Development of a novel Hybrid Hydrodynamic Particle Simulation Methodology for Estimating Discharge Coefficient of Broad-Crested Weirs

Abstract

Weirs are crucial for flow measurement and water level regulation, with the discharge coefficient (C_d) influenced by factors such as crest length, height, upstream head, and slope. This study optimizes C_d estimation for broad-crested weirs using hybrid hydrodynamic particle simulation and physics-enhanced machine learning models. It investigates the impact of geometric parameters, crest length, weir height, slope angles on C_d by conducting 432 simulations. The primary outcome is the development of multi-variable regression equations to predict C_d, along with detailed water level and velocity profile analyses. Three advanced models: Physics-Enhanced Machine Learning (PEML), Physics-Regularized Regression Trees (PRRT), and Hybrid Hydrodynamic Particle Simulation (HHPS) are evaluated. The HHPS model outperforms others with DC of 0.998 and 0.996, RMSE of 0.013 and 0.017, WI of 0.999 and 0.998, and NSE of 0.998 and 0.997 for training and testing dataset, respectively, showing exceptional predictive accuracy. A sensitivity analysis using SHapley Additive exPlanations (SHAP) was used in this study. Upstream head-to-weir height ratio (H₁/P) and flow rate (Q) with SHAP values of +0.15 and +0.11, respectively, have the greatest impact on C_d modeling. Also, this study enhances the understanding of weir flow dynamics and provides practical tools for engineers and hydrologists. By integrating physics-based simulations with machine learning, it sets a new precision benchmark for hydraulic structure design and analysis, impacting water resource management and environmental engineering.