Diagnosis of Hybrid Dynamic Systems Based on the Behavior Automaton Abstraction

  • Ramon Sarrate
  • Vicenç Puig
  • Louise Travé-Massuyès
Chapter

Abstract

This chapter focuses on the use of the hybrid automaton framework to develop a method for diagnosing hybrid systems. A hybrid automaton models the behavior of the system through a set of operation modes and a set of transitions between modes which trigger upon discrete events or based on continuous state conditions. Continuous dynamics within each mode are described by a set of differential equations which constrain the continuous state, input and output variables. The discrete event part constrains the possible transitions among modes and is referred to as the underlying DES. The restriction of the hybrid system to the continuously-valued part of the model is defined as the multimode system. The diagnosis method relies on abstracting the continuous dynamics by defining a set of “distinguishability-aware” events, called signature-events, associated to mode signature changes across modes. Signature-events are used to enrich appropriately the underlying DES to obtain the so-called behavior automaton from which a diagnoser can be built following standard methods of the discrete event system field. The diagnostic task involves detecting and isolating two types of faults: structural and non-structural faults. Structural faults are represented by a dynamic model as in the case of nominal modes and they are identified thanks to the diagnoser. Non-structural faults do not change the structure of the model in a given operation mode and are identified by a proper residual pattern. The proposed hybrid diagnosis method can operate in a non-incremental and an incremental manner. In the non-incremental form, algorithms are executed taking into account global models whereas in the incremental form only the useful parts of the diagnoser are built, developing the branches that are needed to explain the occurrence of incoming events. Thus, the resulting diagnoser adapts to the system operation life and is less demanding in terms of memory storage than building the full diagnoser offline. The incremental method is illustrated by the application to a case study based on a representative part of the Barcelona sewer network and its complexity is compared to the non-incremental method.

Notes

Acknowledgements

This work has been partially funded by the Spanish Government (MINECO) through the project ECOCIS (ref. DPI2013-48243-C2-1-R), by MINECO and FEDER through the project HARCRICS (ref. DPI2014-58104-R).

References

  1. 1.
    Arogeti, A., Wang, D., & Low, C. B. (2010). Mode identification of hybrid systems in the presence of fault. IEEE Transactions on Industrial Electronics, 57(4), 1452–1467.Google Scholar
  2. 2.
    Bayoudh, M. (2009). Active Diagnosis of Hybrid Systems Guided by Diagnosability Properties- Application to Autonomous Satellites. PhD thesis, l’Université de Toulouse, Institut National Polytechnique, Toulouse, France.Google Scholar
  3. 3.
    Bayoudh, M., & Travé-Massuyès, L. (2014). Diagnosability analysis of hybrid systems cast in a discrete-event framework. Discrete Event Dynamic Systems, 24(3), 309–338.Google Scholar
  4. 4.
    Bayoudh, M., Travé-Massuyès, L., & Olive, X. (2007). State tracking in the hybrid space. In 18th International Workshop on Principles of Diagnosis (DX-07), May 2007 (pp. 221–228).Google Scholar
  5. 5.
    Bayoudh, M., Travé-Massuyès, L., & Olive, X. (2008). Coupling continuous and discrete event system techniques for hybrid system diagnosability analysis. In 18th European Conference on Artificial Intelligence (ECAI 2008), July 2008 (pp. 219–223).Google Scholar
  6. 6.
    Bayoudh, M., Travé-Massuyès, L., & Olive, X. (2008). Hybrid systems diagnosis by coupling continuous and discrete event techniques. In 17th IFAC World Congress (Vol. 41, pp. 7265–7270).Google Scholar
  7. 7.
    Bayoudh, M., Travé-Massuyès, L., & Olive, X. (2009). On-line analytic redundancy relations instantiation guided by component discrete-dynamics for a class of non-linear hybrid systems. In Proceedings of the Decision and Control Conference CDC/CCC 2009, Shanghai (China) (pp. 6970–6975).Google Scholar
  8. 8.
    Benazera, E., & Travé-Massuyès, L. (2009). Set-theoretic estimation of hybrid system configurations. IEEE Transactions on Systems, Man and Cybernetics—Part B: Cybernetics, 39(5), 1277–1291.Google Scholar
  9. 9.
    Blanke, M., Kinnaert, M., Lunze, J., & Staroswiecki, M. (2006). Diagnosis and fault tolerant control (2nd ed.). New York: Springer.Google Scholar
  10. 10.
    Blom, H. A. P., & Bar-Shalom, Y. (1988) The interacting multiple model algorithm for systems with Markovian switching coefficients. IEEE Transactions on Automatic Control, 33, 780–783 (1988)Google Scholar
  11. 11.
    Bregon, A., Alonso, C., Biswas, G., Pulido, B., & Moya, N. (2012). Fault diagnosis in hybrid systems using possible conflicts. In 8th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (pp. 132–137).Google Scholar
  12. 12.
    Cassandras, C., & Lafortune, S. (2008). Introduction to discrete event systems. New York: Springer.Google Scholar
  13. 13.
    Chow, E., & Willsky, A. (1984). Analytical redundancy and the design of robust failure detection systems. IEEE Transactions on Automatic Control, 29(7), 603–614.Google Scholar
  14. 14.
    Cocquempot, V., Staroswiecki, M., & El Mezyani, T. (2003). Switching time estimation and fault detection for hybrid systems using structured parity residuals. In Proceedings of the 15th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (pp. 681–686).Google Scholar
  15. 15.
    Daigle, M. (2008). A Qualitative Event-Based Approach to Fault Diagnosis of Hybrid Systems. PhD thesis, Faculty of the Graduate School of Vanderbilt University, Nashville, TN.Google Scholar
  16. 16.
    de Freitas, N. (2002). Rao-Blackwellised particle filtering for fault diagnosis. In Proceedings of the IEEE Aerospace Conference 2002 (Vol. 4, pp. 1767–1772).Google Scholar
  17. 17.
    Ding, X., Kinnaert, M., Lunze, J., & Staroswiecki, M. (2008). Model based fault diagnosis techniques. Berlin: Springer.Google Scholar
  18. 18.
    Georges, J.-P., Theilliol, D., Cocquempot, V., Ponsart, J.-C., & Aubrun, C. (2011). Fault tolerance in networked control systems under intermittent observations. International Journal of Applied Mathematics and Computer Science, 21(4), 639–648.Google Scholar
  19. 19.
    Hofbaur, M., & Williams, B. (2004). Hybrid estimation of complex systems. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 34(5), 2178–2191.Google Scholar
  20. 20.
    Krysander, M., Åslund, J., & Nyberg, M. (2008). An efficient algorithm for finding minimal over-constrained sub-systems for model-based diagnosis. IEEE Transactions on Systems, Man, and Cybernetics—Part A: Systems and Humans, 38(1), 197–206.Google Scholar
  21. 21.
    Lygeros, J., Henrik, K., & Zhang, J. (2003). Dynamical properties of hybrid automata. IEEE Transactions on Automatic Control, 48, 2–17.Google Scholar
  22. 22.
    Meseguer, J., Puig, V., & Escobet, T. (2010). Fault diagnosis using a timed discrete-event approach based on interval observers: Application to sewer networks. IEEE Transactions on Systems, Man, and Cybernetics—Part A: Systems and Humans, 40(5), 900–916.Google Scholar
  23. 23.
    Meseguer, J., Puig, V., & Escobet, T. (2010). Observer gain effect in linear interval observer-based fault detection. Journal of Process Control, 20(8), 944–956.Google Scholar
  24. 24.
    Narasimhan, S., & Biswas, G. (2007). Model-based diagnosis of hybrid systems. IEEE Transactions on Systems, Man and Cybernetics, 37(3), 348–361.Google Scholar
  25. 25.
    Pencolé, Y. (2006–2015). Diades: Diagnosis of discrete-event systems. http://homepages.laas.fr/ypencole/DiaDes/
  26. 26.
    Rienmuller, T., Hofbaur, M.W., Travé-Massuyès, L., & Bayoudh, M. (2013). Mode set focused hybrid estimation. International Journal of Applied Mathematics and Computer Science, 23(1), 13 pp.Google Scholar
  27. 27.
    Sampath, M., Sengupta, R., & Lafortune, S. (1995). Diagnosability of discrete-event system. IEEE Transactions on Automatic Control, 40(9), 1555–1575.Google Scholar
  28. 28.
    Travé-Massuyès, L., Bayoudh, M., & Olive, X. (2008). Hybrid systems diagnosis by coupling continuous and discrete event techniques. In Proceedings of the 17th World Congress, Seoul, Korea, July 2008 (pp. 7265–7270).Google Scholar
  29. 29.
    Travé-Massuyès, L., Bayoudh, M., & Olive, X. (2009). On-line analytic redundancy relations instantiation guided by component discrete-dynamics for a class of non-linear hybrid systems. In Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, December 2009, Shanghai, P.R. China (pp. 6970–6975).Google Scholar
  30. 30.
    Vento, J., Puig, V., & Sarrate, R. (2010). Fault detection and isolation of hybrid system using diagnosers that combine discrete and continuous dynamics. In 2010 Conference on Control and Fault-Tolerant Systems (SysTol), October 2010 (pp. 149–154).Google Scholar
  31. 31.
    Vento, J., Puig, V., & Sarrate, R. (2011). A methodology for building a fault diagnoser for hybrid systems. In 9th European Workshop on Advance Control and Diagnosis, Budapest, Hungry, November 2011.Google Scholar
  32. 32.
    Vento, J., Puig, V., & Sarrate, R. (2012). Parity space hybrid system diagnosis under model uncertainty. In 2012 20th Mediterranean Conference on Control Automation (MED), July 2012 (pp. 685–690).Google Scholar
  33. 33.
    Vento, J., Puig, V., Sarrate, R., & Travé-Massuyès, L. (2012). Fault detection and isolation of hybrid systems using diagnosers that reason on components. IFAC Proceedings Volumes, 45(20), 1250–1255. 8th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes.Google Scholar
  34. 34.
    Vento, J., Travé-Massuyès, L., Puig, V., & Sarrate, R. (2015). An incremental hybrid system diagnoser automaton enhanced by discernibility properties. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 45(5), 788–804.CrossRefGoogle Scholar
  35. 35.
    Vento, J., Travé-Massuyès, L., Sarrate, R., & Puig, V. (2013). Hybrid automaton incremental construction for online diagnosis. In International Workshop on Principles of Diagnosis, October 2013 (pp. 186–191).Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ramon Sarrate
    • 1
  • Vicenç Puig
    • 1
  • Louise Travé-Massuyès
    • 2
  1. 1.Automatic Control DepartmentUniversitat Politècnica de Catalunya (UPC)TerrassaSpain
  2. 2.Laboratoire d’Analyse et d’Architecture des Systèmes, Centre National de la Recherche Scientifique (LAAS-CNRS)Université de ToulouseToulouseFrance

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