A Forecasting Framework Based on Kalman Filter Integrated Multivariate Local Polynomial Regression: Application to Urban Water Demand

摘要

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.