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Lsqcurvefit nonlinear model: experimental data with model prediction

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Kaouthar Kaouthar
编辑： Matt J 2019-4-1
Hello, I am trying to fit a curve with non linear model (as shown in the caption). I used lsqcurvefit. The fitted curve is bad. How can I get a better fit and another question how can i fit two data simultaneously (same xdata but different ydata, for each ydata same function but i just want to change the value "80"). Thank you in advance. (the data is in attachment)
figure;
A=importdata('ouss.xlsx');
xdata = ...
(A(:,1));
ydata = ...
(A(:,2));
%%
% Create a simple exponential decay model.
fun = @(x,xdata)(x(1)*exp(-(x(2)*(80-x(4)))/(x(3)+80-x(4))))...
./(1+(xdata*(x(1)*exp(-(x(2)*(80-x(4)))/(x(3)+80-x(4))))./x(6)).^(1-x(5)));
%%
% Fit the model using the starting point
x0 = [2e+05,12.3,10.12,335,0.37,12.3];
% x0 = [1,1,1,1,1,1];
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt','Display','iter','TolX', 1e-20, 'TolFun', 1e-20, 'MaxFunEvals', 40000, 'MaxIter', 4000000);
lb = [1 1 1 1 0 1];
ub = [1e17 100 100 1000 1 1e9];
[x] = lsqcurvefit(fun,x0,xdata,ydata,lb,ub,options)
%%
% Plot the data and the fitted curve.
times = linspace(xdata(1),xdata(end));
loglog(xdata,ydata,'ko',times,fun(x,times),'b-')
legend('Data','Fitted exponential')
title('Data and Fitted Curve')

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Matt J
Matt J 2019-4-1
编辑：Matt J 2019-4-1
how can i fit two data simultaneously (same xdata but different ydata, for each ydata same function but i just want to change the value "80").
Just concatenate the data together and write a bigger model function with more variables that describes both.
https://www.mathworks.com/matlabcentral/answers/431697-make-curve-fitting-faster
For a small number of fits, however, it's usually not worthwhile.
How can I get a better fit
I find that fitting the log of the data gives better results,
[x] = lsqcurvefit(@(p,xd)log(fun(p,xd)),x0,xdata,log(ydata),lb,ub,options);
  2 个评论
Kaouthar Kaouthar
Kaouthar Kaouthar 2019-4-1
Thank you for your quick response.
Thank you for the response of the first question.
As for the second one, in order to better visualize the error between the experimental curve and the fitted one, i move to a log scale and the difference is still very big.
I attached the result.
Thank you.
Matt J
Matt J 2019-4-1
编辑：Matt J 2019-4-1
I don't think you're going to do better with this model. The exitflag that I received is 1.
[x,resnorm,residual,exitflag,stats] = ...
lsqcurvefit(@(p,xd)log(fun(p,xd)),x0,xdata,log(ydata),lb,ub,options);
That's the best. It means lsqcurvefit thinks it converged.

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