Predicting air-demand ratio in high-head rectangular conduits with a sluice gate

Abstract

Accurate estimation of the air-demand ratio (Qa/Qw) is essential for maintaining flow stability, preventing cavitation, and ensuring structural safety in high-head gated conduit systems. Existing empirical and CFD-based methods often fall short in capturing the nonlinear, multivariate interactions inherent in such flows, especially under variable geometric and hydraulic conditions. This study presents a machine learning-based predictive framework using four advanced algorithms—Gradient Boosting Machine (GBM), Distributed Random Forest (DRF), Deep Neural Network (DNN), Stacked Ensemble Learning and Multiple Linear Regression (MLR) Baseline—trained on 336 experimentally derived samples. The input variables include the cross-sectional flow area ratio (?: 10–60), conduit height (Lc: 60–100 mm), conduit width (Wc: 60–100 mm), normalized gate opening (h/L: 0.0009–0.0564), hydraulic radius ratio (R/L: 0.0004–0.0138), and Froude number (Fr: 1.85–57.35). The output variable, Qa/Qw, ranged from 0.00 to 7.28 across all flow scenarios. The GBM model achieved the best performance among all methods, with training metrics of CC = 0.9975, MAE = 0.1018, RMSE = 0.1311, NME = 0.9950, and SI = 0.0679, and testing metrics of CC = 0.9812, MAE = 0.2807, RMSE = 0.3686, NME = 0.9614, and SI = 0.1930. Sensitivity analysis using the Cosine Amplitude Method (CAM) identified Froude number (Fr) as the most influential predictor (Rij = 0.937), followed by conduit width (Wc: Rij = 0.719) and conduit height (Lc: Rij = 0.696). The proposed framework not only surpasses traditional modeling approaches in accuracy and scalability but also provides critical design insights into the governing parameters of aeration behavior in gated hydraulic structures. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2026.