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
am 28 Mär. 2023
Kommentiert: Mathieu NOE
am 29 Mär. 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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Davide Masiello
am 29 Mär. 2023
Bearbeitet: Torsten
am 29 Mär. 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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