System Identification: gradient warning with pem

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Hello,
here is my Problem: I try to identify 3 parameters in a nonlinear Greybox-Model (4 States, 2 Inputs). I actually "copied" the example for this task provided by matlab (Estimating Nonlinear Grey-Box Models).
To test it, I simulated the model with knwon parameters and used the in- and output for the identification. While running pem I get the following warning:
"Warning: Gradient calculation using numerical differentiation failed. Check parameter values"
After that warning the identification process terminates (reason: near local minimum, but it did not change the values of the parameters) I get that error even if i start with the right values for the parameters.
So I changed the Gradient calculation to 'Basic' and get the following Warning:
"Warning: Gradient calculation using numerical differentiation failed for expermiment 1. Check parameter values"
But this time the identfication process runs until the cost function is not decreasing any further. During the process it only changes the values of 2 out of the 3 parameters.
Is it possible that my third parameter is not identifiable (and is this a typicall warning you get then)?
Edit: Parameter is very small (10e-12), could this be the problem?
EditEdit: Estimating only the parameter which isnt changing, removes the warning, the cost function decreases during the identification process, but the parameter remains still the same?!
Thanks
  1 Comment
Alan Liang
Alan Liang on 17 Jun 2021
Hi, I ran into the same problem with the warning "Warning: Gradient calculation using numerical differentiation failed for expermiment 1. Check parameter values" except that the model is never iterated and none of the parameters are changed.
I don't know how to make it work to fit the data. Have you ever solve the problem?

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