Cole Cole Fitting to data

Question

Jasmine Boparai 2021-9-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1445479-cole-cole-fitting-to-data

回答： Maha 2022-11-12

采纳的回答： Star Strider

I am having an experimental data and I want to do cole cole fitting using the equation

εr(ω) = ε' r(ω) - jε'' r(ω) = εro + Δεr/1 + (jωτ)^1-α +σs/jωε0

I am trying to do this with curve fitting toolbox, but not able to do it.

Then I want to find coefficientf from the equation.

I have attached csv file and code i was using this:

fid = fopen('Ist.csv');

out = textscan(fid,'%f %f %f', 'Headerlines', 1, 'delimiter',',');

fclose(fid);

%date = datevec(out{1});

col1 = out{1}

col2 = out{2}

Matlab form of equation:

output = e + d./((1-(j.*omega.*t).^(1-a)))+s./(j.*omega.*es);

16 个评论
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Jasmine Boparai 2021-9-3

As you said fitting real data to complex model is not possible, but if we have complex data, then would it be possible?

Star Strider 2021-9-3

I have no idea.

I have no idea what your data are, the rationale behind the model you are fitting, or anything else.

All I know is that I cannot get either GlobalSearch or ga to fit it.

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Answer 1

Star Strider 2021-9-2

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1445479-cole-cole-fitting-to-data#answer_779754

在 MATLAB Online 中打开

In electrical engineering terminology,

, where f is the frequency in Hz. I defined ω that way here.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/727854/Ist.csv', 'VariableNamingRule','preserve')

T1 = 1001×2 table

frequency(Hz) Tr 2 Data(e') _____________ ______________ 5e+08 52.4 5.26e+08 52.8 5.52e+08 52 5.78e+08 51.7 6.04e+08 52.3 6.3e+08 52.2 6.56e+08 51.4 6.82e+08 51.6 7.08e+08 52 7.34e+08 51.5 7.6e+08 51.2 7.86e+08 51.6 8.12e+08 51.6 8.38e+08 51 8.64e+08 51.2 8.9e+08 51.4

omega = 2*pi*T1{:,1};

y = T1{:,2};

es = 8.85e-12;

output = @(ero,d,t,s,a,omega) ero + d./((1-(1j.*omega.*t).^(1-a)))+s./(1j.*omega.*es);

[B,fval] = fminsearch(@(b) norm(y - imag(output(b(1),b(2),b(3),b(4),b(5),omega))), rand(5,1)*1000)

B = 5×1

615.4022 702.8629 10.1123 -4.5173 688.4702

fval = 697.6694

result = output(B(1),B(2),B(3),B(4),B(5),omega)

result =

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figure

plot(omega, y, '.')

hold on

plot(omega, imag(result), '-r')

hold off

grid

xlabel('\omega')

ylabel('Something')

legend('Data','Fit', 'Location','best')

The imaginary result appears to be the most appropriate fit, since the real result is a straight line, and the abs result is not much better. Regardless, the function and initial parameter estimates need to be examined closely to be certain that they actually describe the data. Other solvers (such as lsqcurvefit) might be more appropriate here. I use fminsearch because everyone has it.

.

8 个评论
显示 6更早的评论隐藏 6更早的评论

Star Strider 2021-9-3

在 MATLAB Online 中打开

I cannot help any more than I already have.

I even tried GlobalSearch on this and could not get a good fit, regardless of fitting the real, imag or abs values of the function to the data.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/727854/Ist.csv', 'VariableNamingRule','preserve');
omega = 2*pi*T1{:,1};
y = T1{:,2};
es = 8.85e-12;
output = @(ero,d,t,s,a,omega) ero + d./((1-(1j.*omega.*t).^(1-a)))+s./(1j.*omega.*es);
fitfcn = @(b) norm(y - abs(output(b(1),b(2),b(3),b(4),b(5),omega)));
B0 = randn(5,1)*10000;
problem = createOptimProblem('fmincon', 'x0',B0, 'objective',fitfcn);
gs = GlobalSearch('PlotFcns',@gsplotbestf);
[B,fval] = run(gs,problem)
B(:)
result = output(B(1),B(2),B(3),B(4),B(5),omega);
figure
plot(omega, y, '.')
hold on
plot(omega, real(result), '-r')
plot(omega, imag(result), '--r')
plot(omega, abs(result), '-g')
hold off
grid
xlabel('\omega')
ylabel('Something')
legend('Data','Fit', 'Location','best')

The model does not describe the data, so any further efforts to fit this are likely not worthwhile.

Stopping here.

Good luck!

.

Star Strider 2021-9-3

在 MATLAB Online 中打开

Attempting the fit using the genetic algorithm —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/727854/Ist.csv', 'VariableNamingRule','preserve');

omega = 2*pi*T1{:,1};

y = T1{:,2};

es = 8.85e-12;

outputfcn = @(ero,d,t,s,a,omega) ero + d./((1-(1j.*omega.*t).^(1-a)))+s./(1j.*omega.*es);

ftns = @(b) norm(y - real(outputfcn(b(1),b(2),b(3),b(4),b(5),omega)));

PopSz = 50;

Parms = 5;

opts = optimoptions('ga', 'PopulationSize',PopSz, 'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-3, 'MaxGenerations',2E3); %, 'PlotFcn',@gaplotbestf, 'PlotInterval',1);

[theta,fval,exitflag,output] = ga(ftns, Parms, [],[],[],[],zeros(Parms,1),Inf(Parms,1),[],[],opts)

Optimization terminated: average change in the fitness value less than options.FunctionTolerance.

theta = 1×5

0.0001 18.6955 0.0001 11.3390 1.0617

fval = 303.9269

exitflag = 1

output = struct with fields:

problemtype: 'boundconstraints' rngstate: [1×1 struct] generations: 1119 funccount: 52646 message: 'Optimization terminated: average change in the fitness value less than options.FunctionTolerance.' maxconstraint: 0 hybridflag: []

format long

B = theta(:)

B = 5×1

0.000082602500916 18.695516696453094 0.000073242187500 11.338973423600198 1.061712076544762

format short

result = outputfcn(B(1),B(2),B(3),B(4),B(5),omega);

figure

plot(omega, y, '.')

hold on

plot(omega, real(result), '-r')

% plot(omega, imag(result), '--r')

% plot(omega, abs(result), '-g')

hold off

grid

xlabel('\omega')

ylabel('Something')

legend('Data','Fit Real', 'Location','best')

.

Star Strider 2021-9-3

My pleasure!

Alex Sha 2021-9-4

编辑：Alex Sha 2021-9-4

在 MATLAB Online 中打开

Hi, Jasmine, the results provided above are obtained by one other package other than Matlab, the code looks simple like:

Constant es = 8.85e-12;
ComplexStr = j;
Variable omega,y[realPart];
Function y = real(e + d/((1-(j*omega*t)^(1-a)))+s/(j*omega*es));
DataFile "Sheet1[A2:B1002]";