Problem with nonlinear curve fitting (lsqcurvefit and Multistart)

Question

Faezeh Manesh 2020-4-30

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/522074-problem-with-nonlinear-curve-fitting-lsqcurvefit-and-multistart

编辑： Faezeh Manesh 2020-5-5

Hello all,

Actually, I am dealing with an issue that I can't get desirable results out of my curve-fitting problem. I used lsqcurvefit in the first place. Then, 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')

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Ameer Hamza 2020-5-1

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/522074-problem-with-nonlinear-curve-fitting-lsqcurvefit-and-multistart#answer_429681

在 MATLAB Online 中打开

I am not sure why you wrote the function firstorderDSC1 like that, but reviewing it briefly, it appears that the ode function you have written inside it to fit the data is wrong. Check the differences of your code with this code

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 =rand(1,3);
%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')
function dndt2 = firstorderDSC1(B, T)
%my differential equation
    function denaturate = firstorderDSC(T, n)
        a= (exp(183.8)./1.5); %(1/s)
        dndT=B(1)*exp(-((T-B(2))/B(3)).^2);
        denaturate=dndT;
    end
%solving my differential equation
options = odeset('AbsTol', 1e-8,'RelTol',1e-8);%,'OutputFcn',@odeplot);
[temp,num] = ode23s(@firstorderDSC, T, 0, options);
dndt2 = firstorderDSC(temp,num);
end

Both lines overlap.

12 个评论
显示 10更早的评论隐藏 10更早的评论

Ameer Hamza 2020-5-2

编辑：Ameer Hamza 2020-5-2

在 MATLAB Online 中打开

Finding a good initial guess can really be considered a theoretical problem. You need to analyze your ODEs to see what type of initial guess will lead to a good solution. For example, you can see that the solution to your ODE has a global peak when you plot T against dn/dT. Is there a way to write down the location of that peak in terms of a and deltaE/R? If yes, you can see that if the peak in the dataset to find the good initial guess for a and deltaE/R (B in your code).

Also, I don't see the reason why you need to use numbers of such large magnitude, e.g., a~1e79. Is there some way to rewrite this system of ODE such that this can be avoided?

In your code, you have fixed the value of parameter 'a'. I have modified your code to tell the optimization algorithm to find both parameters. I have also placed bound on the value of 'a', after some trial and error, I found that it will be useful. Now the solution converges sometime, but the performance is still not reliable enough.

clc
clear all;
close all;
%xdata
T = 294:0.1:361;
T=T';
%ydata
f1 =  0.2099*exp(-((T-340.2)/2.439).^2);
%Initial value for unknown coefficient
B0 =[-6.1e+04 3];
%find the local fit using lsqcurvefit
options = optimoptions('lsqcurvefit','FiniteDifferenceType','central','OptimalityTolerance',1e-12,'FunctionTolerance',1e-12, 'MaxFunctionEvaluations',1500);
lb = [-Inf 1];
ub = [Inf 10];
[B,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(@firstorderDSC1,B0,T,f1,lb,ub,options);
figure;
plot(T,f1,T,firstorderDSC1(B,T),'LineWidth',3)
legend('Data','Fitted result')
function dndt2 = firstorderDSC1(B, T)
    %my differential equation
    function denaturate = firstorderDSC(T, n)
        dndT=B(2)*1e79*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);
    dndt2 = firstorderDSC(temp, num);
end