How to obtain model parameters by fitting experimental data to the monod model. monod model.

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O'Brien Ikart
O'Brien Ikart 2021-7-30
评论： Alex Sha 2021-7-31
t= [0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 48]
x= [15, 18.3, 22, 23.4, 23.8, 24.1, 24.5, 24.8, 24.87, 24.9, 24.95, 25, 25]
S= [49.7, 28, 26.1, 18.1, 13.7, 10.1, 4.1, 1.2, 0.3, 0.08, 0.05, 0.05, 0.05 ]
P= [0, 5.2, 8.1, 9.3, 10.5, 12.3, 12.8, 13.2, 13.6, 13.8, 13.9, 13.95, 13.95]
I used initial guess values of umax, ks, y1 and y2 as 0.5, 55, 5 and 1.4 respectively. dx/dt= umax*s*x/(ks + s); ds/dt= -y1*umax*s*x/(ks + s) dp/dt= y2*umax*s*x/(ks +s). I used the code provided by star strider on a similar question but I keep getting errors, I also have to fit the data to other fermentation models. Also can simulink be used for the fitting?
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O'Brien Ikart
O'Brien Ikart 2021-7-30
I tried using that code to numerically integrate the models from 0 to 48 with the guess values for the model parameters. I kept getting errors.... I have to fit the model to the experimental parameters. It was easier to numerically integrate the models using simulink but I dunno how to do the fitting on either Matlab or simulink.

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Alex Sha
Alex Sha 2021-7-31
Refer to the results below:
Root of Mean Square Error (RMSE): 1.50437634361661
Sum of Squared Residual: 81.4733345963976
Correlation Coef. (R): 0.97672011839718
R-Square: 0.9539821896818
Parameter Best Estimate
-------------------- -------------
umax -0.0619295716977556
ks -88.5509341201568
y1 4.65073776898894
y2 1.33836136350295
  2 个评论
Alex Sha
Alex Sha 2021-7-31
If you want all parameters to be positive without upper bound limition, the result will be a bit strange as below:
Root of Mean Square Error (RMSE): 1.70454457017103
Sum of Squared Residual: 104.596998901184
Correlation Coef. (R): 0.976253765588915
R-Square: 0.953071414826535
Parameter Best Estimate
-------------------- -------------
y1 4.78475504434034
y2 1.35947688117111
umax 515071175352863
ks 5.10885251418351E17

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