Fit data with a given equation for 3 variables

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Tesla
Tesla 2022-5-24
评论： Tesla 2022-5-24
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 个评论
Torsten
Torsten 2022-5-24
How should it be possible to have the value for b if you don't know the value for a ?

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采纳的回答

Torsten
Torsten 2022-5-24
编辑：Torsten 2022-5-24
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 个评论
Tesla
Tesla 2022-5-24
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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更多回答（1 个）

Hiro Yoshino
Hiro Yoshino 2022-5-24
Ran in:
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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