How can I force my curve fit to respect physical limits using MATLAB?
Conditions
- Requires an optimization solver like lsqnonlin.
- Objective function must be defined based on the model equation (e.g., minimizing sum of squared errors).
- Physical or mathematical constraints on coefficients are known.
Reasoning, step by step
- Open the Optimization Toolbox in MATLAB.
- Define the model coefficients as optimization variables.
- Set lower and upper bounds for each variable based on physical limits.
- Define the objective function as the sum of squared errors between data and model predictions.
- Select a solver (e.g., lsqnonlin) to minimize the objective subject to the bounds.
- Run the optimization to obtain the constrained curve fit.
Example
The speaker explains adding bounds and constraints using the Optimization Toolbox to create a more precise model reflecting physical limitations. The MATLAB Live Editor shows an 'Optimize' task with variables x1 to x6, lower and upper bounds, and an objective function defined as sum((clean_turbine_data.power - (x1 ./ ((-x2 * clean_turbine_da...)))^2).
Common misconceptions
- Assuming standard curve fitting automatically respects physical constraints without explicit bounds.
- Believing that constrained optimization always yields a worse fit than unconstrained fitting, whereas it often improves robustness.
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