Nonlinear Dynamic Modeling of Urban Water Consumption Using Chaotic Approach (Case Study: City of Kelowna)

Abstract

This study investigated urban water consumption complexity using chaos theory to improve forecasting performance to help optimize system management, reduce costs and improve reliability. The objectives of this study were to (1) investigate urban water distribution consumption complexity and its role in forecasting technique performance, (2) evaluate forecasting models by periodicity and lead time, and (3) propose a suitable forecasting technique based on operator applications and performance through various time scales. An urban consumption dataset obtained from the City of Kelowna (British Columbia, Canada) was used as a test case to forecast future consumption values using varying lead times under different temporal scales to identify models which may improve forecasting performance. Chaos theory techniques were employed to inform model optimization. This study attempted to address the paucity of studies on chaos theory applications in water consumption forecasting. This was accomplished by applying non-linear approximation, dynamic investigation, and phase space reconstruction for input variables, to improve the accuracy in various periodicity and lead time. To reconstruct the phase space, lag time was calculated using average mutual information for daily resolution as 17 days to reconstruct the phase space. The optimum embedding dimension and correlation exponent for the phase space were 18 and 3.5, respectively. Comparing the results, the non-linear local approximation model provided the best performance. The forecasting horizon for the models was 122 days. Moreover, phase space reconstruction improved the accuracy of the models for the different lead times. The findings of this study may improve forecasting performance and provide evidence to support further investigation of the chaotic behaviour of water consumption values over different time scales.