Fit computation did not converge:Success, but fitting stopped because change in residuals less than tolerance (TolFun)

Recently I am trying to measure the thickness of different materials in micron level and when I tried to fit the phase of different materials. Normally, I set +-10% tolerance to my actual value for each parameters. However when I use the tolerance values for upper and lower limits, my fitting function cannot fit the phase oscillation(e.g. refractive index of silicon is 3.416 and I took lower limit: 3.0744 and upper limit:3.7576). my fitting function works for 525 um thickness measurements but it does not work for 280 um and below. And I got the message of ''Fit computation did not converge:Success, but fitting stopped because change in residuals less than tolerance (TolFun)''

Does anybody know the reason for that? when I increased the tolerance more than 200%, it gets better but increasing tolerance is not helping me for the project.

Your help would be appreciated.

Thank you.

Answer 1

[Avadhoot]

Hi Korhan,

I understand that you are working on fitting your model to your data. As you correctly mentioned, the error you're encountering is due to the residuals falling below the tolerance limits. One possible solution is to increase the tolerance by adjusting the "TolFun" parameter. However, I understand that you prefer not to do that. Based on the information you've provided, here are a few options you can consider:

1. Data characteristics: Noisy data can slow down the convergence of the model or prevent it from converging at all. Be sure to thoroughly check the data for any inconsistencies or noise.
2. Choice of model: The model you have selected might have inherent limitations that hinder its convergence. Consider exploring alternative models that may provide a better fit to your data.
3. Initial parameters: The initial parameter values you provide to the model can significantly impact the convergence speed. If the initial parameters are far from the optimal solution, the fitting process may be slower. Ensuring that your initial parameter estimates are closer to the expected values can help improve convergence.

To provide more specific help, please share additional details about the data and the specific model you are working with.

For more information about the “fit” function, refer to the below documentation:

https://www.mathworks.com/help/curvefit/fit.html

I hope it helps.