Studying the Effect of Wavelet Transform on the Uncertainty of Artificial Neural Network-based Models and Extreme Learning Machines for the Prediction of Urban Water Demand

Urban water demand prediction has been one of the contemporary concerns of modern urban societies. In this vein, many studies have been carried out comparing the performance of different models. By the introduction of artificial neural networks (ANNs), the discussion about the accuracy improvement of ANNs using wavelet transforms (WTs) was heated up. In many research, the effect of using WTs on the performance and the accuracy of ANNs drew many attentions. However, the effect of using WTs on the uncertainties associated with ANNs has not been investigated. In this study, the performance and the uncertainty of two ANN-based models, i.e., nonlinear autoregressive network with exogenous inputs (NARX) and extreme learning machines (ELM) were studied and the wavelet version of those, i.e., W_NARX and W_ELM were used for the prediction of urban water demand of Mahdie Residential Complex. The results indicated that NARX (regression coefficient (R) of 0.955) is more accurate than ELM (R of 0.787). On the other, the WT version of these models had the R of 0.960 and 0.847, respectively, indicating the outperformance of W_NARX model. The reason for the lower accuracy of ELM could be found in the complexity of the water consumer behavior and the simpler structure of ELM than NARX. Besides, the implementation of WTs had a positive effect on both models, but ELM more. The results of the uncertainty analysis of both models indicated a decrease in uncertainty. However, this was more considerable in W_NARX with the confidence interval of 98.75%.