Urban water demand forecasting and uncertainty assessment using ensemble wavelet-bootstrap-neural network models

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 naive 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.