Factor Graph Optimization for Leak Localization in Water Distribution Networks

2025-09-13

AI Summary

Leak detection and precise localization in water distribution networks (WDNs) are critical for ensuring water resource security. This paper proposes a novel joint state estimation method based on dual factor graph optimization—the first application of factor graphs to leak localization. It introduces a synergistic architecture comprising a “leak-free reference graph” and a “leak localization graph,” enabling simultaneous estimation of both current and historical spatiotemporal network states—overcoming the limitation of conventional methods that model only instantaneous states. By fusing pressure and flow sensor measurements and employing nonlinear optimization, the method achieves robust joint inference. Experiments on the Modena, L-TOWN, and synthetic benchmark networks demonstrate superior localization accuracy compared to state-of-the-art approaches, while exhibiting significantly higher computational efficiency than nonlinear Kalman filters such as the unscented Kalman filter (UKF).

Technology Category

• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements

Abstract

Detecting and localizing leaks in water distribution network systems is an important topic with direct environmental, economic, and social impact. Our paper is the first to explore the use of factor graph optimization techniques for leak localization in water distribution networks, enabling us to perform sensor fusion between pressure and demand sensor readings and to estimate the network's temporal and structural state evolution across all network nodes. The methodology introduces specific water network factors and proposes a new architecture composed of two factor graphs: a leak-free state estimation factor graph and a leak localization factor graph. When a new sensor reading is obtained, unlike Kalman and other interpolation-based methods, which estimate only the current network state, factor graphs update both current and past states. Results on Modena, L-TOWN and synthetic networks show that factor graphs are much faster than nonlinear Kalman-based alternatives such as the UKF, while also providing improvements in localization compared to state-of-the-art estimation-localization approaches. Implementation and benchmarks are available at https://github.com/pirofti/FGLL.

Problem

• Localizing leaks in water distribution networks
• Fusing pressure and demand sensor data
• Estimating temporal and structural network state evolution

Innovation

• Factor graph optimization for leak localization
• Sensor fusion between pressure and demand readings
• Two-factor graph architecture for state estimation