How to find coefficients A, B, C,...F...?
Input = x1, x2 .... x15
Output =Y1
Prefixed equation = (Ax1.^B.*x2.*x3*x4./C).^D +E.*x5+F.*x6+... x15
From experimental results, x1, x2... and Y1 are known.
Condition Mean of experimental and predicted should be 1.0, standard deviation preferably less than 0.20.
Please provide solution, MATLAB code or suggest me any software to solve this problem.
Thanks in advance.
Hi Leon,
The easiest way is using MATLAB built-in Genetic Algorithm (GA) optimization code. If you have enough data (with 15 dependent variables you should have > 30 data points) then you can use this:
1) assign 16 coefficients as the output of the GA model (one intercept and 15 for variables)
2) set boundaries for each variable in GA
3) in your function script define an error like this:
Error1= sum ((Model output (using variables from real data and coefficients from GA) - Real data)^2)
Error2= Something related to mean
Error3= Something related to SD
Error=Error1+Error2+Error3
Make sure the errors are in the same range, otherwise multiply to a constants to make them close (you can think of weights as well to make one Error more important than others)
4) Run GA and ask to minimize the function (Error)
Hope this helps.
Dear Harald,
Very nice solution. I think nonlinear least squares algorithm will only take care of the fitting not conditional mean and SD (ot sure what the exact restrictions are here).
Best Regards,
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