Discharge coefficient of combined rectangular-triangular weirs using soft computing models

Document Type : Research Paper


1 Department of Water Engineering, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran.

2 Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran.

3 Department of Civil Engineering, Faculty of Engineering, Recep Tayyip Erdogan University, Rize, Turkey.


This study investigates the potential of Adaptive Neuro-fuzzy inference system (ANFIS), M5P, and Gaussian Process regression (GP) approaches to predict discharge coefficient (Cd) of chimney weir with different apex angles. Out of 110 data points, 77 arbitrarily selected observations were used for training, whereas the remaining 77 data points were used for testing. Input data consisted of h/p, y/p, L/p, and w/z, whereas Cd was an output. Four shapes of membership functions, i.e., triangular, trapezoidal, generalized bell-shaped, and Gaussian, were used for the ANFIS-based model development. Five different goodness-of-fit parameters and various graphical presentations were used to evaluate the performance of the machine-learning models. It was found that the M5P-based model was superior to other implemented models in predicting the Cd with Correlation Coefficient (CC) (0.9532 and 0.9472), Mean Absolute Error (MAE) (0.0024 and 0.0026), (Root Mean Square Error) RMSE (0.0032 and 0.0033), Scattering Index (SI) (0.0048 and 0.0050), and Nash Sutcliffe Efficiency (NSE) (0.9085 and 0.9925) values in the training and testing stages, respectively. Another major outcome of this study was that the ANFIS model was better than GP and other MFs-based ANFIS-ti models. The sensitivity of the Cd variables is also investigated, which showed h/p and L/p as major influencing factors in the Cd.


Main Subjects

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