Redundancy relations for fault diagnosis in nonlinear uncertain systems

Alexey Shumsky

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 4, page 477-489
  • ISSN: 1641-876X

Abstract

top
The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.

How to cite

top

Shumsky, Alexey. "Redundancy relations for fault diagnosis in nonlinear uncertain systems." International Journal of Applied Mathematics and Computer Science 17.4 (2007): 477-489. <http://eudml.org/doc/207853>.

@article{Shumsky2007,
abstract = {The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.},
author = {Shumsky, Alexey},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {full decoupling; algebraic approach; fault detection and isolation; redundancy relations; nonlinear systems; geometric approach},
language = {eng},
number = {4},
pages = {477-489},
title = {Redundancy relations for fault diagnosis in nonlinear uncertain systems},
url = {http://eudml.org/doc/207853},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Shumsky, Alexey
TI - Redundancy relations for fault diagnosis in nonlinear uncertain systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 4
SP - 477
EP - 489
AB - The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.
LA - eng
KW - full decoupling; algebraic approach; fault detection and isolation; redundancy relations; nonlinear systems; geometric approach
UR - http://eudml.org/doc/207853
ER -

References

top
  1. Chow E. Y. and A.S. Willsky. (1984): Analytical redundancy and the design of robust failure detection systems. IEEE Transactions on Automatic Control, Vol.AC-29,No.7, pp.603-614. Zbl0542.90040
  2. Comtet-Varga G., C. Christophe, V. Cocquempot and M. Staroswiecki. (1999): F.D.I. For the induction motor using elimination theory. Proceedings of the European Control Conference, Karlsruhe, Germany, (on CD-ROM) 
  3. Cox D., Ltle J. and D. O'Shea. (1992): Ideals, Varieties and Algorithms. New York: Springer. 
  4. De Persis C. and A. Isidori. (2001): A geometric approach to nonlinear fault detection and isolation. IEEE Transactions on Automatic Control, Vol.AC-46, No.6, pp.853-865. Zbl1009.93003
  5. De Persis C. and A. Isidori. (2002): Fault detection filters. International Journal of Robust and Nonlinear Control, Vol.12, No.6, pp.729-747. Zbl1003.93019
  6. Ding X. and P.M. Frank. (1993): An adaptive observer-based fault detection scheme for nonlinear dynamic systems. Proceedings of the 12-th IFAC World Congress, Sydney, Australia, Vol.8, pp.307-310 
  7. Diop S. (1991): Elimination in control theory. - Mathematics of Control, Signals, and Systems, Vol.14, No.1, pp.459-474 Zbl0727.93025
  8. Frank P.M. (1990): Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy- A survey and some new results. Automatica, Vol.26, No3, pp.459-474. Zbl0713.93052
  9. Gertler J. and M.M. Kunwer. (1993): Optimal residual decoupling for robust fault diagnosis. Proceedings of the International Conference Tooldiag'93, Toulouse, France, pp.436-452. Zbl0817.93039
  10. Isermann R. (1984): Process fault detection based on modeling and estimationmethods: A survey. Automatica, Vol.20, No.4, pp.387-404. Zbl0539.90037
  11. Isidori A. (1989): Nonlinear Control Systems. Berlin: Springer. Zbl0693.93046
  12. Lou X.C., Willsky A.S. and G.L. Verghese.(1986): Optimally robust redundancy relations for failure detection in uncertain systems. Automatica, Vol.22, No.3,pp.333-344. Zbl0596.93019
  13. Massoumnia M. A. (1986): A geometric approach to the synthesis of failure detection filters. IEEE Transactions on Automatic Control, Vol.AC-31, No.9, pp.839-846. Zbl0599.93017
  14. Massoumnia M. A., G. C. Verghese and A.S. Willsky. (1989): Failure detection and identification. IEEE Transactions on Automatic Control, Vol.AC-34,No.3, pp.316-323. Zbl0682.93061
  15. Medvedev A. (1994): Pary space method: A continuous time approach. Proceedings of the American Control Conference, Baltimore, Vol.1, pp.662-665. 
  16. Mironovskii L.A. (1980): Functional diagnosis of dynamic systems. Automation and Remote Control, Vol.41, No.8, pp.1122-1143. 
  17. Park J., G. Rizzoni and W.B. Ribbens. (1994): On the representation of sensor faults in fault detection filters. Automatica, Vol.30, No.11, pp.1793-1795. Zbl0925.93875
  18. Patton R. and S. Kangethe. (1989): Robust fault diagnosis using eigen structure assignment of observers. In: Fault Diagnosis in Dynamic Systems. Theory and Application (Patton R.J., Frank P.M., Clark R.N. N.Y., Eds.), Englewood Cliffs: Prentice Hall,pp.99-154. 
  19. Pekpe, K. M., G. Mourot and J. Ragot. (2004): Subspace method for sensors fault detection and isolation -application to grinding circuit monitoring. Proceedings of the 11th IFAC Symposium on Automation in Mining, Mineral and Metal Processing, Nancy, France. 
  20. Rt J.F. (1950): Differential Algebra. New York, American Math. Society. 
  21. Seliger R. and P.M. Frank. (1991): Robust component fault detection and isolation in nonlinear dynamic systems using nonlinear unknown input observers. Proceedings of the IFAC Symposium SAFEPROCESS'91, Baden-Baden, Germany, pp.313-318. 
  22. Shumsky, A.Ye. (1991): Fault isolation in nonlinear systems via functional diagnosis. Automation and Remote Control, Vol.52, No.12, pp.1759-1765. 
  23. Shumsky, A.Ye. (1992): Diagnosis of parametric errors in dynamic objects by the hypothesizes testing method. Avtomatika i telemehanika, Vol.53, No.10, pp.171-177 (in Russian). 
  24. Shumsky, A.Ye. (2002): Robust analytical redundancy relations for fault diagnosis in nonlinear systems. Asian Journal of Control, Vol.4, No2, pp.159-170. 
  25. Shumsky, A. Ye. and A. N. Zhirabok. (2006): Nonlinear diagnostic filter design: Algebraic and geometric points of view. International Journal of Applied Mathematics and Computer Science, Vol.16, No.1, pp.115-127. Zbl1334.93081
  26. Shumsky, A. Ye. (2006): Fault diagnosis of sensors in autonomous underwater vehicle: Adaptive quasi-linear parity relations method. Proceedings of the International Symposium SAFEPROCESS, Beijing, PR China, pp.415-520 

Citations in EuDML Documents

top
  1. Abed Alrahim Yassine, Stéphane Ploix, Jean-Marie Flaus, A method for sensor placement taking into account diagnosability criteria
  2. Dezhi Xu, Bin Jiang, Peng Shi, Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy model
  3. Denis Berdjag, Vincent Cocquempot, Cyrille Christophe, Alexey Shumsky, Alexey Zhirabok, Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems
  4. Wei Chen, Abdul Q. Khan, Muhammmad Abid, Steven X. Ding, Integrated design of observer based fault detection for a class of uncertain nonlinear systems

NotesEmbed ?

top

You must be logged in to post comments.