A Forecasting Framework Based on Kalman Filter Integrated Multivariate Local Polynomial Regression: Application to Urban Water Demand
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In this study, a forecasting framework for daily urban water demand has been proposed. It was developed based on the extended Kalman filter (EKF) which consists of state estimation, forecasting and error correction. The forecasting and error correction models can be substituted. As an example, a multivariate local polynomial regression (MLPR) was used to linearize the complex system which is essential for EKF. A correctional prediction of residual based on relevance vector regression was employed to update and substitute error estimation value in the EKF. To improve the precision of the forecasts, the historical data series was decomposed into low- and high-frequency subseries using discrete wavelet transformation. Five category forecasts with the lead time of 1-day were assessed in comparison of the proposed model: MLPR, multi-scale relevance vector regression, autoregressive moving average, Back Propagation neural network and multiple linear regression. According to the performance criteria, the MLPR is slightly beneficial in capturing the basic dynamics of the daily urban water demand in the short term, but the state estimation and error correction can greatly improve the results. The proposed model obtains better forecasting performances than existing models, which is attributed to good state estimation from the Kalman transmission gain and favorable feature learning performance using MLPR.
KeywordsKalman filter Multivariate local polynomial regression Water demand Forecast Relevance vector regression
This work is supported by the Natural Science Foundation of China (71801044), the Humanities and Social Science Foundation of Ministry of Education of China (17YJC630003), the Natural Science Foundation of Chongqing (cstc2018jcyjAX0436), and the Research Start-Up Funds of CTBU (1756012). In addition, the authors would also like to thank the editors/reviewers for their valuable suggestions and comments that have helped improve this paper.
TL and YB conceived and designed the experiments; GC performed the experiments, analyzed the data and wrote the paper; JZ contributed to the scientific discussion and editing. The authors thank JX for supplying the dataset.
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Conflicts of interest
The authors declare no conflict of interest.
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