Towards attack detection in multimodal cyber-physical systems with sticky HDP-HMM based time series analysis
Open accessAbstract
Automatic detection of the precise occurrence and duration of an attack reflected in time-series logs generated by cyber-physical systems is a challenging problem. This problem is exacerbated when performing this analysis using logs with limited system information. In a realistic scenario, multiple and differing attack methods may be employed in rapid succession. Modern or legacy systems operate in multiple modes and contain multiple devices recording a variety of continuous and categorical data streams. This work presents a non-parametric Bayesian framework that addresses these challenges using the sticky Hierarchical Dirichlet Process Hidden Markov Model (sHDP-HMM) . Additionally, we explore metrics for measuring the accuracy of the detected events, their timings and durations, and compare the computational efficiency of different inference implementations of the model. The efficacy of attack detection is demonstrated in two settings: an avionics testbed and a consumer robot.
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In many works, a model predicts the next-step sensor or control-signal values and computes prediction residuals, or derives an anomaly score that functions as a probabilistic or density-based residual, so that small but systematic deviations in process dynamics can be detected even when they are not visible at the network layer.
“In many of these works, a model predicts the next-step sensor or control-signal values and computes prediction residuals, or derives an anomaly score that functions as a probabilistic or density-based residual, so that small but systematic deviations in process dynamics can be detected even when they are not visible at the network layer [67,69,70,72,73,75].”
From AI-Based Anomaly Detection in Industrial Control and Cyber–Physical Systems: A Data-Type-Oriented Systematic Review (2025) · cites this paper as [70]
Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe distribution of datasets shows a strong reliance on SWaT and WADI for benchmarking prediction-residual-based methods, with additional evidence from custom-built avionics, robotics, temperature-control, offshore wind farm, and simulation-based CPS testbeds.
“Finally, the distribution of datasets shows a strong reliance on SWaT and WADI for benchmarking prediction-residual-based methods, with additional evidence from custombuilt avionics, robotics, temperature-control, offshore wind farm, and simulation-based CPS testbeds [67-73,75,76].”
From AI-Based Anomaly Detection in Industrial Control and Cyber–Physical Systems: A Data-Type-Oriented Systematic Review (2025) · cites this paper as [70]
Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredStudies that explicitly model multiple normal modes or use probabilistic residuals address operating-mode changes by representing them and assigning anomaly scores based on deviation probabilities.
“Studies that explicitly model multiple normal modes or use probabilistic residuals address this by representing operating-mode changes and assigning anomaly scores based on deviation probabilities [70,75].”
From AI-Based Anomaly Detection in Industrial Control and Cyber–Physical Systems: A Data-Type-Oriented Systematic Review (2025) · cites this paper as [70]
Section 4.2 models changing CPS behavior as latent HMM states, and the Additional information section identifies novel states by comparing normal and attack recordings. These passages support representing operating modes and detecting anomalous changes, but they do not describe assigning anomaly scores based on deviation probabilities. Section 3.3 mentions residuals and log-likelihood spikes as other approaches, not as this paper’s scoring method; page numbers were not available in our copy. (LLM, conf=0.84)
Experimental — accuracy not yet measuredProcess data are particularly suitable for attacks that perturb the physical process state while keeping network-level statistics relatively unchanged, such as false data injection, malicious command or parameter manipulation, process-oriented attacks, and stealthy drifts in sensor trajectories.
“First, process data are particularly suitable for attacks that perturb the physical process state while keeping network-level statistics relatively unchanged-such as false data injection, malicious command or parameter manipulation, process-oriented attacks, and stealthy drifts in sensor trajectories [67,69-73,75,76].”
From AI-Based Anomaly Detection in Industrial Control and Cyber–Physical Systems: A Data-Type-Oriented Systematic Review (2025) · cites this paper as [70]
Section 7 (Consumer Robot) and Section 7.1 (Attacks; page unavailable) describe using sensor and actuator readings to detect attacks that alter a robot’s physical behavior. The paper does not establish that network-level statistics remain relatively unchanged, nor does it substantiate the listed examples of false data injection, malicious command or parameter manipulation, and stealthy sensor-trajectory drift. (LLM, conf=0.85)
Experimental — accuracy not yet measuredHong et al. [70] proposed a nonparametric Bayesian framework based on a Sticky Hierarchical Dirichlet Process Hidden Markov Model (Sticky HDP-HMM) for time-series analysis of multimodal CPS using log data from avionics and robot testbeds.
“Using log data from an in-house avionics testbed and a consumer robot testbed, Hong et al. [70] proposed a nonparametric Bayesian framework based on a Sticky Hierarchical Dirichlet Process Hidden Markov Model (Sticky HDP-HMM) for time-series analysis of multimodal CPS.”
From AI-Based Anomaly Detection in Industrial Control and Cyber–Physical Systems: A Data-Type-Oriented Systematic Review (2025) · cites this paper as [70]
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- Authors
- Hong, A. E., Malinovsky, P. P., & Damodaran, S. K.
- Affiliations
- The MITRE Corporation, McLean, USA
- Venue
- Digital Threats: Research and Practice
- Published
- 2024-03-21
- Volume
- 5
- Issue
- 1
- Pages
- 1-21
- ISSN
- 2576-5337 (ISSN-L)
- 2692-1626
- OpenAlex
- W4381052590
- Cited by
- 11
- References
- 76
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 4
- FWCI
- 1.22
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- Locations
- Digital Threats Research and Practice (publishedVersion, cc-by)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Network Security and Intrusion Detection
- Physical Sciences › Engineering › Control and Systems Engineering › Smart Grid Security and Resilience
- Physical Sciences › Computer Science › Artificial Intelligence › Adversarial Robustness in Machine Learning
- Keywords
- attack detection, cyber-physical systems, multimodal data, time series analysis, hidden Markov models, non-parametric Bayesian inference, log analysis, event detection, avionics, consumer robots, inference efficiency
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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