A spillway discharging a high-speed flow is susceptible to cavitation damages. As a countermeasure, an aerator is often used to artificially entrain air into the flow. Its air demand is of relevance to cavitation reduction and requires accurate estimations. The main contribution of this study is to establish an embedded multi-gene genetic programming (EMGGP) model for improved prediction of air demand. It is an MGGP-based framework coupled with the gene expression programming acting as a pre-processing technique for input determination and the Pareto front serving as a post-processing measure for solution optimization. Experimental data from a spillway aerator are used to develop and validate the proposed technique. Its performance is statistically evaluated by the coefficient of determination (CD), Nash–Sutcliffe coefficient (NSC), root-mean-square error (RMSE) and mean absolute error (MAE). Satisfactory predictions are yielded with CD = 0.95, NSC = 0.94, RMSE = 0.17 m³/s and MAE = 0.12 m³/s. Compared with the best empirical formula, the EMGGP approach enhances the fitness (CD and NSC) by 23% and reduces the errors (RMSE and MAE) by 48%. It also exhibits higher prediction accuracy and a simpler expressional form than the genetic programming solution. This study provides a procedure for the establishment of parameter relationships for similar hydraulic issues.

排放高速水流的溢洪道容易受到气蚀损坏。作为对策，经常使用曝气器来人为地将空气吸入流中。它的空气需求与减少气蚀有关，需要准确估计。本研究的主要贡献是建立嵌入式多基因遗传编程 (EMGGP) 模型，以改进对空气需求的预测。它是一个基于 MGGP 的框架，结合基因表达编程作为输入确定的预处理技术和帕累托前沿作为解决方案优化的后处理措施。溢洪道曝气器的实验数据用于开发和验证所提出的技术。其性能通过决定系数 (CD)、纳什-萨特克利夫系数 (NSC)、均方根误差 (RMSE) 和平均绝对误差 (MAE)。CD = 0.95，NSC = 0.94，RMSE = 0.17 m 产生令人满意的预测³ /s 和 MAE = 0.12 m ³ /s。与最佳经验公式相比，EMGGP 方法将适应度（CD 和 NSC）提高了 23%，并将误差（RMSE 和 MAE）降低了 48%。它还表现出比遗传编程解决方案更高的预测精度和更简单的表达形式。本研究提供了为类似的水力问题建立参数关系的程序。