Stochastic Fault Diagnosability in Parity Spaces

Gustafsson, Fredrik

doi:10.3182/20020721-6-es-1901.00738

Cited by 22 publications

(13 citation statements)

References 6 publications

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“…Main differences compared to this paper are that the analysis in [7] assumes a known fault size, which is not assumed in this work, and also focuses on the performance of a set of tests rather than properties of the model. This paper presents a theory for quantified isolability analysis of linear static models.…”

Section: Introductionmentioning

confidence: 98%

“…FNR is, in the normally distributed case, the ratio between fault influence of the system, λ, and the standard deviation, σ, of the noise, see e.g. [7]. For simplicity in this example, for each fault pair the highest FNR of the residuals which isolate the fault pair is used to quantify isolability.…”

Section: An Introductory Examplementioning

confidence: 99%

“…In [7], a quantitative analysis of isolability performance in dynamic linear models is made using parity spaces. Main differences compared to this paper are that the analysis in [7] assumes a known fault size, which is not assumed in this work, and also focuses on the performance of a set of tests rather than properties of the model.…”

Section: Introductionmentioning

confidence: 99%

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Quantitative stochastic fault diagnosability analysis

Eriksson

Krysander

Frisk

2011

2011 50th IEEE Conference on Decision and Control and European Control Conference

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Abstract-A theory is developed for quantifying fault detectability and fault isolability properties of static linear stochastic models. Based on the model, a stochastic characterization of system behavior in different fault modes is defined and a general measure, based on the Kullback-Leibler information, is proposed to quantify the difference between the modes. This measure, called distinguishability, of the model is shown to give sharp upper limits of the fault to noise ratios of residual generators. Finally, a case-study of a diesel engine model shows how the general framework can be applied to a dynamic and nonlinear model.

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Section: Introductionmentioning

confidence: 98%

Section: An Introductory Examplementioning

confidence: 99%

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Quantitative stochastic fault diagnosability analysis

Eriksson

Krysander

Frisk

2011

2011 50th IEEE Conference on Decision and Control and European Control Conference

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“…The original parity space approach is a deterministic one, so this residual is non-zero for non-zero faults. The extension to process and measurement noise was done in (Gustafsson 2002), and analytical results on detectability of an all-one fault vector F was derived.…”

Section: Introductionmentioning

confidence: 99%

GLR Tests for Fault Detection Over Sliding Data Windows

Törnqvist

Gustafsson

Klein

2005

IFAC Proceedings Volumes

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The Generalized Likelihood Ratio (GLR) test for fault detection as derived by Willsky and Jones is a recursive method to detect additive changes in linear systems in a Kalman filter framework. Here, we evaluate the GLR test on a sliding window and compare it to stochastic parity space approaches. Robust fault detection defined as being insensitive to faults in the signal space is also studied in the GLR framework.

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“…Finally, x t−L+1 is the initial state of the measurement window. For a more complete description of this way to view the system see e.g., [13,14]. In order to get a low order parameterization of the fault profile, and a non-ambiguous distinction between fault and noise, assume that the fault profile is a smooth function (rather than noise).…”

Section: B Modelsmentioning

confidence: 99%

Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems

Hendeby

Gustafsson

Proceedings of the 44th IEEE Conference on Decision and Control

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Abstract-Sophisticated fault detection (FD) algorithms often include nonlinear mappings of observed data to fault decisions, and simulation studies are used to support the methods. Objective statistically supported performance analysis of FD algorithms is only possible for some special cases, including linear Gaussian models. The goal here is to derive general statistical performance bounds for any FD algorithm, given a non-linear non-Gaussian model of the system. Recent advances in numerical algorithms for nonlinear filtering indicate that such bounds in many practical cases are attainable. This paper focuses on linear non-Gaussian models. A couple of different fault detection setups based on parity space and Kalman filter approaches are considered, where the fault enters a computable residual linearly. For this class of systems, fault detection can be based on the best linear unbiased estimate (BLUE) of the fault vector. Alternatively, a nonlinear filter can potentially compute the maximum likelihood (ML) state estimate, whose performance is bounded by the Cramér-Rao lower bound (CRLB). The contribution in this paper is general expressions for the CRLB for this class of systems, interpreted in terms of fault detectability. The analysis is exemplified for a case with measurements affected by outliers.

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Stochastic Fault Diagnosability in Parity Spaces

Cited by 22 publications

References 6 publications

Quantitative stochastic fault diagnosability analysis

Quantitative stochastic fault diagnosability analysis

GLR Tests for Fault Detection Over Sliding Data Windows

Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems

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