**Shan Wu 1, Hongquan Han 1, Benwei Hou 1,\* and Kegong Diao <sup>2</sup>**


Received: 13 April 2020; Accepted: 9 June 2020; Published: 12 June 2020

**Abstract:** Short-term water demand forecasting plays an important role in smart management and real-time simulation of water distribution systems (WDSs). This paper proposes a hybrid model for the short-term forecasting in the horizon of one day with 15 min time steps, which improves the forecasting accuracy by adding an error correction module to the initial forecasting model. The initial forecasting model is firstly established based on the least square support vector machine (LSSVM), the errors time series obtained by comparing the observed values and the initial forecasted values is next transformed into chaotic time series, and then the error correction model is established by the LSSVM method to forecast errors at the next time step. The hybrid model is tested on three real-world district metering areas (DMAs) in Beijing, China, with different demand patterns. The results show that, with the help of the error correction module, the hybrid model reduced the mean absolute percentage error (MAPE) of forecasted demand from (5.64%, 4.06%, 5.84%) to (4.84%, 3.15%, 3.47%) for the three DMAs, compared with using LSSVM without error correction. Therefore, the proposed hybrid model provides a better solution for short-term water demand forecasting on the tested cases.

**Keywords:** water demand forecasting; hybrid model; error correction; chaotic time series; least square support vector machine
