From 857502792d0ddd8785b7e78d9b649bc004263ad2 Mon Sep 17 00:00:00 2001 From: Dimitris Tsapetis Date: Wed, 26 Jul 2023 19:40:25 +0300 Subject: [PATCH] Corrects SORM documentation --- docs/source/reliability/sorm.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/reliability/sorm.rst b/docs/source/reliability/sorm.rst index 80f51b13..dc6b09cf 100644 --- a/docs/source/reliability/sorm.rst +++ b/docs/source/reliability/sorm.rst @@ -4,7 +4,7 @@ SORM In SORM the performance function is approximated by a second-order Taylor series around the design point according to -.. math:: G(\textbf{U}) = G(\textbf{U}^\star) + \nabla G(\textbf{U}^\star)(\textbf{U}-\textbf{U}^\star)^\intercal + \frac{1}{2}(\textbf{U}-\textbf{U}^\star)\textbf{H}(\textbf{U}-\textbf{U}^\star) +.. math:: G(\textbf{U}) = G(\textbf{U}^\star) + \nabla G(\textbf{U}^\star)(\textbf{U}-\textbf{U}^\star)^\intercal + \frac{1}{2}(\textbf{U}-\textbf{U}^\star)\textbf{H}(\textbf{U}-\textbf{U}^\star)(\textbf{U}-\textbf{U}^\star)^T where :math:`\textbf{H}` is the Hessian matrix of the second derivatives of :math:`G(\textbf{U})` evaluated at :math:`\textbf{U}^*`. After the design point :math:`\textbf{U}^*` is identified and the probability of failure