lsqcurvefit for global fitting gives bad parameters

Hello Dear Matlab-Community,

I am trying to do a Butterworth-Van Dyke (BVD) siumulation. I calculated my startparameters. Common X-values are between 1 and 3000. Common Y-values are between 1E-2 and 1E-4. I want to optimize 4 parameter (R_m, L_m, C_m, C_0) with TypicalX like [1000, 1, 1e-10, 1e-8].

My Programm is:

if true
% clear all;
% close all;
% 
% Folder = 'xxx';
% FileName = [Folder 'Daten_Aktor1.xls'];
% fid = fopen(FileName, 'r');
% if fid == -1
%     error('Cannot open file %s', FileName);
% end
% Data = xlsread(FileName);
% fclose(fid);
% 
% t=Data(:,1)     %x-values
% y=Data(:,2)     %y-values
% 
% %Calculated startparameters
% % R_m = 7120
% % L_m = 26.60811
% % C_m = 5.94902E-10
% % C_0 = 3.762756E-8
% 
% %Borders
% lb = [6500,1,5E-11,5E-009]
% ub = [7800,100,5E-09,5E-007]
% 
% x0 = [3.762756E-8,7120,26.6,5.94902E-10]
% 
% Fun = @(x,xdata) abs(i*2*pi*x(1)*xdata+1./(x(2)+i*(2*pi*x(3)*xdata-1./(2*pi*x(4)*xdata))))
% 
% options = optimset('TolX',1e-10,'TolFun',1e-10, 'TypicalX', [1000, 1, 1e-10, 1e-8]);
% x = lsqcurvefit(Fun,x0,t,y,lb,ub,options)
% 
% hold all
% plot(t,Fun(x,t),'r', 'LineWidth',2)
% plot(t, y,'k', 'LineWidth',2)
% xlabel('Frequenz [Hz]')
% ylabel('Amplitude [a.u.]')

end

The main problem is, that the Parameter C_0 and C_m are very small. For the algorithm it seems to be not possible to optimize both parameters. For this purpose I did not optimize the value directly. I defined a the value of C_0 and C_m as fix, and changed a percentage of the calculated value, like C_calculated * x(1) = C_optimized. But still, the steptolerance seems to be to tiny. I can not change that. Do you have an idea for me. I am trying to achieve a global fit.

I hope you can help me. Best regards Henrik

[Eugênio Sabatini]

Could you solve it?

Answer 1

[Alex Sha]

Hi, I have just try to solve this complex fitting problem by using another math package, the result is as following, seems to be prefect:

Fun = @(x,xdata) abs(i*2*pi*x(1)*xdata+1./(x(2)+i*(2*pi*x(3)*xdata-1./(2*pi*x(4)*xdata))))

Root of Mean Square Error (RMSE): 1.55596435380165E-6
Sum of Squared Residual: 9.70831053190858E-10
Correlation Coef. (R): 0.999930645831277
R-Square: 0.999861296472554
Adjusted R-Square: 0.999860599469904
Determination Coef. (DC): 0.999861282770118
F-Statistic: 953637.344478172

Parameter          	Best Estimate
--------------------	-------------
x1	3.80465879533941E-8
x2	8071.77174563029
x3	15.4842218863772
x4	1.0150335453685E-9

[Eugênio Sabatini]

Do you have the code for this approach?

[Alex Sha]

Hi, looks like below:

ComplexStr = i;
Parameter x(4);
Variable xdata,ydata;
Function ydata=abs(i*2*pi*x(1)*xdata+1/(x(2)+i*(2*pi*x(3)*xdata-1./(2*pi*x(4)*xdata))));
Data; 
500	0.00012322
504.999	0.00012447
509.999	0.0001257
514.999	0.00012694
519.999	0.00012817
524.999	0.00012942
529.999	0.000131
....

[Eugênio Sabatini]

Hi! Which package did you use to obtain this solution?

[Alex Sha]

Hi, it's a package named 1stOpt