Comparing Sigmoid Transfer Functions for Neural Network Multistep Ahead Streamflow Forecasting

Abstract

One of the main problems of neural networks is the lack of consensus on how to best implement them. This work targets the question of the transfer function selection—a vital part of neural network providing nonlinear mapping potential. Three nonlinear transfer functions bounded by −1 and 1 are selected for testing, based on a literature review: the Elliott sigmoid, the bipolar sigmoid, and the tangent sigmoid. They are used to design multilayer perceptron neural networks for multistep ahead streamflow forecasting over five diverse watersheds and lead times from 1 to 5 days. All multilayer perceptrons have shown a good performance on the account of the four selected criteria, which confirms that the selected multilayer perceptron implementation procedure was adequate, namely, the data set length, the Kohonen network clustering method to create the training and testing sets, and the Levenberg-Marquardt back-propagation training procedure with Bayesian regularization. Specifically, results endorsed the tangent sigmoid as the most pertinent transfer function for streamflow forecasting, over the bipolar (logistic) and Elliott sigmoids, but the latter requires less computing time and as such may be a valuable option for operational hydrology. Also, results averaged over five lead times confirmed the universal approximation theorem that a linear transfer function is suitable for the output layer—a nonlinear transfer function in the output layer failed to improve performance values.