Radial gates are widely used hydraulic structures for flow control in irrigation canals.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 input parameters of the ratio of the downstream flow depth to the gate opening (y3/w) and submergence ratio (y1-y3/w) 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. 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.

Accurate determination of discharge capacity in radial gates as commonly designed check structures is of great importance in hydraulic engineering research. The discharge coefficient plays the most dominant role in calculating the flow discharge through the radial gates. The main goal of this study is to adopt Grey Wolf Optimization-based Kernel Extreme Learning Machine (KELM-GWO) to further improve the prediction accuracy of the discharge coefficient of radial gates. To compare the supreme performance of the proposed model, kernel-depend support vector machine (SVM) and Gaussian process regression (GPR) were employed. An extensive field database consisting of 546 data samples gathered from different types of radial gates was established for building prediction models. The modeling results indicated that the proposed KELM-GWO model (correlation coefficient [R] = 0.927, and root mean squared error [RMSE] = 0.018) and SVM model (correlation coefficient [R] = 0.940, and root mean squared error [RMSE] = 0.022) demonstrated better performance under free and submerged flow conditions, respectively. Moreover, it was found that the applied kernel-depend approaches can be suitable options to predict the discharge coefficient of radial gates under varied submergence conditions with a satisfactory level of accuracy.

Radial gates are widely used hydraulic structures for flow control in irrigation canals. 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 input parameters of the ratio of the downstream flow depth to the gate opening (y3/w) and submergence ratio (y1-y3/w) 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. 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.