Estimate differential equation parameters
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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
采纳的回答
Shashank Prasanna
2013-1-31
1 个投票
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
Alessandro Antonini
2013-2-1
Shashank Prasanna
2013-2-1
编辑：Shashank Prasanna
2013-2-1
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
更多回答（1 个）
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.
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