Dear all,
I'm working on an inverse problem to identify material parameters. This problem involves looking for a minimum of a cost function that is built using the sought parameters. What happens is that my cost function is much more sensitive to a certain parameters so that the others are not correctly identified. I found that it is common to use cost function scaling but I'm not entirely sure how to do that in my case since my parameters have physical meaning.
I use following code to run the optimization:
[optiParams, phi, ~, output] = fmincon(@(plasParams)...
VFOptimisation(plasParams, strain, area, FGlob, VF, 'optimised', meshData,...
options), inpParams, [], [], [], [], LB, UB, [], ...
optimoptions('fmincon', 'TolFun', 1e-10, 'TolX', 1e-10, 'algorithm', 'sqp',...
'MaxFunEvals', 3000, 'TypicalX', [1e2 1e4], 'PlotFcn',[@optimplotx],...
'GradObj', 'off', 'Display', 'iter'))
I investigated multiple starting points and only rarely my identification finds the minimum (which I roughly know where is), see the picture (the contour plot is actually log of my cost fun so the real function is more flat in y direction):
My reference parameters have order : sigma_0 = 297.5 MPa, H = 3170 MPa, so I tried to fiddle with TypicalX parameters in optimization varying it from 1e3-1e10 for the 2nd component (H) but I didn't see improvement. The problem is even more profound when I investigate 4 parameters model.
I found that when the optimization fails (TolX is reached) it ends up much faster with no change in H from initial point:
However, I successful trial, more iterations are performed and eventually H is changed:
Any ideas how could I improve my optimization so it's more reliable?
Cheers,
Aleksander Marek
