Explainable Machine Learning to Analyze the Optimized Reverse Curve Geometry for flow over Ogee Spillways

Spillways regulate water flow rates to maintain optimum levels in reservoirs. These come in different designs; the ogee spillways are some of the most safe and effective. In this paper, the impact of reverse curve geometry modifications on the water surface profile and pressure profile is tested to help bridge the deficiency in the understanding of ogee spillway hydraulic performance under variable conditions. This study embodies the use of machine learning models and SHAP analysis to enhance interpretability and optimization in spillway design using fresh approaches different from those traditionally used. Utilizing ANSYS Fluent software, the investigation employs the realizable k-epsilon turbulence model and incorporates the model to accurately capture water-air interactions. Three different head ratios, specifically 0.5, 1, and 1.33, were investigated to understand their influence. The simulation results were validated against data from the US Army Corps of Engineers - Waterways Experiment Station (USACE-WES). For example, the water surface profile showing the highest discrepancy-a discrepancy of 12% for a head ratio of 1.33-was considered to have occurred within the upper nappe of the spillway. The flow dynamics for such conditions would be highly sensitive with respect to changes within this operating variable. Interestingly, Changing the reverse curve geometry from a circular arc to an elliptical arc did not have much effect on either water surface or pressure profiles. The maximum water surface elevation difference was just 2.5 cm, and pressure profiles showed less than a 3% variation for all head ratios investigated, namely 0.5, 1, and 1.33. This finding suggests that such modifications may not significantly alter the hydraulic behavior of the spillway under consideration. To enhance the analysis, machine learning models were developed to predict the head ratio from the vertical face of the spillway based on the total pressure for reverse curve circular and elliptical designs, as well as the horizontal distance from the vertical face of the spillway. Multiple models were trained, and their accuracies were compared, with the Random Forest model yielding the best performance. Furthermore, SHapley Additive explanations (SHAP) analysis was employed to interpret the contributions of each feature to the model's predictions. SHAP analysis showed that head ratio contributed 45% to the predictions, making it the most critical factor affecting spillway performance. In comparison, the total pressure for a reverse curve circular design contributed 30%, while the horizontal distance from the vertical face accounted for 25%. This distribution underlines how dominant head ratio is in determining water flow characteristics over the spillway.