Machine learning prediction of air entrainment rate in triangular broad-crested weirs

Air entrainment in weir flows plays a critical role in enhancing oxygen transfer, improving flow stability, and mitigating cavitation in hydraulic systems. However, predicting air entrainment in triangular broad-crested weirs remains challenging due to complex interactions between flow conditions and geometric configurations. To address this, a data-driven modelling framework based on machine learning was developed using experimental observations of triangular weir flows, supported by dimensional and non-dimensional analysis. Four models – MARS, M5P, random forest, and Gaussian process regression (GPR) – were trained and evaluated to simulate air entrainment behaviour under varying hydraulic conditions. The analysis was conducted using a structured dataset and validated through statistical and graphical diagnostics. Among the tested models, GPR demonstrated the highest predictive performance, achieving a correlation coefficient of 0.9918, root mean square error of 2.509 × 10⁻⁴ m³/s, mean absolute error of 1.977 × 10⁻⁴ m³/s, and NSE of 0.9818. Additional indices (scatter index = 0.0877, Legates–McCabe index = 0.8641, Willmott’s index = 0.9953) further confirmed its robustness and reliability. Sensitivity analysis revealed that discharge and drop height are the dominant parameters governing air entrainment. The results highlight the effectiveness of machine learning, particularly GPR, in accurately modelling complex aeration processes in triangular broad-crested weirs.