Deep fuzzy mapping nonparametric model for real-time demand estimation in water distribution systems: A new...

Hydraulic modeling has been recognized as a valuable tool for improving the design, operation, and management of water distribution systems (WDSs) as it allows engineers to simulate and analyze behaviors of WDSs in real time and help them make scientific decisions. The informatization of urban infrastructure has motivated the real-time fine-grained control of WDSs, making it one of the hotspots in recent years, thereby putting higher requirements on WDS online calibration in terms of efficiency and accuracy, especially when dealing with large-complex WDSs. To achieve this purpose, this paper proposes a novel approach (i.e., deep fuzzy mapping nonparametric model (DFM)) from a new perspective for developing a real-time WDS model. To our knowledge, this is the first work that considers uncertainties in modeling problems using fuzzy membership functions and establishes the precise inverse mapping from pressure/flow sensors to nodal water consumption for a given WDS based on the proposed DFM framework. Unlike most traditional calibration methods that require time to optimize model parameters, the DFM approach has a unique analytical solution derived through rigorous mathematical theory, thus the DFM is computationally fast as a result of sensibly handling the problems whose solutions typically require iterative numerical algorithms and large computational time. The proposed method is applied to two case studies and the results obtained show that it can produce a real-time estimation of nodal water consumption with higher accuracy, computational efficiency, and robustness relative to traditional calibration methods.