Optimal fault detection with nuisance parameters and a general covariance matrix

Fouladirad, Mitra; Freitag, Lori A.

doi:10.1002/acs.976

Cited by 14 publications

(18 citation statements)

References 18 publications

(31 reference statements)

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“…The Monte-Carlo simulation with trails shows that the false alarm rate of the test is about , where represents the 99% confidence interval. In other words, the upper bound of is close to its true value which is explained by the existence of the dominant term in the sum given by (22) in Appendix A-A.…”

Section: B a Toy Example-continuedmentioning

confidence: 84%

“…This transformation to the initial hypothesis testing problem (2) is based on the invariance properties of the Gaussian family (see details in [21]). To avoid the discussion of astuteness and consequences of such a transformation, the interested readers are referred to the following publication where mathematical aspect and proofs are provided [22]. The very last comment is that the aforementioned transformation does not degrade the optimality of the test.…”

Section: General Covariance Matrixmentioning

confidence: 97%

“…1) Conservative Threshold: Let be the false alarm probability of and its threshold. From (22), it follows that:…”

Section: B Bayesian Test With Uniform Weightsmentioning

confidence: 98%

“…Let be the weighted log-likelihood ratio defined by (19) where Let be the test of level between given by (20) and for (21) where is chosen such that . 2) False Alarm Probability: The false alarm probability of the Bayesian test given by (20), (21) This yields to (22) Analogously, it is straightforward to verify that is lower bounded by (23) 3) False Isolation Probabilities: By definition, the false isolation probability of the Bayesian test given by (20), (21) is (24) where is the notation that stands for the probability of event occurring when follows the distribution and . The most common upper bound for is the union bound given by (see the Boole's inequality in [33]) (25) From (19), it follows that: Hence, for , is a Gaussian random variable with the following mean and variance under : (26) since and .…”

Section: A Bayesian Test Between Simple Hypothesesmentioning

confidence: 98%

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Asymptotically Uniformly Minimax Detection and Isolation in Network Monitoring

Fillatre

Nikiforov

2012

IEEE Trans. Signal Process.

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This paper addresses the problem of multiple hypothesis testing (detection and isolation of mean vectors) in the case of Gaussian linear model with nuisance parameters. An invariant constrained asymptotically uniformly minimax test is proposed to solve this problem. The invariance of the test with respect to the nuisance parameters is obtained by projecting the measurement vector onto a subspace of invariant statistics. The proposed test minimizes the maximum probability of false isolation uniformly with respect to the lower bounded projections of the vectors defining the alternative hypotheses. This minimization is achieved provided that the signal-to-noise ratio (SNR) becomes arbitrary large. The asymptotic probabilities of false alarm and false isolations and their nonasymptotic bounds are analytically established. To illustrate the practical relevance of the proposed test, it is applied to the problem of network monitoring. It is aimed to detect and isolate volume anomalies in network origin-destination (OD) traffic demands from simple link load measurements. The ambient traffic, i.e. the OD traffic matrix corresponding to the nonanomalous network state, is unknown and considered as a nuisance parameter. An original linear parsimonious model of the ambient traffic which is indispensable for the proposed asymptotically optimal test is designed. The statistical performances of this approach to detect and isolate the anomalies are evaluated by using real data from the Abilene network.

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Section: B a Toy Example-continuedmentioning

confidence: 84%

Section: General Covariance Matrixmentioning

confidence: 97%

“…1) Conservative Threshold: Let be the false alarm probability of and its threshold. From (22), it follows that:…”

Section: B Bayesian Test With Uniform Weightsmentioning

confidence: 98%

Section: A Bayesian Test Between Simple Hypothesesmentioning

confidence: 98%

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Asymptotically Uniformly Minimax Detection and Isolation in Network Monitoring

Fillatre

Nikiforov

2012

IEEE Trans. Signal Process.

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“…[31]. A test statistic g(k) is computed based on S(k) using cumulative sum (CUSUM) algorithms for known changes, generalised likelihood (GLR) methods or others to detect an unknown change.…”

Section: Evaluation Of Residualsmentioning

confidence: 99%

Diagnosis for Control and Decision Support for Autonomous Vehicles

Blanke

Hansen

Blas³

2016

Complex Systems

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Abstract. Diagnosis and, when possible, prognosis of faults are essential for safe and reliable operation. The area of fault diagnosis has emerged over three decades. The majority of studies are related to linear systems but real-life systems are complex and nonlinear. The development of methodologies coping with complex and nonlinear systems have matured and even though there are many unsolved problems, methodology and associated tools have become available in the form of theory and software for design. Genuine industrial cases have also become available. Analysis of system topology, referred to as structural analysis, has proven to be unique and simple in use and a recent extension to active structural techniques have made fault isolation possible in a wide range of systems. Following residual generation using these topology-based methods, deterministic and statistical change detection has proven very useful for online prognosis and diagnosis. For complex systems, results from nonGaussian detection theory have been employed with convincing results. The chapter presents the theoretical foundation for design methodologies that now appear as enabling technology for a new area of design of systems that are reliable in practise. Yet they are also affordable due to the use of fault-tolerant philosophies and tools that make engineering efforts minimal for their implementation. The chapter includes examples for an autonomous aircraft and a baling system for agriculture to illustrate the generic design procedures and real life results.

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Bridges between Diagnosis Theories from Control and AI Perspectives

Travé-Massuyès¹

2014

Advances in Intelligent Systems and Computing

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Optimal fault detection with nuisance parameters and a general covariance matrix

Cited by 14 publications

References 18 publications

Asymptotically Uniformly Minimax Detection and Isolation in Network Monitoring

Asymptotically Uniformly Minimax Detection and Isolation in Network Monitoring

Diagnosis for Control and Decision Support for Autonomous Vehicles

Bridges between Diagnosis Theories from Control and AI Perspectives

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