Neural Processing Letters

, Volume 50, Issue 2, pp 1173–1189 | Cite as

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

  • Yuebing XuEmail author
  • Jing Zhang
  • Zuqiang Long
  • Mingyang Lv


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.


Daily water demand forecasting Deep belief networks CDBNN model Chaotic theory 



This work was supported in part by the National Natural Science Foundation of China (No. 61573299), the Science and Technology Plan Project of Hunan Province (2016TP1020), the Open Fund Project of Hunan Provincial Key Laboratory of Intelligent Information Processing and Application for Hengyang Normal University (2017IIPAYB04), the Natural Science Foundation of Hunan Province (No. 2017JJ2011), and the Research Project of the Education Department of Hunan Province (No. 17A031).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflicts of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Electrical and Information EngineeringHunan UniversityChangshaChina
  2. 2.Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, College of Physics and Electronic EngineeringHengyang Normal UniversityHengyangChina

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