Reliable prediction of the discharge coefficient of triangular labyrinth weir based on soft computing techniques

Weirs are important hydraulic structures widely used to control the flow rates in open channels and rivers. As a remarkable parameter, the discharge coefficient (Cd) determines the weirs' passing capacity. In this research, to more accurately predict the Cd of triangular labyrinth weir, the machine learning (ML) models, including least square support vector machine (LS-SVR), quantile regression forest (QRF), and Gaussian process regression (GPR) were developed and assessed. Several statistical and visual methods were utilized to assess ML accuracy. Data management was performed to objectively evaluate these models' performance, and the optimal training/testing proportion was determined reliably. Sensitivity analysis determined that the highest effective parameters in prediction Cd are l/h and Froude number (Fr). The prediction results of the GPR model with R2 = 0.986 and RMSE = 0.009 are superior to those of the QRF and LSSVR. Compared to empirical models, GPR provides much better accuracy and stability. Furthermore, ML models were adopted for probabilistic Cd prediction for its nature of high variability. The examination of models demonstrates that GPR can obtain an appropriate prediction interval on the Cd prediction of triangular labyrinth weir in comparison with LSSVR and QRF. Furthermore, the GPR model is strongly recommended for predicting Cd; because this model indicates good learning performance and can represent point prediction coupled with prediction intervals. •In this research, to more accurately predict the Cd of triangular labyrinth weir, the machine learning (ML) models, including least square support vector machine (LS-SVR), quantile regression forest (QRF), and gaussian process regression (GPR) were developed.•Sensitivity analysis determined that the highest effective parameters in prediction Cd are l/h and Fr.•The prediction results of the GPR model are superior to those of the QRF and LSSVR.•The examination of models demonstrates that GPR can obtain an appropriate prediction interval on the Cd prediction of triangular labyrinth weir in comparison with LSSVR and QRF.