An efficient hybrid grey wolf optimization-based KELM approach for prediction of the discharge coefficient of submerged radial gates

Accurately prediction of discharge coefficient through radial gates is considered as a challenging hydraulic subject, particularly under highly submerged flow conditions. Incurring the advantages of kernel-depend extreme learning machine (KELM), this study offers a grey wolf optimization-based KELM (GWO-KELM) for effective prediction of discharge coefficient through submerged radial gates. Additionally, support vector machine (SVM) and Gaussian process regression (GPR) methods are also presented for comparative purposes. To build prediction models using GWO-KELM, GPR, and SVM, an extensive experimental database was established, consisting of 2125 data samples gathered by the US Bureau of Reclamation. From simulation results, it is observed that the proposed GWO-KELM approach with radial basis function and input parameters of the ratio of the downstream flow depth to the gate opening and submergence ratio provides the best performance with the correlation coefficient (R) of 0.983, the determination coefficient (DC) of 0.966 and the root-mean-squared error (RMSE) of 0.027. The obtained results showed that the proposed GWO-KELM with RBF kernel function gives better prediction accuracy than employed GPR and SVM approaches. Furthermore, the obtained results showed that the employed kernel-depend methods are capable of a statistically predicting the discharge coefficient under varied submergence conditions with satisfactory level of accuracy. Amon theme, proposed hybrid GWO-KELM method gave the most accurate results (R = 0.873, DC = 0.744, and RMSE = 0.035) for extremely highly submerged flow. Moreover, the results reflected that the employed kernel-depend methods give better predictions than the developed dimensionless formulas.