lsqnonlin (lsqcurvefit , fmincon) does not change the variables in an optimization process to find the best fit

I'm perfoming an optimization of parameters. The main difference between my work and a regular curvefiiting problem is that the function that should be fitted is one that obtains x-y data from a third party simulation software. Here is the main section of the code:

u_test = []; f_test = []; % Anything

x0 = [22,280]; 

force = @(x) sim_res(x,u_test,f_test) - f_test;

x = lsqnonlin(force,x0,[4,199],[40,350]);

and here is the function that goes into another software (ABAQUS) and obtains some simulation results (a set of x-y data):

function force = sim_res(x,u_test,f_test)

inp_initial(x(1),x(2)); % Replaces new coefficients for new iteration

pause(2) 

system('abaqus job=Al.inp user=NONLINEAR.for cpus=4 interactive' )

pause(2)

while exist('Al.lck','file')==2 % Some files have to be deleted
   pause(0.1) 
end
while exist('Al.odb','file')==0 % Some files have to be deleted 
   pause(0.1)
end 

[dis,force] = Read_ODB_outputs_node(); % Another function that obtains results

plot(dis,force,u_test,f_test)

% Some files have to be deleted 
delete('Al.prt'); 
delete('Al.com'); 
delete('Al.sim'); 
delete('Al.dat'); 
delete('Al.log');
end

The problem is that lsqnonlin does not change the initial values of x and after 2-3 iterations, the process stops and converges. The same happens with lsqcurvefit and fmincon. Can anyone find a solution for this?

Thanks in advance

Answer 1

[Torsten]

We don't know if you get modified values for the array "force" from "ABAQUS" if the input vector "x" to "sim_res" is slightly changed by "lsqnonlin". If this is not the case, "lsqnonlin" will think that changing the parameters does not change the objective function and stops - usually with the message that the initial point is optimal.

[Esi Tesi]

Thank you Torsten.

Looks like you're right. So, is there any way to force lsqnonlin start adjusting variables? Or make it think the way it should? I still don't get any solution.

[Torsten]

As already written: it's necessary that the force vector changes when the x-vector changes. We don't know what ABAQUS returns ...

Often choosing a bigger value than sqrt(eps) for the FiniteDifferenceStepSize under the options setting for "lsqnonlin" helps:

FiniteDifferenceStepSize

Scalar or vector step size factor for finite differences. When you set FiniteDifferenceStepSize to a vector v, the forward finite differences delta are

delta = v.*sign′(x).*max(abs(x),TypicalX);where sign′(x) = sign(x) except sign′(0) = 1. Central finite differences are

delta = v.*max(abs(x),TypicalX);

A scalar FiniteDifferenceStepSize expands to a vector. The default is sqrt(eps) for forward finite differences, and eps^(1/3) for central finite differences.

For optimset, the name is FinDiffRelStep. See Current and Legacy Option Names.

Maybe it will also be necessary to choose a higher precision of the ABAQUS computations.

By the way: What does the line "inp_initial(x(1),x(2));" do ?

[Esi Tesi]

It only passes new x vector into an input file (related to ABAQUS) to run a new simulation in ABAQUS and then obtain new force vector.

[Esi Tesi]

Thank you

Your suggestion worked well. I increased FiniteDifferenceStepSize to 0.1 and parameters get changed in next iterations and fitting improves.

But what if the lengths of f_test and force do not match? I tried spline and interp1 to adjust the length of force vector inside sim_res() but some critical points get lost and appears like the attached curves.

Is there anyway to fix this?

[Torsten]

You cannot make ABAQUS output "force" at the "u_test" values instead of the "dis" values ?

[Esi Tesi]

As far as I know and searched for a few days, there is no way to obtain the way you said.

It will be very much easier to process in Matlab and adjust number of variables.

Will lsqcurvefit have the same problem? because it won't need f_test to be included in cost function.

[Torsten]

Every interpolation of the ABAQUS results will make it more difficult for lsqnonlin to succeed. So I would strongly recommend to make ABAQUS output its results at the u_test instead of the dis values.

And choose FiniteDifferenceStepSize as small as possible for lsqnonlin to vary the respective parameter. A value of 0.1 is very big.

And you should try to choose a higher precision for the results in ABAQUS.

lsqcurvefit is the same as lsqnonlin - only more comfortable to handle curve fitting problems.

Of course, there are other nonlinear optimizers in MATLAB you could try, e.g. fminsearch, fmincon or fitnlm.

[Esi Tesi]

Thank you for your notes and time.

I found a function which performs well and interpolates without any change in the main curve, named interparc. Access here:

https://www.mathworks.com/matlabcentral/fileexchange/34874-interparc

Now everything looks fine and optimization goes forward but after a few iterations (like 10) I get an error such this:

Output argument "D_sim" (and maybe others) not assigned during call to "Read_ODB_outputs_node".

Error in Optimize>sim_res

Error in Optimize>@(x)sim_res(x,u_test,f_test)-f_test

Error in finDiffEvalAndChkErr

Error in finitedifferences

Error in computeFinDiffGradAndJac

Error in sfdnls (line 54)

computeFinDiffGradAndJac(x,funfcn,confcn,valx, ...

Error in snls (line 343)

[newA, findiffevals] = sfdnls(xcurr,newfvec,Jstr,group,alpha, ...

Error in lsqncommon (line 167)

snls(funfcn,xC,lb,ub,flags.verbosity,options,defaultopt,initVals.F,initVals.J,caller, ...

Error in lsqnonlin (line 253)

lsqncommon(funfcn,xCurrent,lb,ub,options,defaultopt,allDefaultOpts,caller,...

Error in Optimize (line 103)

x = lsqnonlin(force,x0,[4 199],[40 350],options)

Do you have any experience on this?

[Torsten]

I don't see a variable with name "D_sim" in the code you posted.

Maybe ABAQUS failed in an iteration step and an output is missing to make MATLAB start ?

[Esi Tesi]

I looked into the dis and force vectors at last iteration and they had gotten zero and NaN values at some elements respectively but until then, new values of constants (x(1) & x(2)) do not get closer to the objective and only oscillate between two specific set of values. Is it because I've chosen a large value for FiniteDifferenceStepSize?

[Torsten]

Is it because I've chosen a large value for FiniteDifferenceStepSize?

I don't know. I told you to test for the smallest possible values for FiniteDifferenceStepSize for x(1) and x(2) to make MATLAB move away from the initial guesses for the two parameters.

[Esi Tesi]

I've tried these vaues (1e-6, 1e-3, 1e-2, 1e-1) for FiniteDifferenceStepSize and got the same result that after a few iterations, the solver gets stuck at some specific x value and iterates on them without any progress. Is there any option or parameter that controls this action?

[Torsten]

I don't know the reason. Most probably, the values coming from ABAQUS are too inexact. This would cause that computing reliable derivatives with respect to the parameters being fitted fails.

Answer 2

[Matt J]

Consider the various recommendations at,

https://www.mathworks.com/help/optim/ug/optimizing-a-simulation-or-ordinary-differential-equation.html

I suspect that Suggestions for Finite Differences may be particularly relevant.