parameter estimation and minimization
9 ビュー (過去 30 日間)
古いコメントを表示
I have to estimate parameters(k1 ,k2) of the following equation
dx/dt=k1(3-x)-k2*ca0*x^2
I have data available of x vs t at different inital ca0.I have minimization function as follows.
where N=total no. of runs at different ca0(=6) and N'= total no. of runs at same ca0(=12). kindly help me to build a matlab code for the same bcoz i have done only with one summation error minimization.
4 件のコメント
採用された回答
Star Strider
2014 年 6 月 28 日
Your ODE is not well-behaved. I had problems fitting it with synthesised data with even a small noise component, particularly with respect to k1 (or p(1) in my code). It is very sensitive to the initial parameter estimates. I have no idea what your parameters actually are, so you will have to experiment with the starting estimates to get a good fit to your data. I also used ‘0’ as an initial condition for x in the data synthesis and the DevyaniODEFIT function. Change this if it is not correct. I used a time vector of [0:12] for the independent variable. Change this to reflect the values of your actual independent variable.
I attached the objective function that integrates your ODE and is used by the main script as an objective function that the parameter estimation routine uses to fit your data. I used fminsearch here because I do not know if you have access to the Statistics Toolbox function nlinfit or the Optimization Toolbox function lsqcurvefit. They are more robust and will give a better fit than fminsearch, so you can easily change my code here to use them instead. Note that your paraesti function does not pass Ca0 as a parameter, so either include it in yours, or use my function instead.
The main code:
Ca0=[6 9 12 18];
DE = @(p,t,x,Ca0) p(1).*(3-x)-p(2).*Ca0.*x.^2; % ODE function to create data
% CREATE DATA:
for k1 = 1:length(Ca0)
p(:,k1) = rand(2, 1)*0.1; % Random parameters k1, k2
[t x(:,k1)] = ode45(@(t,x) DE(p(:,k1),t,x,Ca0(k1)), [0:12], 0);
x(:,k1) = x(:,k1) + 0.005*randn(size(x(:,k1))); % Add noise for realism
end
% ESTIMATE PARAMETERS:
for k1 = 1:length(Ca0)
xest = @(B) DevyaniODEFIT(B,t,Ca0(k1)); % Calls ODE function
OLS = @(B) sum( (x(:,1) - xest(B) ).^2); % Least squares objective function
B0 = rand(2,1)*0.1; % Initial parameter estimates
B(:,k1) = fminsearch(OLS, B0); % Optimise parameters to fit data
xgrf(:,k1) = DevyaniODEFIT(B,t,Ca0(k1)); % Generated fitted data to plot
end
figure(1)
plot(t, x, '-x', 'MarkerSize',2, 'LineWidth',1) % Plot original data
hold on % Plot estimated data
plot(t, xgrf, '-p', 'LineWidth',1.5, 'MarkerSize',3);
hold off
grid
The function DevyaniODEFIT.m is attached.
The code definitely works. I documented it with comments as well as I can, so you can easily understand it. You will probably have to experiment with different starting values it to fit your data.
15 件のコメント
その他の回答 (0 件)
参考
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!