genetic algorithm for curve fitting

I know this question have been extensively asked previously,

However, I want to fit an exponontial equation y = a*(1-b*exp(-c*x)) where a,b and c are constants to be optimized, y and x are experimental data obtained as follows

xx=[0.001,5,10,20,40,80];

yy=[0,5,8,11.2,18.3,25.3];

From previous threads I read in the fourm, I ended up forming the below function:

function x = material(y)

xx=[0.001,5,10,20,40,80];

yy=[0,5,8,11.2,18.3,25.3];

a=y(1); b=y(2); c=y(3);

for j=1:6

x=(a)*(1-b*exp(-c*xx(j)))-yy(j);

end

end

I used the function above with GA toolbox in MATLAB 2017b, the results are way wrong

49.98723904071618 49.939937193013776 0.011881054853272788 for a,b and c respictevely

what i have missed?

Thanks for your help!

Answer 1

[Ameer Hamza]

Try this

xx=[0.001,5,10,20,40,80];
yy=[0,5,8,11.2,18.3,25.3];

fun = @(p) p(1)*(1-p(2)*exp(-p(3)*xx));
objFun = @(p) norm(fun(p)-yy);

sol = ga(objFun, 3);

figure()
axes();
plot(xx, yy, 'b+');
hold on
plot(xx, fun(sol), 'r-');
legend({'Data points', 'Fitted Curve'})

[Emran Alotaibi]

Thanks for your help!

that is exactly what I was looking for.

[Ameer Hamza]

I am glad to be of help! :)

[Divya Thokala]

I have ran a code similar to this. Actually I am not aware of how to optimize it. My graph is coming like slopy as in the figure shown. please help me

xx=xlsread('wave.xlsx','A:A');

yy=xlsread('wave.xlsx','B:B');

fun = @(p) p(1)+p(2)*cos(2*3.14*xx/12)+p(3)*sin(2*3.14*xx/12)+p(4)*xx;

objFun = @(p) norm(fun(p)-yy);

sol = ga(objFun, 4);

figure()

axes();

plot(xx, yy, 'b+');

hold on

plot(xx, fun(sol), 'r-');

legend({'Data points', 'Fitted Curve'})