How fit experimental data to mathematical equation with 10 parameters??

I have experimental data of a polymer for storage, loss modulus and loss factor.

And I have mathematical equations for storage, loss moudlus and loss factor. These equations contains 10 parameters I need to obtain them by curve fitting. How to obtain these parameters (These parameters also have some constrains) ??

[Torsten]

help lsqcurvefit

help fmincon

[Anil Kumar Mekala]

I have to fit all three equations simultaneously and get the 10 parameters will these functions work for this kind of problems??

[Torsten]

Yes. E.g. for lsqcurvefit, you could supply a vector yexp with your experimental data for storage, loss modulus and loss factor: yexp = [storage_exp;loss_modulus_exp;loss_factor_exp] and supply the simulated vector that depends on the parameters in the same format: ysim=[storage_sim;loss_modulus_sim;loss_factor_sim].

lsqcurvefit will then try to arrange the parameter vector such that norm(yexp-ysim) is approximately 0.

But to fit 10 parameters, you should have quite a lot of measurement data ...

[Anil Kumar Mekala]

Would you please elaborate the code little bit to get the complete idea??

[Torsten]

Sorry, no. There are lots of examples for lsqcurvefit that demonstrate how to proceed. And I explained how you can overcome the little difference for your problem with the three different experimental data to be fitted.

[Alex Sha]

@Anil Kumar Mekala

It is better for you giving out the details of the data, fitting functions and the parameters you want to estimate.

[Anil Kumar Mekala]

I am attaching my code which is not working.

You may find the data and equations within that file,

Thank you,

If you find any leads please let me know ASAP.

[Shivansh]

Hi Anil!

I understand that you are trying to obtain the ten parameters involved in your model of equations using the curve fitting. The code you have attached is not working as all the three equations are producing “NaN” values on the initial parameters.

You can verify it using the following code after the line where you have initialised the upper bounds by “ub”:

testEquation1 = equation1(initialParams, xData);
testEquation2 = equation2(initialParams, xData);
testEquation3 = equation3(initialParams, xData);

if any(isnan(testEquation1))
    error('Equation 1 produces NaN at the initial parameters');
end
if any(isnan(testEquation2))
    error('Equation 2 produces NaN at the initial parameters');
end
if any(isnan(testEquation3))  
    error('Equation 3 produces NaN at the initial parameters');
end

The above results clearly indicate that there is some issue with the handling of equations on initial parameters.

You can use a for loop to find the corresponding x values resulting in NaN values for corresponding equations. You can do the same for the first equation by using the following code snippet:

x_resultingToNaN=[];
for i = 1:779
    if isnan(testEquation1(i))
        x_resultingToNaN(end+1)= xData(i);
    end
end

You are currently taking an array of zeros as initial parameters. You can also try experimenting with it and observe any changes.

Hope it helps!