Enhancing discharge prediction over Type-A piano key weirs: An innovative machine learning approach

Abstract

Piano key weirs (PKWs) are an increasingly popular hydraulic structure due to their higher discharge capacity than linear weirs. Accurately predicting the discharge of PKWs is essential for appropriate design and operation. This study utilized eight Machine Learning algorithms, including non-ensemble and ensemble models to predict the discharge of type-A PKWs. Multiple-Linear-Regression (MLR), Support-Vector-Machine (SVM), Gene-Expression-Programming (GEP), and Artificial-Neural-Network (ANN) were adopted as non-ensemble models. While the ensemble models comprised Random-Forest (RF), Adaptive-Boosting (AdaBoost), Extreme-Gradient-Boosting (XGBoost), and Categorical-Boosting (CatBoost). A total of 476 experimental datasets were collected from previous research considering three critical dimensionless input parameters: PKW key widths, PKW height, and total upstream head. The models were trained on 70 % of the dataset and tested on the remaining 30 %. The hyperparameters of the models were optimized using the Bayesian Optimization technique, with 5-fold cross-validation ensuring high performance. Comprehensive analyses, including visual and quantitative methods, were employed to validate model effectiveness. CatBoost model consistently outperformed the other models, achieving the highest Determination-coefficient (R² = 0.998) and lowest Root-Mean-Squared-Error (RMSE = 0.002), highlighting its ability to handle complex data patterns and its superior optimization process. XGBoost follows closely behind, showing strong generalization, while ANN and RF perform well, but it's a slight increase in error metrics. The study also incorporated Shapley-Additive-exPlanations (SHAP) and Partial-Dependence-Plot (PDP) analyses, revealing that the total upstream head variable had the most significant impact on the discharge predictions. An interactive Graphical-User-Interface was developed to facilitate practical applications, enabling engineers to predict discharge quickly and economically.