What is the mathematical form of the nonlinear model used for multiple wind factors?

Conditions

• Multiple predictor factors are to be modeled together.
• Wind speed is known to have a sigmoidal relation to power output.
• Other factors are assumed linear for simplicity.

Reasoning, step by step

1. Identify the primary predictor (wind speed) and its known non-linear (sigmoidal) relationship with the response (power output).
2. Identify secondary predictors (wind direction, air density, turbulence, wind shear).
3. Formulate a sigmoid function for the primary predictor using parameters $b_1, b_2, b_3$.
4. Add linear terms for the secondary predictors using parameters $b_4, b_5, b_6, b_7$.
5. Combine these components into a single nonlinear model function to be fitted using MATLAB's fitnlm command.

Example

The code overlay defines the model as `modelFun = @(b,x) $b(1)$./($1+\exp$(-b(2)*(x(:,1)-b(3)))) + $b(4)$.*x(:,2) + $b(5)$.*x(:,3) + $b(6)$.*x(:,4) + $b(7)$.*x(:,5)`. The speaker explains that a nonlinear model can be created from the Statistics and Machine Learning Toolbox to understand the effects of all these factors.

Common misconceptions

• Assuming all factors, including wind speed, have a linear relationship with power output.
• Believing the model parameters $b_1-b_7$ have fixed universal physical meanings rather than being fitted to the specific dataset.

Watch the explanation

Connected concepts

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