Hi Muralidhar,
I understand that you are trying to calculate 12 experimental coefficients from a set of 200 samples.
As the model for relating ('F'n') and ('F't') to the coefficients and variables '((V_w), (V_c), (a), (de), (Cs))' is complex, using 'fmincon' from MATLAB's Optimization Toolbox is a suitable approach.'fmincon' is used for finding the minimum of a constrained multivariable function.
The general approach involves defining an objective function that calculates the sum of squared errors (SSE) between the experimental values and the values predicted by the model(F'n and F't). Then, 'fmincon' is used to find the set of coefficients that minimizes this SSE.
Please go through the following code sample to proceed further,
function [sse] = objectiveFunction(coeffs, Vw, Vc, a, de, Cs, F)
% coeffs are the coefficients (define these for the unknown variables)
F_pred = coeffs(1)*Vw + coeffs(2)*Vc + coeffs(3)*a + coeffs(4)*de + coeffs(5)*Cs + coeffs(6); % This is just an example model
sse = sum((F - F_pred).^2);
end
initialGuess = zeros(6, 1);
% Bounds and constraints (if you have any, otherwise set these to [])
A = []; b = [];
Aeq = []; beq = [];
lb = []; % Lower bounds of coefficients
ub = []; % Upper bounds of coefficients
nonlcon = []; % Non-linear constraints
% For F'n
options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'sqp');
[coeffs_Fn, sse_Fn] = fmincon(@(coeffs)objectiveFunction(coeffs, Vw, Vc, a, de, Cs, Fn), initialGuess, A, b, Aeq, beq, lb, ub, nonlcon, options);
The initial guess, bounds, and constraints ('initialGuess', 'lb', 'ub', etc.) are crucial to finding a good solution with 'fmincon'.With this approach, we can find the set of coefficients that best fit the experimental data by minimizing the error between the predicted and actual values.
For a comprehensive understanding of the 'fmincon' MATLAB function, please go through the following documentation.
I hope this helps!
