Estimation of aerator air demand by an embedded multi-gene genetic programming

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 m(3)/s and MAE = 0.12 m(3)/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.