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

TL;DR

The paper tackles the challenge of accurately modeling the full wind-turbine wake, including the near-wake region, where traditional analytical models falter. It introduces a domain knowledge–driven symbolic regression (SR) framework that embeds a double-Gaussian (DG) wake profile and searches for simple, interpretable expressions for the DG parameters $a$, $\mu$, and $\sigma$ as functions of downstream distance. The approach leverages LES/SOWFA CFD data, a hierarchical model structure, and a Pareto-front–based fitness to yield a concise, physically informed wake expression that predicts the mean velocity deficit across the full wake with high accuracy, including the near rotor region, and shows advantages over conventional Gaussian models in critical regions. Validation against experimental and high-fidelity simulation data confirms robustness and practical relevance for wind-farm design and control, illustrating the power of knowledge-discovery methods to transcend limitations of theory-only wake models.

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.

Figures (14)

• Figure 1: Schematic figure showing a wind turbine wake featuring a DG velocity deficit.
• Figure 2: Profiles of the velocity deficit at different downstream locations. Circles represent LES results and dashdotted lines represent DG fittings. Vertical red dashed lines are at $\dot{y}=\pm0.29$.
• Figure 3: The workflow scheme of SR. The blue box represents operations within a population.
• Figure 4: The Schematic diagram of domain knowledge-driven genetic SR framework for the turbine-wake modeling, a real-world problem.
• Figure 5: The relationship between the logarithmic loss and the complexity of the expressions obtained in $\mathbb{P}$. The green line denotes the Pareto curve, which consists of blue points representing the expressions in $\mathbb{P}$. The red dashed line represents the threshold, and the red point corresponds to the optimal expression.