Problem with nonlinear curve fitting - lsqcurvefit

Hello!

I'm trying to fit a nonlinear curve with constrains, so I use lsqcurvefit to get the parameters of my function. After applying lsqcurvefit I obtain this output:

Local minimum possible.

So I use MultiStart in order to get the global minimum, but it is not able to obtain the parameters of the function. In this case the output is:

MultiStart encountered failures in the user provided functions. All 100 local solver runs failed in a user supplied function

Searching on Matlab answers I came across this post

http://www.mathworks.es/matlabcentral/answers/49057-nonlinear-curve-fitting-issue

They suggest patternsearch in situations where an objective function has many local minima. However, it is not clear how to use pattern search to fit a nonlinear curve.

How can I obtain an optimal fitting? How can I use pattern search when fitting a nonlinear curve?

Any help will be appreciated. Thanks!

[Matt J]

It could be worthwhile seeing your code, your curve model, and how you are initializing the iterations. Sometimes, it takes some problem-specific artistry, to avoid naive initial guesses.

Answer 1

[Shashank Prasanna]

Hi Alex, this link may help you get started:

http://www.mathworks.com/help/matlab/math/example-curve-fitting-via-optimization.html

Using optimization routines in MATLAB are very similar across functions. The idea in fitting a curve is to set up an error function usually sum of squared errors, and ask the optimization tool (your choice) to minimize it.

x = patternsearch(@err,x0)

Answer 2

[Alan Weiss]

If your first run with lsqcurvefit produced a local solution, as it seems, then there is no reason I know that MultiStart would fail every time. I would look into the syntax you used to call MultiStart. This example show how to use lsqcurvefit with MultiStart. In particular, you might need to set bounds for the MultiStart object.

Also, the exit message you quoted (Local minimum possible) means that lsqcurvefit did not obtain a sufficiently low value of its first-order optimality measure, but it might have succeeded in minimizing the model discrepancy anyway. It is not clear from that message whether you need MultiStart, but if you want a global optimum then it is a good idea to use it.

I would avoid using patternsearch or any other solver just yet, lsqcurvefit should provide more accurate answers if you can get it to work with MultiStart.

Alan Weiss

MATLAB mathematical toolbox documentation

[Faezeh Manesh]

Dear Alan,

Actually, I am dealing with the same issue that I can't get desirable results out of my curve-fitting problem. I used lsqcurvefit in the first pplace. Then based on your suggestion, I added MultiStart to my code as well but my result didn't change. I don't know why MATLAB gives the unknown model coefficient the same value as I entered for MATLAB. I bring my code in the following along with the results. I would really appreciate it if you can help me fix this problem and get better results:

clc
clear all;
close all;
%xdata
T = 294:0.1:361;
T=T';

%ydata
for i=1:size(T,1)
f1(i)=  0.2099*exp(-((T(i)-340.2)/2.439).^2);
end
f1=f1';

%Initial value for unknown coefficient
B0 =[-6.1e+04];

%find the local fit using lsqcurvefit
options = optimoptions('lsqcurvefit','FiniteDifferenceType','central','OptimalityTolerance',1e-12,'FunctionTolerance',1e-12, 'MaxFunctionEvaluations',1500);
 lb = [-Inf];
 ub = [Inf];
 [B,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(@firstorderDSC1,B0,T,f1,lb,ub,options);
 
% Set up the problem for MultiStart
problem = createOptimProblem('lsqcurvefit','x0',B0,'objective',@firstorderDSC1,...
    'lb',lb,'ub',ub,'xdata',T,'ydata',f1);
ms = MultiStart('PlotFcns',@gsplotbestf);
[xmulti,errormulti] = run(ms,problem,50);

%plot the result
figure;
plot(T,f1,T,firstorderDSC1(xmulti,T),'LineWidth',3)
legend('Data','Fitted result')

And here is my @firstorderDSC1 function:

function dndt2 = firstorderDSC1(B, T)

%my differential equation
    function denaturate = firstorderDSC(T, n)
          a= (exp(183.8)/1.5); %(1/s)
          dndT=a*exp(B(1)/T)*(1-n);
          denaturate=dndT;
    end 
    
%solving my differential equation
options = odeset('AbsTol', 1e-8,'RelTol',1e-8);%,'OutputFcn',@odeplot);
[temp,num] = ode23s(@firstorderDSC, T, 0, options);

  for i=1:size(num,1)
     dndt2(i,1) = firstorderDSC(temp(i),num(i));
  end
end

And here are my results:

[Deniz Toprak]

Hi Alan and Shashank,

I have problem with lsqcurvefit function. I couldn't get good results from parameters. I used multistart with lsqcurvefit. The results are worse than before. I mean without multistart results are more approximate to the real parameter. What the problem should be?

How can I get good parameter results ?

Please help me with this?

Answer 3

[Alex]

Hi Alan and Shashank,

I solved the problem following the example that Alan posted. Thanks to your comments it is more clear for me not only MultiStart function but also pattersearch.

Many thanks for your help!