Computation of energy dissipation across the type-A piano key weir by using gene expression programming technique

Abstract

Abstract Energy dissipation across the weir and dam structures is a vital economic and technical solution for designing the downstream morphology of any hydraulic system. Accurately estimating the energy over any hydraulic system using traditional empirical formulas is tedious and challenging. Consequently, employing new and precise techniques still in high demand is crucial. In this study, the authors developed an empirical model for estimating the residual energy downstream of the type-A piano key weir (PKW) using gene expression programming (GEP) by considering six non-dimensional parameters: headwater ratio, magnification ratio, inlet to outlet width ratio, inlet to outlet key bottom slopes, inlet to outlet overhang portions and the number of cycles. The performance of the proposed models has been compared to empirical equations using the statistical factors coefficient of determination (R2), concordance coefficient (CC), and root mean square error (RMSE). The computed relative residual energy values using the proposed models are within ±10% of the observed ones. The proposed GEP model predicted the relative residual energy satisfactorily, with coefficients of determination of R2 = 0.978 for training, 0.980 for testing and root mean square errors (RMSE) of 0.032 and 0.029 for the training and testing datasets, respectively.