MATLAB: Fit Powerlaw to Data

Question

Hi all!

I need to fit following Power Law to some experimental data.

y = C(B+x)^n

The data I have is as the following:

    STRESS = [0.574,    367.364,    449.112,    531.087,    596.241,    649.097,    695.038,    737.173,    815.008];
    STRAIN = [2.8746e-04,    0.00063,    0.0459,    0.0901,    0.1320,    0.1725,    0.2132,    0.2557,    0.3579];

The variables are x and y are STRAIN and STRESS respectively, and I would like estimates for C, B and n.

I'm not sure how to use the fitting tool for this kind of specific model.

Any ideas or suggestions would be greatly appreciated!

Thank you very much!

Answer 1

Try this:

STRESS = [0.574,    367.364,    449.112,    531.087,    596.241,    649.097,    695.038,    737.173,    815.008];
STRAIN = [2.8746e-04,    0.00063,    0.0459,    0.0901,    0.1320,    0.1725,    0.2132,    0.2557,    0.3579];
yfcn = @(b,x) b(1).*(b(2)+x).^b(3);
B0 = [1E-6; 100; 2];
B = fminsearch(@(b) norm(STRAIN - yfcn(b,STRESS)), B0);
xv = linspace(min(STRESS), max(STRESS), 50);
yv = yfcn(B,xv);
figure
plot(STRESS, STRAIN, 'pg')
hold on
plot(xv, abs(yv), '-r')
hold off
grid
text(150, 0.27, sprintf('y = %.3E \\cdot (%.3f + x)^{%.3f}', B))
xlabel('STRESS')
ylabel('STRAIN')

Experiment to get different results.

EDIT — (6 Dec 2019 at 17:50)

Added plot image: