Problem in the data fitting with custom equation

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.

Answer 1

[Mathieu NOE]

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

[Somnath Kale]

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]

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.