Enhanced prediction of discharge coefficients in Harmonic Plan Circular Weirs using advanced machine learning and ensemble techniques

Abstract

This study leverages advanced machine learning models—Natural Gradient Boosting (NGBoost), Categorical Boosting (CatBoost), and Tabular Network (TabNet)—to predict the discharge coefficients (C_d) of Harmonic Plan Circular Weirs (HPCWs). To achieve enhanced predictive accuracy, a Stacking Ensemble-based Hybrid (StEH) model was developed, integrating the strengths of the individual models. The methodology involved a comprehensive experimental dataset, split into 75 % for training and 25 % for testing. Key performance metrics, including R², RMSE, Symmetric Mean Absolute Percentage Error (sMAPE), Scatter Index (SI), and Weighted Mean Absolute Percentage Error (WMAPE), were employed to assess model accuracy. Additionally, the Regression Error Characteristic (REC) curve, Kling-Gupta Efficiency (KGE), and Taylor diagram provided statistical and visual insights into model performance. During the training stage, the NGBoost model emerged as the best-performing model, achieving an exceptional R² of 0.9999, an RMSE of 0.0009, an sMAPE of 0.1100 %, an SI of 0.0014, and a WMAPE of 0.1063 %. The StEH model closely followed in second place, with strong performance metrics including an R² of 0.9986 and an RMSE of 0.0034. In the testing stage, the TabNet model outperformed the other models, with an R² of 0.9893, an RMSE of 0.0095, an sMAPE of 1.0191 %, an SI of 0.0144, and a WMAPE of 1.0444 %. The CatBoost model secured the second position during this phase, demonstrating reliable performance with an R² of 0.9779 and an RMSE of 0.0136. Additionally, sensitivity analysis using ANOVA and SHAP methods identified the ratio of the head to weir height (h/P) as the most significant parameter affecting C_d, followed by the net crest length to weir height ratio (l_C/P) and the number of cycles (N). This research underscores the efficacy of ensemble learning techniques, providing valuable insights into the design and optimization of weirs.