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
on 28 Mar 2023
Commented: Mathieu NOE
on 29 Mar 2023
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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Accepted Answer
Davide Masiello
on 29 Mar 2023
Edited: Torsten
on 29 Mar 2023
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]);
a = P(1)
b = P(2)
hold on
plot(z,u_exp,'o')
plot(z,u_mod(P))
hold off
grid on
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