[1] A new hybrid wavelet-bootstrap-neural network (WBNN) model is proposed in this study for short term (1, 3, and 5 day; 1 and 2 week; and 1 and 2 month) urban water demand forecasting. The new method was tested using data from the city of Montreal in Canada. The performance of the WBNN method was compared with the autoregressive integrated moving average (ARIMA) and autoregressive integrated moving average model with exogenous input variables (ARIMAX), traditional NNs, wavelet analysis-based NNs (WNN), bootstrap-based NNs (BNN), and a simple naïve persistence index model. The WBNN model was developed as an ensemble of several NNs built using bootstrap resamples of wavelet subtime series instead of raw data sets. The results demonstrated that the hybrid WBNN and WNN models produced significantly more accurate forecasting results than the traditional NN, BNN, ARIMA, and ARIMAX models. It was also found that the WBNN model reduces the uncertainty associated with the forecasts, and the performance of WBNN forecasted confidence bands was found to be more accurate and reliable than BNN forecasted confidence bands. It was found in this study that maximum temperature and total precipitation improved the accuracy of water demand forecasts using wavelet analysis. The performance of WBNN models was also compared for different numbers of bootstrap resamples (i.e., 25, 50, 100, 200, and 500) and it was found that WBNN models produced optimum results with different numbers of bootstrap resamples for different lead time forecasts with considerable variability.

A new hybrid model, the wavelet–bootstrap–ANN (WBANN), for daily discharge forecasting is proposed in this study. The study explores the potential of wavelet and bootstrapping techniques to develop an accurate and reliable ANN model. The performance of the WBANN model is also compared with three more models: traditional ANN, wavelet-based ANN (WANN) and bootstrap-based ANN (BANN). Input vectors are decomposed into discrete wavelet components (DWCs) using discrete wavelet transformation (DWT) and then appropriate DWCs sub-series are used as inputs to the ANN model to develop the WANN model. The BANN model is an ensemble of several ANNs built using bootstrap resamples of raw datasets, whereas the WBANN model is an ensemble of several ANNs built using bootstrap resamples of DWCs instead of raw datasets. The results showed that the hybrid models WBANN and WANN produced significantly better results than the traditional ANN and BANN, whereas the BANN model is found to be more reliable and consistent. The WBANN and WANN models simulated the peak discharges better than the ANN and BANN models, whereas the overall performance of WBANN, which uses the capabilities of both bootstrap and wavelet techniques, is found to be more accurate and reliable than the remaining three models.