Enhancing rectangular side weir discharge prediction using stacking technique

In this paper, the impact of different variables on discharge coefficients in sharp-crested rectangular side weirs was investigated utilizing 559 experimental data points. Various methodologies, including De Marchi, Traditional weir equation (TWE), Domínguez, adjusted Domínguez, and Schmidt procedures, were employed for the analysis. Novel equations were developed to predict the discharge coefficients with greater accurately, surpassing the predictive capabilities of previous studies' equations. Additionally, three supervised machine learning algorithms, namely extreme gradient boosting (XGBoost), Light gradient boosting machine (LightGBM), and support vector regression (SVR), were employed to enhance the precision of discharge coefficient estimation. Among these algorithms, the XGBoost model exhibited superior performance compared to LightGBM and SVR models for forecasting discharge coefficients. Furthermore, using a stacking technique, hybrid models were constructed by combining XGBoost, LightGBM, and SVR. The hybrid models showed enhanced performance and generalization capacities than the individual models. Notably, the HYBRID₅ model, specifically designed for estimated the Schmidt coefficient, achieved outstanding statistical indices (R² = 0.995, MSE = 1.378, MRPE = 3.73 %) for calculating discharge of rectangular side weirs.