Optimal Adaptive Threshold and Mode Fault Detection for Model-Based Fault Diagnosis of Hybrid Dynamical Systems

  • Om Prakash
  • A. K. Samantaray
  • R. Bhattacharyya


Selection of suitable residual thresholds is a crucial factor for robust model-based fault diagnosis of a dynamical system. Usually, the residual thresholds for robust diagnosis, called adaptive thresholds, are generated based on the worst case conditions of parameter and measurement uncertainties. The adaptive thresholds are robust because they consider that all parameters can have maximum possible deviations in arbitrary directions, i.e. either higher or lower than the corresponding measured or estimated parameter values. This inflates the thresholds and for small faults, the residuals may not cross the adaptive thresholds. For larger faults, the time taken to cross the thresholds may be significant leading to detection delay. The situation is more complex in a hybrid dynamical system because both discrete mode faults and parametric faults are possible and the diagnosis scheme must discriminate between those two types of faults. This chapter presents a common bond graph model-based framework for the hybrid system modelling, simulation, residual and threshold equations derivation, and parametric and discrete mode fault detection and isolation. To improve the fault detection and isolation, an optimization technique is proposed to select a set of optimal adaptive thresholds in the presence of uncertainties. Also, a new technique is proposed to discriminate the parametric faults from the discrete mode faults by an initial hypothesis based on magnitude of residual deviation after a fault. This discrimination improves further diagnosis tasks, especially the parameter estimation process. The proposed diagnosis and thresholding techniques are applied to an academic example system.


  1. 1.
    Gertler, J. (1998). Fault detection and diagnosis in engineering systems. New York: Dekker. ISBN 0-8247-9427-3.Google Scholar
  2. 2.
    Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M., & Schröder, J. (2006). Diagnosis and fault-tolerant control. Berlin: Springer.Google Scholar
  3. 3.
    Chen, J., & Patton, R. J. (2012). Robust model-based fault diagnosis for dynamic systems. Berlin: Springer Science Business Media.Google Scholar
  4. 4.
    Gelso, E. R., Biswas, G., Castillo, S., & Armengol, J. (2008, September). A comparison of two methods for fault detection: A statistical decision, and an interval-based approach. In 19th International Workshop on Principles of Diagnosis DX (pp. 261–268).Google Scholar
  5. 5.
    Borutzky, W. (2015). Bond graph model-based fault diagnosis of hybrid systems. Cham, Switzerland: Springer.Google Scholar
  6. 6.
    Mukherjee, A., Karmakar, R., & Samantaray, A. K. (2006). Bond graph in modelling, simulation and fault identification. New Delhi: I. K. International Pvt. Ltd.Google Scholar
  7. 7.
    Samantaray, A. K., & Ould Bouamama, B. (2008). Model-based process supervision: A bond graph approach. London: Springer.Google Scholar
  8. 8.
    Karnopp, D. C., Margolis, D. L., & Rosenberg, R. C. (2012). System dynamics: Modelling, simulation, and control of mechatronic systems (5th ed.). Hoboken, NJ: Wiley.Google Scholar
  9. 9.
    Mosterman, P. J., & Biswas, G. (1995). Behaviour generation using model switching: A hybrid bond graph modelling technique. Transactions of The Society for Computer Simulation, 27(1), 177–182.Google Scholar
  10. 10.
    Roychoudhury, I., Daigle, M. J., Biswas, G., & Koutsoukos, X. (2011). Efficient simulation of hybrid systems: A hybrid bond graph approach. Simulation, 87(6), 467–498.Google Scholar
  11. 11.
    Ghoshal, S. K., Samanta, S., & Samantaray, A. K. (2012). Robust fault detection and isolation of hybrid systems with uncertain parameters. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 226(8), 1013–1028.Google Scholar
  12. 12.
    Wang, D., Yu, M., Low, C. B., & Arogeti, S. (2013). Model-based health monitoring of hybrid systems. New York: Springer Science Business Media.Google Scholar
  13. 13.
    Djeziri, M. A., Merzouki, R., Ould Bouamama, B., & Dauphin-Tanguy, G. (2007). Robust fault diagnosis by using bond graph approach. IEEE/ASME Transactions on Mechatronics, 12(6), 599–611.Google Scholar
  14. 14.
    Merzouki, R., Samantaray, A. K., Pathak, P. M., & Ould Bouamama, B. (2012). Intelligent mechatronic systems: Modelling, control and diagnosis. London: Springer.Google Scholar
  15. 15.
    Touati, Y., Merzouki, R., & Ould Bouamama, B. (2012). Robust diagnosis to measurement uncertainties using bond graph approach: Application to intelligent autonomous vehicle. Mechatronics, 22(8), 1148–1160.Google Scholar
  16. 16.
    Arogeti, S., 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
  17. 17.
    Daigle, M., Bregon, A., & Roychoudhury, I. (2016). A qualitative fault isolation approach for parametric and discrete faults using structural model decomposition. In Annual Conference of PHMS.Google Scholar
  18. 18.
    Prakash, O., & Samantaray, A. K. (2017). Model-based diagnosis and prognosis of hybrid dynamical systems with dynamically updated parameters. In Bond graphs for modelling, control and fault diagnosis of engineering systems (pp. 195–232). Cham, Switzerland: Springer.Google Scholar
  19. 19.
    Samantaray, A. K., Ghoshal, S. K., Chakraborty, S., & Mukherjee, A. (2005). Improvements to single-fault isolation using estimated parameters. Simulation, 81(12), 827–845.Google Scholar
  20. 20.
    Samantaray, A. K., & Ghoshal, S. K. (2007). Sensitivity bond graph approach to multiple fault isolation through parameter estimation. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 221(4), 577–587.Google Scholar
  21. 21.
    Low, C. B., Wang, D., Arogeti, S. A., & Luo, M. (2009, July). Fault parameter estimation for hybrid systems using hybrid bond graph. In Control Applications, (CCA) Intelligent Control, (ISIC), 2009 IEEE (pp. 1338–1343). New York: IEEE.Google Scholar
  22. 22.
    Bregon, A., Biswas, G., & Pulido, B. (2012). A decomposition method for nonlinear parameter estimation in TRANSCEND. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 42(3), 751–763.Google Scholar
  23. 23.
    Jha, M. S., Dauphin-Tanguy, G., & Ould Bouamama, B. (2014, June). Robust FDI based on LFT BG and relative activity at junction. In European on Control Conference (ECC) (pp. 938–943). New York: IEEE.Google Scholar
  24. 24.
    Touati, Y., Mellal, M. A., & Benazzouz, D. (2016). Multi-thresholds for fault isolation in the presence of uncertainties. ISA Transactions, 62, 299–311.Google Scholar
  25. 25.
    Khorasgani, H., Eriksson, D., Biswas, G., Frisk, E., & Krys, M. (2014). Off-line robust residual selection using sensitivity analysis. 25th International Workshop on Principles of Diagnosis (DX-14). Graz, Austria, September 8–11, 2014.
  26. 26.
    Borutzky, W. (2014). Bond graph model-based system mode identification and mode-dependent fault thresholds for hybrid systems. Mathematical and Computer Modelling of Dynamical Systems, 20(6), 584–615.Google Scholar
  27. 27.
    Levy, R., Arogeti, S., Wang, D., & Fivel, O. (2015). Improved diagnosis of hybrid systems using instantaneous sensitivity matrices. Mechanism and Machine Theory, 91, 240–257.Google Scholar
  28. 28.
    Alonso, N. M., Bregon, A., Alonso-González, C. J., & Pulido, B. (2013, September). A common framework for fault diagnosis of parametric and discrete faults using possible conflicts. In Conference of the Spanish Association for Artificial Intelligence (pp. 239–249). Berlin, Heidelberg: Springer.Google Scholar
  29. 29.
    Bregon, A., González, C. A., & Pulido, B. (2015). Improving fault isolation and identification for hybrid systems with hybrid possible conflicts. In DX@ Safeprocess (pp. 59–66).Google Scholar
  30. 30.
    Vento, J., Blesa, J., Puig, V., & Sarrate, R. (2015). Set-membership parity space hybrid system diagnosis. International Journal of Systems Science, 46(5), 790–807.Google Scholar
  31. 31.
    Rahal, M. I., Ould Bouamama, B., & Meghebbar, A. (2016, May). Hybrid bond graph for robust diagnosis to measurement uncertainties. In 2016 5th International Conference on Systems and Control (ICSC) (pp. 439–444). New York: IEEE.Google Scholar
  32. 32.
    Louajri, H., & Sayed-Mouchaweh, M. (2014, September). Decentralized approach for fault diagnosis of three cell converters. In Annual Conference of the Prognostics and Health Management Society, Fort Worth, TX, USA (pp. 265–277).Google Scholar
  33. 33.
    Toubakh, H., & Sayed-Mouchaweh, M. (2016). Hybrid dynamic classifier for drift-like fault diagnosis in a class of hybrid dynamic systems: Application to wind turbine converters. Neurocomputing, 171, 1496–1516.Google Scholar
  34. 34.
    Kościelny, J. M. (1995). Fault isolation in industrial processes by the dynamic table of states method. Automatica, 31(5), 747–753.Google Scholar
  35. 35.
    Cordier, M. O., Dague, P., Lévy, F., Montmain, J., Staroswiecki, M., & Travé-Massuyés, L. (2004). Conflicts versus analytical redundancy relations: A comparative analysis of the model based diagnosis approach from the artificial intelligence and automatic control perspectives. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34(5), 2163–2177.Google Scholar
  36. 36.
    Puig, V., Schmid, F., Quevedo, J., & Pulido, B. (2005, December). A new fault diagnosis algorithm that improves the integration of fault detection and isolation. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain (pp. 3809–3814).Google Scholar
  37. 37.
    Petti, T. F., Klein, J., & Dhurjati, P. S. (1990). Diagnostic model processor: Using deep knowledge for process fault diagnosis. AIChE Journal, 36(4), 565–575.Google Scholar
  38. 38.
    Samantaray, A. K., Medjaher, K., Ould Bouamama, B., Staroswiecki, M., & Dauphin-Tanguy, G. (2006). Diagnostic bond graphs for online fault detection and isolation. Simulation Modelling Practice and Theory, 14(3), 237–262.Google Scholar
  39. 39.
    Low, C. B., Wang, D., Arogeti, S., & Luo, M. (2010). Quantitative hybrid bond graph-based fault detection and isolation. IEEE Transactions on Automation Science and Engineering, 7(3), 558–569.Google Scholar
  40. 40.
    Brandt, A. (2011). Noise and vibration analysis: Signal analysis and experimental procedures. New York: Wiley.Google Scholar
  41. 41.
    Nocedal, J., & Wright, S. (2006). Numerical optimization. New York: Springer Science and Business Media.Google Scholar
  42. 42.
    Oukl Bouamama, B., Staroswiecki, M., & Samantaray, A. K. (2006). Software for supervision system design in process engineering industry. IFAC Proceedings Volumes, 39(13), 646–650.Google Scholar
  43. 43.
    Prakash, O., Samantaray, A. K., & Bhattacharyya, R. (2017). Model-based diagnosis of multiple faults in hybrid dynamical systems with dynamically updated parameters. IEEE Transactions on Systems, Man, and Cybernetics: Systems.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Om Prakash
    • 1
  • A. K. Samantaray
    • 1
  • R. Bhattacharyya
    • 1
  1. 1.Systems, Dynamics and Control Laboratory, Department of Mechanical EngineeringIndian Institute of Technology-KharagpurKharagpurIndia

Personalised recommendations