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Breaking the Flow and the Bank: Stealthy Cyberattacks on Water Network Hydraulics

Abdallah Alalem Albustami, Ahmad F. Taha

arXiv:2504.17211v1eess.SYcs.CRcs.SY

TL;DR

WDNs face stealthy sensor attacks, while the relationship between attack sophistication, required system knowledge, and impact remains insufficiently explored. The paper analyzes attack formulations across hydraulic and detection constraints, finding that localized manipulations can affect operations while evading checks.

  • Problem

    Prior work has often examined specific WDN attack scenarios or detection methods in isolation, leaving the relation between attacker knowledge, constraints, and impact underexplored.

    Source: §1 · p. 1, §1.2 · p. 2

  • Method

    The paper formulates sensor attacks with varying physical, state-estimation, and intrusion-detection constraints and evaluates them using WLS, CUSUM, and chi-squared detection.

    Source: §1.2 · p. 2

  • Results

    Local hydraulic relationships constrain attacks but also permit targeted manipulations that increase operational costs and alter water flows while maintaining physical and detection stealth; Net3 results show similar success at larger scale.

    Source: §1.2 · p. 3, §5.6 · p. 12

  • Takeaways & Limitations

    The analysis offers utilities a way to assess vulnerabilities across security configurations and highlights localized subsystems for enhanced monitoring.

    Source: §1.2 · p. 3, §8 · p. 15

    The approach relies on a deterministic hydraulic model and static WLS estimation, without fully accounting for epistemic parameter uncertainty or temporal correlations.

    Source: §7 · p. 15

Abstract

from arXiv · show

As water distribution networks (WDNs) become increasingly connected with digital infrastructures, they face greater exposure to cyberattacks that threaten their operational integrity. Stealthy False Data Injection Attacks (SFDIAs) are particularly concerning, as they manipulate sensor data to compromise system operations while avoiding detection. While existing studies have focused on either detection methods or specific attack formulations, the relationship between attack sophistication, system knowledge requirements, and achievable impact remains unexplored. This paper presents a systematic analysis of sensor attacks against WDNs, investigating different combinations of physical constraints, state monitoring requirements, and intrusion detection evasion conditions. We propose several attack formulations that range from tailored strategies satisfying both physical and detection constraints to simpler measurement manipulations. The proposed attacks are simple and local -- requiring knowledge only of targeted sensors and their hydraulic connections -- making them scalable and practical. Through case studies on Net1 and Net3 benchmark networks, we demonstrate how these attacks can persistently increase operational costs and alter water flows while remaining undetected by monitoring systems for extended periods. The analysis provides utilities with insights for vulnerability assessment and motivates the development of protection strategies that combine physical and statistical security mechanisms.

1. Introduction

Connected WDNs face cybersecurity vulnerabilities, and stealthy false-data attacks can mislead monitoring while threatening operations. The paper analyzes attacks across hydraulic constraints, state estimation, detection evasion, and attacker knowledge.

1. Introduction

  • The 2021 Oldsmar attack attempted to alter chemical levels, while a 2024 Texas incident caused tank overflow and SCADA disruption.Many attacks also go unnoticed or undisclosed [17].Source: §1 · p. 1

1.1. Literature Review

  • Prior WDN studies addressed particular attacks or detectors, leaving systematic analysis of hydraulic constraints, monitoring, and attacker knowledge limited.Earlier work included treatment-system attacks, sensor interruptions, random injections, and selected stealthy attack scenarios.Source: §1.1 · p. 2

1.2. Paper Contributions

  • The paper formulates four attack strategies and evaluates how CUSUM, chi-squared tests, and physical checks respond to their hydraulic impacts.The analysis considers pump scheduling and water-flow management.Source: §1.2 · pp. 2–3
  • The methodology guides target selection and attack assessment, including how topology affects complexity and how few sensor manipulations may suffice.The stated aim is to help utilities assess vulnerabilities across security configurations.Source: §1.2 · p. 3

2. Preliminaries

The hydraulic model represents network components under mass and energy conservation, providing the physical relationships used in the analysis.

2.1.1. Reservoirs

  • Reservoirs are modeled as infinite water sources with constant hydraulic head over time.The paper treats this assumption as appropriate for elevated reservoirs supplying water under gravity.Source: §2.1.1 · p. 3

2.1.2. Tanks

  • Tank head changes with the net inflow and outflow, with tank cross-sectional area relating flow balance to head variation.The model assumes constant tank cross-sectional areas.Source: §2.1.2 · p. 3

2.1.3. Junctions

  • Junction mass balance equates incoming water with outgoing flow plus local demand.The equation accounts for flows on links connected to each junction.Source: §2.1.3 · p. 3

2.1.4. Pipes

  • Pipe head loss is modeled with the Hazen-Williams relationship between flow and head loss.The paper states that its attack methods also apply to hydraulic models based on mass and energy conservation.Source: §2.1.4 · p. 3

2.1.5. Pumps

  • Pump head gain depends on pump speed and flow, with speed bounded between zero and its maximum.The model uses pump-specific shutoff-head and curve coefficients.Source: §2.1.5 · p. 3

2.1.6. Valves

  • Valves are on-off components: an open valve permits flow with head loss, while a closed valve stops flow and decouples its nodes.The open-valve model includes a minor-loss coefficient.Source: §2.1.6 · p. 4
  • Piecewise linear segments approximate pipe and valve head-loss curves, while quadratic functions approximate pump characteristics for tractable optimization.The linear formulation selects a segment and constrains flow within its bounds; the pump approximation preserves the speed, discharge, and head-gain relationship.Source: §2.1.6 · p. 4

2.2. Hydraulics State Estimation in WDNs

Hydraulic state estimation reconstructs network conditions from sensor measurements, although practical adoption depends on adequate observability and calibrated models.

2.2. Hydraulics State Estimation in WDNs

  • State estimation can provide real-time snapshots and support intrusion detection, but adoption is limited by calibrated-model and sensor-observability requirements.The literature includes static residual-minimization methods and dynamic estimators such as the extended Kalman filter.Source: §2.2 · p. 4

2.2.1. Weighted Least Squares State Estimation

  • The paper uses weighted least squares (WLS), minimizing weighted squared residuals between measured and predicted values to estimate state.The state includes pipe flows and junction heads; measurement noise is assumed Gaussian with known covariance.Source: §2.2.1 · p. 4
  • WLS sensors are distributed to make the system observable, with inverse measurement variances used as weights.The work does not solve a formal sensor-placement optimization problem.Source: §2.2.1 · p. 4

2.3. Intrusion Detection

The study uses residual-based intrusion detection with both cumulative and single-time-step tests, which address different anomaly patterns.

2.3.1. CUSUM Detection

  • CUSUM accumulates residual deviations over time and alarms when its statistic exceeds a threshold, making it suited to persistent anomalies.Its bias adjusts sensitivity, and the study empirically tunes threshold and bias to reach a desired false-alarm rate.Source: §2.3.1 · p. 5

2.3.2. Chi-squared (χ2) Detector

  • The chi-squared detector tests whether the current residual vector falls within its expected distribution and alarms above a threshold.The threshold is set to maintain a desired false-alarm rate based on the number of independent measurements and desired mean time between false alarms.Source: §2.3.2 · p. 5

2.3. Intrusion Detection

  • CUSUM targets subtle, long-term deviations, whereas the chi-squared test identifies sudden residual anomalies; the paper then introduces attacks with varying constraints and knowledge.The attack overview identifies FS-FDI, HU-FDI, HA-FDI, and R-FDI variants interacting with system security mechanisms.Source: §2.3.2 · p. 5, Figure 1 · p. 5

3. Full-Stealth Attack Design

The Full-Stealth FDI strategy formulates sensor manipulation as an optimization problem that combines detection evasion, state-estimation convergence, and hydraulic feasibility. Its objective encourages sparse attacks on selected measurements.

3. Full-Stealth Attack Design

  • FS-FDI jointly enforces intrusion-detection bypass, state-estimation convergence, and hydraulic constraints in a nonlinear optimization formulation.The hydraulic constraints encode mass and energy balance.Source: §3 · p. 5
  • The objective minimizes the sum of absolute attack values, promoting sparse manipulations of specific measurements.The attack vectors represent head, flow, and demand measurements.Source: §3 · p. 6
  • The state-estimation constraint models the attacker applying state estimation to attacked measurements and their hydraulically connected components.For WLS, the passage gives the estimator as a function of the attacked measurements.Source: §3 · p. 6

k. The convergence constraint (13j) ensures

The formulation combines local hydraulic and monitoring constraints with an iterative attack procedure. It is presented as a benchmark for assessing resilience and identifying monitoring vulnerabilities.

k. The convergence constraint (13j) ensures

  • Mass and energy balance constraints need only cover the local subnetwork and paths containing attacked measurements, requiring relevant connectivity and hydraulic parameters.The local subnetwork is defined by hydraulically connected components around targeted sensors.Source: k. The convergence constraint (13j)… · p. 6
  • With piecewise-linearized hydraulic constraints, the optimization is a MILP whose localized scope keeps it computationally tractable regardless of overall network size.The passage says even one-minute hydraulic time steps remain computationally feasible with standard MILP solvers.Source: k. The convergence constraint (13j)… · p. 6
  • The attack algorithm iteratively computes residuals, solves for attack vectors, updates measurements, and checks detector statistics and physical feasibility.Its stated inputs include measurements, state estimates, local topology and hydraulic parameters, and detector parameters.Source: k. The convergence constraint (13j)… · p. 7
  • FS-FDI provides a benchmark for analyzing worst-case stealthy sensor attacks and identifying vulnerabilities in monitoring systems.The formulation combines intrusion-detection bypass, state-estimation convergence, and physical constraint satisfaction.Source: k. The convergence constraint (13j)… · p. 7
  • The framework is intended to support vulnerability assessment and targeted protection strategies, using standard hydraulic principles and common operational data.The passage also notes that WDN hydraulic timescales allow implementation within feasible operational intervals.Source: k. The convergence constraint (13j)… · p. 7
  • The next strategies relax different combinations of FS-FDI constraints to examine their effects on attack capabilities and impact.Source: k. The convergence constraint (13j)… · p. 7

4. Constraint-Relaxed Attack Strategies

The section compares attack strategies that relax different combinations of physical and monitoring constraints, spanning tailored stealthy attacks to random manipulations. It also evaluates impacts on pump scheduling and water flow.

4.1. Hydraulics-Unaware FDI (HU-FDI)

  • HU-FDI preserves detection evasion and state-estimation convergence while dropping hydraulic consistency, reducing optimization requirements to detection parameters and targeted measurements.Hydraulic violations may still produce obvious deviations that alert operators.Source: §4.1 · pp. 7–8
  • For scalar detection statistics, closed-form HU-FDI requires comprehensive measurement, state-estimate, covariance, and detector knowledge; optimization needs only targeted measurements and corresponding detector parameters.The optimization-based alternative is described as more practical for scalar detection schemes.Source: §4.1 · p. 8

4.2. Hydraulics-Aware FDI (HA-FDI)

  • HA-FDI preserves physical plausibility while removing ID- and SE-related constraints, requiring local topology and hydraulic parameters.It is a benchmark for physical-validation-only defenses, but may be less algorithmically stealthy where detection systems are present.Source: §4.2 · p. 8

4.3. Random FDI (R-FDI)

  • R-FDI is a minimal-knowledge baseline combining random-walk drift, high-frequency noise, and occasional spikes, with attack magnitude bounded for basic operational plausibility.The strategy is meant to reflect patterns possible from automated scripts or basic manipulation tools.Source: §4.3 · p. 8

4.4. Impact on Hydraulic Operations

  • Figure 2 guides strategy selection by available knowledge, including measurement access, SE/ID understanding, and network topology or parameters.Source: §4.3 · p. 9, Figure 2 · p. 9
  • The operational-impact evaluation considers pump scheduling costs and water-flow feasibility under mass- and energy-balance constraints.The study tests whether manipulated measurements can induce suboptimal pump schedules or false feasibility assessments while appearing physically consistent.Source: §4.4 · p. 9

5. Case Studies

Case studies on Net1 and Net3 examine whether sensor attacks can evade intrusion detection and physical validation, affect operations, and scale.

5.1. Full-Stealth FDI Analysis

  • From hours 15–20, FS-FDI increased pumping costs while evading detection and physical validation; no feasible increase was found during hours 11–15.The earlier interval likely coincided with pump inactivity, when sudden changes could trigger CUSUM detection; coordinated sensor changes maintained hydraulic consistency.Source: §5.1 · p. 10

5.2. Constraint-Relaxed FDI Analysis

  • HA-FDI had marginally greater pump impact than FS-FDI, but hydraulic balance bounded its effects; HU-FDI caused mass-balance violations up to 400 GPM.HA-FDI maintained mass conservation errors below 10^-7 GPM, while HU-FDI violations could be flagged by physical validation.Source: §5.2 · pp. 10–11

5.3. Comparison of Attack Strategies

  • FS-FDI and HA-FDI achieved similar cost increases while maintaining physical plausibility; HU-FDI and Random FDI had greater impact but failed validation or detection.The benchmark results suggest that a sustained 5% cost increase could accumulate to millions in annual excess costs in metropolitan networks, though the results are from a benchmark network.Source: §5.3 · p. 11

5.4. Impact on Water Flow Operations

  • Random FDI drew an additional 4,874 ft3 from a tank during an eight-hour attack, illustrating impacts beyond pump-cost manipulation.Attack effectiveness depends on measurement access and the operational objective; even random measurement selection typically had detrimental operational effects.Source: §5.4 · pp. 11–12

5.5. Evaluation of Intrusion Detection Methods

  • Chi-squared detection allowed larger measurement manipulations than CUSUM, whose per-measurement accumulation better detected persistent changes but could increase false alarms.Tighter thresholds improved attack detection while raising false alarms; relaxed thresholds reduced false alarms but created larger exploitable blind spots.Source: §5.5 · p. 12

5.6. Scalability and Implementation on Larger Networks

  • A 5% attack on Net3 increased operational costs by 62.74% over 24 hours, with effects persisting beyond the attack window.Local modifications to Pump 1 flow and adjacent-junction demand readings pushed the pump into less-efficient operating regions.Source: §5.6 · p. 12

6. Systematic Approach to Attack Design and Execution

The section maps attack targets to local hydraulic relationships, then describes a workflow for designing and implementing attacks under physical and detection constraints. It also discusses practical deployment conditions and utility defenses.

6.1. Strategic Measurement Selection for Attacks

  • Physically consistent attacks can target boundary-demand nodes, source-consumer paths, storage interfaces, or flow-distribution points, with topology shaping the required manipulations.Radial networks can permit localized changes along unique flow paths; looped networks may use loop manipulation, demand absorption, or loop-breaking. Potential targets in Net1 and Net3 can require access to only 2–3 measurements.Source: §6.1 · p. 13, Figure 12 · p. 14

6.2. Attack Implementation Workflow

  • The workflow selects measurements, checks hydraulic connectivity and feasibility, then optimizes attack vectors for impact under physical and detection constraints.The Net1 example manipulates pump flow and Junction 1 demand while preserving their mass-balance relationship; the framework also proposes alternative sensor groupings or parameter adjustments when constraints cannot be met.Source: §6.2 · pp. 13–14
  • 62.74% cost increase in Net3 and 7–15% in Net1 were achieved while attacks remained physically plausible and evaded detection.The Net1 example coordinates pump-flow and demand manipulations during hours 15–20; the Net3 implementation uses the same algorithmic approach.Source: §6.2 · p. 14

6.3. Implementation Considerations and Practical Aspects

  • Practical attack deployment depends on network topology and the attacker’s access to system information.The implementation discussion focuses on measurement selection and real-world execution constraints.Source: §6.3 · p. 14

6.3.1. State Estimation Robustness

  • State-estimation robustness depends on measurement noise, sensor density, and parameter uncertainty, while sparse sensing can both increase vulnerability and limit coordinated attack options.The section identifies redundant sensors at hydraulic bottlenecks and critical control points as a possible robustness improvement.Source: §6.3.1 · p. 14

6.3.2. Implementation and Technical Reproducibility

  • Implementation requires access to field devices, and optimization scales with targeted sensors and nearby hydraulic connections rather than total network size.For typical configurations targeting 2–3 sensors, the MILPs use approximately O(10–20) binary variables and solve in 0.5–2 seconds on Net3 in the reported experiments.Source: §6.3.2 · p. 14

6.3.3. Security Recommendations

  • Utilities are advised to cross-validate hydraulically coupled measurements, add redundant monitoring at critical subsystems, and combine physical checks with statistical monitoring where resources permit.The recommendations also call for SCADA segmentation that accounts for hydraulic relationships and for verifying control decisions using multiple independent measurements.Source: §6.3.3 · pp. 14–15

7. Paper Limitations and Future Work

The authors identify modeling, estimator, attack-scope, and network-scale limits, and propose corresponding extensions and larger-network validation.

Limitations

  • The analysis uses a deterministic hydraulic model, static WLS estimation, localized attack strategies, and benchmark networks smaller and less complex than metropolitan systems.The model includes measurement noise but does not fully account for epistemic uncertainty in network parameters.Source: §7 · p. 15

Future Work

  • Future work includes uncertainty-aware optimization, time-series state estimation, hydraulic-constraint-based detection, distributed observers, and experiments on larger operational networks.The paper also notes potential integration with industry-standard tools such as EPANET.Source: §7 · p. 15

8. Summary and Concluding Remarks

The paper analyzes stealthy false data injection attacks on water networks and shows that local hydraulic relationships can support feasible attacks without complete network knowledge. It concludes that the approach can inform vulnerability assessment, while future work should address uncertainty and resilient monitoring.

Summary and Concluding Remarks

  • The proposed strategies can bypass physical validation and intrusion detection while disrupting pump control and water-flow management.Simulations show sensor manipulations can degrade operational efficiency and hydraulic performance while maintaining apparent physical consistency.Source: §8 · p. 15
  • Local hydraulic relationships can support feasible attacks without complete network knowledge, highlighting subsystems that merit enhanced monitoring.The conclusion also notes that missing basic validation mechanisms in many utilities can leave even straightforward sensor attacks capable of significant operational disruption.Source: §8 · p. 15
  • Future work should develop resilient control and distributed detection methods that use spatial and temporal measurement correlations while accounting for model uncertainty and sensor-calibration errors.Source: §8 · p. 15

Appendix A. Weighted Least Squared State Estimation

The appendix describes the WLS state-estimation system used in the paper, combining sensor measurements with hydraulic constraints to estimate pipe flows and junction heads.

State and objective

  • The state vector contains pipe flows and junction heads, and the WLS estimate minimizes weighted squared residuals while incorporating hydraulic constraints.Source: Appendix A · p. 17

Measurements and noise

  • The measurement system represents sensor readings and noise, with a diagonal weighting matrix whose entries are inverse measurement variances.The implementation sets σflow = 0.05 and σhead = 0.1.Source: Appendix A · p. 17

Hydraulic constraints and solution

  • Mass-balance constraints at junctions and linearized energy-balance equations across pipes are combined with the measurement system for WLS estimation.The combined system is expressed using a system matrix and vector, and the appendix gives the resulting WLS solution.Source: Appendix A · p. 17

Appendix B. Comprehensive SFDIA Implementation Framework

Algorithm 3 provides an implementation framework for four SFDIA strategies, taking users from sensor selection through attack execution and hydraulic impact assessment. Validation checks identify infeasible attacks and suggest alternatives based on system knowledge and sensor access.

Appendix B. Comprehensive SFDIA Implementation Framework

  • Algorithm 3 implements four attack strategies, applies modified measurements, and uses a hydraulic solver to assess projected operational effects.It accepts network configuration, measurements, and a target set, and returns modified measurements for vulnerability assessment.Source: Appendix B · pp. 17–18
  • Full-Stealth FDI requires state-estimation and intrusion-detection settings plus local hydraulic parameters, and verifies sensor connectivity before optimization.If connectivity validation fails or the optimization is infeasible, the framework exits with an explanation and may suggest alternative sensor groupings.Source: Appendix B · p. 18
  • Hydraulics-Aware FDI verifies hydraulic connectivity among targeted sensors before solving its attack optimization with local pipe parameters.A failed topology check exits with a message that the selected sensors cannot satisfy physical constraints.Source: Appendix B · p. 18
  • Hydraulics-Unaware FDI uses state-estimation and detector settings, then generates an attack through either optimization without physical constraints or a closed-form approach.The closed-form branch selects among vectorized or scalar CUSUM and chi-squared detectors.Source: Appendix B · p. 18
  • Random FDI initializes drift, generates drift, noise, and spike components, combines them, and applies magnitude bounds.The attack bounds are typically 5–10% of original values.Source: Appendix B · p. 18
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