In Simulink, when performing parameter estimation with multiple outputs that have different levels of importance or reliability, it is indeed important to use a weighted objective function. This ensures that each output is appropriately considered during the parameter estimation process according to its weight.
Here's how to use a weighted objective function in the parameter estimation process in Simulink:
- Define Output Weights: Determine the weights for each output (y1, y2, y3) based on their importance or the inverse of their variance if you are considering measurement noise.
- Create a Custom Objective Function: You will need to create a custom objective function that computes the weighted sum of squared errors between the measured outputs and the simulated outputs from the model.
- Use the Parameter Estimation Tool: Open the Parameter Estimation tool in Simulink. Import the measured data for your outputs and set up the parameters you wish to estimate.
- Specify the Custom Objective Function: In the Parameter Estimation tool, you can specify the custom objective function by selecting "New" > "Custom Objective Function" and then entering your function that computes the weighted error.
Here is an example of how you might define a custom objective function in MATLAB:
function weightedError = customObjectiveFunction(params, measuredData, simOptions)
% Set the parameter values in the model
set_param('model_name', 'parameter_name1', num2str(params(1)), ...
'parameter_name2', num2str(params(2)), ...
'parameter_name3', num2str(params(3)));
% Simulate the model with the current parameter values
simOut = sim('model_name', simOptions);
% Extract the simulated outputs
y1_sim = simOut.yout.getElement('y1').Values.Data;
y2_sim = simOut.yout.getElement('y2').Values.Data;
y3_sim = simOut.yout.getElement('y3').Values.Data;
% Compute the weighted error for each output
error1 = measuredData.y1 - y1_sim;
error2 = measuredData.y2 - y2_sim;
error3 = measuredData.y3 - y3_sim;
% Define the weights for each output
weight1 = measuredData.weight1;
weight2 = measuredData.weight2;
weight3 = measuredData.weight3;
% Compute the weighted sum of squared errors
weightedError = sum(weight1 * error1.^2 + weight2 * error2.^2 + weight3 * error3.^2);
end
Replace 'model_name', 'parameter_name1', 'parameter_name2', 'parameter_name3', and the measuredData structure with the actual names and data relevant to your model.
