3) Comparison of theoretical "Ratio" measurements and practical "Sensor" measurements in 3D graphics
- ppm = a*ratio^b (a: valuea b: valueb)
- ppm = 10^[(log10(ratio)-b)/m] (m: logm b: logb)
If R^2 equals 1 :
a*ratio^b = 10^[(log10(ratio)-b)/m]
logm = valueb, logb = log10(valuea)
[(1,10), (2,4), (3,3)]
loge(b) = ln(b)
(ln(1),ln(10)) for ≈ (0,2.3026)
(ln(2),ln(4)) ≈ (0.6931,1.3863) and
(ln(3),ln(3)) ≈ (1.0986,1.0986)
b = ∑ i=1 n (x i − x ˉ ) 2 ∑ i=1 n (xi − xˉ)(yi−yˉ)
ln(x):(0,0.6931,1.0986)ln(y):(2.3026,1.3863,1.0986)ln(y)ˉ=(2.3026+1.3863+1.0986)/3≈1.5958
ln(x)ˉ=(0+0.6931+1.0986)/3≈0.5972
b = (0−0.5972)(2.3026−1.5958)+(0.6931−0.5972)(1.3863−1.5958)+(1.0986−0.5972)(1.0986−1.5958)/(0−0.5972)^2+(0.6931−0.5972)^2+(1.0986−0.5972)^2 ≈ -1.2
ln(a) = − ln ˉ (y) - b ln ˉ (x) ≈ 1.5958−(−1.2)⋅0.5972≈2.31244
a=e^2.31244 ≈ 9.947
y = mx+ n
n = b
log10(y) = m*log10(x) + b
-b = m*log10(x) - log10(y)
last b = log10(y) - m*log10(x)
m = (y - y0) / (x - x0)
m = (log10(y) - log10(y0)) / (log10(x) - log10(x0))
if y= a*x^b:
last m = log10(y/y0) / log10(x/x0)
m = slope of the line
b = intersection point
m = log10(y/y0) / log10(x/x0)
b = log10(y) - m*log10(x)
if r_squared >= 0.9995:
print("R-squared value for {gas name} is above 0.9995, plotting against first and last values.")
x0, y0 = x[0], y[0]
xn, yn = x[-1], y[-1]
b = np.log10(yn/y0) / np.log10(xn/x0)
a = 10**(np.log10(yn) - b * np.log10(xn))
b2 = np.log10(yn) - b * np.log10(xn)
b2_rounded = round(b2, 4)
a_rounded = round(a, 4)
b_rounded = round(b, 4)
The first formula is determined according to all points (OldCurve.py, OldCurve), while the second formula is determined according to the first and last point. Therefore, in order to collect them all in the same formula and to increase the accuracy rate, we used the method in the second formula and took the logarithm (if R^2 = 1 (%100) always: logm = valueb, logb = log10(valuea)) for slopes greater than 99.95% and collected them all in the first formula, thus we increased the accuracy rate without having to use 2 different formulas (Regression.py, NewCurve).
V = I x R -> VRL = [VC / (RS + RL)] x RL -> VRL = (VC x RL) / (RS + RL)
RS: -> VRL x (RS + RL) = VC x RL -> (VRL x RS) + (VRL x RL) = VC x RL -> (VRL x RS) = (VC x RL) - (VRL x RL)
RS = [(VC x RL) - (VRL x RL)] / VRL -> RS = [(VC x RL) / VRL] – RL
Rs = (voltage * Rload) / (voltage/2^n-1)) - (Rload)
SensorValue / 2^(AdcBitResulation1-1) -> SensorCalibrationValue / 2^(AdcBitResulation2-1)
Rs = 2^(AdcBitResulation1-1) * [Rload / SensorValue - Rload] -> calibrationRs = 2^(AdcBitResulation2-1) * [Rload / SensorCalibrationValue – Rload]
Ro = calibrationRs / Air ||| ratio = Rs / Ro -> ratio = Rs / (calibrationRs / Air) -> ratio = Rs x Air / calibrationRs
Ratio = (2^(AdcBitResulation1-1) * [Rload1 / SensorValue – Rload1]) * RsRoMQAir / (2^(AdcBitResulation2-1) * [Rload2 / SensorCalibrationValue – Rload2]) [Rs / Ro]
If Sensor Calibration and Sensor Measurement are Under the Same Conditions:
Rload1 = Rload2 && 2^(AdcBitResulation1-1) = 2^(AdcBitResulation2-1)
SensorRange = [0 - 2^(AdcBitResulation-1)]
if MinSensorValue == 0 && MaxSensorValue == 1: SensorRange [0 - 1]
if SensorRange [0 - 1]: 0 <= (SensorValue) <= 1 && 0 <= SensorCalibrationValue <= 1
Ratio = (MaxSensorValue * [Rload / SensorValue – Rload]) * RsRoMQAir / (MaxSensorValue * [Rload / SensorCalibrationValue – Rload]) [Rs / Ro]
Ratio = [Rload / SensorValue – Rload] * RsRoMQAir / [Rload / SensorCalibrationValue – Rload] [Rs / Ro]
Ratio = f(R) * RsRoMQAir
f(R) = [R / S - R] / [R / C - R] -> [(R - RS) / S] / [(R - RC) / C] -> [(R - RS) / S] * [C / (R - RC)]
f(R) = [(R - RS) / S] * [C / (R - RC)] = [C * (R - RS) / S (R - RC)]
g(x) = (R - Rx1) / (R - Rx2) -> g(x) = (1 - x1) / (1 - x2)
f(R) = [(R - RS) / S] * [C / (R - RC)] = [C * (1 - S) / S (1 - C)]
Ratio = [SensorCalibrationValue * (1 - SensorValue)] * RsRoMQAir / [SensorValue * (1 - SensorCalibrationValue)] [Rs / Ro]
(1) if ratio = Rs / Ro:
ratio = [SensorCalibrationValue * (1 - SensorValue)] * RsRoMQAir / [SensorValue * (1 - SensorCalibrationValue)]
(2) if ratio = Rs / Rs:
ratio = [SensorCalibrationValue * (1 - SensorValue)] / [SensorValue * (1 - SensorCalibrationValue)] [No RsRoMQAir]
(3) if ratio = Ro / Rs:
ratio = [SensorCalibrationValue * (1 - SensorValue)] / [SensorValue * (1 - SensorCalibrationValue)] * RsRoMQAir
STATUS 1: MQ-2, MQ-3, MQ-4, MQ-5, MQ-6, MQ-7, MQ-8, MQ-9, MQ-135, MQ-136, MQ-137 [Almost All & Standart]
STATUS 2: MQ303A, MQ307A, MQ309A [A models]
STATUS 3: MQ131 [MQ131 only]
"The first and only Arduino library where Geiger Counter and MQ Sensors combine with Data Science"
NOTE: [For detailed explanation, You can also check out the github wiki page] https://github.com/abcdaaaaaaaaa/MQSpaceData.h/wiki
MQ Sensor List: [MQ-2, MQ-3, MQ-4, MQ-5, MQ-6, MQ-7, MQ-8, MQ-9, MQ131, MQ-135, MQ-136, MQ-137, MQ303A, MQ307A, MQ309A]
