Minimize the sum of squared errors between the experimental and predicted data in order to calculate two parameters

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ORESTE SAINT-JEAN 2023-3-28

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评论： Mathieu NOE 2023-3-29

In my research work, I use a model and I want to minimize the sum of squared errors between the experimental and predicted data in order to calculate two parameters.

The experimental data are:

u exp: [0.709; 0.773 ;0.823 ;0.849 ;0.884 ;0.927 ;0.981 ;1.026 ;1.054 ;1.053 ;1.048;1.039] ;

observed at z=[ 0.006;0.012;0.018;0.024;0.03;0.046;0.069;0.091;0.122;0.137;0.152;0.162];

The equation of the model that I use is:

u model=0.1073*((log(0.13/z)-1/3*(1-(z/0.13)^3)+2*a*(1+(b)^0.5)*cos(11.89*z)); and I want to calculate the parameters “a” et “b” by minimizing the sum of squared errors between “u exp” and “u model”.

Someone here can help me please?

Thank you already for your help!

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Answer 1

Davide Masiello 2023-3-29

编辑：Torsten 2023-3-29

在 MATLAB Online 中打开

You can use MatLab's fmincon.

z = [0.006;0.012;0.018;0.024;0.03;0.046;0.069;0.091;0.122;0.137;0.152;0.162];

u_exp = [0.709;0.773;0.823;0.849;0.884;0.927;0.981;1.026;1.054;1.053;1.048;1.039];

u_mod = @(P) 0.1073*(log(0.13./z)-1/3*(1-(z/0.13).^3)+2*P(1).*(1+P(2).^0.5).*cos(11.89*z));

sum_sq_err = @(P) sum((u_exp-u_mod(P)).^2);

P = fmincon(sum_sq_err,[0.1,0.1]);

Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.

a = P(1)

a = 2.0158

b = P(2)

b = 0.3185

hold on

plot(z,u_exp,'o')

plot(z,u_mod(P))

hold off

grid on

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ORESTE SAINT-JEAN 2023-3-29

移动：Star Strider 2023-3-29

z = [0.006;0.012;0.018;0.024;0.03;0.046;0.069;0.091;0.122;0.137;0.152;0.162];

u_exp = [0.345;0.281;0.231;0.205;0.17;0.127;0.073;0.028;0.00;0.0010;0.0060;0.015];

u_mod = @(P) 0.1073*((log(0.132./z)-(1/3)*(1-(z/0.132).^3)+2*P(2).*(1+(P(1)).^0.5).*(cos(pi*z/0.264)).^2));

sum_sq_err = @(P) sum((u_exp-u_mod(P)).^2);

P = fminsearch(sum_sq_err,[0.01,0.01])

hold on

plot(z,u_exp,'o')

plot(z,u_mod(P))

hold off

grid on

P =

0.0506 0.2198

With the god data, everything it's ok.

THANK YOU FOR YOUR HELPS!!

Mathieu NOE 2023-3-29

I feel better now :)

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Minimize the sum of squared errors between the experimental and predicted data in order to calculate two parameters

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