How to optimize the Parameters in my code

9 次查看（过去 30 天）
Mathematics
Mathematics 2011-5-2
评论： yem 2014-12-15
Dear All,
I have a problem regarding the optimization of parameters such that the error should be minimized. As given in the code below, I want to find the best values of parameters (UP1 and UP2) in the given range such that my error minimizes. Can anybody help me in this regard. If there is any example similar to my problem, please let me know. I will be very thankful to you.
Best Regards
------------------------------
clear,clc
global XX
tend = 40;
tspan=1:1:40;
cp1 = 5; cp2 = 3; A1 = 2; rst = 2;
UP1=.2; %%%parameter to be optimized range = [.01 1] %%%
UP2=.7; %%%parameter to be optimized range = [0.5 3] %%%
M =[cp1 0 0 0; 0 cp1 0 0; 0 0 cp2 0; 0 0 0 cp2];
XX=[-rst-cp1*UP1 0 rst 0;
UP1*cp1 0 0 0;
rst 0 -rst-UP2*cp2 0;
0 0 UP2*cp2 0];
options = odeset('AbsTol',1e-10,'RelTol',1e-10,'InitialStep',1e-2, ...
'Mass',M,'Jacobian',XX);
u0 = zeros(4,1);
u0(1) = 1;
[t,u] = ode15s(@call, tspan, u0,options);
n1=[u(3,2) u(7,2) u(end,2)];
n2=[u(3,4) u(7,4) u(end,4)];
e1=[0.3 0.8 1];
e2=[0.5 2 5];
%%%% Objective is to minimize the following error %%%%
error = abs((n1(1)-e1(1))^2+(n1(3)-e1(2))^2+(n1(3)-e1(3))^2+...
(n2(1)-e2(1))^2+(n2(2)-e2(2))^2+(n2(3)-e2(3))^2)
------------------------------
function du = call( t,u )
global XX
du=XX*u;
end
------------------------------

请先登录，再回答此问题。

采纳的回答

Teja Muppirala
Teja Muppirala 2011-5-2
People often ask how to do this. Basically you need to pass your ODE solver to your optimization solver. This is an example of how to do it:
http://www.mathworks.com/matlabcentral/answers/5054-solving-an-ode-with-best-fit-adjustment-to-empirical-observations
  2 个评论
Teja Muppirala
Teja Muppirala 2011-5-2
If that example doesn't make sense, or you don't know how to apply that to your problem, feel free to ask for more clarification.
Mathematics
Mathematics 2011-5-2
Dear Teja,
First of all, I am really thankful to you for your kind help. Your example is really good but I could not implement it in my problem. Can you please help me in implementing this in my problem. I have tried the following:
function xout = do_optimization_mine
% The true parameters
e1=[0.3 0.8 1]; % the actual data
T = [3 7 40]'; % need to optimize at three time steps.
hold on;
plot(T,e1);
x0 = [0.2 .7]; % Just some Initial Condition
ub = [5 5]; % Upper bounds
lb = [0 0]; % Lower bounds
F = @(x) COST_mine(x,T,e1);
xout = fmincon(F,x0,[],[],[],[],lb,ub); %<-- FMINCON is the optimizer
legend({'Experimental Data','Fitted Data'});
-------------------------------
function COST = COST_mine(x,T,e1)
A = x(1);
B = x(2);
cp1 = 5; cp2 = 3; A1 = 2; rst = 2;
M =[cp1 0 0 0; 0 cp1 0 0; 0 0 cp2 0; 0 0 0 cp2];
XX=[-rst-cp1*A 0 rst 0;
A*cp1 0 0 0;
rst 0 -rst-B*cp2 0;
0 0 B*cp2 0];
options = odeset('AbsTol',1e-10,'RelTol',1e-10,'InitialStep',1e-2, ...
'Mass',M,'Jacobian',XX);
u0 = zeros(4,1);
u0(1) = 1;
% The cost function calls the ODE solver.
[tout,yout] = ode15s(@call, T, u0,options);
COST = sum((yout - e1).^2);
h = findobj('tag','solution');
set(h,'ydata',yout);
title(['y0 = ' num2str(u0) ' ' 'A = ' num2str(A) ' B = ' num2str(B)]);
drawnow;
-----------------------------------
function du = call( T,XX,A,B )
global XX
du=XX*yout;
end

请先登录，再进行评论。

更多回答（1 个）

Teja Muppirala
Teja Muppirala 2011-5-2
Your answer is actually close, but maybe it wasn't entirely straightforward to match it to the other example without some more experience with seeing these types of problems.
This is (just one) correct implementation of your problem. Make sure you understand why it works. You can see that the answer occurs at a corner, [0.01 3.0].
function [x,f] = dooptim
tspan=1:1:40;
cp1 = 5; cp2 = 3; A1 = 2; rst = 2;
lb = [0.01 0.5]; %Upper bounds on the variables
ub = [1 3]; %Lower bounds on the variables
x0 = [0.2 0.7] % Some initial condition
mycostfun = @(x) dosolve(x,cp1,cp2,A1,rst,tspan);
[x,f] = fmincon(mycostfun,x0,[],[],[],[],lb,ub,[])
function error = dosolve(x,cp1,cp2,A1,rst,tspan)
UP1=x(1); %%%parameter to be optimized range = [.01 1] %%%
UP2=x(2); %%%parameter to be optimized range = [0.5 3] %%%
M =[cp1 0 0 0; 0 cp1 0 0; 0 0 cp2 0; 0 0 0 cp2];
XX=[-rst-cp1*UP1 0 rst 0;
UP1*cp1 0 0 0;
rst 0 -rst-UP2*cp2 0;
0 0 UP2*cp2 0];
options = odeset('AbsTol',1e-10,'RelTol',1e-10,'InitialStep',1e-2, ...
'Mass',M,'Jacobian',XX);u0 = zeros(4,1);
u0(1) = 1;
call = @(t,u) XX*u;
[t,u] = ode15s(call, tspan, u0,options);
n1=[u(3,2) u(7,2) u(end,2)];
n2=[u(3,4) u(7,4) u(end,4)];
e1=[0.3 0.8 1];
e2=[0.5 2 5];
%%%%Objective is to minimize the following error %%%%
error = abs((n1(1)-e1(1))^2+(n1(3)-e1(2))^2+(n1(3)-e1(3))^2+...
(n2(1)-e2(1))^2+(n2(2)-e2(2))^2+(n2(3)-e2(3))^2);
  2 个评论
Mathematics
Mathematics 2011-5-2
Dear Teja,
I am very thankful to you for your kind and prompt help.
God bless you.
Best Regards
yem
yem 2014-12-15
hi i have a system with 2 delays i want to identify these delays with optimisations tools(Newton algorithm)

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Surrogate Optimization 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by