Predicting discharge coefficient of triangular labyrinth weir using extreme learning machine, artificial neural network and genetic programming

Abstract

Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient (C _d). The aim of this study is accurate determination of the C _d in triangular labyrinth side weirs by applying three intelligence models [i.e., artificial neural network (ANN), genetic programming (GP) and extreme learning machine (ELM)]. The calculated discharge coefficients were then compared with some experimental results. In order to examine the accuracy of C _d predictions by ANN, GP and ELM methods, five statistical indices including coefficient of determination (R ²), root-mean-square error (RMSE), mean absolute percentage error (MAPE), SI and δ have been used. Results showed that R ² values in the ELM, ANN and GP methods were 0.993, 0.886 and 0.884, respectively, at training stage and 0.971, 0.965 and 0.963, respectively, at test stage. The ELM method, having MAPE, RMSE, SI and δ values of 0.81, 0.0059, 0.0082 and 0.81, respectively, at the training stage and 0.89, 0.0063, 0.0089 and 0.88, respectively, at the test stage, was superior to ANN and GP methods. The ANN model ranked next to the ELM model.