Advertisement

Fault Diagnosis of Nonlinear Differential-Algebraic Systems Using Hybrid Estimation

  • Dirk WeidemannEmail author
  • Ilja Alkov
Chapter
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

Modern technical systems often contain components capable for extensive autonomous actions. Thus, an integrated system supervision is essential in enabling an adequate reaction for compensation of unpredictable substantial variations. This is addressed by fault detection, isolation and identification techniques discussed in this article. Therefore, an overview is given about modelling of systems subject to faults, continuous state estimation utilizing an unscented Kalman filter and hybrid state estimation by the interacting multiple model approach. These methods are generalized for application to nonlinear differential-algebraic equations, i.e. DAE systems. DAE systems arise in such fields as discretization of partial differential equations or optimization problems. However, the appearance of DAE systems most often results from an object-oriented modelling (OOM) approach. Since OOM is probably the most relevant approach for modelling complex systems, the generalization and adaptation of supervision methods to DAE is the principal subject of this contribution. Finally, the proposed fault identification approach is applied to a hydraulic system, and the related results are discussed in detail.

Keywords

Kalman Filter Unscented Kalman Filter Algebraic State Hybrid Automaton Differential State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Alkov I, Weidemann D (2013) Fault detection with unscented Kalman filter applied to nonlinear differential-algebraic systems. In: Proceedings of the 18th international conference on methods and models in automation and robotics (MMAR), Miedzyzdroje, Poland, pp 166–171Google Scholar
  2. 2.
    Alkov I, Weidemann D (2014) Unscented Kalman filter for higher index nonlinear differential-algebraic equations. In: Proceedings of the 19th international conference on methods and models in automation and robotics (MMAR), Miedzyzdroje, Poland, pp 88–93Google Scholar
  3. 3.
    Åslund J, Frisk E (2006) An observer for non-linear differential-algebraic systems. Automatica 42(6):959–965MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bar-Shalom Y, Li X-R, Kirubarajan T (2001) Estimation with applications to tracking and navigation. Wiley, New YorkCrossRefGoogle Scholar
  5. 5.
    Becerra VM, Roberts PD, Griffiths GW (1999) Dynamic data reconciliation for a class of nonlinear differential-algebraic equation models using the extended Kalman filter. In: Proceedings of the 14th IFAC world congress, Oxford, UK, pp 303–308Google Scholar
  6. 6.
    Blanke M, Kinnaert M, Lunze J, Staroswiecki M (2006) Diagnosis and fault-tolerant control. Springer, BerlinzbMATHGoogle Scholar
  7. 7.
    Brenan KE, Petzold LR (1989) The numerical solution of higher index differential/algebraic equations by implicit methods. SIAM J Numer Anal 26(4):976–996MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Campbell SL, Gear CW (1995) The index of general nonlinear DAEs. Numerische Mathematik 72(2):173–196MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chen DW, Saif M (2007) Observer-based strategies for actuator fault detection, isolation and estimation for certain class of nonlinear systems. IET Control Theory Appl 1(6):1672–1680CrossRefGoogle Scholar
  10. 10.
    Chen J, Patton RJ (2005) Robust model-based fault diagnosis for dynamic systems. Kluwer Academic Publisher, BostonzbMATHGoogle Scholar
  11. 11.
    Deuflhard P, Hairer E, Zugck J (1987) One-step and extrapolation methods for differential-algebraic systems. Numerische Mathematik 51(5):501–516MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Ding SX (2008) Model-based fault diagnosis techniques. Springer, BerlinGoogle Scholar
  13. 13.
    Gear C (1988) Differential-algebraic equation index transformations. SIAM J Sci Stat Comput 9(1):39–47MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gerdin M, Sjoberg J (2006) Nonlinear stochastic differential-algebraic equations with application to particle filtering. In: Proceedings of the 45th IEEE conference on decision and control (CDC), San Diego, CA, USA, pp 6630–6635Google Scholar
  15. 15.
    Hedengren JD, Shishavan RA, Powell KM, Edgar TF (2014) Nonlinear modeling, estimation and predictive control in APMonitor. Comput Chem Eng 70:133–148CrossRefGoogle Scholar
  16. 16.
    Hofbaur MW (2005) Hybrid estimation of complex systems. Springer, BerlinzbMATHGoogle Scholar
  17. 17.
    Hofbaur MW, Williams BC (2002) Mode estimation of probabilistic hybrid systems. In: Proceedings on the international conference on hybrid systems: computation and control, Springer, pp 253–266Google Scholar
  18. 18.
    Isermann R (1993) Fault diagnosis of machines via parameter estimation and knowledge processing—tutorial paper. Automatica 29(4):815–835MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Isermann R (2006) Fault-diagnosis systems. Springer, BerlinCrossRefzbMATHGoogle Scholar
  20. 20.
    Julier S J (2002) The scaled unscented transformation. In: Proceedings of the American control conference (ACC), vol 6, Anchorage, AK, USA, pp 4555–4559Google Scholar
  21. 21.
    Julier S J, Uhlmann J K, Durrant-Whyte H F (1995) A new approach for filtering nonlinear systems. In: Proceedings of the American control conference (ACC), vol 3, Seattle, WA, USA, pp 1628–1632Google Scholar
  22. 22.
    Kunkel P, Mehrmann V, Seufer I (2002) GENDA: A software package for the solution of general nonlinear differential-algebraic equations. Technical report 730-02, Institut für Mathematik, Technische Universität Berlin, 2002Google Scholar
  23. 23.
    Mandela RK, Rengaswamy R, Narasimhan S (2009) Nonlinear state estimation of differential-algebraic systems. Adv Control Chem Process 7:792–797Google Scholar
  24. 24.
    Mattsson SE, Söderlind G (1993) Index reduction in differential-algebraic equations using dummy derivatives. SIAM J Sci Stat Comput 14(3):677–692MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Mehrmann V (2012) Index concepts for differential-algebraic equations. Technical report 2012-03, Institut für Mathematik, Technische Universität Berlin, 2012Google Scholar
  26. 26.
    Nedialkov NS, Pryce JD (2005) Solving differential-algebraic equations by Taylor series (i): computing Taylor coefficients. BIT Numer Math 45(3):561–591MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Pantelides CC (1988) The consistent initialization of differential-algebraic systems. SIAM J Sci Stat Comput 9(2):213–231MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Rao C, Rawlings J, Mayne D (2003) Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations. IEEE Trans Autom Control 48:246–258MathSciNetCrossRefGoogle Scholar
  29. 29.
    Tan CP, Edwards C (2003) Sliding mode observers for reconstruction of simultaneously actuator and sensor faults. In: Proceedings of the IEEE conference on decision and control, pp 1455–1460Google Scholar
  30. 30.
    van der Merwe R, Wan E A (2001) The square-root unscented Kalman filter for state and parameter-estimation. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing, vol 6, Salt Lake City, UT, USA, pp 3461–3464Google Scholar
  31. 31.
    Zhang YM, Jiang J (2002) Active fault-tolerant control system against partial actuator failures. IEE Proc Control Theory Appl 149(1):95–104CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of System Dynamics and Mechatronics, University of Applied Sciences BielefeldBielefeldGermany

Personalised recommendations