Distributionally Robust Tuning of Anomaly Detectors in Cyber-Physical Systems with Stealthy Attacks

Renganathan, Venkatraman; Hashemi, Navid; Ruths, Justin; Summers, Tyler H.

doi:10.23919/acc45564.2020.9147661

Cited by 12 publications

(7 citation statements)

References 13 publications

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“…Due to its distribution-free nature, the Chebyshev inequality constitutes the foundation of a variety of probabilistic methods such as the minimax probability machines and DRFD design [14], [16], [37]. Note that the Chebyshev bound is tight due to the existence of an extremal distribution making (10) an equality.…”

Section: Optimal Inequalities In Probability Theorymentioning

confidence: 99%

“…Very often, CPS is modelled as a discrete-time linear time-invariant system. Using a state estimator, one defines residuals as output errors, based on which a quadratic failure detector is commonly constructed [14], [51]. • Control performance monitoring (CPM).…”

Section: Safe Thresholding For Change Detectionmentioning

confidence: 99%

“…[11]- [13]. Recently, distributionally robust fault detection (DRFD) has been extensively investigated [14]- [16], where robust integrated design of residual generator and alarm threshold are obtained, reliably enforcing constraints on FAR, FDR and other indices irrespective of imprecisely known distributions [15]- [17].…”

mentioning

confidence: 99%

“…In fact, evaluating the FAR is simply a quantification problem of tail probability that a random vector deviates from its mean in the multi-dimensional setting. Thus, given the mean and covariance, the worst-case FAR is nothing but an extension of the classic univariate Chebyshev bound [14]. With unimodality further considered, the worst-case FAR can be also viewed as generalizing the Gauss bound.…”

mentioning

confidence: 99%

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From Generalized Gauss Bounds to Distributionally Robust Fault Detection with Unimodality Information

Chen

Hao

Huang

et al. 2021

Preprint

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Probabilistic methods have attracted much interest in fault detection design, but its need for complete distributional knowledge is seldomly fulfilled. This has spurred endeavors in distributionally robust fault detection (DRFD) design, which secures robustness against inexact distributions by using moment-based ambiguity sets as a prime modelling tool. However, with the worst-case distribution being implausibly discrete, the resulting design suffers from over-pessimisim and can mask the true fault. This paper aims at developing a new DRFD design scheme with reduced conservatism, by assuming unimodality of the true distribution, a property commonly encountered in real-life practice. To tackle the chance constraint on false alarms, we first attain a new generalized Gauss bound on the probability outside an ellipsoid, which is less conservative than known Chebyshev bounds. As a result, analytical solutions to DRFD design problems are obtained, which are less conservative than known ones disregarding unimodality. We further encode bounded support information into ambiguity sets, derive a tightened multivariate Gauss bound, and develop approximate reformulations of design problems as convex programs. Moreover, the derived generalized Gauss bounds are broadly applicable to versatile change detection tasks for setting alarm thresholds. Results on a laborotary system shown that, the incorporation of unimodality information helps reducing conservatism of distributionally robust design and leads to a better tradeoff between robustness and sensitivity.

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Section: Optimal Inequalities In Probability Theorymentioning

confidence: 99%

Section: Safe Thresholding For Change Detectionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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From Generalized Gauss Bounds to Distributionally Robust Fault Detection with Unimodality Information

Chen

Hao

Huang

et al. 2021

Preprint

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“…Contributions: This paper is part of our ongoing work [7], [8] to leverage results from distributionally robust optimization to design robust anomaly detectors. Specifically, the detector threshold corresponding to a desired false alarm rate in the setting considered in this paper can be effectively computed only through the moment-based approaches explained [7].…”

Section: Introductionmentioning

confidence: 99%

Anomaly Detection Under Multiplicative Noise Model Uncertainty

Renganathan,

Gravell,

Ruths

et al. 2021

Preprint

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State estimators are crucial components of anomaly detectors that are used to monitor cyber-physical systems. Many frequently used state estimators are susceptible to model risk as they rely critically on the availability of an accurate state-space model. Modeling errors make it more difficult to distinguish whether deviations from expected behavior are due to anomalies or simply a lack of knowledge about the system dynamics. In this research, we account for model uncertainty through a multiplicative noise framework. Specifically, we propose two different state estimators in this setting to hedge against the model uncertainty risk namely, 1) multiplicative noise LQG, and 2) Wasserstein distributionally robust Kalman filter. The size of the residual from either estimator can then be compared against a threshold to detect anomalies. Finally, the proposed detectors are validated using numerical simulations. Extension of state-of-the-art anomaly detection in cyber-physical systems to handle model uncertainty represents the main novel contribution of the present work.

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