Explainable machine learning for hydraulic engineering: sensitivity and uncertainty aware prediction of air-demand ratio in gated conduits

This study explores how hydraulic and geometric factors influence the air-demand ratio (ζ) in high-head, sharp-crested gated conduits, emphasizing conduit design and flow conditions. The analysis uses dimensional inputs: gate opening (Ø), height (y), conduit length (L), water flow area (Aw), and velocity (V), alongside non-dimensional variables (Ø, L/y, Aw/y2, and Fr2 (square of Froude number)) to predict ζ. Machine learning (ML) models- Artificial Neural Networks (ANN), Deep Neural Networks (DNN), Neuro-Fuzzy Systems (NFS), Gradient Boosting Machines (GBM), and Generalized Linear Models (GLM) were applied and benchmarked against Multiple Linear Regression (MLR), Multiple Nonlinear Regression (MNLR), and classical empirical formulas. Statistical metrics and visual tools-scatter plots, Taylor diagrams, box plots, and performance diagrams showed GBM as the top performer, followed by DNN, across both dimensional and non-dimensional datasets. Uncertainty analysis via Monte Carlo simulations and the interval methods confirmed GBM’s robustness, with DNN showing narrow uncertainty bands. ANOVA revealed minimal deviation between predicted and experimental results for all ML models, unlike empirical relations. Sensitivity (one-factor-at-a-time, Morris, Sobol), correlation, and SHapley analyses identified V and Aw as key factors in dimensional datasets, and Fr2 and Ø in non-dimensional ones.