Estimating Discharge Coefficient of PK-Weir Under Subcritical Conditions Based on High-Accuracy Machine Learning Approaches

Abstract

This article adopts four high-accuracy machine learning-based approaches for the prediction of discharge coefficient of a Piano Key Weir (PK-weir) under subcritical condition located on the straight open-channel flume. These approaches consist of least-square support vector machine (LS-SVM), extreme learning machine (ELM), Bayesian ELM (BELM), and logistic regression (LR). For this purpose, 70 laboratory test results are used for determining discharge coefficient of PK-weir for a wide range of discharge values. Root-mean-squared error (RMSE), Nash–Sutcliffe model efficiency coefficient (NSE), the coefficient of correlation (R), threshold statistics (TS), and scatter index (SI) are used for comparing the performance of the models. The simulation results indicate that an improvement in predictive accuracy could be achieved by the ELM approach in comparison with LS-SVM and LR (RMSE of 0.016 and NSE of 0.986), while the BELM model’s generalization capacity enhanced, with RMSE of 0.011 and NSE of 0.989 in validation dataset. The results show that BELM is a simple and efficient algorithm which exhibits good performance; hence, it can be recommended for estimating discharge coefficient.