Enhanced prediction of energy dissipation rate in hydrofoil-crested stepped spillways using novel advanced hybrid machine learning models - Ehsan Afaridegan; Nosratollah Amanian (Results in Engineering)
Accurately estimating the Energy Dissipation Rate (EDR) in Hydrofoil-Crested Stepped Spillways (HCSSs) is crucial for ensuring the safety and optimizing the performance of these hydraulic structures. This study investigates the prediction of EDR using advanced hybrid Machine Learning (ML) models, including the Tabular Neural Network with Moth Flame Optimization (TabNet-MFO), Long Short-Term Memory with Ant Lion Optimizer (LSTM-ALO), Extreme Learning Machine with Jaya and Firefly Optimization (ELM-JFO), and Support Vector Regression with Improved Whale Optimization (SVR-IWOA). Notably, two novel models—TabNet-MFO and SVR-IWOA—are introduced for the first time, providing dynamic hyperparameter optimization to enhance prediction accuracy in complex hydraulic conditions. To develop the models, a dataset comprising 462 laboratory data points from HCSS experiments was used, with 75 % allocated for the training stage and 25 % for the testing stage. The Isolation Forest (IF) algorithm was employed to detect and remove outliers, resulting in the exclusion of 5 % of the original dataset. Dimensional analysis was conducted to identify key factors influencing EDR, including step number (NS), chute angle (θ), hydrofoil formation index (t), and the ratio of critical depth to total chute height (yC / PS). ANOVA and SHAP analyses confirmed the significant impact of the yC / PS ratio on EDR. Model performance was evaluated using metrics such as 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). Performance was further compared using Taylor diagrams, residual error curves (REC), and the Performance Index (PI). During the training stage, TabNet-MFO outperformed the other models with a PI of 0.784 and a normalized Root Mean Squared Error (E') of 1.231, followed by ELM-JFO with a PI of 0.605 and E' of 1.125. In the testing stage, TabNet-MFO maintained strong performance, achieving a PI of 0.692, while SVR-IWOA showed robust results with a PI of 0.631. At this stage, the models TabNet-MFO, LSTM-ALO, and ELM-JFO ranked first through third with R² values of 0.977, 0.972, and 0.954, respectively. These findings demonstrate the robustness and effectiveness of the innovative ML models in predicting EDR in HCSSs. The results emphasize the importance of parameter optimization and highlight that the hybrid ML models introduced in this study can significantly enhance the accuracy of EDR prediction for HCSSs compared to other models.