MATLAB: Parameter Estimation for Differential Equation according to data measured

parameter estimation

Thanks in advance to all supporters, this is the first time a ask a question – that's because there are answers to most of the problems i had.
After reviewing the proposed solution :
  • i tried to apply "Star Strider" ‘Igor_Moura’ function to another ode problem i have but get Error "using lsqcurvefit"
  • i did a modification to your code to solve the eq:
  • A,B,C are parameters i look for ([A B C] inside the code are theta(1:3). [y,y'] are c(1:2), dcdt(2) is [y''] and x is t)
function C=kinetics(theta,t)
c0=[293;0]; %initial condition
[T,Cv]=ode45(@DifEq,t,c0);
%
    function dC=DifEq(t,c)
    dcdt=zeros(2,1);
    dcdt(1)=c(2);
    dcdt(2)=theta(3)-theta(2).*c(1)-theta(1).*t.*c(2);
    dC=dcdt;
    end
C=Cv;
end
global t c 
load('t.mat'); t=t*1000;
load('c.mat');
theta0=[1;1;1]; % initial guess
[theta,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat]=lsqcurvefit(@kinetics,theta0,t,c);
fprintf(1,'\tRate Constants:\n')
for k1 = 1:length(theta)
    fprintf(1, '\t\tTheta(%d) = %8.5f\n', k1, theta(k1))
end
  • unfortunately, I encounter a problem of dimensions :
Error using lsqcurvefit (line 248)
Function value and YDATA sizes are not equal.
  • at line 199 :
  • initVals.F get the size :
  • so at line 248 :
  • i got the err because YDATA length is 18896X1 so their sizes are not equal.
any idea?? thanks Netanel

Best Answer

I will now delete your Comment from the other post.
I found the problem, and your code now works. Your ‘kinetics’ function should be:
function C=kinetics(theta,t)
c0=[0;293]; %initial condition
[T,Cv]=ode45(@DifEq,t,c0);
%
    function dC=DifEq(t,c)
    dcdt=zeros(2,1);
    dcdt(1)=c(2);
    dcdt(2)=theta(3)-theta(2).*c(1)-theta(1).*t.*c(2);
    dC=dcdt;
    end
C=Cv(:,2);
end
Your parameters are very difficult to estimate. After failing to get a good fit with lsqcurvefit, I decided to let ga (Genetic Algorithm) estimate them. That has now been going for 11 hours, and does not appear close to converging.
EDIT — (11 Oct 2018 at 20:16)
The best parameters I can estimate (unconstrained genetic algorithm) are:
  Rate Constants:
    Theta(1) =      98063.79853
    Theta(2) =      99458.01337
    Theta(3) =      97298.39633
They do not come close to approximating your data, and have a residual norm of 1543.5.
I suspect that your model is not appropriate to your data.
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