Advanced hybrid techniques for predicting discharge coefficients in ogee-crested spillways: integrating physical, numerical, and machine learning models

Abstract The primary objective of this work was to examine the flow characteristics over an ogee spillway using both a numerical model and the Machine Learning (ML) approach. A 3D computational fluid dynamics (CFD) model was employed to simulate the flow over an ogee spillway, utilizing the Reynolds averaged Navier–Stokes equations. The simulation encompassed a wide variety of head ratios, ranging from 0.1 to 6.0, to extend the rating curve of discharge coefficient ( C ) and head ratio ( H e /H 0 ). The formation of the negative pressure zone rapidly occurred, and the maximum velocity area developed from toe to top of the spillway surface as the head ratio increased. Then, four ML models—RF, FNN, ADB, and KNN—were utilized to estimate the discharge coefficient of the spillway. Hyperparameter tuning using the Tree-Structured Parzen Estimator (TPE) and five-fold cross-validation ensured robust model performance. The ML model’s efficacy was assessed by conducting 200 random seed simulations. The RF and ADB models exhibited the highest predictive accuracy and consistency, with mean correlation coefficient (CC) values of 0.979 and 0.975, respectively. FNN and KNN also performed well but showed greater variability in their prediction. The results demonstrated reasonably good agreement between the physical, numerical, and ML models. Both numerical simulation methods and ML models, particularly RF, proved to be cost-efficient and reliable tools for designing and analyzing flow over an ogee spillway. These findings highlight the potential of integrating numerical simulations and advanced ML techniques to enhance the prediction and analysis of hydraulic structures, providing valuable insights for the design and management of spillway systems.