Hi, I have these two functions:
sigma_11_fun = @(a, lambda) (-1/lambda(2)^2) * (2*a(1) + 4*a(2)*(lambda(1)^2 + lambda(2)^2 + (1/(lambda(1)^2 * lambda(2)^2))-3)) + 2*a(1)*lambda(1)^2 + 4*a(2)*lambda(1)^2*(lambda(1)^2 + lambda(2)^2 + (1/(lambda(1)^2 * lambda(2)^2))-3) + 2*lambda(1)^2*a(3)*(lambda(1)^2-1)*exp(a(4)*(lambda(1)^2-1));
sigma_22_fun = @(a, lambda) (-1/lambda(1)^2) * (2*a(1) + 4*a(2)*(lambda(1)^2 + lambda(2)^2 + (1/(lambda(1)^2 * lambda(2)^2))-3)) + 2*a(1)*lambda(2)^2 + 4*a(2)*lambda(2)^2*(lambda(1)^2 + lambda(2)^2 + (1/(lambda(1)^2 * lambda(2)^2))-3);
As you can see, sigma_11_fun is a functions of lambda_1, lambda_2, a(1), a(2), a(3) and a(4) while sigma_22_fun is a function of lambda_1, lambda_2, a(1) and a(2).
I have the data for sigma_11, sigma_22, lambda_1 and lambda_2. Now using this data and functions above, I want to do a curve-fitting to obtain a(1), a(2), a(3) and a(4) constant parameters and of course, a(1) and a(2) which are mutual in both functions should have one value which is similar for both functions.
I defined this error function for the optimization process:
err_fun = @(a, lambda) (sigma_11 - sigma_11_fun(a, lambda)).^2 + (sigma_22 - sigma_22_fun(a, lambda)).^2;
I tried both fmincon and ga functions to do the optimization using the defined error function and initial guess of "a0 = [1, 1, 1, 1]" but results are completly wrong and not even close. I tried to increase maximum generation etc, but nothing helped.
Can someone please help with this?
Thanks in advance.
Diagram of data
