Statistical inference for fault detection: a complete algorithm based on kernel estimators

Piotr Kulczycki

Kybernetika (2002)

  • Volume: 38, Issue: 2, page [141]-168
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Kulczycki, Piotr. "Statistical inference for fault detection: a complete algorithm based on kernel estimators." Kybernetika 38.2 (2002): [141]-168. <http://eudml.org/doc/33572>.

@article{Kulczycki2002,
abstract = {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.},
author = {Kulczycki, Piotr},
journal = {Kybernetika},
keywords = {fault detection; kernel estimator; trend estimation; fault detection; kernel estimator; trend estimation},
language = {eng},
number = {2},
pages = {[141]-168},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Statistical inference for fault detection: a complete algorithm based on kernel estimators},
url = {http://eudml.org/doc/33572},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Kulczycki, Piotr
TI - Statistical inference for fault detection: a complete algorithm based on kernel estimators
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 2
SP - [141]
EP - 168
AB - 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.
LA - eng
KW - fault detection; kernel estimator; trend estimation; fault detection; kernel estimator; trend estimation
UR - http://eudml.org/doc/33572
ER -

References

top
  1. Abraham B., Ledolter J., Statistical Methods for Forecasting, Wiley, New York 1983 Zbl1082.62079MR0719535
  2. Basseville M., Nikiforov I. V., Detection of Abrupt Changes – Theory and Applications, Prentice–Hall, Englewood Cliffs, N.J. 1993 MR1210954
  3. Berger J. O., Statistical Decision Theory, Springer–Verlag, New York 1980 Zbl0782.00068MR0580664
  4. Billingsley P., Probability and Measure, Wiley, New York 1979 Zbl0822.60002MR0534323
  5. Chen J., Patton R. J., Robust Model–Based Fault Diagnosis for Dynamic Systems, Kluwer, Boston 1999 Zbl0920.93001
  6. Devroe L., Györfi L., Nonparametric Density Estimation: the L 1 View, Wiley, New York 1985 MR0780746
  7. Dertouzos M. L., Athans M., Spann R. N., Mason S. J., Systems, Networks, and Computation, McGraw–Hill, New York 1972 Zbl0355.93001
  8. Fisz M., Probability Theory and Mathematical Statistics, Wiley, New York 1963 Zbl0656.60001MR0164358
  9. Gertler J. J., Fault Detection and Diagnosis in Engineering Systems, Dekker, New York 1998 
  10. Kulczycki P., 10.1093/imamci/13.1.63, IMA J. Math. Control Inform. 13 (1996), 63–77 (1996) Zbl0852.49007MR1387021DOI10.1093/imamci/13.1.63
  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 Zbl1122.93082
  12. Kulczycki P., A random approach to time-optimal control, Trans. ASME: Journal of Dynamic Systems, Measurement, and Control 121 (1999), 542–543 (1999) 
  13. Kulczycki P., A test for comparing distribution functions with strongly unbalanced samples, Statistica, to appear MR1985551
  14. Kulczycki P., Fault Detection in Automated Systems by Statistical Methods, Alfa, Warsaw 1998 
  15. Kulczycki P., 10.1109/91.873587, IEEE Trans. on Fuzzy Systems 8 (2000), 645–652 DOI10.1109/91.873587
  16. Kulczycki P., Dawidowicz A. L., Kernel estimator of quantile, Univ. Iagel, Acta Math. 37 (1999), 325–336 (1999) Zbl1180.62043MR1729545
  17. Kulczycki P., Wisniewski R., Fuzzy controller for a system with uncertain load, Fuzzy Sets and Systems, to appear Zbl1010.93514MR1930739
  18. Mangoubi R. S., Robust Estimation and Failure Detection, Springer–Verlag, London 1998 
  19. Parrish R. S., 10.2307/2531649, Biometrics 46 (1990), 247–257 (1990) Zbl0715.62076DOI10.2307/2531649
  20. Rao B. L. S. Prakasa, Nonparametric Functional Estimation, Academic Press, Orlando 1983 MR0740865
  21. Schiøler H., Kulczycki P., 10.1109/72.623203, IEEE Trans. Neural Networks 8 (1997), 1015–1025 (1997) DOI10.1109/72.623203
  22. Sheather S. J., Marron J. S., 10.1080/01621459.1990.10476214, J. Amer. Statist. Assoc. 85 (1990), 410–416 (1990) Zbl0705.62042MR1141741DOI10.1080/01621459.1990.10476214
  23. Silverman B. W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, London 1986 Zbl0617.62042MR0848134
  24. Sohlberg B., Supervision and Control for Industrial Processes, Springer–Verlag, London 1998 
  25. Wand M. P., Jones M. C., Kernel Smoothing, Chapman and Hall, London 1994 Zbl0854.62043MR1319818
  26. West M., Harrison J., Bayesian Forecasting and Dynamic Models, Springer–Verlag, New York 1989 Zbl0871.62026MR1020301

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.