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.

水力建模已被认为是改进配水系统 (WDS) 设计、操作和管理的重要工具，因为它允许工程师实时模拟和分析 WDS 的行为，并帮助他们做出科学决策。城市基础设施的信息化推动了WDS的实时细粒度控制，使其成为近年来的热点之一，从而对WDS在线标定的效率和精度提出了更高的要求，特别是在处理大型复杂的情况时WDS。为了实现这一目的，本文从新的角度提出了一种开发实时WDS模型的新方法（即深度模糊映射非参数模型（DFM））。据我们所知，这是第一个使用模糊隶属函数考虑建模问题的不确定性的工作，并基于所提出的 DFM 框架为给定的 WDS 建立从压力/流量传感器到节点水消耗的精确逆映射。与大多数需要时间来优化模型参数的传统校准方法不同，DFM 方法具有通过严格的数学理论得出的独特解析解，因此 DFM 的计算速度很快，因为它能够合理地处理通常需要迭代数值算法和大量数据才能解决的问题。计算时间。该方法应用于两个案例研究，结果表明，该方法可以实时估计节点耗水量，具有较高的精度、计算效率、