Daily Urban Water Demand Forecasting Based on Chaotic Theory and Continuous Deep Belief Neural Network

The prediction of daily water demands is a crucial part of the effective functioning of the water supply system. This work proposed that a continuous deep belief neural network (CDBNN) model based on the chaotic theory should be implemented to predict the daily water demand time series in Zhuzhou, China. CDBNN should initially be used to predict the urban water demand time series. First, the power spectrum and the largest Lyapunov exponent is used to determine the chaotic characteristic of the daily water demand time series. Second, C–C method is utilized to reconstruct the water demand time series’ phase space. Lastly, the forecasting model should be produced with the continuous deep belief network and neural network algorithms implemented for feature learning and regression, respectively, and the CDBNN input established by the best embedding dimension of the reconstructed phase space. The proposed method is contrasted with the support vector regression, generalized regression neural networks and feed forward neural networks, and they are accepted with the identical dataset. The predictive performance of the models is examined using normalized root-mean-square error (NRMSE), correlation coefficient (COR), and mean absolute percentage error (MAPE). The results suggest that the hybrid model has the smallest NRMSE and MAPE values, and the largest COR.