Problem in the data fitting with custom equation

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Somnath Kale
Somnath Kale 2021-4-29
评论： Mathieu NOE 2021-4-29
Hi
I am facing some issue in the data fitting with the equation. I wanted to fit to my data with eqauation
P(t) = 2Pr (1- exp(-(t/t0)^n) (also attached in the image). and Pr <= 40 and n <=2 are the upper limits.
I wanted to fit my function for n, Pr and t0.
t = 1.00E-07 2.00E-07 5.00E-07 1.00E-06 2.00E-06 5.00E-06 1.00E-05 2.00E-05 5.00E-05 1.00E-04 2.00E-04 5.00E-04 1.00E-03 2.00E-03 5.00E-03
P(t) = 2.3800 4.4800 6.4500 9.0200 13.2400 16.2600 18.9700 22.9900 26.3300 28.7800 30.3100 31.6500 31.9500 32.0500 32.3400
if possible let me know the code also.

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Mathieu NOE
Mathieu NOE 2021-4-29
hello
here you are :
t = [1.00E-07 2.00E-07 5.00E-07 1.00E-06 2.00E-06 5.00E-06 1.00E-05 2.00E-05 5.00E-05 1.00E-04 2.00E-04 5.00E-04 1.00E-03 2.00E-03 5.00E-03];
P = [2.3800 4.4800 6.4500 9.0200 13.2400 16.2600 18.9700 22.9900 26.3300 28.7800 30.3100 31.6500 31.9500 32.0500 32.3400];
f = @(a,b,c,x) 2*a.*(1-exp(-(x./b).^c));
obj_fun = @(params) norm(f(params(1), params(2), params(3),t)-P);
sol = fminsearch(obj_fun, [P(end)/2,1,1]);
Pr = sol(1)
t0 = sol(2)
n = sol(3)
figure;
semilogx(t, P, '+', 'MarkerSize', 10, 'LineWidth', 2)
hold on
semilogx(t, f(Pr, t0,n, t), '-');grid on
xlabel('time t');
ylabel('P(t)');
% % gives :
% Pr = 15.9313
% t0 = 1.2114e-05
% n = 0.4339
  2 个评论
Somnath Kale
Somnath Kale 2021-4-29
Hello @Mathieu NOE
Thanks for your kind reply!
I have one dbout: how do you seted the upper limit fot n t0 and Pr ?
is it here?
sol = fminsearch(obj_fun, [P(end)/2,1,1]);
please let know!
I also fitted the equation with fmincon but I was uable to set the upper bound.
Mathieu NOE
Mathieu NOE 2021-4-29
hello
these are initial guesses , not limits;
fminsearch Multidimensional unconstrained nonlinear minimization (Nelder-Mead).
X = fminsearch(FUN,X0) starts at X0 and finds a local minimizer X of the
function FUN. FUN accepts input X and returns a scalar function value
F evaluated at X. X0 can be a scalar, vector or matrix.

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