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Localizing Anomalies in Critical Infrastructure using Model-Based Drift Explanations

Valerie Vaquet, Fabian Hinder, Jonas Vaquet, Kathrin Lammers, Lars Quakernack, Barbara Hammer

TL;DR

This work models critical infrastructure as graphs and treats anomalies as concept drift within a dynamic Bayesian network, distinguishing Type I global demand anomalies (e.g., leaks) from Type II sensor faults. By introducing a time latent variable and applying model-based drift explanations, the authors enable anomaly detection and localization without requiring precise topology or leakage-free historical data, and they validate the approach on water distribution networks and electrical grids. The key findings show that drift effects decay exponentially with graph distance, and tree-based explanation methods can effectively localize anomalies, offering a topology-agnostic, computationally lightweight alternative to hydraulic models with practical applicability to real-world critical infrastructure. Overall, the methodology advances explainable AI for infrastructure monitoring by linking drift detection to localized explanations, enabling robust anomaly localization under data scarcity and changing demands.

Abstract

Facing climate change, the already limited availability of drinking water will decrease in the future rendering drinking water an increasingly scarce resource. Considerable amounts of it are lost through leakages in water transportation and distribution networks. Thus, anomaly detection and localization, in particular for leakages, are crucial but challenging tasks due to the complex interactions and changing demands in water distribution networks. In this work, we analyze the effects of anomalies on the dynamics of critical infrastructure systems by modeling the networks employing Bayesian networks. We then discuss how the problem is connected to and can be considered through the lens of concept drift. In particular, we argue that model-based explanations of concept drift are a promising tool for localizing anomalies given limited information about the network. The methodology is experimentally evaluated using realistic benchmark scenarios. To showcase that our methodology applies to critical infrastructure more generally, in addition to considering leakages and sensor faults in water systems, we showcase the suitability of the derived technique to localize sensor faults in power systems.

Localizing Anomalies in Critical Infrastructure using Model-Based Drift Explanations

TL;DR

This work models critical infrastructure as graphs and treats anomalies as concept drift within a dynamic Bayesian network, distinguishing Type I global demand anomalies (e.g., leaks) from Type II sensor faults. By introducing a time latent variable and applying model-based drift explanations, the authors enable anomaly detection and localization without requiring precise topology or leakage-free historical data, and they validate the approach on water distribution networks and electrical grids. The key findings show that drift effects decay exponentially with graph distance, and tree-based explanation methods can effectively localize anomalies, offering a topology-agnostic, computationally lightweight alternative to hydraulic models with practical applicability to real-world critical infrastructure. Overall, the methodology advances explainable AI for infrastructure monitoring by linking drift detection to localized explanations, enabling robust anomaly localization under data scarcity and changing demands.

Abstract

Facing climate change, the already limited availability of drinking water will decrease in the future rendering drinking water an increasingly scarce resource. Considerable amounts of it are lost through leakages in water transportation and distribution networks. Thus, anomaly detection and localization, in particular for leakages, are crucial but challenging tasks due to the complex interactions and changing demands in water distribution networks. In this work, we analyze the effects of anomalies on the dynamics of critical infrastructure systems by modeling the networks employing Bayesian networks. We then discuss how the problem is connected to and can be considered through the lens of concept drift. In particular, we argue that model-based explanations of concept drift are a promising tool for localizing anomalies given limited information about the network. The methodology is experimentally evaluated using realistic benchmark scenarios. To showcase that our methodology applies to critical infrastructure more generally, in addition to considering leakages and sensor faults in water systems, we showcase the suitability of the derived technique to localize sensor faults in power systems.
Paper Structure (21 sections, 4 theorems, 16 equations, 7 figures, 2 tables)

This paper contains 21 sections, 4 theorems, 16 equations, 7 figures, 2 tables.

Table of Contents

  1. Keywords
  2. Introduction
  3. Modeling Critical Infrastructure
  4. A Causal Model for Modeling Anomalies in Critical Infrastructure
  5. Methodology
  6. Modelling Anomalies as Concept Drift
  7. Anomaly Detection
  8. Anomaly Localization
  9. Type II
  10. Type I
  11. Baseline Methodology for Anomaly Localization
  12. Experiments
  13. Setup, Data, and Metrics
  14. Case Studies
  15. Used Methods
  16. ...and 6 more sections

Key Result

Lemma 1

Let $D_\cdot : \mathbb{Z} \to \mathbb{R}^{V(G)}, t \mapsto D_t$ be a demand pattern and assume that the transition function $O(\cdot, d)$ is uniformly Lipschitz continuous for all $d \in \mathbb{R}^{V(G)}$, i.e. we have $\sup_{d \in \mathbb{R}^{V(G)}} \Vert O(p,d) - O(p',d) \Vert_1 \leq C_s \Vert p- In particular, $t \mapsto O_t(D_\cdot) := \lim_{n \to \infty} O_{t+n}^{(-n)}(p,D_\cdot)$ is well de

Figures (7)

  • Figure 1: L-Town topology. Diamonds mark the position of pressure sensors, red dot marks the leakage position.
  • Figure 2: Pressures at sensors in Figure \ref{['fig:ltwon:map']} (colors match), black line marks occurrence time of leakage.
  • Figure 4: Visualization of modeling of anomalies in critical infrastructure
  • Figure 5: Visualization of model-based drift explanation scheme
  • Figure 6: FI (ET)
  • ...and 2 more figures

Theorems & Definitions (10)

  • Definition 1
  • Definition 2
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof