Pressure Gradient Driven Multistage Leak Localization for Multiple Simultaneous Leaks in Water Distribution Networks under Uncertainty

Abstract

Abstract Leak localization in water distribution networks (WDNs) is inherently challenging due to the nonuniqueness of solutions, where different leak configurations can produce similar pressure responses at monitoring sensors. These challenges are further exacerbated by uncertainties in hydraulic model parameters, particularly nodal demands and pipe roughness coefficients, as well as by the unknown number of simultaneous leaks present in the system. This study proposes a multistage clustering-based methodology for leak localization that systematically addresses these issues. The approach groups network nodes into clusters and identifies leaky regions by minimizing discrepancies between measured data and hydraulic model simulations. The objective function jointly incorporates pressures at sensor locations, flow rates, and pressure gradients between sensors, while explicitly accounting for hydraulic model uncertainties without requiring prior knowledge of the number of leaks. The methodology employs an iterative refinement strategy, whereby suspected leaky clusters are progressively subdivided into smaller groups at successive localization stages, thereby reducing the search space and improving localization accuracy. The proposed approach is validated using three benchmark networks and one real-world WDN, covering both looped and branched topologies with single and multiple supply source configurations. The evaluation considers simultaneous uncertainties in nodal demands and pipe roughness coefficients, with mean uncertainties ranging from 20% to 25% across networks and maximum uncertainties reaching approximately 50% at the node level for demands and pipe level for roughness for each network. Results show that for scenarios involving up to four concurrent leaks, with individual leak sizes between 2.4 and 4.0 m 3 / h and total leakage ranging from approximately 1.5% to 10% of the total system demand, the proposed method successfully localizes at least three leaks in the majority of cases, even under high uncertainty conditions. These results demonstrate the robustness and practical applicability of the methodology across diverse network configurations and operational scenarios.