Find the parameters of integration

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Kim Jeong Min 2018-7-2

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评论： Ameer Hamza 2018-7-3

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.

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Walter Roberson 2018-7-2

It is not necessary -- it just makes it easier, probably.

Kim Jeong Min 2018-7-2

If the problem is very easy to solve using "Curve Fitting Toolbox" (or the problem is too complicated without "Curve Fitting Toolbox"). Please tell me the solution with "Curve Fitting Toolbox".

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回答（1 个）

Ameer Hamza 2018-7-2

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在 MATLAB Online 中打开

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.

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Kim Jeong Min 2018-7-3

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 2018-7-3

As Walter pointed out, the difficulty is finding a suitable starting point for optimization. After the introduction of exp() term, it is even more difficult. The new integrand is very sensitive to the value of b and c, for the given value of integral limits. I don't have curve fitting toolbox but maybe it is able to estimate parameters for this new integrand.

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