Fit data with a given equation for 3 variables

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I want to fit my data to the following equation, but I dont know how to force the program to take the b values which i have, instead of calculating them automatically, I attached here my code which i wrote
fy = @(a,b,x) ((1-(x/a)).^(-a*b));
x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001, 0.00111499, 0.0011926, 0.0013699, 0.00161633, 0.00192075, 0.00274991, 0.00357156];
b = [0, 1.1499, 0.963, 1.233, 1.540825, 2.001630435, 3.181654545, 4.285933333];
B = fmincon(@(c) norm(y - fy(c(1),c(2),x)), [1; 1], [],[],[],[], [0 0],[1 90]);
fprintf('PhiMax = %.15f\nVisco = %.15f\n', B)
xv = linspace(min(x), max(x));
figure(1)
plot(x, y, 'pg')
hold on
plot(xv, fy(B(1),B(2),xv), '-r')
hold off
grid
  2 Commenti
Torsten
Torsten il 24 Mag 2022
How should it be possible to have the value for b if you don't know the value for a ?
Tesla
Tesla il 24 Mag 2022
Indeed i am looking for the value of a

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Risposta accettata

Torsten
Torsten il 24 Mag 2022
Modificato: Torsten il 24 Mag 2022
Your function is not suited to reflect your data.
x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001, 0.00111499, 0.0011926, 0.0013699, 0.00161633, 0.00192075, 0.00274991, 0.00357156];
b = [0, 1.1499, 0.963, 1.233, 1.540825, 2.001630435, 3.181654545, 4.285933333];
p0 = 1;
B = lsqnonlin(@(a)fy(a,x,y,b),p0,max(x),Inf)
fprintf('PhiMax = %.15f\nVisco = %.15f\n', B)
figure(1)
plot(x, y, 'pg')
hold on
plot(x, fy(B(1),x,y,b)+y, '-r')
hold off
grid
function res = fy(a,x,y,b)
res = ((1-(x/a)).^a).^b - y;
end
  1 Commento
Tesla
Tesla il 24 Mag 2022
Thanks a lot, it works, I just need to multipy the function by 0.001.
function res = fy(a,x,y,b)
res = 0.001*((1-(x/a)).^a).^b - y;
end

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Più risposte (1)

Hiro Yoshino
Hiro Yoshino il 24 Mag 2022
How about this?
You only need to think about c as follows:
fy = @(a,b,x) ((1-(x/a)).^(-a*b));
x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001, 0.00111499, 0.0011926, 0.0013699, 0.00161633, 0.00192075, 0.00274991, 0.00357156];
b = [0, 1.1499, 0.963, 1.233, 1.540825, 2.001630435, 3.181654545, 4.285933333];
B = fmincon(@(c) norm(y - fy(c,b,x)),1,[],[],0,1)
Converged to an infeasible point. fmincon stopped because the size of the current step is less than the value of the step size tolerance but constraints are not satisfied to within the value of the constraint tolerance. Consider enabling the interior point method feasibility mode.
B = 6.6511e+03

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