fminsearch gives weird zick zack solution

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sbr
sbr 2023-6-10
编辑： Torsten 2023-6-11
So, I wanna implement a parameter fit to fit meassurement data to an equation (specifically, I wanna fit data to the "improved generalised steinmetz equation", which you can see here. The average over time period T from eq 1.11 is ignored, since I want the current value).
For a reason I don't understand, the solution fminsearch (and also lsqcurvefit) delivers is just completely off and goes zick-zack through my meassured data. Can someone of you maybe spot the flaw? In my mind it has to be somewhere in the implementation of the 2 equations, which are linked above too, since lsqcurvefit and fminsearch both deliver the same bs.
EDIT: Here is a screenshot of the plot:
Here is my code: At the beginning, I import data (B, P) from a file (which is not included below):
B_pp = max(B) - min(B); % peak-to-peak flux density
T = 1./f;
dt = T ./ 1000;
t = 0:dt:T;
k1 = @(x) x(1)./( (2*pi).^(x(2)-1) .* ...
integral(@(theta) abs(cos(theta)).^x(2) .* 2.^(x(3)-x(2)), 0, 2*pi) );
pv = @(x) k1(x) .* abs(gradient(B, t(2)-t(1))).^x(2) .* B_pp.^(x(3)-x(2));
x = fminsearch(@(x) vecnorm(pv(x) - P), [1,1,1]);
%[x, resnorm, residual] = lsqcurvefit(pv, [0,0,0], B, P, [-Inf, -Inf, -Inf],[Inf, Inf, Inf],opts);
figure; grid on;
plot(B, P, 'bo', B, pv(x), 'r-');
xlabel('Magnetic field B [T]'); ylabel('Power loss p [W/m^3]');
legend('Experimental data', 'Fitted function'); title('Experimental vs. fitted');
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sbr
sbr 2023-6-11
Sure. It is more or less exactly the fitted function without a weight (same zick-zack, different amplitudes).
Torsten
Torsten 2023-6-11
编辑：Torsten 2023-6-11
And by multiplication by a constant and an exponentiation you expect a smooth curve like the blue one ? No chance. I think you have to reconsider if delta B in your integral really means max(B) - min(B). I doubt it. If it wouldn't depend on t as your setting implies , it could have been taken out of the integral.

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回答（1 个）

Matt J
Matt J 2023-6-10
编辑：Matt J 2023-6-10
It seems unlikely to me that x0=[1,1,1] would be an accurate initial guess. Surely, you chose that arbitrarily. Since you only have 3 unknown parameters, it shouldn't be too computationally expensive to do a discrete grid search for a better initial point.
  2 个评论
sbr
sbr 2023-6-11
Normal values for or in this case x(1), x(2), x(3) are [10, 1.5, 3], but setting the initial guess to that doesn't improve the result sadly.
Matt J
Matt J 2023-6-11
Then your model (as coded currently) may be inconsistent with your data. But that is an additional reason a grid search could help you. If you get poor agreement even after a grid search, you know you have bug in your model function code.

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