Cole Cole Fitting to data
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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 Comments
John D'Errico
on 2 Sep 2021
Edited: John D'Errico
on 2 Sep 2021
It looks like as I was writing this comment, you did attach two csv files, but the rest of my comment still applies.
Can we assume that e and d are unknowns? omega? a? s? How about j? Is es one unknown, or a product of two unknowns? After all, s and e both appear to be possibly uknowns. So what is es?
Is t the independent variable, represented by what? out(1)? Or something else?
Jasmine Boparai
on 2 Sep 2021
Edited: Jasmine Boparai
on 2 Sep 2021
Star Strider
on 2 Sep 2021
What variables are the data, what variables are known, and what variables (parameters) are to be estimated?
Is ‘j’ a variable or the imaginary operator?
.
Jasmine Boparai
on 2 Sep 2021
Edited: Jasmine Boparai
on 2 Sep 2021
Star Strider
on 2 Sep 2021
What variables are the data to be fitted? Independent variable? Dependent variable?
Apparently ‘es’ now has a value assigned to it. What value is assigned to ω?
.
Jasmine Boparai
on 2 Sep 2021
Edited: Jasmine Boparai
on 2 Sep 2021
Star Strider
on 2 Sep 2021
Fitting real data to a complex model is not possible.
Jasmine Boparai
on 2 Sep 2021
Star Strider
on 2 Sep 2021
I tried with abs, not real, and could not get it to fit.
Jasmine Boparai
on 2 Sep 2021
Alex Sha
on 3 Sep 2021
if taking equation as:
output = real(e + d./((1-(j.*omega.*t).^(1-a)))+s./(j.*omega.*es))
result:
Root of Mean Square Error (RMSE): 0.301453065843602
Sum of Squared Residual: 90.9648248574138
Correlation Coef. (R): 0.999593118288108
R-Square: 0.999186402128943
Parameter Best Estimate
-------------------- -------------
ero 8.667518205328
d 42.2642835242029
t -8.6912938387384E-11
a -0.493793750300934
s -1270059.74250092
parameter s can be any value, others keep stable values；
while if taking equation as:
output = abs(e + d./((1-(j.*omega.*t).^(1-a)))+s./(j.*omega.*es))
result (stable and unique):
Root of Mean Square Error (RMSE): 0.164575686925224
Sum of Squared Residual: 27.1122418836362
Correlation Coef. (R): 0.999878747426502
R-Square: 0.99975750955519
Parameter Best Estimate
-------------------- -------------
ero 7.32134313693091
d 43.9926893787809
t 9.44768896632764E-11
a -0.364142224570391
s 0.659065621688692
Jasmine Boparai
on 3 Sep 2021
Star Strider
on 3 Sep 2021
That uses different software, not MATLAB, to estimate the parameters. The code would therefore not be at all helpful unless you also have that software.
Jasmine Boparai
on 3 Sep 2021
Jasmine Boparai
on 3 Sep 2021
Star Strider
on 3 Sep 2021
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.
Accepted Answer
In electrical engineering terminology, 
, where f is the frequency in Hz. I defined ω that way here.
, 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')
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)
result = output(B(1),B(2),B(3),B(4),B(5),omega)
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 Comments
Jasmine Boparai
on 2 Sep 2021
Star Strider
on 2 Sep 2021
If you already have the estimated parameters, then just use them.
.
Jasmine Boparai
on 3 Sep 2021
Star Strider
on 3 Sep 2021
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!
.
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)
format long
B = theta(:)
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')
.
Jasmine Boparai
on 3 Sep 2021
Star Strider
on 3 Sep 2021
My pleasure!
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]";
More Answers (1)
Maha
on 12 Nov 2022
0 votes
can i get the script code working on matlab to solve the same prob debye eq
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