Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression

TL;DR

This paper introduces an AI-enhanced symbolic regression method to discover an interpretable mathematical model for wind-turbine wake velocity deficits, improving prediction accuracy in the near-wake region.

Contribution

The study develops a novel genetic symbolic regression algorithm incorporating domain knowledge to derive a concise, physically informed wake model with high predictive accuracy.

Findings

The model accurately predicts wake velocity deficits across the full wake region.

Incorporating domain knowledge reduces search space and improves model robustness.

Validated with experimental and numerical data.

Abstract

The rapid expansion of wind power worldwide underscores the critical significance of engineering-focused analytical wake models in both the design and operation of wind farms. These theoretically-derived ana lytical wake models have limited predictive capabilities, particularly in the near-wake region close to the turbine rotor, due to assumptions that do not hold. Knowledge discovery methods can bridge these gaps by extracting insights, adjusting for theoretical assumptions, and developing accurate models for physical processes. In this study, we introduce a genetic symbolic regression (SR) algorithm to discover an interpretable mathematical expression for the mean velocity deficit throughout the wake, a previously unavailable insight. By incorporating a double Gaussian distribution into the SR algorithm as domain knowledge and designing a hierarchical equation structure, the search space is reduced, thus efficiently finding a concise, physically informed, and robust wake model. The proposed mathematical expression (equation) can predict the wake velocity deficit at any location in the full-wake region with high precision and stability. The model's effectiveness and practicality are validated through experimental data and high-fidelity numerical simulations.