Enhanced prediction of discharge coefficient in sharp-edged width constrictions using a novel hybrid SVR-IWOA and machine learning models

Sharp-Edged Width Constrictions (SEWC) are hydraulic structures designed to measure flow in open channels. Accurate prediction of the discharge coefficient (C_d) in SEWC is crucial for determining water discharge in these channels. This information plays a key role in effective water resource management, supporting decision-making regarding the allocation and conservation of water for agricultural, industrial, and municipal purposes. This study introduces a novel hybrid machine learning model, combining Support Vector Regression (SVR) with the Improved Whale Optimization Algorithm (IWOA). Additionally, advanced machine learning models such as NGBoost, AutoInt, and TabNet were employed to predict C_d in SEWC. The SVR-IWOA model offers automatic hyperparameter tuning, significantly enhancing prediction accuracy in complex flow conditions. To develop these models, a dataset consisting of 156 laboratory data points from SEWC experiments was utilized, with 75 % of the data allocated for training and 25 % for testing. The Isolation Forest (IF) algorithm was applied to detect and remove outliers, leading to the exclusion of 5.1 % of the original dataset. Dimensional analysis identified critical factors influencing C_d, including the ratio of upstream depth to opening width (h/b) and the constriction ratio (β = b/B, where B is the channel width). The validity of these dimensionless parameters was confirmed using ANOVA and SHAP analyses, which highlighted β as the most influential factor affecting C_d. Model performance was rigorously evaluated using multiple metrics, including the coefficient of determination (R²), Root Mean Squared Error (RMSE), Scatter Index (SI), Weighted Mean Absolute Percentage Error (WMAPE), and symmetric Mean Absolute Percentage Error (sMAPE). Comparative evaluations were conducted using Taylor Diagrams, Residual Error Curves (REC), and the Performance Index (PI). In the training stage, NGBoost demonstrated superior performance with a PI of 4994 and a normalized Root Mean Squared Error (E′) of 0.00021, followed by SVR-IWOA with a PI of 2490 and E′ of 0.00035. During the testing stage, the SVR-IWOA model maintained strong performance, achieving a PI of 1986 and a low E′ of 0.00046, while TabNet closely followed with a PI of 1986 and E′ of 0.00047. In terms of R² values, the models ranked as follows during testing: SVR-IWOA and TabNet tied for first with R² = 0.993, followed by NGBoost (R² = 0.992) and AutoInt (R² = 0.973). These findings highlight the effectiveness of the proposed SVR-IWOA model in accurately predicting C_d and its strong generalization capabilities, positioning it as a robust tool for hydraulic applications.