Prediction of the Coefficient of Pressure Fluctuations during the Hydraulic Jump Using ELM, GMDH, and M5MT

Abstract

Pressure fluctuations are a critical phenomenon that can endanger the safety and stability of hydraulic structures, especially stilling basins. Hence, the accurate estimation of the dimensionless coefficient of pressure fluctuations ( $C_P^{\prime }$ ) is critical for hydraulic engineers. This study proposed predictive soft computing models to estimate $C_P^{\prime }$ on sloping channels. Therefore, three robust soft computing methods, including extreme learning machine (ELM), group method data of handling (GMDH), and M5 model tree (M5MT), were used to estimate $C_P^{\prime }$ . The results revealed that ELM was more accurate than GMDH and M5MT methods when comparing statistical indices, including correlation coefficient (CC), root mean square error (RMSE), mean absolute error (MAE), scatter index (SI), index agreement ( $I_{\mathrm{a}}$ ), and BIAS values. The performance of ELM was found to be more accurate (CC = 0.9183, RMSE = 0.0067, MAE = 0.0051, SI = 11.88%, Ia = 0.9569) when compared with the results of GMDH (CC = 0.8818, RMSE = 0.0078, MAE = 0.0058, SI = 13.89%, Ia = 0.9361) and M5MT (CC = 0.6883, RMSE = 0.0120, MAE = 0.0090, SI = 21.28%, Ia = 0.7905) in the testing stage. In addition, the BIAS values revealed that ELM slightly overestimated the values of $C_P^{\prime }$ , especially at the peak point compared with GMDH and M5MT results. Overall, the suggested soft computing techniques worked well for predicting pressure fluctuation changes in the hydraulic jump.