Estimate differential equation parameters

Question

Alessandro Antonini 2013-1-31

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/60726-estimate-differential-equation-parameters

Dear all,

I need to estimate a parameter of a second order differential equation. This equation is a law of the displacement of a floating body. I know a solution in time domain coming from the experimental investigation but the roblem are the values of the parameters. Is there any function to estimate a differetial equation parameters?

Thanking in advance

Alessandro Antonini

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Shashank Prasanna 2013-1-31

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/60726-estimate-differential-equation-parameters#answer_73099

You can set up an optimization problem to 'fit' your ode to the experimental data for certain parameters that minimize the error between the fitted and real data.

Here is a link in the documentation that explains how to go about this: http://www.mathworks.com/help/optim/ug/optimizing-a-simulation-or-ordinary-differential-equation.html

3 个评论
显示 1更早的评论隐藏 1更早的评论

Shashank Prasanna 2013-2-1

编辑：Shashank Prasanna 2013-2-1

在 MATLAB Online 中打开

Ok, at this point i am assuming you know how to set up an ode and solve it using ODE45, if you are not sure then please look through some examples in: http://www.mathworks.com/help/matlab/ref/ode45.html

I am going to assume you ode function is 'odefun' as in some examples in the link, but with an extra parameter p passed by the optimizer.

Create your objective function such that it minimizes the error between your fitted ode result for a given parameter(s) p.

function err = odefit(exp_t,exp_y,p)
[t,y] = ode45(@(t,y)odefun(t,y,p),exp_t,0) % i am using y0=0 you can choose whatever.
err = sum((y-exp_y).^2); % compute error between experimental y and fitted y
end
p_estimate = fminsearch(@(p)odefit(exp_t,exp_y,p),p0);

Choice of optimization function is left to you and some dangers are listed in the link i gave in the previous post.

Alessandro Antonini 2013-2-1

Yes I know how set up ODE. Thanks

请先登录，再进行评论。

Answer 2

Matt J 2013-1-31

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/60726-estimate-differential-equation-parameters#answer_73098

编辑：Matt J 2013-1-31

在 MATLAB Online 中打开

If it's a linear differential equation with constant unknown coefficients, just evaluate both sides of your differential equation at lots of time points. This will result in a linear system of equalities in the unknown parameters x(i), representable in matrix/vector form as

A*x=b

Then solve by doing x=A\b.