MATLAB code to find unknown parameters in ODEs using LM method

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nado 2022-10-14

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https://ww2.mathworks.cn/matlabcentral/answers/1825813-matlab-code-to-find-unknown-parameters-in-odes-using-lm-method

编辑： nado 2022-10-14

Hello, I am trying to write a code for solving system of linear ODE with unknown parameters that need to fit the experimental data. I tried doing it by using this:

https://fr.mathworks.com/matlabcentral/answers/160452-matlab-code-for-solving-system-of-ode-with-unknown-parameters

But it didn't work. Or maybe I didn't do it properly because I didn't really understand what was what and how the variables were defined. My problem is:

[M]x_double_dot + [C]x_dot + [K]x = {0};

The experimental data is called "exp_open". I won't show exp_open here because it contains 15001 samples. I don't know if i did a mistake when writing the system in a state space form in order to use ode45.

The code i write is the same as : https://fr.mathworks.com/matlabcentral/answers/160452-matlab-code-for-solving-system-of-ode-with-unknown-parameters

But i obtain an error that said y and exp_open has not the same dimension.

Thank u for your help.

Here is my code :

km11=5.44e+5;

km15=-4.85e+7;

km55=-2073095808.81460221;

km51=-4.85e+7;

km0(1)=km11;

km0(2)=km15;

km0(3)=km55;

km0(4)=km51;

km_estimate=lsqnonlin(@(km)odefit_lm(t,exp_open,km),km0);

function [ err ] = odefit_lm( t,exp_open,km )

time=0:0.1:1500;

km11=km(1);

km15=km(2);

km55=km(3);

km51=km(4);

y0=[0;pi/18;0;0;0;0];

[t,y]=ode45(@(t,y)f_lm(t,y,km11,km15,km55,km51),time,y0);

err=y-exp_open;

end

function [dydt] = f_lm( t,y,km11,km15,km55,km51 )

M(1,1)=8.3163e+7;

M(1,2)=-2.6982e+9;

M(1,3)=1.8107e+6;

M(2,2)=5.6542e+11;

M(2,3)=3.4131e+8;

M(3,3)=1.4249e+6;

M(2,1)=M(1,2);

M(3,1)=M(1,3);

M(3,2)=M(2,3);

K(1,1)=km11;

K(1,2)=km15;

K(1,3)=0;

K(2,1)=km51;

K(2,2)=1.4604e+10+km55;

K(2,3)=0;

K(3,1)=0;

K(3,2)=0;

K(3,3)=1.4249e+6;

C(1,1)=1.8448e+5;

C(2,2)=1.8286e+10;

C(3,3)=4.0008e+10;

C(1,2)=5.8081e+7;

C(1,3)=-8.5911e+7;

C(2,3)=-2.7048e+10;

C(2,1)=C(1,2);

C(3,1)=C(1,3);

C(3,2)=C(2,3);

dydt(1)= y(4);

dydt(2)=y(5);

dydt(3)=y(6);

dydt(4:6)=-(M^(-1))*K*y(1:3)-(M^(-1))*C*y(4:6);

dydt=dydt';

end

In fact, i made some modifications to the code and i obtained another error:

Attempted to access y(5); index out of bounds because numel(y)=4.

Error in f_lm (line 49)

dydt(2)=y(5);

Error in odefit_lm>@(t,y)f_lm(t,y,km) (line 3)

[t,y]=ode45(@(t,y)f_lm(t,y,km),time,[5.44e+5 -4.85e+7 -2073095808.81460221 -4.85e+7]);

Error in odearguments (line 87)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 113)

[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in odefit_lm (line 3)

[t,y]=ode45(@(t,y)f_lm(t,y,km),time,[5.44e+5 -4.85e+7 -2073095808.81460221 -4.85e+7]);

Error in @(km)odefit_lm(time,exp_y,km)

Error in lsqnonlin (line 194)

initVals.F = feval(funfcn{3},xCurrent,varargin{:});

Error in test_lm (line 45023)

km_estimate=lsqnonlin(@(km)odefit_lm(time,exp_y,km),km0);

Caused by:

Failure in initial user-supplied objective function evaluation. LSQNONLIN cannot continue.

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Jan 2022-10-14

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