Incorrect lsqcurvefit fitting, stays in initial guess

Question

hg song 2022-6-24

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1747040-incorrect-lsqcurvefit-fitting-stays-in-initial-guess

评论： hg song 2022-6-26

采纳的回答： Matt J

在 MATLAB Online 中打开

hello all,

I am trying to fitting the data with the following function:

y = a*exp(-x/b)+c*exp(-x/d) , where a,b,c,d are 4 free parameters.

a range from (1e9,5e10), b range from (0,100) ,c range from (5e8,5e9), d range from (100,500);

x range from (1e-5, 1.2e-3)

Saying b = 20, the (-x*1e6/b) could range vastly.

This problem might be similar to this post:https://ww2.mathworks.cn/matlabcentral/answers/255480-lsqcurvefit-does-not-change-the-initial-values

After applied the method in my code, it barely improved the performance.

Here are the codes:

xdata =[2.00E-05 2.45E-05 3.00E-05 3.70E-05 4.55E-05 5.55E-05 6.75E-05 8.25E-05 1.01E-04 ...

1.24E-04 1.51E-04 1.85E-04 2.26E-04 2.76E-04 3.37E-04 4.12E-04 5.03E-04 6.15E-04 7.52E-04 9.19E-04 1.12E-03];

ydata =[2.51E+10 1.68E+10 1.24E+10 8.10E+09 6.33E+09 4.73E+09 3.28E+09 1.88E+09 1.26E+09 ...

7.77E+08 5.17E+08 3.45E+08 2.34E+08 1.57E+08 9.70E+07 5.35E+07 2.94E+07 1.53E+07 7.77E+06 3.89E+06 1.82E+06];

a0=[5; 1; 2; 1.5];

options = optimset('TolFun',1e-28);

lb = [0 ; 0; 1; 1];

ub = [10;10;10;10];

fun=@(x,xdata)(x(1)*1e10)*exp(-xdata*1e6/x(3)/10)+(x(2)*1e9)*exp(-xdata*1e6/x(4)/100);

for i = 1:100

x = lsqcurvefit(fun,a0,xdata,ydata,lb,ub,options);

a0 = x;

end

Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. 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Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance.

semilogy(xdata,fun(x,xdata),xdata,ydata,'+');

And the best fit could be （5.5e10, 26, 1e9, 160)

Is there anybody with a suggestion for improvement?

Best wishes