Hourly Urban Water Demand Forecasting Using the Continuous Deep Belief Echo State Network

Yuebing Xu,Jing Zhang,Zuqiang Long,Hongzhong Tang,Xiaogang Zhang

doi:10.3390/w11020351

Yuebing Xu, Jing Zhang + Show 3 more

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https://doi.org/10.3390/w11020351

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Abstract

Effective and accurate water demand prediction is an important part of the optimal scheduling of a city water supply system. A novel deep architecture model called the continuous deep belief echo state network (CDBESN) is proposed in this study for the prediction of hourly urban water demand. The CDBESN model uses a continuous deep belief network (CDBN) as the feature extraction algorithm and an echo state network (ESN) as the regression algorithm. The new architecture can model actual water demand data with fast convergence and global optimization ability. The prediction capacity of the CDBESN model is tested using historical hourly water demand data obtained from an urban waterworks in Zhuzhou, China. The performance of the proposed model is compared with those of ESN, continuous deep belief neural network, and support vector regression models. The correlation coefficient (r2), normalized root-mean-square error (NRMSE), and mean absolute percentage error (MAPE) are adopted as assessment criteria. Forecasting results obtained in the testing stage indicate that the CDBESN model has the largest r2 value of 0.995912 and the smallest NRMSE and MAPE values of 0.027163 and 2.469419, respectively. The prediction accuracy of the proposed model clearly outperforms those of the models it is compared with due to the good feature extraction ability of CDBN and the excellent feature learning ability of ESN.

Highlights

Precise short-term prediction of urban water demand provides guidance for the planning and management of water resources and plays an important role in the economic operation of a water supply system
A new continuous deep belief echo state network (CDBESN) model is proposed for the prediction of the original hourly urban water demand
The continuous deep belief network (CDBN) model is a stack of multiple continuous RBM (CRBM) with continuous state values, which can deal with actual hourly water demand data

Summary

Introduction

Precise short-term prediction of urban water demand provides guidance for the planning and management of water resources and plays an important role in the economic operation of a water supply system. Research regarding water demand prediction generally focuses on methods involving ANN, which are nonparametric data-driven approaches applicable for building nonlinear mapping from input to output variables for estimating nonlinear continuous functions with an arbitrary accuracy [10]. Jain et al [11] compared ANNs, a time series model, and a regression model for the weekly water demand prediction of the Indian Institute of Technology in Kanpur, India, and found that the ANNs outperformed the two other methods. Adamowski [12] applied an ANN model to forecast peak daily urban water demands and achieved a high prediction accuracy. Bennett et al [13]

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