The interpretable model for the discharge coefficient of a contraction flume under free and submerged flows

The flow measurement flume effectively solves the problem of sediments being discharged downstream by the water flow, and the existing computational methods make it challenging to reveal the interactions between different hydraulic parameters. In particular, submerged flow increases the complexity of discharge calculation. This study proposes an integrated learning model based on physical characteristics to predict the discharge coefficient of the shrinkage flume. It introduces the SHAP (Shapley Additive exPlanation) theory to explain the model's prediction results and validate the credibility of the model's outputs. The research shows that the XGBoost (eXtreme Gradient Boosting) has stable prediction and generalization ability under free and submerged flows. In free flow conditions, the ratio of upstream water depth to throat width h/W influences the model results most. When the value of h/W gradually increases, the corresponding SHAP value is greater than zero, positively affecting the model prediction. When the value of h/W gradually decreases, the corresponding SHAP value is less than zero, which has a pronounced negative influence on the prediction results. In submerged flow conditions, the ratio of channel width to throat width B/W influences the model results most; when the eigenvalue of B/W increases, the corresponding SHAP value is less than zero and also decreases, which hurts the model prediction value, and when its eigenvalue decreases, the corresponding SHAP value is more than zero, which has a positive effect on the model prediction value. Overall, this study provides a new perspective on understanding the complex discharge process and demonstrates the potential for obtaining scientific insights from the model.