Estimation of discharge with free overfall in rectangular channel using artificial intelligence models

Abstract

In open channels, free overfall can be used as a flow-measuring device in various flow regimes for different shapes of channels. The aim of this paper is to accurately estimate the discharge in rectangular channels by applying four soft computing models [i.e., artificial neural network (ANN), gene expression programming (GEP), multivariate adaptive regression spline (MARS) and M5 tree model]. The variables including brink depth, roughness coefficient, channel width and channel bed slope taken from earlier published works were used as inputs for the models. Data were divided according to three different splitting scenarios, 50%–50%, 60%–40% and 75%–25%, for training-testing phases to obtain more robust evaluation of the models. The computed discharges were then compared with experimental results. In order to evaluate the accuracy of discharge estimations by ANN, GEP, MARS and M5 tree models, six statistical measures including correlation coefficient (R), mean absolute error (MAE), root mean square error (RMSE), Nash-Sutcliffe (NS), Willmott index (WI) and Legates and McCabe index (LMI) have been applied. For different training-testing scenarios, the performance of the ANN model is better than the other methods. Regarding 50%–50% training-testing scenario, ANN has the best accuracy with R, RMSE, MAE, NS, WI and LMI of 0.994, 0.004 m3/s/m, 0.002 m3/s/m, 0.986, 0.999 and 0.909 by considering all inputs.