Fit data with a given equation for 3 variables

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Tesla
Tesla on 24 May 2022
Commented: Tesla on 24 May 2022
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 Comments
Tesla
Tesla on 24 May 2022
Indeed i am looking for the value of a

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Accepted Answer

Torsten
Torsten on 24 May 2022
Edited: Torsten on 24 May 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 Comment
Tesla
Tesla on 24 May 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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More Answers (1)

Hiro
Hiro on 24 May 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
  1 Comment
Tesla
Tesla on 24 May 2022
Thank you for the suggestion but the fitting plot is not working

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