Prediction and Uncertainty Quantification of Flow Rate Through Rectangular Top-Hinged Gate Using Hybrid Gradient Boosting Models

Accurate estimation of flow discharge, Q, through hydraulic structures such as spillways and gates is of great importance in water resources engineering. Each hydraulic structure, due to its unique characteristics, requires a specific and comprehensive study. In this regard, the present study innovatively focuses on predicting Q through Rectangular Top-Hinged Gates (RTHGs) using advanced Gradient Boosting (GB) models. The GB models evaluated in this study include Categorical Boosting (CatBoost), Histogram-based Gradient Boosting (HistGBoost), Light Gradient Boosting Machine (LightGBoost), Natural Gradient Boosting (NGBoost), and Extreme Gradient Boosting (XGBoost). One of the essential factors in developing artificial intelligence models is the accurate and proper tuning of their hyperparameters. Therefore, four powerful metaheuristic algorithms—Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Sparrow Search Algorithm (SSA), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA)—were evaluated and compared for hyperparameter tuning, using LightGBoost as the baseline model. An assessment of error metrics, convergence speed, stability, and computational cost revealed that SSA achieved the best performance for the hyperparameter optimization of GB models. Consequently, hybrid models combining GB algorithms with SSA were developed to predict Q through RTHGs. Random split was used to divide the dataset into two sets, with 70% for training and 30% for testing. Prediction uncertainty was quantified via Confidence Intervals (CI) and the R-Factor index. CatBoost-SSA produced the most accurate prediction performance among the models (R2 = 0.999 training, 0.984 testing), and NGBoost-SSA provided the lowest uncertainty (CI = 0.616, R-Factor = 3.596). The SHapley Additive exPlanations (SHAP) method identified h/B (upstream water depth to channel width ratio) and channel slope, S, as the most influential predictors. Overall, this study confirms the effectiveness of SSA-optimized boosting models for reliable and interpretable hydraulic modeling, offering a robust tool for the design and operation of gated flow control systems.