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Efficient computation of minmax tests for fault isolation and their application to structural damage localization

  • Fault detection and isolation can be handled by many different approaches. This paper builds upon a hypothesis test that checks whether the mean of a Gaussian random vector has become non-zero in the faulty state, based on a chi2 test. For fault isolation, it has to be decided which components in the parameter set of the Gaussian vector have changed, which is done by variants of the chi2 hypothesis test using the so-called sensitivity and minmax approaches. While only the sensitivity of the tested parameter component is taken into account in the sensitivity approach, the sensitivities of all parameters are used in the minmax approach, leading to better statistical properties at the expense of an increased computational burden. The computation of the respective test variable in the minmax test is cumbersome and may be ill-conditioned especially for large parameter sets, asking hence for a careful numerical evaluation. Furthermore, the fault isolation procedure requires the repetitiveFault detection and isolation can be handled by many different approaches. This paper builds upon a hypothesis test that checks whether the mean of a Gaussian random vector has become non-zero in the faulty state, based on a chi2 test. For fault isolation, it has to be decided which components in the parameter set of the Gaussian vector have changed, which is done by variants of the chi2 hypothesis test using the so-called sensitivity and minmax approaches. While only the sensitivity of the tested parameter component is taken into account in the sensitivity approach, the sensitivities of all parameters are used in the minmax approach, leading to better statistical properties at the expense of an increased computational burden. The computation of the respective test variable in the minmax test is cumbersome and may be ill-conditioned especially for large parameter sets, asking hence for a careful numerical evaluation. Furthermore, the fault isolation procedure requires the repetitive calculation of the test variable for each of the parameter components that are tested for a change, which may be a significant computational burden. In this paper, dealing with the minmax problem, we propose a new efficient computation for the test variables, which is based on a simultaneous QR decomposition for all parameters. Based on this scheme, we propose an efficient test computation for a large parameter set, leading to a decrease in the numerical complexity by one order of magnitude in the total number of parameters. Finally, we show how the minmax test is useful for structural damage localization, where an asymptotically Gaussian residual vector is computed from output-only vibration data of a mechanical or a civil structure.zeige mehrzeige weniger

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Metadaten
Autoren/innen:Michael Döhler, L. Mevel, Falk Hille
Dokumenttyp:Beitrag zu einem Tagungsband
Veröffentlichungsform:Graue Literatur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):19th World congress of the international federation of automatic control (Proceedings)
Jahr der Erstveröffentlichung:2014
Organisationseinheit der BAM:7 Bauwerkssicherheit
7 Bauwerkssicherheit / 7.2 Ingenieurbau
Verlag:IFAC
Erste Seite:7382
Letzte Seite:7387
Freie Schlagwörter:Fault isolation; Mechanical systems; Numerical computation; Residual evaluation; Statistical tests
Veranstaltung:19th World congress of the international federation of automatic control
Veranstaltungsort:Cape Town, South Africa
Beginndatum der Veranstaltung:24.08.2014
Enddatum der Veranstaltung:29.08.2014
Verfügbarkeit des Volltexts:Volltext-PDF im Netzwerk der BAM verfügbar ("Closed Access")
Datum der Freischaltung:20.02.2016
Referierte Publikation:Nein