Predicting Critical Submergence in Horizontal Circular Intakes Using Meta-Heuristic Optimized Gradient Boosting Ensembles

Abstract

This study evaluates critical submergence depth (Sc) in horizontal circular intakes using a dataset compiled from two controlled laboratory experiments conducted under varying hydraulic and geometric configurations. A total of 324 experimental measurements were obtained across two intake-clearance scenarios: (i) zero bottom clearance (C = 0) and (ii) partial elevation (C = d_i/2). The dataset included four primary input variables—intake diameter, approach flow velocity, Froude number, and bottom clearance ratio—which were used as predictors of the dimensionless submergence depth. To enhance predictive accuracy, an automated machine-learning framework was developed using Gradient Boosting (GB) and Extreme Gradient Boosting (XGB), combined with five meta-heuristic optimizers: Artificial Hummingbird Algorithm (AHA), Victoria Amazonica Optimization (VAO), Turbulent Flow of Water- based Optimization (TFWO), Smell Agent Optimization (SAO), and Tasmania Devil Optimizer (TDO). Model training used a 70/30 train–test split, with 10-fold cross-validation applied exclusively to the training portion for hyperparameter tuning. A custom empirical adjustment equation was incorporated to further enhance physical consistency and model stability. Performance evaluation based on the independent test set showed that VAO-enhanced models provided the highest predictive accuracy. The XGVO model achieved R² = 0.993 and RMSE = 0.082 for the C = 0 configuration, while the GBVA model achieved R² = 0.993 and RMSE = 0.118 for the C = d_i/2 case. These findings demonstrate that hybrid ensemble techniques can reliably estimate Sc across varying hydraulic scenarios and outperform standard boosting algorithms.