MATLAB: Fitting data to an equation with complex part

curve fittingnonlinear equationnonlinear fitting

Hi,
I hope you are all well.
I have experimental data for a diaphragm displacement and want to fit it to the following equation. The experimental data is displacement (H in meters) and frequency (w in rad/s).
I have a working code but it is changes a lot with the initial guess. I need help to improve this.
x(1) is the alpha (numerator) and x(2) is the damping. omega_r is the resonant frequency and it is known. Gamma should be between 0.04 and 0.07. I am interested in gamma, the damping term in the denominator.
% non linear fitting
fun = @(x,omega)(x(1)./(omega_r^2 - omega.^2 + 1i*(2*x(2)*omega_r.*omega)));
x0 = [-35.9811 + 1i*23.8154,0.06];
opts = optimoptions(@lsqcurvefit,'Display','off','Algorithm','trust-region-reflective');
[vestimated,resnorm] = lsqcurvefit(fun,x0,omega,H,[],[],opts);
Looking forward to your suggestions.
Best regards,
Baris
Edit: x0 is changed.

Best Answer

lsqcurvefit is seneitive to initial start-values since it use local optimization algorithm, same as cftool, there is a GA toolbox with global optimization algorithm in Matlab, unfortunately, the effects of GA are not so good as expected.
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