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Title: Statistical inference for fault detection: a complete algorithm based on kernel estimators (English)
Author: Kulczycki, Piotr
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 38
Issue: 2
Year: 2002
Pages: [141]-168
Summary lang: English
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Category: math
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Summary: This article presents a new concept for a statistical fault detection system, including the detection, diagnosis, and prediction of faults. Theoretical material has been collected to provide a complete algorithm making possible the design of a usable system for statistical inference on the basis of the current value of a symptom vector. The use of elements of artificial intelligence enables self-correction and adaptation to changing conditions. The mathematical apparatus is founded on the methodology of testing statistical hypotheses, and on kernel estimators; the theoretical aspects have been documented by mathematical theorems. The work is oriented towards the problem of fault detection in dynamic systems under automatic control, but the basic formula is of a universal nature and can be used in a broad range of applications, including those outside the scope of engineering. (English)
Keyword: fault detection
Keyword: kernel estimator
Keyword: trend estimation
MSC: 62G05
MSC: 62G07
MSC: 62N05
MSC: 93E10
idZBL: Zbl 1265.93226
idMR: MR1916448
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Date available: 2009-09-24T19:44:36Z
Last updated: 2015-03-24
Stable URL: http://hdl.handle.net/10338.dmlcz/135452
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Reference: [1] Abraham B., Ledolter J.: Statistical Methods for Forecasting.Wiley, New York 1983 Zbl 1082.62079, MR 0719535
Reference: [2] Basseville M., Nikiforov I. V.: Detection of Abrupt Changes – Theory and Applications.Prentice–Hall, Englewood Cliffs, N.J. 1993 MR 1210954
Reference: [3] Berger J. O.: Statistical Decision Theory.Springer–Verlag, New York 1980 Zbl 0782.00068, MR 0580664
Reference: [4] Billingsley P.: Probability and Measure.Wiley, New York 1979 Zbl 0822.60002, MR 0534323
Reference: [5] Chen J., Patton R. J.: Robust Model–Based Fault Diagnosis for Dynamic Systems.Kluwer, Boston 1999 Zbl 0920.93001
Reference: [6] Devroe L., Györfi L.: Nonparametric Density Estimation: the $L_1 $ View.Wiley, New York 1985 MR 0780746
Reference: [7] Dertouzos M. L., Athans M., Spann R. N., Mason S. J.: Systems, Networks, and Computation.McGraw–Hill, New York 1972 Zbl 0355.93001
Reference: [8] Fisz M.: Probability Theory and Mathematical Statistics.Wiley, New York 1963 Zbl 0656.60001, MR 0164358
Reference: [9] Gertler J. J.: Fault Detection and Diagnosis in Engineering Systems.Dekker, New York 1998
Reference: [10] Kulczycki P.: Almost certain time-optimal positional control.IMA J. Math. Control Inform. 13 (1996), 63–77 Zbl 0852.49007, MR 1387021, 10.1093/imamci/13.1.63
Reference: [11] Kulczycki P.: An algorithm for Bayes parameter identification.Trans. ASME: Journal of Dynamic Systems, Measurement, and Control, Special Issue on the Identification of Mechanical Systems 123 (2001), 611–614 Zbl 1122.93082
Reference: [12] Kulczycki P.: A random approach to time-optimal control.Trans. ASME: Journal of Dynamic Systems, Measurement, and Control 121 (1999), 542–543
Reference: [13] Kulczycki P.: A test for comparing distribution functions with strongly unbalanced samples.Statistica, to appear MR 1985551
Reference: [14] Kulczycki P.: Fault Detection in Automated Systems by Statistical Methods.Alfa, Warsaw 1998
Reference: [15] Kulczycki P.: Fuzzy controller for mechanical systems.IEEE Trans. on Fuzzy Systems 8 (2000), 645–652 10.1109/91.873587
Reference: [16] Kulczycki P., Dawidowicz A. L.: Kernel estimator of quantile.Univ. Iagel, Acta Math. 37 (1999), 325–336 Zbl 1180.62043, MR 1729545
Reference: [17] Kulczycki P., Wisniewski R.: Fuzzy controller for a system with uncertain load.Fuzzy Sets and Systems, to appear Zbl 1010.93514, MR 1930739
Reference: [18] Mangoubi R. S.: Robust Estimation and Failure Detection.Springer–Verlag, London 1998
Reference: [19] Parrish R. S.: Comparison of quantile estimators in normal sampling.Biometrics 46 (1990), 247–257 Zbl 0715.62076, 10.2307/2531649
Reference: [20] Rao B. L. S. Prakasa: Nonparametric Functional Estimation.Academic Press, Orlando 1983 MR 0740865
Reference: [21] Schiøler H., Kulczycki P.: Neural network for estimating conditional distributions.IEEE Trans. Neural Networks 8 (1997), 1015–1025 10.1109/72.623203
Reference: [22] Sheather S. J., Marron J. S.: Kernel quantile estimators.J. Amer. Statist. Assoc. 85 (1990), 410–416 Zbl 0705.62042, MR 1141741, 10.1080/01621459.1990.10476214
Reference: [23] Silverman B. W.: Density Estimation for Statistics and Data Analysis.Chapman and Hall, London 1986 Zbl 0617.62042, MR 0848134
Reference: [24] Sohlberg B.: Supervision and Control for Industrial Processes.Springer–Verlag, London 1998
Reference: [25] Wand M. P., Jones M. C.: Kernel Smoothing.Chapman and Hall, London 1994 Zbl 0854.62043, MR 1319818
Reference: [26] West M., Harrison J.: Bayesian Forecasting and Dynamic Models.Springer–Verlag, New York 1989 Zbl 0871.62026, MR 1020301
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