Joint Anomaly Detection and Topology Inference for Dynamic Water Distribution Networks Monitoring

The reliable and efficient operation of Water Distribution Networks (WDNs), in the context of water scarcity and deteriorating infrastructure, requires advanced monitoring strategies. In this paper, we propose a a joint framework for dynamic modeling and anomaly detection in WDNs based on Topological Signal Processing (TSP) that enables the representation and processing of IoT sensor data over cell complexes, i.e. higher-order network structures that capture multi-way interactions among network variables. The higher order topology is inferred in a data-driven manner from flow observations. Our dynamic flow model simultaneously accounts for both temporally sparse and spatially distributed water demands, as well as persistent, spatially sparse leakages. Within this framework, we formulate a principled optimization problem for the joint inference of the underlying higher-order topology and the detection of leakages in water flow signals. This joint formulation allows the topology to adapt to the observed dynamics, improving the representation of flow interactions and enhancing detection accuracy. Numerical experiments on synthetic and realistic WDNs demonstrate that the proposed framework outperforms graph-based approaches, achieving improved leakage detection performance across different operating conditions.