt) in enumerate(t) - l = t[1]:dt:nt - push!(Φ, sum(dt .* weights(ni, nj) .* H[ns(std) * (nj-1) + st] - for (nj,nl) in enumerate(l))) + τ = t[1]:dt:nt + + p[ni] -= init * cdf(dst, nt, t[1]) + p[ni] -= sum(dt * weights(ni,nj) * h[nj] * cdf(dst, nt-nτ, nτ) + for (nj,nτ) in enumerate(τ)) end else for (ni,nt) in enumerate(t) - l = t[1]:dt:nt - push!(Φ, sum(dt .* weights(ni, nj) .* H[ns(std) * (nj-1) + st] - for (nj,nl) in enumerate(l))) - for dst in dst_v - Φ[ni] -= sum(dt .* weights(ni, nj) .* H[ns(std) * (nj-1) + st] .* - cdf(dst, nt-nl, nl) - for (nj,nl) in enumerate(l)) - end - end - end - return Φ -end + τ = t[1]:dt:nt -function set_int(std, st, dst_v, t, h, init, tol) - if init > 0.0 - p = init .* ccdf.(std, st, t, zero(t[1])) .+ integral(dst_v, t, h, tol) - else - p = integral(dst_v, t, h, tol) + p[ni] -= sum(dt * weights(ni,nj) * h[nj] * cdf(dst, nt-nτ, nτ) + for (nj,nτ) in enumerate(τ)) + end end - return p end +function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; + tsim::Number=1.0u"yr", dt::Number=4u"hr", tol::Real=1e-8) + # get the input + dt = dt |> unit(tsim) + t = zero(dt):dt:tsim + # solve the problem + U = get_U(std,t,tol) + A = ustrip(get_A(std,t,tol)) + H = U \ A * unit(1/dt) -""" - MultiStateSystems.weights(x::Int) - -Determine integration weights based on Simpson's rule. -w[1] and w[end] = 1/2, other weights = 1. -""" - -function weights(N::Int, p::Int) - if p == 1 || p == N - return 0.5 - else - return 1.0 - end -end + set_p!(std, t, H, tol) + + # set the output + set_prop!(std, :cls, cls) + set_prop!(std, :time, t) -# TOM: added functionality to enable \ with units. -elunit(A::Matrix{U}) where U = _UF.unit(U) -elunit(b::Vector{U}) where U = _UF.unit(U) -_LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = - (ustrip.(A) \ ustrip(b)) * (elunit(b) / elunit(A)) + # set the solved status + set_info!(std, :solved, true) +end \ No newline at end of file diff --git a/src/io/utils.jl b/src/io/utils.jl index eb06ded..0320474 100644 --- a/src/io/utils.jl +++ b/src/io/utils.jl @@ -67,4 +67,13 @@ reduce(kwargs::Iterators.Pairs, nc; excl=[]) = # UNITS """ Base.log(a::Quantity{T,D,U}) where T <: Real where D where U = log(a.val)unit(a) -Base.exp(a::Quantity{T,D,U}) where T <: Real where D where U = exp(a.val)unit(a) \ No newline at end of file +Base.exp(a::Quantity{T,D,U}) where T <: Real where D where U = exp(a.val)unit(a) + +elunit(A::Matrix{U}) where U = _UF.unit(U) +elunit(b::Vector{U}) where U = _UF.unit(U) +_LA.:\(A::Matrix{<:Number}, b::Vector{<:Number}) = (ustrip.(A) \ ustrip(b)) * (elunit(b) / elunit(A)) + +""" +# Integral +""" +weights(N::Int, p::Int) = p == 1 || p == N ? 0.5 : 1.0 ; \ No newline at end of file From d892cd6d21562c43f1ab4b25172c07f81e2df4df Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 22 Dec 2023 11:13:23 +0100 Subject: [PATCH 52/56] Adding the LVDC Battery system paper model as example to the github --- .../Pluto.jl_notebook/LVDC1.jl | 2414 + .../LVDC_Battery_systems/data/std_DCDC_40.csv | 43832 ++++++++++++++++ .../LVDC_Battery_systems/elements/CAP_L1.jl | 29 + .../LVDC_Battery_systems/elements/CAP_L2.jl | 28 + .../LVDC_Battery_systems/elements/CAP_ac.jl | 27 + .../LVDC_Battery_systems/elements/CAP_dc.jl | 28 + .../LVDC_Battery_systems/elements/acdc.jl | 26 + .../LVDC_Battery_systems/elements/battery.jl | 27 + .../elements/dcdc copy.jl | 30 + .../LVDC_Battery_systems/elements/dcdc.jl | 30 + .../LVDC_Battery_systems/elements/inv1.jl | 27 + .../LVDC_Battery_systems/elements/inv2.jl | 27 + .../LVDC_Battery_systems/elements/test.jl | 36 + .../LVDC_Battery_systems/elements_m/CAP_L1.jl | 29 + .../LVDC_Battery_systems/elements_m/CAP_L2.jl | 28 + .../LVDC_Battery_systems/elements_m/CAP_ac.jl | 27 + .../LVDC_Battery_systems/elements_m/CAP_dc.jl | 28 + .../LVDC_Battery_systems/elements_m/acdc.jl | 27 + .../elements_m/battery.jl | 27 + .../LVDC_Battery_systems/elements_m/dcdc.jl | 30 + .../LVDC_Battery_systems/elements_m/inv1.jl | 27 + .../LVDC_Battery_systems/elements_m/inv2.jl | 27 + .../networks/LVDC_grid_sm.jl | 100 + 23 files changed, 46911 insertions(+) create mode 100644 examples/LVDC_Battery_systems/Pluto.jl_notebook/LVDC1.jl create mode 100644 examples/LVDC_Battery_systems/data/std_DCDC_40.csv create mode 100644 examples/LVDC_Battery_systems/elements/CAP_L1.jl create mode 100644 examples/LVDC_Battery_systems/elements/CAP_L2.jl create mode 100644 examples/LVDC_Battery_systems/elements/CAP_ac.jl create mode 100644 examples/LVDC_Battery_systems/elements/CAP_dc.jl create mode 100644 examples/LVDC_Battery_systems/elements/acdc.jl create mode 100644 examples/LVDC_Battery_systems/elements/battery.jl create mode 100644 examples/LVDC_Battery_systems/elements/dcdc copy.jl create mode 100644 examples/LVDC_Battery_systems/elements/dcdc.jl create mode 100644 examples/LVDC_Battery_systems/elements/inv1.jl create mode 100644 examples/LVDC_Battery_systems/elements/inv2.jl create mode 100644 examples/LVDC_Battery_systems/elements/test.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/CAP_L1.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/CAP_L2.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/CAP_ac.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/CAP_dc.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/acdc.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/battery.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/dcdc.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/inv1.jl create mode 100644 examples/LVDC_Battery_systems/elements_m/inv2.jl create mode 100644 examples/LVDC_Battery_systems/networks/LVDC_grid_sm.jl diff --git a/examples/LVDC_Battery_systems/Pluto.jl_notebook/LVDC1.jl b/examples/LVDC_Battery_systems/Pluto.jl_notebook/LVDC1.jl new file mode 100644 index 0000000..80c76be --- /dev/null +++ b/examples/LVDC_Battery_systems/Pluto.jl_notebook/LVDC1.jl @@ -0,0 +1,2414 @@ +### A Pluto.jl notebook ### +# v0.19.32 + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═╡ 24e9a358-8387-42a4-9e38-47c3452a20af +using MultiStateSystems + +# ╔═╡ 57f41984-7f99-4b82-93d1-397d8cf80534 +using SpecialFunctions + +# ╔═╡ c56064ac-35d9-44d3-ad0c-87e6ee5d6bc1 +using Plots + +# ╔═╡ 5555e94d-6e98-4c6c-8d28-024fc337d97d +using Unitful + +# ╔═╡ da1eb8ad-a83d-4485-939e-cf264cf8e764 +using CSV + +# ╔═╡ 148e95ae-8ef4-458e-939a-16a27fd895f5 +using DataFrames + +# ╔═╡ 604ac5a0-0f72-4a9f-ae12-23865f842bb4 +using PlutoUI + +# ╔═╡ 30bfc652-de3d-47d1-bc93-ed4166cddecf +md""" +# Simulation variables + +Be careful when changing the simulation variables. These variables determine the calculation of the entire semi-Markov process. Changing them will cause these simulations to run again, which will take a lot of time and could impact the results! +""" + +# ╔═╡ 2c97acb4-9c6c-4f6e-95a6-1cae897dbbb2 +# Defining the simulation variables +begin + tsim = 40.0u"yr"; + dt = 8.0u"hr"; + t = zero(dt):dt:tsim .|> u"yr"; + const _MSS = MultiStateSystems + cls = SemiMarkovProcess() + cls1 = MarkovProcess() +end + +# ╔═╡ 73890b8b-c585-49bb-87f1-92e47f8da3a1 +stdᵃᶜᵈᶜ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/acdc.jl")); + +# ╔═╡ 8b4f434b-d1f3-4217-b439-c0c6ef547214 +stdⁱⁿᵛ¹ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/inv1.jl")); + +# ╔═╡ 7dfa474c-fb70-4d82-b2fa-26cfd71e6f56 +stdⁱⁿᵛ² = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/inv2.jl")); + +# ╔═╡ e9a896df-3443-48c6-a786-21538604ed43 +stdᶜᵃᵖᵃᶜ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/CAP_ac.jl")); + +# ╔═╡ cb5ae9ee-a1d4-42d0-add1-81a7249bfba5 +stdᶜᵃᵖᵈᶜ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/CAP_dc.jl")); + +# ╔═╡ c54d1e5a-ab14-4179-9e1d-a193c522ae52 +stdᶜᵃᵖᴸ¹ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/CAP_L1.jl")); + +# ╔═╡ 1e093c6c-2f2f-4fd6-9ddc-bec451728eb2 +stdᶜᵃᵖᴸ² = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/CAP_L2.jl")); + +# ╔═╡ c2dd4e66-ddb3-4928-86fb-e69ce603bfae +stdᵇᵃᵗ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements/battery.jl")); + +# ╔═╡ 1d4b223e-af9e-49f2-a3a8-f97da6fe4796 +stdmᵃᶜᵈᶜ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/acdc.jl")); + +# ╔═╡ 46ccc9eb-5a5a-49bc-8792-9dc98c96a47a +stdmᵈᶜᵈᶜ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/dcdc.jl")); + +# ╔═╡ 54ad935a-f5ab-4dde-bf33-b349c17efdca +stdmⁱⁿᵛ¹ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/inv1.jl")); + +# ╔═╡ a58db239-8ca1-4c0c-b97a-6be7ae4463b1 +stdmⁱⁿᵛ² = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/inv2.jl")); + +# ╔═╡ d394788d-8181-49ac-9b72-7ee8f5572b43 +stdmᶜᵃᵖᵃᶜ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/CAP_ac.jl")); + +# ╔═╡ 2b2736b4-4e3d-4fb0-b447-49e38b826e4a +stdmᶜᵃᵖᵈᶜ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/CAP_dc.jl")); + +# ╔═╡ c73cbbde-b4e9-44c6-ab24-dade0407706e +stdmᶜᵃᵖᴸ¹ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/CAP_L1.jl")); + +# ╔═╡ 4b852660-2472-452f-8c8b-5d959f9c56a8 +stdmᶜᵃᵖᴸ² = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/CAP_L2.jl")); + +# ╔═╡ 8331f4c9-9d5d-486a-9f24-8eece99a0596 +stdmᵇᵃᵗ = include(joinpath(_MSS.BASE_DIR,"examples/LVDC_Battery_systems/elements_m/battery.jl")); + +# ╔═╡ 6998b663-a5d9-43f9-ad57-487d7754720f +md""" +# Other variables + +These are the variables that do not trigger recalculation of the entire semi-Markov process. Changing them will effect in quick outcome changes +""" + +# ╔═╡ 3e1a1a05-fa19-4cb5-a5cc-3e78ad1b8ead +md""" +Battery reserve time +""" + +# ╔═╡ 803a934b-6f04-463a-9a28-15d100f78000 +@bind T Slider(1.0u"d":0.5u"d":10.0u"d", default = 4.0u"d") + +# ╔═╡ c29efeea-4b9f-42b4-9785-55caaa4bf69a +T + +# ╔═╡ d1212301-11dd-4cc3-919e-3f6629b519f3 +md""" +AC grid availability +""" + +# ╔═╡ 8d25a896-b7c4-47c8-9aa2-9d7ca48ead6d +@bind AC_Grid_av Slider(1 .- 10 .^ range(-7, -1, 7), default=1-10^-4) + +# ╔═╡ ed104a66-a4e5-47cc-bf74-01813588a5ec +AC_Grid_av + +# ╔═╡ 914ce2c2-8348-454e-9880-9b52556651a0 +md""" +Amount of AC/DC converters in parallel +""" + +# ╔═╡ 3fa956a9-eba3-442f-8046-af339b754577 +@bind nr_acdc Slider(1:10, default = 1) + +# ╔═╡ 3e15829e-1d90-4a60-8a2e-5e0bf522a2ea +nr_acdc + +# ╔═╡ 290c60dd-e96e-4948-95d6-f0ebeaf3297e +md""" +Amount of DC/DC converters in parallel +""" + +# ╔═╡ 455072a0-5f9c-4caf-9f8a-3589a6368aca +@bind nr_dcdc Slider(1:10, default = 1) + +# ╔═╡ affb9ea8-3887-43ae-a924-2618061f1b19 +nr_dcdc + +# ╔═╡ 37212910-4c12-4116-a8cb-36b2097e042d +md""" +Amount of batteries in parallel +""" + +# ╔═╡ fc23c215-562e-4d7b-b769-fda4416a92cc +@bind nr_bat Slider(1:10, default = 1) + +# ╔═╡ 3ec1c941-937b-4133-b75e-375cd0af250e +nr_bat + +# ╔═╡ b0a6acb6-ece8-4691-8229-9f26f60f0b3c +md""" +Additional capacitors +""" + +# ╔═╡ f77de149-1449-4e87-b427-79ae9e3fc655 +@bind adcap Slider(0:4, default = 0) + +# ╔═╡ d0288530-028b-4c4b-bfc6-4908dcd7ffa4 +adcap + +# ╔═╡ 5553b12b-317e-47b9-8c94-f3c7839f6cd5 +md""" +# Plotting +""" + +# ╔═╡ 666877a8-04f3-4d6b-bb3b-1f5d0f413954 +md""" +![LVDC system user overview](https://i.postimg.cc/DfDXMwLV/users-LVDC1.png) +""" + +# ╔═╡ 4fc373f9-f2c6-4b0c-8066-c66691e4b197 +md""" +User +""" + +# ╔═╡ 3c66ce37-112c-40f8-80aa-7137d18a7b88 +@bind user Slider(3:7) + +# ╔═╡ a4e3b35c-f9a8-4202-80c0-b7758ac7e498 +user + +# ╔═╡ d5d6af32-ac71-4163-85f3-27b39b932244 +@bind plotting Select(["Markov", "Semi-Markov", "Both"]) + +# ╔═╡ 164b2bd4-1201-4ca0-8998-536138d61950 +md""" +Single plot +""" + +# ╔═╡ 2354e834-7360-4473-8586-3e8ce8bb60de +@bind singleplot CheckBox(default=true) + +# ╔═╡ f914541a-ced5-4fa7-85a9-359f5c445fc7 +md""" +# Solving the networks +""" + +# ╔═╡ 1e190326-d0f7-432b-a226-7c5639260b49 +ac_av = AC_Grid_av*ones(length(t)); + +# ╔═╡ f301d353-3a28-423e-b581-1d8fc1bc0441 +stdᵃᶜ = solvedSTD(prob = [ac_av, 1 .- ac_av], time = collect(t), power = [10.0u"MW", 0.0u"MW"]); + +# ╔═╡ 2650f4df-b3f2-4bb0-90c3-74b796d6fbe9 +stdᵖ = solvedSTD(prob = [ones(length(t))], time = collect(t), power = [10.0u"MW"]); + +# ╔═╡ d21ce9bc-aae4-4fd5-b433-376e5db96941 +begin + ntwmᵃᶜ = Network() + add_user!(ntwmᵃᶜ, node = 2) + add_sources!(ntwmᵃᶜ, node = 1, std = stdᵃᶜ) + add_components!(ntwmᵃᶜ, edge = [(1,2)], + std = [stdmᵃᶜᵈᶜ]); + + solve!(ntwmᵃᶜ) + ntwm_ac = 1 .- ntwmᵃᶜ.usr[1][:ugf].prb[1]; +end + +# ╔═╡ b65662d9-d397-4e43-9c70-0cad46d08f7d +md""" +Solving the network of the battery and then dc/dc converter for both the Markov and the semi-Markov cases.\ +_____________________ +""" + +# ╔═╡ 28422021-1e05-4bb7-a229-455f28bc9e69 +plotly() + +# ╔═╡ 5e45c319-b462-45e4-8004-f47473e9b125 +md""" +Determining unavailability after including battery reserve time for both Markov and semi-Markov. +""" + +# ╔═╡ e899b8f6-ebe8-44ed-a914-58e64ec092ba +md""" +Solving the entire LVDC network +""" + +# ╔═╡ 1d1a63e6-f076-413d-81de-cb5c6469aab0 +md""" +# Functions + +Function to determine probability of repair before battery reserve time is reached for repair rates described by lognormal distributions. +""" + +# ╔═╡ cafd2c3d-d2c1-44a6-bb56-b44c4d27b4fb +function battery_system_availability(i, T, ntw_av, μ, σ) + # Calculate the probability that the battery does not run out of charge before + # the power sources are repaired at time t. With a lognormal distribution for + # the repair time with mean μ and standard deviation σ. + p_failure = 1 - ntw_av[i] + p_repair_time_ge_T = _MSS.ccdf(LogNormal(μ, σ),T) + return 1-p_failure*p_repair_time_ge_T +end + +# ╔═╡ 608611ac-a8d9-4a2f-8ab7-aafb1a83b110 +md""" +Function to determine probability of repair before battery reserve time is reached for repair rates described by exponential distributions. +""" + +# ╔═╡ 5a2199a1-7b8b-4af3-a34b-0392f8cf14c9 +function battery_system_availability(i, T, ntw_av, θ) + # Calculate the probability that the battery does not run out of charge before + # the power sources are repaired at time t. With a lognormal distribution for + # the repair time with mean μ and standard deviation σ. + p_failure = 1 - ntw_av[i] + p_repair_time_ge_T = _MSS.ccdf(Exponential(θ),T) + return 1-p_failure*p_repair_time_ge_T +end + +# ╔═╡ 6f4a10e4-18d7-4cfe-9208-ffbfa994da0d +begin + bat_av_m = Float64[] + append!(bat_av_m, ones(Int64(round(T/dt)))) + append!(bat_av_m,[battery_system_availability(i, T, ntwm_ac, (exp(log(4)+(0.3^2)/2))u"d") for i in 1:1:length(t)-Int64(round(T/dt))]) + stdmᵇᵃᵛ = solvedSTD(prob = [bat_av_m, 1 .- bat_av_m], time = collect(t), power = [10.0u"MW", 0.0u"MW"]) +end + +# ╔═╡ 4f13e38a-0075-4edd-8169-838ffb7134cd +md""" +Function to automotically change the amount of components in parallel between a pre-defined edge. +Inputs:\ + - Edge (between two nodes) or State Transition Diagram of the component to be put in parallel\ + - Amount of components in parallel\ +Output: String formatted in such a way that it fits as input to the add_components! command + +""" + +# ╔═╡ f9a371e8-203c-48a3-9335-1cdf8bc39d8b +function parallel(input, amount) + return [input for i in 1:amount] +end + +# ╔═╡ bb7d9dd8-6340-45a5-a59d-38d771b83a99 +begin + ntwᵃᶜ = Network() + add_user!(ntwᵃᶜ, node = 2) + add_sources!(ntwᵃᶜ, node = 1, std = stdᵃᶜ) + add_components!(ntwᵃᶜ, edge = parallel((1,2), nr_acdc), + std = parallel(stdᵃᶜᵈᶜ, nr_acdc)); + + solve!(ntwᵃᶜ) + ntw_ac = 1 .- ntwᵃᶜ.usr[1][:ugf].prb[1]; +end + +# ╔═╡ 6782a8b8-0a27-4221-a89b-b4197a2e2902 +begin + bat_av = Float64[] + append!(bat_av, ones(Int64(round(T/dt)))) + append!(bat_av,[battery_system_availability(i, T, ntw_ac, log(4)u"d", 0.3u"d") for i in 1:1:length(t)-Int64(round(T/dt))]) + stdᵇᵃᵛ = solvedSTD(prob = [bat_av, 1 .- bat_av], time = collect(t), power = [10.0u"MW", 0.0u"MW"]) +end + +# ╔═╡ a8c2acc2-6079-43a9-84ea-b19b85616538 +begin + ntwᵇᵃᵗ = Network() + add_user!(ntwᵇᵃᵗ, node = 2) + add_sources!(ntwᵇᵃᵗ, node = 1, std = stdᵖ) + add_components!(ntwᵇᵃᵗ, edge = parallel((1,2), nr_bat), + std = parallel(stdᵇᵃᵗ, nr_bat)) + solve!(ntwᵇᵃᵗ) + ntw_bat = 1 .- ntwᵇᵃᵗ.usr[1][:ugf].prb[1] +end + +# ╔═╡ 8cad16a1-71c9-498c-b3ab-2b954fb02c67 +begin + ntwmᵇᵃᵗ = Network() + add_user!(ntwmᵇᵃᵗ, node = 2) + add_sources!(ntwmᵇᵃᵗ, node = 1, std = stdᵖ) + add_components!(ntwmᵇᵃᵗ, edge = parallel((1,2), nr_bat), + std = parallel(stdᵇᵃᵗ, nr_bat)) + solve!(ntwmᵇᵃᵗ) + ntwm_bat = 1 .- ntwmᵇᵃᵗ.usr[1][:ugf].prb[1] +end + +# ╔═╡ 139ac22d-06db-434b-b224-6dcbb3b55e1f +begin + ntwmᴸⱽᴰᶜ = Network() + add_users!(ntwmᴸⱽᴰᶜ, node = [1,2,3,4,7,8,9]) + add_sources!(ntwmᴸⱽᴰᶜ, node = 1, std = stdᵃᶜ) + add_sources!(ntwmᴸⱽᴰᶜ, node = 2, ntw = (ntwmᵇᵃᵗ,1)) + add_components!(ntwmᴸⱽᴰᶜ, edge = [(3,4),(4,5),(4,5),(5,6),(6,7),(7,8),(7,9)], + std = [stdmᵇᵃᵛ, stdmᶜᵃᵖᴸ¹, stdmᶜᵃᵖᴸ², stdmᶜᵃᵖᵃᶜ, stdmᶜᵃᵖᵈᶜ, stdmⁱⁿᵛ¹, stdmⁱⁿᵛ²]) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((1,3), nr_acdc), + std = parallel(stdmᵃᶜᵈᶜ, nr_acdc)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((2,3), nr_dcdc), + std = parallel(stdmᵈᶜᵈᶜ, nr_dcdc)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((4,5), nr_acdc - 1 ), + std = parallel(stdmᶜᵃᵖᵃᶜ, nr_acdc - 1)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((5,6), nr_acdc - 1), + std = parallel(stdmᶜᵃᵖᵃᶜ, nr_acdc - 1)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((6,7), nr_acdc - 1), + std = parallel(stdmᶜᵃᵖᵃᶜ, nr_acdc - 1)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((4,5), nr_dcdc - 1 ), + std = parallel(stdmᶜᵃᵖᵈᶜ, nr_dcdc - 1)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((5,6), nr_dcdc - 1), + std = parallel(stdmᶜᵃᵖᵈᶜ, nr_dcdc - 1)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((6,7), nr_dcdc - 1), + std = parallel(stdmᶜᵃᵖᵈᶜ, nr_dcdc - 1)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((4,5), adcap ), + std = parallel(stdmᶜᵃᵖᵈᶜ, adcap)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((5,6), adcap), + std = parallel(stdmᶜᵃᵖᵈᶜ, adcap)) + add_components!(ntwmᴸⱽᴰᶜ, edge = parallel((6,7), adcap), + std = parallel(stdmᶜᵃᵖᵈᶜ, adcap)) + solve!(ntwmᴸⱽᴰᶜ) +end + +# ╔═╡ 2032520c-c8b9-44a1-970d-649d7c9b9783 +md""" +# State Transition Diagrams + +Importing the Semi-Markov State Transition Diagrams +""" + +# ╔═╡ da734f64-5a5a-4e74-ac4e-b9f095162a44 +dcdc_data = CSV.read("C:/Users/gemmers/Documents/GitHub/SemiMarkov.jl/examples/Journal/semi-Markov/std_DCDC_40.csv", DataFrame); + +# ╔═╡ 30d044ef-80e9-4c15-9b2c-d5e9f9e4c105 +md""" +Solving the Semi-Markov State Transition Diagrams +""" + +# ╔═╡ 3b700e3c-de15-4e4b-9618-6cbb24373d67 +stdᵈᶜᵈᶜ = solvedSTD(prob = [dcdc_data[!, :dcdc_state1], dcdc_data[!, :dcdc_state2], dcdc_data[!, :dcdc_state3]], time = collect(t), power = [10.0u"MW", 0.0u"MW", 0.0u"MW"]); + +# ╔═╡ 46a887c4-a9a0-496e-ab75-753ad9ebe2cb +begin + ntwᴸⱽᴰᶜ = Network() + add_users!(ntwᴸⱽᴰᶜ, node = [1,2,3,4,7,8,9]) + add_sources!(ntwᴸⱽᴰᶜ, node = 1, std = stdᵃᶜ) + add_sources!(ntwᴸⱽᴰᶜ, node = 2, ntw = (ntwᵇᵃᵗ,1)) + add_components!(ntwᴸⱽᴰᶜ, edge = [(3,4),(4,5),(4,5),(5,6),(6,7),(7,8),(7,9)], + std = [stdᵇᵃᵛ, stdᶜᵃᵖᴸ¹, stdᶜᵃᵖᴸ², stdᶜᵃᵖᵃᶜ, stdᶜᵃᵖᵈᶜ,stdⁱⁿᵛ¹, stdⁱⁿᵛ²]) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((1,3), nr_acdc), + std = parallel(stdᵃᶜᵈᶜ, nr_acdc)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((2,3), nr_dcdc), + std = parallel(stdᵈᶜᵈᶜ, nr_dcdc)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((4,5), nr_acdc - 1 ), + std = parallel(stdᶜᵃᵖᵃᶜ, nr_acdc - 1)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((5,6), nr_acdc - 1), + std = parallel(stdᶜᵃᵖᵃᶜ, nr_acdc - 1)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((6,7), nr_acdc - 1), + std = parallel(stdᶜᵃᵖᵃᶜ, nr_acdc - 1)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((4,5), nr_dcdc - 1 ), + std = parallel(stdᶜᵃᵖᵈᶜ, nr_dcdc - 1)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((5,6), nr_dcdc - 1), + std = parallel(stdᶜᵃᵖᵈᶜ, nr_dcdc - 1)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((6,7), nr_dcdc - 1), + std = parallel(stdᶜᵃᵖᵈᶜ, nr_dcdc - 1)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((4,5), adcap), + std = parallel(stdᶜᵃᵖᵈᶜ, adcap)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((5,6), adcap), + std = parallel(stdᶜᵃᵖᵈᶜ, adcap)) + add_components!(ntwᴸⱽᴰᶜ, edge = parallel((6,7), adcap), + std = parallel(stdᶜᵃᵖᵈᶜ, adcap)) + solve!(ntwᴸⱽᴰᶜ) +end + +# ╔═╡ 17d989ce-929b-499c-9012-e713c5a41684 +if singleplot == true + if plotting == "Markov" + plot(t, 1 .- ntwmᴸⱽᴰᶜ.usr[user][:ugf].prb[1]) + elseif plotting == "Semi-Markov" + plot(t, 1 .- ntwᴸⱽᴰᶜ.usr[user][:ugf].prb[1]) + else + plot(t, [1 .- ntwᴸⱽᴰᶜ.usr[user][:ugf].prb[1], 1 .- ntwmᴸⱽᴰᶜ.usr[user][ :ugf].prb[1]]) + end +else + if plotting == "Markov" + plot!(t, 1 .- ntwmᴸⱽᴰᶜ.usr[user][:ugf].prb[1]) + elseif plotting == "Semi-Markov" + plot!(t, 1 .- ntwᴸⱽᴰᶜ.usr[user][:ugf].prb[1]) + else + plot!(t, [1 .- ntwᴸⱽᴰᶜ.usr[user][:ugf].prb[1], 1 .- ntwmᴸⱽᴰᶜ.usr[user][ :ugf].prb[1]]) + end +end + +# ╔═╡ c12c9752-0186-4e91-bde2-eef78348a801 +@time solve!(stdᵃᶜᵈᶜ, cls; tsim, dt) + +# ╔═╡ 11db6494-3541-45c7-b7d3-1ea41d0b04eb +@time solve!(stdⁱⁿᵛ¹, cls; tsim, dt) + +# ╔═╡ d25a9fd9-93b9-4706-86ca-f916f1078e8a +@time solve!(stdⁱⁿᵛ², cls; tsim, dt) + +# ╔═╡ 6eebd299-7b8e-4e8b-be6c-77d8b7bac529 +@time solve!(stdᶜᵃᵖᵃᶜ, cls; tsim, dt) + +# ╔═╡ 83e3dd80-ba02-46d5-aa44-9a4dcc11dc9d +@time solve!(stdᶜᵃᵖᵈᶜ, cls; tsim, dt) + +# ╔═╡ c9464a8d-c489-47ee-877e-fd3d00334a4a +@time solve!(stdᶜᵃᵖᴸ¹, cls; tsim, dt) + +# ╔═╡ 10ba43fe-fee3-4d2c-b44f-a00e4a8022db +@time solve!(stdᶜᵃᵖᴸ², cls; tsim, dt) + +# ╔═╡ 74462966-5771-4eab-91f9-107c62542883 +@time solve!(stdᵇᵃᵗ, cls; tsim, dt) + +# ╔═╡ 857a2bbd-bed7-465c-a8f8-b8ed6c2e92ad +md""" +Markov State Transition Diagrams +""" + +# ╔═╡ 2732f05b-2987-420b-8115-d97620965f34 +md""" +Solution of the Markov State Transition Diagrams +""" + +# ╔═╡ 0959477d-5fce-449d-bef0-310e344cb874 +@time solve!(stdmᵃᶜᵈᶜ, cls1; tsim, dt) + +# ╔═╡ 4a1a9fd3-cc09-40f7-bd0c-7bad5cddfd98 +@time solve!(stdmᵈᶜᵈᶜ, cls1; tsim, dt) + +# ╔═╡ ba55d4f8-7636-46a3-9ef6-fd1d3e2b611a +@time solve!(stdmⁱⁿᵛ¹, cls1; tsim, dt) + +# ╔═╡ 9bdcc2e5-1a36-4439-8fb6-19556127aba8 +@time solve!(stdmⁱⁿᵛ², cls1; tsim, dt) + +# ╔═╡ 92988b50-06f7-4d3d-8d37-f6fd93f5be36 +@time solve!(stdmᶜᵃᵖᵃᶜ, cls1; tsim, dt) + +# ╔═╡ ad7fc263-31a7-4b50-90b5-55868579f653 +@time solve!(stdmᶜᵃᵖᵈᶜ, cls1; tsim, dt) + +# ╔═╡ 63f18789-cf2c-45f3-92ba-553592fe69e6 +@time solve!(stdmᶜᵃᵖᴸ¹, cls1; tsim, dt) + +# ╔═╡ 7f4f75e5-9497-4ac9-9318-3e272e02e1fe +@time solve!(stdmᶜᵃᵖᴸ², cls1; tsim, dt) + +# ╔═╡ b65ef768-843b-4b6a-8df1-4b9f861a4b07 +@time solve!(stdmᵇᵃᵗ, cls1; tsim, dt) + +# ╔═╡ fa8bdadb-6ba8-4fcd-82c3-7987cf12e4fc +md""" +# Package management +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" +DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" +MultiStateSystems = "63dd226a-9d27-42a2-9f4c-7f7a071798e0" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" +SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" +Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" + +[compat] +CSV = "~0.10.11" +DataFrames = "~1.3.6" +MultiStateSystems = "~0.1.2" +Plots = "~1.39.0" +PlutoUI = "~0.7.54" 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"Libdl", "Pkg"] +git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.5.0+0" + +[[deps.xkbcommon_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37" +uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "1.4.1+1" +""" + +# ╔═╡ Cell order: +# ╟─30bfc652-de3d-47d1-bc93-ed4166cddecf +# ╠═2c97acb4-9c6c-4f6e-95a6-1cae897dbbb2 +# ╟─6998b663-a5d9-43f9-ad57-487d7754720f +# ╟─3e1a1a05-fa19-4cb5-a5cc-3e78ad1b8ead +# ╟─c29efeea-4b9f-42b4-9785-55caaa4bf69a +# ╟─803a934b-6f04-463a-9a28-15d100f78000 +# ╟─d1212301-11dd-4cc3-919e-3f6629b519f3 +# ╟─ed104a66-a4e5-47cc-bf74-01813588a5ec +# ╟─8d25a896-b7c4-47c8-9aa2-9d7ca48ead6d +# ╟─914ce2c2-8348-454e-9880-9b52556651a0 +# ╟─3e15829e-1d90-4a60-8a2e-5e0bf522a2ea +# ╟─3fa956a9-eba3-442f-8046-af339b754577 +# 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file mode 100644 index 0000000..f554939 --- /dev/null +++ b/examples/LVDC_Battery_systems/data/std_DCDC_40.csv @@ -0,0 +1,43832 @@ +time,unit,dcdc_state1,dcdc_state2,dcdc_state3 +0.0,yr,1.0,0.0,0.0 +0.0009126169290440336,yr,0.9999999999955693,0.0,0.0 +0.0018252338580880673,yr,0.9999999999780129,0.0,0.0 +0.002737850787132101,yr,0.9999999999438627,0.0,0.0 +0.0036504677161761346,yr,0.9999999998908153,0.0,0.0 +0.004563084645220168,yr,0.9999999998170547,0.0,0.0 +0.005475701574264202,yr,0.9999999997210525,0.0,0.0 +0.006388318503308236,yr,0.9999999996014721,0.0,0.0 +0.007300935432352269,yr,0.9999999994571173,0.0,0.0 +0.008213552361396302,yr,0.9999999992868982,0.0,0.0 +0.009126169290440337,yr,0.9999999990898097,0.0,0.0 +0.01003878621948437,yr,0.999999998864916,0.0,0.0 +0.010951403148528403,yr,0.9999999986113386,0.0,0.0 +0.011864020077572437,yr,0.9999999983282482,0.0,0.0 +0.012776637006616472,yr,0.9999999980148571,0.0,0.0 +0.013689253935660504,yr,0.9999999976704148,0.0,0.0 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+39.99999999999999,yr,0.9996883306327708,0.00013712224098283432,0.0001745236615681156 diff --git a/examples/LVDC_Battery_systems/elements/CAP_L1.jl b/examples/LVDC_Battery_systems/elements/CAP_L1.jl new file mode 100644 index 0000000..e54859c --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/CAP_L1.jl @@ -0,0 +1,29 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs + +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the load 1 capacitance +stdᶜᵃᵖᴸ¹ = STD() + +# add the states to the std +add_states!(stdᶜᵃᵖᴸ¹, name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + + +# add the transitions to the std +add_transitions!(stdᶜᵃᵖᴸ¹, states = [(1,2),(2,1)], + distr = [ Weibull(52.0u"yr", 5.12), + LogNormal(log(4)u"d", 0.3u"d")]) + +# solve the std +return stdᶜᵃᵖᴸ¹ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/CAP_L2.jl b/examples/LVDC_Battery_systems/elements/CAP_L2.jl new file mode 100644 index 0000000..6832500 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/CAP_L2.jl @@ -0,0 +1,28 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the load 2 capacitance +stdᶜᵃᵖᴸ² = STD() + +# add the states to the std +add_states!(stdᶜᵃᵖᴸ², name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + + +# add the transitions to the std +add_transitions!(stdᶜᵃᵖᴸ², states = [(1,2),(2,1)], + distr = [ Weibull(60.0u"yr", 5.12), + LogNormal(log(4)u"d", 0.3u"d")]) + +# solve the std +return stdᶜᵃᵖᴸ² diff --git a/examples/LVDC_Battery_systems/elements/CAP_ac.jl b/examples/LVDC_Battery_systems/elements/CAP_ac.jl new file mode 100644 index 0000000..4c50c41 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/CAP_ac.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc capacitance +stdᶜᵃᵖᵃᶜ = STD() + +# add the states to the std +add_states!(stdᶜᵃᵖᵃᶜ, name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdᶜᵃᵖᵃᶜ, states = [(1,2),(2,1)], + distr = [ Weibull(50.0u"yr", 5.12), + LogNormal(log(4)u"d", 0.3u"d")]) + +# solve the std +return stdᶜᵃᵖᵃᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/CAP_dc.jl b/examples/LVDC_Battery_systems/elements/CAP_dc.jl new file mode 100644 index 0000000..92d2fd2 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/CAP_dc.jl @@ -0,0 +1,28 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the dc/dc converter capacitance +stdᶜᵃᵖᵈᶜ = STD() + +# add the states to the std +add_states!(stdᶜᵃᵖᵈᶜ, name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + + +# add the transitions to the std +add_transitions!(stdᶜᵃᵖᵈᶜ, states = [(1,2),(2,1)], + distr = [ Weibull(31.65u"yr", 8.502), + LogNormal(log(4)u"d", 0.3u"d")]) + +# solve the std +return stdᶜᵃᵖᵈᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/acdc.jl b/examples/LVDC_Battery_systems/elements/acdc.jl new file mode 100644 index 0000000..94a2b13 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/acdc.jl @@ -0,0 +1,26 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdᵃᶜᵈᶜ = STD() + +# add the states to the std +add_states!(stdᵃᶜᵈᶜ, name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +add_transitions!(stdᵃᶜᵈᶜ, states = [(1,2),(2,1)], + distr = [Weibull(20.0u"yr", 2.38), + LogNormal(log(4)u"d", 0.3u"d")]) + +# solve the std +return stdᵃᶜᵈᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/battery.jl b/examples/LVDC_Battery_systems/elements/battery.jl new file mode 100644 index 0000000..605bbc8 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/battery.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acke, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc +# converter +stdᵇᵃᵗ = STD() + +# add the states to the std +add_states!(stdᵇᵃᵗ, name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdᵇᵃᵗ, states = [(1,2),(2,1)], + distr = [Exponential(55.0u"yr"), + LogNormal(log(4)u"d", 0.3u"d")]) +# return the std +return stdᵇᵃᵗ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/dcdc copy.jl b/examples/LVDC_Battery_systems/elements/dcdc copy.jl new file mode 100644 index 0000000..5bb5c85 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/dcdc copy.jl @@ -0,0 +1,30 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +std = STD() + +# add the states to the std +add_states!(std, name = ["available", "unavailable_igbt1", "unavailable_igbt2"], + power = [10.0u"MW", 0.0u"MW", 0.0u"MW"], + init = [1.0, 0.0, 0.0]) + +# add the transitions to the std +add_transitions!(std, states = [(1,2),(2,1),(1,3),(3,1)], + distr = [ Exponential(2*55.6u"yr"), + Exponential(10.0u"d"), + Exponential(2*21.1u"yr"), + Exponential(10.0u"d")]) + + +# solve the std +return std \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/dcdc.jl b/examples/LVDC_Battery_systems/elements/dcdc.jl new file mode 100644 index 0000000..4a1a5bb --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/dcdc.jl @@ -0,0 +1,30 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdᵈᶜᵈᶜ = STD() + +# add the states to the std +add_states!(stdᵈᶜᵈᶜ, name = ["available", "unavailable_igbt1", "unavailable_igbt2"], + power = [10.0u"MW", 0.0u"MW", 0.0u"MW"], + init = [1.0, 0.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdᵈᶜᵈᶜ, states = [(1,2),(2,1),(1,3),(3,1)], + distr = [ Weibull(55.6u"yr", 2.31, t -> 0.00004u"1/d" * t + 0.5), + LogNormal(log(4)u"d", 0.3u"d"), + Weibull(21.1u"yr", 3.24, t -> -0.00004u"1/d" * t + 0.5), + LogNormal(log(4)u"d", 0.3u"d")]) + + +# solve the std +return stdᵈᶜᵈᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/inv1.jl b/examples/LVDC_Battery_systems/elements/inv1.jl new file mode 100644 index 0000000..c942158 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/inv1.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdⁱⁿᵛ¹ = STD() + +# add the states to the std +add_states!(stdⁱⁿᵛ¹, name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdⁱⁿᵛ¹, states = [(1,2),(2,1)], + distr = [ Weibull(19.2u"yr", 2.64), + LogNormal(log(4)u"d", 0.3u"d")]) + +# solve the std +return stdⁱⁿᵛ¹ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/inv2.jl b/examples/LVDC_Battery_systems/elements/inv2.jl new file mode 100644 index 0000000..67e9707 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/inv2.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdⁱⁿᵛ² = STD() + +# add the states to the std +add_states!(stdⁱⁿᵛ², name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdⁱⁿᵛ², states = [(1,2),(2,1)], + distr = [ Weibull(22.1u"yr", 2.13), + LogNormal(log(4)u"d", 0.3u"d")]) + +# solve the std +return stdⁱⁿᵛ² \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements/test.jl b/examples/LVDC_Battery_systems/elements/test.jl new file mode 100644 index 0000000..67c5e85 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements/test.jl @@ -0,0 +1,36 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdᵃᶜᵈᶜ = STD() + +# add the states to the std +add_states!(stdᵃᶜᵈᶜ, name = ["available", "unavailable_weibull", "unavailable_weibull", "unavailable_weibull", "unavailable_weibull", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW", 0.0u"MW"], + init = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0]) + +add_transitions!(stdᵃᶜᵈᶜ, states = [(1,2),(2,1),(1,3),(3,1),(1,4),(4,1),(1,5),(5,1),(1,6),(6,1),(1,7),(7,1)], + distr = [Weibull(20.0u"yr", 2.38, 1/6), + LogNormal(log(10)u"d", 0.25u"d"), + Weibull(20.0u"yr", 2.38, 1/6), + LogNormal(log(10)u"d", 0.25u"d"), + Weibull(20.0u"yr", 2.38, 1/6), + LogNormal(log(10)u"d", 0.25u"d"), + Weibull(20.0u"yr", 2.38, 1/6), + LogNormal(log(10)u"d", 0.25u"d"), + Weibull(20.0u"yr", 2.38, 1/6), + LogNormal(log(10)u"d", 0.25u"d"), + Weibull(20.0u"yr", 2.38, 1/6), + LogNormal(log(10)u"d", 0.25u"d")]) + +# solve the std +return stdᵃᶜᵈᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/CAP_L1.jl b/examples/LVDC_Battery_systems/elements_m/CAP_L1.jl new file mode 100644 index 0000000..a8e3d26 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/CAP_L1.jl @@ -0,0 +1,29 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs + +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the load 1 capacitance +stdmᶜᵃᵖᴸ¹ = STD() + +# add the states to the std +add_states!(stdmᶜᵃᵖᴸ¹, name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + + +# add the transitions to the std +add_transitions!(stdmᶜᵃᵖᴸ¹, states = [(1,2),(2,1)], + distr = [ Exponential((52.0*gamma(1+1/5.12))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + +# solve the std +return stdmᶜᵃᵖᴸ¹ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/CAP_L2.jl b/examples/LVDC_Battery_systems/elements_m/CAP_L2.jl new file mode 100644 index 0000000..de10b86 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/CAP_L2.jl @@ -0,0 +1,28 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the load 2 capacitance +stdmᶜᵃᵖᴸ² = STD() + +# add the states to the std +add_states!(stdmᶜᵃᵖᴸ², name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + + +# add the transitions to the std +add_transitions!(stdmᶜᵃᵖᴸ², states = [(1,2),(2,1)], + distr = [ Exponential((60.0*gamma(1+1/5))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + +# solve the std +return stdmᶜᵃᵖᴸ² diff --git a/examples/LVDC_Battery_systems/elements_m/CAP_ac.jl b/examples/LVDC_Battery_systems/elements_m/CAP_ac.jl new file mode 100644 index 0000000..b4b185d --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/CAP_ac.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc capacitance +stdmᶜᵃᵖᵃᶜ = STD() + +# add the states to the std +add_states!(stdmᶜᵃᵖᵃᶜ, name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdmᶜᵃᵖᵃᶜ, states = [(1,2),(2,1)], + distr = [ Exponential((50.0*gamma(1+1/5.12))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + +# solve the std +return stdmᶜᵃᵖᵃᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/CAP_dc.jl b/examples/LVDC_Battery_systems/elements_m/CAP_dc.jl new file mode 100644 index 0000000..90f5c61 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/CAP_dc.jl @@ -0,0 +1,28 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the dc/dc converter capacitance +stdmᶜᵃᵖᵈᶜ = STD() + +# add the states to the std +add_states!(stdmᶜᵃᵖᵈᶜ, name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + + +# add the transitions to the std +add_transitions!(stdmᶜᵃᵖᵈᶜ, states = [(1,2),(2,1)], + distr = [ Exponential((31.65*gamma(1+1/8.5))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + +# solve the std +return stdmᶜᵃᵖᵈᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/acdc.jl b/examples/LVDC_Battery_systems/elements_m/acdc.jl new file mode 100644 index 0000000..00380cc --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/acdc.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems +using SpecialFunctions + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdmᵃᶜᵈᶜ = STD() + +# add the states to the std +add_states!(stdmᵃᶜᵈᶜ, name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +add_transitions!(stdmᵃᶜᵈᶜ, states = [(1,2),(2,1)], + distr = [ Exponential((20.0*gamma(1+1/2.38))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + +# solve the std +return stdmᵃᶜᵈᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/battery.jl b/examples/LVDC_Battery_systems/elements_m/battery.jl new file mode 100644 index 0000000..91af5f2 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/battery.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acke, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc +# converter +stdmᵇᵃᵗ = STD() + +# add the states to the std +add_states!(stdmᵇᵃᵗ, name = ["available", "unavailable"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdmᵇᵃᵗ, states = [(1,2),(2,1)], + distr = [Exponential(55.0u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) +# return the std +return stdmᵇᵃᵗ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/dcdc.jl b/examples/LVDC_Battery_systems/elements_m/dcdc.jl new file mode 100644 index 0000000..63244a9 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/dcdc.jl @@ -0,0 +1,30 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdmᵈᶜᵈᶜ = STD() + +# add the states to the std +add_states!(stdmᵈᶜᵈᶜ, name = ["available", "unavailable_igbt1", "unavailable_igbt2"], + power = [10.0u"MW", 0.0u"MW", 0.0u"MW"], + init = [1.0, 0.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdmᵈᶜᵈᶜ, states = [(1,2),(2,1),(1,3),(3,1)], + distr = [ Exponential(2*(55.6*gamma(1+1/2.31))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d"), + Exponential(2*(21.1*gamma(1+1/3.24))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + + +# solve the std +return stdmᵈᶜᵈᶜ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/inv1.jl b/examples/LVDC_Battery_systems/elements_m/inv1.jl new file mode 100644 index 0000000..dce6939 --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/inv1.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdmⁱⁿᵛ¹ = STD() + +# add the states to the std +add_states!(stdmⁱⁿᵛ¹, name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdmⁱⁿᵛ¹, states = [(1,2),(2,1)], + distr = [ Exponential((19.2*gamma(1+1/2.64))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + +# solve the std +return stdmⁱⁿᵛ¹ \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/elements_m/inv2.jl b/examples/LVDC_Battery_systems/elements_m/inv2.jl new file mode 100644 index 0000000..df24e0f --- /dev/null +++ b/examples/LVDC_Battery_systems/elements_m/inv2.jl @@ -0,0 +1,27 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +# load pkgs +using Unitful +using MultiStateSystems + +# initialize the state-transition diagram corresponding to the front-end ac/dc converter +stdmⁱⁿᵛ² = STD() + +# add the states to the std +add_states!(stdmⁱⁿᵛ², name = ["available", "unavailable_weibull"], + power = [10.0u"MW", 0.0u"MW"], + init = [1.0, 0.0]) + +# add the transitions to the std +add_transitions!(stdmⁱⁿᵛ², states = [(1,2),(2,1)], + distr = [ Exponential((22.1*gamma(1+1/2.13))u"yr"), + Exponential((exp(log(4)+(0.3^2)/2))u"d")]) + +# solve the std +return stdmⁱⁿᵛ² \ No newline at end of file diff --git a/examples/LVDC_Battery_systems/networks/LVDC_grid_sm.jl b/examples/LVDC_Battery_systems/networks/LVDC_grid_sm.jl new file mode 100644 index 0000000..49116cd --- /dev/null +++ b/examples/LVDC_Battery_systems/networks/LVDC_grid_sm.jl @@ -0,0 +1,100 @@ +################################################################################ +# Copyright 2022, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ + +""" +This is an example to demonstrate the effect of wear-out failure of power electronic converters +on the system wide availability in an LVDC distribution. + +Pluto.jl environment is also available on at http://github.com/timmyfaraday/MultiStateSystems.jl +""" + +# Load pkgs +using Plots +using Unitful +using MultiStateSystems + +# Pkg const +const _MSS = MultiStateSystems + +# Settings for a specific analysis +cls = SemiMarkovProcess() +tsim = 40.0u"yr"; # Total simulation time +dt = 8.0u"hr"; # Simulation delta time +t = zero(dt):dt:tsim .|> u"yr" # Creating a timeseries of tsim and dt. +T = 2u"d"; #Battery reserve time + +# Function to determine probability of repair before battery reserve time is reached +function battery_system_availability(i, T, ntw_av, μ, σ) + # Calculate the probability that the battery does not run out of charge before + # the power sources are repaired at time t. With a lognormal distribution for + # the repair time with mean μ and standard deviation σ. + p_failure = 1 - ntw_av[i] + p_repair_time_ge_T = _MSS.ccdf(LogNormal(μ, σ),T) + return 1-p_failure*p_repair_time_ge_T +end + +# Include the stochastic models for the wind turbines and cables +stdᵃᶜᵈᶜ = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/acdc.jl")); +stdᵈᶜᵈᶜ = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/dcdc.jl")); +stdⁱⁿᵛ¹ = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/inv1.jl")); +stdⁱⁿᵛ² = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/inv2.jl")); +stdᶜᵃᵖᵃᶜ = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/CAP_ac.jl")); +stdᶜᵃᵖᵈᶜ = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/CAP_dc.jl")); +stdᶜᵃᵖᴸ¹ = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/CAP_L1.jl")); +stdᶜᵃᵖᴸ² = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/CAP_L2.jl")); +stdᵇᵃᵗ = include(joinpath("C:/Users/gemmers/Documents/GitHub/MultiStateSystems.jl/examples/LVDC_Battery_systems/elements/battery.jl")); + +# Solve the state transition diagrams +solve!(stdᵃᶜᵈᶜ, cls; tsim, dt) +solve!(stdᵈᶜᵈᶜ, cls; tsim, dt) +solve!(stdⁱⁿᵛ¹, cls; tsim, dt) +solve!(stdⁱⁿᵛ², cls; tsim, dt) +solve!(stdᶜᵃᵖᵃᶜ, cls; tsim, dt) +solve!(stdᶜᵃᵖᵈᶜ, cls; tsim, dt) +solve!(stdᶜᵃᵖᴸ¹, cls; tsim, dt) +solve!(stdᶜᵃᵖᴸ², cls; tsim, dt) +solve!(stdᵇᵃᵗ, cls; tsim, dt) + +""" +The DC/DC converter can take a lot of memory to solve. +The solved std is provided as data and can be accessed by uncommenting the following two lines: +""" +# dcdc_data = CSV.read("Z:/MyOwn/Journal/semi-Markov/std_DCDC_40.csv", DataFrame) +# stdᵈᶜᵈᶜ = solvedSTD(prob = [dcdc_data[!, :dcdc_state1], dcdc_data[!, :dcdc_state2], dcdc_data[!, :dcdc_state3]], time = collect(t), power = [10.0u"MW", 0.0u"MW", 0.0u"MW"]); + +# Set up the state transition diagram for the AC-grid with a constant availability of four nines. +ac_av = 0.9999*ones(length(t)); +stdᵃᶜ = solvedSTD(prob = [ac_av, 1 .- ac_av], time = collect(t), power = [10.0u"MW", 0.0u"MW"]); + +# Set up a perfectly available state transition diagram as source in some of the networks. +stdᵖ = solvedSTD(prob = [ones(length(t))], time = collect(t), power = [10.0u"MW"]); + +# Solve the availability of the AC side of the network, including AC grid and AC/DC converter. +ntwᵃᶜ = Network() +add_user!(ntwᵃᶜ, node = 2) +add_sources!(ntwᵃᶜ, node = 1, std = stdᵃᶜ) +add_components!(ntwᵃᶜ, edge = [(1,2)], + std = [stdᵃᶜᵈᶜ]); +solve!(ntwᵃᶜ) +ntw_ac = ntwᵃᶜ.usr[1][:ugf].prb[2]; + +# Determining the probability that the AC side network availability has been restored before +# the battery has drained. +bat_av = Float64[] +append!(bat_av, ones(Int64(round(T/dt)))) +append!(bat_av,[battery_system_availability(i, T, ntw_ac, log(4)u"d", 0.3u"d") for i in 1:1:length(t)-Int64(round(T/dt))]) +stdᵇᵃᵛ = solvedSTD(prob = [bat_av, 1 .- bat_av], time = collect(t), power = [10.0u"MW", 0.0u"MW"]) + +#Total system availability, contains the availability at all essential users in the sytem. +ntwᴸⱽᴰᶜ = Network() +add_users!(ntwᴸⱽᴰᶜ, node = [4,5,8,9,10]) +add_sources!(ntwᴸⱽᴰᶜ, node = 1, std = stdᵖ) +add_components!(ntwᴸⱽᴰᶜ, edge = [(1,2),(2,4),(1,3),(3,4),(4,5),(5,6),(5,6),(6,7),(7,8),(8,9),(8,10)], + std = [stdᵃᶜ, stdᵃᶜᵈᶜ, stdᵇᵃᵗ, stdᵈᶜᵈᶜ, stdᵇᵃᵛ, stdᶜᵃᵖᴸ¹, stdᶜᵃᵖᴸ², stdᶜᵃᵖᵃᶜ, stdᶜᵃᵖᵈᶜ, stdⁱⁿᵛ¹, stdⁱⁿᵛ²]) + +solve!(ntwᴸⱽᴰᶜ) \ No newline at end of file From 30870110147a5ce244a771366862862a23bbdccd Mon Sep 17 00:00:00 2001 From: EvilDrVlad Date: Fri, 22 Dec 2023 11:32:19 +0100 Subject: [PATCH 53/56] Create lvdc_resilience.jl Another example of the semi-Markov process, to determine LVDC battery system resilience against AC disturbances. --- examples/semi-markov/lvdc_resilience.jl | 74 +++++++++++++++++++++++++ 1 file changed, 74 insertions(+) create mode 100644 examples/semi-markov/lvdc_resilience.jl diff --git a/examples/semi-markov/lvdc_resilience.jl b/examples/semi-markov/lvdc_resilience.jl new file mode 100644 index 0000000..137a151 --- /dev/null +++ b/examples/semi-markov/lvdc_resilience.jl @@ -0,0 +1,74 @@ +################################################################################ +# Copyright 2023, Tom Van Acker, Glenn Emmers # +################################################################################ +# MultiStateSystems.jl # +# A Julia package to solve multi-state system models. # +# See http://github.com/timmyfaraday/MultiStateSystems.jl # +################################################################################ +""" +This file demonstrates the resilience of LVDC systems with a battery, +against AC side disturbances and outages in function of battery reserve time. +A semi-Markov process strategy is applied to the problem and the state transition +diagram contains three states. + +States: +- 1 : Normal operation state +- 2 : Failed AC state, battery is discharging +- 3 : Shutdown state, battery is empty +""" + +# load pkgs +using Plots +using Unitful +using MultiStateSystems + +# pkg const +const _MSS = MultiStateSystems + +# setting for a specific analysis +cls = SemiMarkovProcess() + +bat = 120.0 +AC_fail = 6.6u"yr" + +function battery_dist(T::Quantity) +# This function determines the transition distribution from an empty battery state to +# a normal operation state. + if T == 120.0u"minute" + return Exponential(51.21u"minute") + elseif T==60.0u"minute" + return Exponential(55.4u"minute") + elseif T==80.0u"minute" + return Exponential(54.39u"minute") + elseif T==100.0u"minute" + return Exponential(53.14u"minute") + elseif T == 140.0u"minute" + return Exponential(47.38u"minute") + end +end + + +# initialize the state-transition diagram +stdᵈᶜ = STD() +stdᵃᶜ = STD() + +# add the states to the std +add_states!(stdᵃᶜ, name = ["normal operation state","failed AC state"], + init = [1.0,0.0]) + +add_states!(stdᵈᶜ, name = ["normal operation state","failed AC state","Battery depletion state"], + init = [1.0,0.0,0.0]) +# add the transitions to the std +add_transitions!(stdᵃᶜ, states = [(1,2),(2,1)], + distr = [ Exponential(AC_fail), + Weibull(95.196u"minute", 2.1)]) + +add_transitions!(stdᵈᶜ, states = [(1,2),(2,1),(2,3),(3,1)], + distr = [ Exponential(AC_fail), + Weibull(95.196u"minute", 2.1, 0.80), + LogNormal(log(bat/60)u"hr", 0.05u"hr", 0.20), + battery_dist((bat)u"minute")]) + +# solve the stds +solve!(stdᵈᶜ, cls, tsim = 7.0u"hr", dt = 1u"minute", tol=1e-10) +solve!(stdᵃᶜ, cls, tsim = 7.0u"hr", dt = 1u"minute", tol=1e-10) \ No newline at end of file From 497c81cbb10c105c499417df51b8f1208e16a6bf Mon Sep 17 00:00:00 2001 From: timmyfaraday Date: Mon, 22 Jan 2024 12:39:23 +0100 Subject: [PATCH 54/56] final commit before merge into main --- Project.toml | 10 +++++----- src/form/semi_markov_process.jl | 5 +++-- 2 files changed, 8 insertions(+), 7 deletions(-) diff --git a/Project.toml b/Project.toml index d259bc6..4284516 100644 --- a/Project.toml +++ b/Project.toml @@ -18,14 +18,14 @@ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" [compat] AdditionalUnits = "0.1.4" -Graphs = "1.8.0" +Graphs = "1.9.0" Interpolations = "0.14.7" -Measurements = "2.9.0" +Measurements = "2.11.0" Multigraphs = "0.3.0" -OrdinaryDiffEq = "6.55.0" -QuadGK = "2.8.2" +OrdinaryDiffEq = "6.58.2" +QuadGK = "2.9.4" SpecialFunctions = "2.3.1" -Unitful = "1.17.0" +Unitful = "1.19.0" julia = "1" [extras] diff --git a/src/form/semi_markov_process.jl b/src/form/semi_markov_process.jl index 2c2f5d3..b79f0bd 100644 --- a/src/form/semi_markov_process.jl +++ b/src/form/semi_markov_process.jl @@ -106,6 +106,7 @@ function _set_p!(std::AbstractSTD, st::Int, init::Real, tol::Real, DST::Vector, _fill_p!(init, dst, t, h, p) end + set_prop!(std, st, :h, h) set_prop!(std, st, :prob, p) end function _fill_p!(init::Real, dst::AbstractDistribution, t::StepRangeLen, @@ -136,8 +137,8 @@ function solve!(std::AbstractSTD, cls::AbstractSemiMarkovProcess; t = zero(dt):dt:tsim # solve the problem - U = get_U(std,t,tol) - A = ustrip(get_A(std,t,tol)) + U = get_U(std, t, tol) + A = ustrip(get_A(std, t, tol)) H = U \ A * unit(1/dt) set_p!(std, t, H, tol) From 9c700d5aaa1fd86af5844f1d4890768bb072b274 Mon Sep 17 00:00:00 2001 From: timmyfaraday Date: Mon, 22 Jan 2024 12:42:45 +0100 Subject: [PATCH 55/56] Update ci.yml --- .github/workflows/ci.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 824e8ab..feb1787 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -13,7 +13,7 @@ jobs: fail-fast: false matrix: version: - - '1.5' + - '1.8' - 'nightly' os: - ubuntu-latest From 57d84f3e65b9bd7cf162522628d181ae61ba6904 Mon Sep 17 00:00:00 2001 From: timmyfaraday Date: Mon, 22 Jan 2024 12:49:29 +0100 Subject: [PATCH 56/56] Update Project.toml --- Project.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Project.toml b/Project.toml index 4284516..5628367 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "MultiStateSystems" uuid = "63dd226a-9d27-42a2-9f4c-7f7a071798e0" authors = ["Tom Van Acker"] -version = "0.1.2" +version = "0.2.0" [deps] AdditionalUnits = "02d9b4f0-7821-44c6-acbd-01a1ab91b72e"