zbMATH — the first resource for mathematics

Detection and diagnosis of changes in the eigenstructure of nonstationary multivariable systems. (English) Zbl 0625.93060
The general theory introduced by the first three authors [IEEE Trans. Autom. Control AC-32, 583-592 (1987)] is used to develop a procedure for detection and diagnosis of changes in the poles of a multivariable linear rational system with possibly time-varying zeros. The procedure, which is based on an instrumental variable test statistics, is used to solve a vibration monitoring problem. This type of problem is described in detail and numerical results obtained from artificially generated as well as real-life data are presented to illustrate the excellent performance that can be achieved.
Reviewer: P.Stoica

93E10 Estimation and detection in stochastic control theory
93C35 Multivariable systems, multidimensional control systems
74H50 Random vibrations in dynamical problems in solid mechanics
93E12 Identification in stochastic control theory
Full Text: DOI
[1] Akaïke, H., Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes, Ann. inst. statist. math., 26, 363-387, (1974) · Zbl 0335.62058
[2] André-Obrecht, R., A new statistical approach for the automatic segmentation of continuous speech signals, Research report IRISA no. 287/INRIA no. 511, (1986)
[3] Basseville, M., Etude des méthodes de surveillance du comportement vibratoire des structures en mer: positionnement optimal des capteurs et détection d’anomalies, IRISA research report no. 268, (1985), (in French)
[4] (), LNCIS no. 77
[5] Basseville, M.; Benveniste, A.; Moustakides, G., Detection and diagnosis of abrupt changes in modal characteristics of nonstationary digital signals, IEEE trans inf. theory, 32, 412-417, (1986) · Zbl 0607.93048
[6] Basseville, M.; Benveniste, A.; Moustakides, G.; Rougée, A., Detection of abrupt changes in the modal characteristics of nonstationary vector signals, (), Stockholm · Zbl 0607.93048
[7] Basseville, M.; Benveniste, A.; Moustakides, G.; Rougée, A., Optimal sensor location for detecting changes in dynamical behavior, Research report IRISA no. 285/INRIA no. 498, (1986) · Zbl 0607.93048
[8] Benveniste, A.; Fuchs, J.J., Single sample modal identification of a nonstationary stochastic process, IEEE trans. aut. control, 30, 66-74, (1985) · Zbl 0557.93066
[9] Bohlin, T., Analysis of EEG signals with changing spectra using a short word Kalman estimator, Math. biosciences, 35, 221-259, (1977) · Zbl 0367.92003
[10] Chow, E.Y.; Lou, X.C.; Verghese, G.C.; Willsky, A.S., Redundancy relations and robust failure detection, ()
[11] Deshayes, J.; Picard, D., Off-line statistical analysis of change-point models using non parametric and likelihood methods, () · Zbl 0534.62044
[12] Isermann, R., Process fault detection based on modeling and estimation methods. A survey, Automatica, 20, 387-404, (1984) · Zbl 0539.90037
[13] Isermann, R., Process fault diagnosis with parameter estimation methods, () · Zbl 0744.93006
[14] Mironovski, L.A., Functional diagnosis of dynamic systems. A survey, Automn remote control, 41, 1122-1143, (1980)
[15] Moustakides, G.; Benveniste, A., Detecting changes in the AR parameters of a nonstationary ARMA process, Stochastics, 16, 137-155, (1986) · Zbl 0598.62105
[16] Nikiforov, I.V., (), (in Russian)
[17] Nikiforov, I.V., Sequential detection of changes in stochastic systems, () · Zbl 0418.93064
[18] Prevosto, M., Algorithmes d’identification des caractéristiques vibratoires de structures mécaniques complexes, (), (in French)
[19] Prevosto, M.; Barnouin, B.; Hoen, C., Frequency versus time domain identification of complex structure modal shapes under natural excitation, () · Zbl 0544.93071
[20] Prevosto, M.; Benveniste, A.; Barnouin, B., Modélisation et identification des caractéristiques d’une structure vibratoire: un problème de réalisation stochastique d’un grand système non-stationnaire, Research report IRISA no. 163/INRIA no. 130, (1982), (in English)
[21] Rougée, A., Détection de changements dans LES paramétres AR d’un processus ARMA vectoriel: application à la surveillance des vibrations, (), (in French)
[22] Rougée, A.; Basseville, M.; Benveniste, A.; Moustakides, G., Optimal robust detection of changes in the AR part of a multivariable ARMA process, Research report IRISA no. 277/INRIA no. 478, (1985)
[23] Söderström, T.; Stoica, P.G., (), LNCIS no. 57
[24] Stoïca, P.G.; Söderström, T.; Friedlander, B., Optimal instrumental variable estimation of the AR parameters of an ARMA process, IEEE trans. aut. control, 30, 1066-1074, (1985) · Zbl 0575.93060
[25] Willsky, A.S., A survey of design methods for failure detection in dynamic systems, Automatica, 12, 601-611, (1976) · Zbl 0345.93067
[26] Willsky, A.S., Detection of abrupt changes in dynamic systems, ()
[27] Yuan, Z.D.; Ljung, L., Black-box identification of multivariable transfer functions, Asymptotic properties and optimal input design, Int. J. control, 40, 233-256, (1984) · Zbl 0545.93075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.