Asked by Kim Jeong Min
on 2 Jul 2018

Hello everyone, I have a question that hasn't been able to find it on my own though, so any help is greatly appreciated.

I try to find the parameters a, b, c, d and e which satisfy below equations.

Where T_1~T_5 and q_1~q_5 are input parameters which already know.

Are there any functions that can solve these kinds of problem in MATLAB?

Thanks for any helpful ideas.

Answer by Ameer Hamza
on 2 Jul 2018

Try this. This requires optimization toolbox. This uses the sum of squared error from your equations as an objective function.

T0 = 1;

Tx = [2; 3; 4; 5; 6]; % from T1 to T5

qx = [2; 3; 4; 5; 6];

f = @(a,b,c,d,e, T) (a+b*T+c*T.^2).^(1./(d+e*T));

f_int = @(a,b,c,d,e, T0, T1) integral(@(T) f(a,b,c,d,e,T), T0, T1);

obj_fun = @(a,b,c,d,e) sum((arrayfun(@(T0, T1) f_int(a,b,c,d,e, T0, T1), T0*ones(size(Tx)), Tx)-qx).^2);

sol = fmincon(@(x) obj_fun(x(1),x(2),x(3),x(4),x(5)), [1;1;1;1;1], [], []);

The sol contain value of a, b, c, d and e in order.

Walter Roberson
on 2 Jul 2018

Could you post some sample T and q values for us to test with?

Kim Jeong Min
on 3 Jul 2018

Thank you for using so much personal time to solve this problem.

The conditions are:

Sorry for the mistake I made (missing exponential) for the specific form of function.

Ameer Hamza
on 3 Jul 2018

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