A hybrid ensemble machine learning model for discharge coefficient prediction of side orifices with different shapes

Side orifices are widely applied for flow control and regulation in channel systems. Accurate estimation of the discharge coefficient of the side orifice is significant for water management. The main objective of current research is to accurately predict the discharge coefficients of circular and rectangular side orifices. Considering that traditional empirical regressions are hard to estimate the discharge coefficient precisely due to the complex nonlinear relationship between the discharge coefficient and relevant parameters, a new hybrid boosting ensemble machine learning model, BO-XGBoost, is developed, which combines the advantages of the boosting ensemble model (XGBoost) and Bayesian Optimization. To further evaluate the proposed hybrid model, it is also compared with other tree-based machine learning models, including standalone XGBoost, Random Forest (RF) and Decision Tree (DT). Literature experimental data of the flow and geometric parameters relevant to the discharge coefficients of circular and rectangular side orifices are collected and applied to develop the models. Four dimensionless parameters of the relative channel width (B/L), the relative bottom height (W/L), the relative upstream depth (Y/L) and the upstream Froude number (Fr) are taken into consideration for the prediction of discharge coefficient (Cd). Furthermore, four different input combinations are designed and then compared to determine the best one on the basis of RMSE. By using the optimal input combination, our results demonstrate that BO-XGBoost provides the best comprehensive performance among all the involved machine learning models in the discharge coefficient prediction for both types of side orifices. Besides, the uncertainty analysis also reveals that BO-XGBoost shows the narrowest uncertainty bandwidth and gives the highest prediction reliability.