How to find parameters that minimize a difference

Question

vinxp 2021-11-8

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1581404-how-to-find-parameters-that-minimize-a-difference

编辑： Alan Stevens 2021-11-10

Hi everyone, I have to solve an equation numerically. I thought to split it into two parts and to calculate the difference between them setting a first try column vector and 4 first try parameters. How can I get the 4 parameters that minimize the obtained column of differences? Thank you.

Here is the code for the first part:

k=1.53E4;
kp=5.8E4;
c=1.11E6;
g=1;             %first try parameters
t=[2:2:480]';
x=Strain;        %Strain is a column vector 240x1
y=[zeros(1,length(x))]';
y1=((c./t).*x.*(exp(-k.*t/c)).*(-1+exp(k.*t./c))+x.*kp);
y2=(54000-x.*g.*(1-exp(x)).^2);
for i=1:(length(x))
    y(i)=y1(i)-y2(i);
end  

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Answer 1

Alan Stevens 2021-11-8

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1581404-how-to-find-parameters-that-minimize-a-difference#answer_826319

在 MATLAB Online 中打开

Use fminsearch and use the norm of the differences.

help fminsearch

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Alan Stevens 2021-11-9

在 MATLAB Online 中打开

More like this (though I can't test it as I don't have the Strain values).

k=1.5E4; 
kp=5.8E4;
c=1.11E6;
k_kp_c0 = [k, kp, c];
s=54000*ones(1,240)'; 
x=Strain;
[K,normval1] = fminsearch(@(k_kp_c) argmin_x(k_kp_c, x), k_kp_c0);
k = K(1);
kp = K(2);
c = K(3);
function F = argmin_x(k_kp_c, x)
            
         k = k_kp_c(1);
         kp = k_kp_c(2);
         c = k_kp_c(3);
         
         g = 1;
         t=(2:2:480)';
         x_comp = ((c./t).*x.*(exp(-k.*t./c)).*(-1+exp(k.*t./c))+x.*kp)-((s-x.*g.*(1-exp(x)).^2));
         F = norm(x_comp - x);
end