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.

翻译：全球风电的快速扩张凸显了面向工程的分析尾流模型在风电场设计和运行中的关键重要性。这些理论推导的分析尾流模型由于存在不成立的假设，其预测能力有限，尤其是在靠近涡轮转子的近尾流区域。知识发现方法能够通过提取洞见、调整理论假设以及为物理过程开发精确模型来弥合这些差距。在本研究中，我们引入了一种遗传符号回归算法，旨在为整个尾流的平均速度亏损发现一个可解释的数学表达式，这是一个先前无法获得的洞见。通过将双高斯分布作为领域知识纳入SR算法，并设计分层方程结构，搜索空间得以缩减，从而高效地找到一个简洁、具有物理依据且稳健的尾流模型。所提出的数学表达式能够以高精度和稳定性预测全尾流区域任意位置的尾流速度亏损。该模型的有效性和实用性已通过实验数据和高保真数值模拟得到验证。