Modeling the discharge coefficient of labyrinth sluice gates using hybrid support vector regression and metaheuristic algorithms

Gates and weirs are frequently used hydraulic structures employed for controlling water flow rates in irrigation and drainage networks. Therefore, accurately estimating the discharge coefficient (Cd) is important for precise flow measurement. The present study used intelligent predictive models for modeling Cd in labyrinth sluice gates. For this purpose, key dimensionless parameters and reliable experimental datasets were used. The support vector regression (SVR) model was hybridized with particle swarm optimization (PSO) and genetic algorithms (GA). The statistical metrics and graphical plots evaluated the performance of the generated models. Three commonly used statistical indicators, namely root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R2), were used for quantitatively evaluating the performance of the proposed models. The SVR-PSO model achieved the lowest values of RMSE (0.0287) and MAE (0.0209) and the highest value of R2 (0.9732), indicating that it was more accurate than SVR-GA (RMSE = 0.0324, MAE = 0.0257, R2 = 0.9685) and SVR (RMSE = 0.0575, MAE = 0.0468, R2 = 0.8958) on the testing data. The findings revealed that the hybrid SVR methods were more accurate than the standalone SVR model. In addition, regarding the value of the objective function criterion (OBF), the SVR-PSO (OBF = 0.0245) and SVR-GA (OBF = 0.0273) had lower OBF values and provided more precise estimates of the Cd compared to existing nonlinear regression-based formulas and existing data-driven approaches. Finally, sensitivity and SHapley Additive exPlanations (SHAP) analyses determined the relative importance of each input variable for the prediction of Cd.