Optimally robust redundancy relations for failure detection in uncertain systems.

*(English)*Zbl 0596.93019A wide variety of techniques has been proposed for the detection, isolation, and accomodation of failures in dynamic systems. All these methods involve the generation of signals that are accentuated by the presence of particular failures. Since the procedures for generating these signals depend on models relating the observed variables, the model errors may also accentuate the signals. The work described in this article focuses on directly designing a failure detection system that is insensitive to model errors.

A new measure of reliability for a redundancy relation is examined. Not only does this measure have a helpful geometric interpretation, but it also leads to a far simpler optimization procedure, involving a single singular value decomposition. It allows issues such as scaling, relative merits of alternative sensor sets and explicit trade-offs between detectability and robustness to be considered.

The main problem of this paper is the determination of optimally robust redundancy relations. The approach used builds on the geometric interpretation of a set of parity checks as an orthogonal projection of a window of observations. The question of whether the constructions developed in this paper provide a useful new method of model reduction remains for further exploration.

A new measure of reliability for a redundancy relation is examined. Not only does this measure have a helpful geometric interpretation, but it also leads to a far simpler optimization procedure, involving a single singular value decomposition. It allows issues such as scaling, relative merits of alternative sensor sets and explicit trade-offs between detectability and robustness to be considered.

The main problem of this paper is the determination of optimally robust redundancy relations. The approach used builds on the geometric interpretation of a set of parity checks as an orthogonal projection of a window of observations. The question of whether the constructions developed in this paper provide a useful new method of model reduction remains for further exploration.

Reviewer: Y.Qu

##### MSC:

93B35 | Sensitivity (robustness) |

90B25 | Reliability, availability, maintenance, inspection in operations research |

93C05 | Linear systems in control theory |

68U20 | Simulation (MSC2010) |

##### Keywords:

failure detection system; measure of reliability; redundancy relation; robustness; model reduction
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##### References:

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