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Selected Estimation Strategies for Fault Diagnosis of Nonlinear Systems

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Fault Diagnosis of Dynamic Systems

Abstract

Fault diagnosis boils down to deciding if a fault occurs (fault detection), locating a faulty component (fault isolation), and assessing the size of a fault (fault identification and estimation) [10, 79]. This causes that fault diagnosis can be perceived as a three-step procedure, which covers fault detection, isolation, and identification. As can be observed in the literature, the problem of Fault Detection and Isolation (FDI) has been studied widely (see [15, 21, 22, 32, 39, 79, 80] and the reference therein).

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References

  1. Abbaszadeh, M., Marquez, H.: LMI optimization approach to robust \(\cal{H}_{\infty }\) observer design and static output feedback stabilization for non-linear uncertain systems. Int. J. Robust Nonlinear Control 19(3), 313–340 (2008)

    MATH  Google Scholar 

  2. Aboky, C., Sallet, G., Vivalda, J.C.: Observers for Lipschitz nonlinear systems. Int. J. Control 75(3), 204–212 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abonyi, J., Babuska, R.: Local and global identification and interpretation of parameters in takagi-sugeno fuzzy models. In: The Ninth IEEE International Conference on Fuzzy Systems, 2000. FUZZ IEEE 2000, vol. 2, pp. 835–840 (2000). https://doi.org/10.1109/FUZZY.2000.839140

  4. Alcorta Garcia, E., Frank, P.M.: Deterministic nonlinear observer-based approaches to fault diagnosis. Control Eng. Pract. 5(5), 663–670 (1997)

    Article  Google Scholar 

  5. Alessandri, A., Baglietto, M., Battistelli, G.: Design of state estimators for uncertain linear systems using quadratic boundedness. Automatica 42(3), 497–502 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Alexiev, K., Georgieva, O.: Improved fuzzy clustering for identification of takagi-sugeno model. In: Intelligent Systems, 2004. Proceedings. 2004 2nd International IEEE Conference, vol. 1, pp. 213–218 (2004). https://doi.org/10.1109/IS.2004.1344669

  7. Amato, F., Cosentino, C., Mattei, M., Paviglianiti, G.: A mixed direct/functional redundancy scheme for the fdi on a small commercial aircraft. In: IFAC Symposium Fault Detection Supervision and Safety of Technical Processes, SAFEPROCESS, pp. 331–339 (2003)

    Article  Google Scholar 

  8. Ashton, S.A., Shields, D.N., Daley, S.: Design of a robust fault detection observer for polynomial non-linearities. In: Proceedings of 14th IFAC World Congress. Beijing, P.R. China (1999). CD-ROM

    Google Scholar 

  9. Bhattacharyya, S.P.: Observer design for linear systems with unknown inputs. IEEE Trans. Autom. Control 23(3), 483–484 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  10. Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M.: Diagnosis and Fault-Tolerant Control, 2nd edn. Springer, Berlin (2006)

    MATH  Google Scholar 

  11. Boutayeb, M., Aubry, D.: A strong tracking extended \(\text{ K }\)alman observer for nonlinear discrete-time systems. IEEE Trans. Autom. Control 44(8), 1550–1556 (1999)

    MATH  Google Scholar 

  12. Busawon, K., Saif, M., Farza, M.: A discrete-time observer for a class of non-linear systems. In: Proceedings of 36th IEEE Conference on Decision and Control, CDC, pp. 4796–4801 (1997)

    Google Scholar 

  13. Califano, C., Monaco, S., Normand-Cyrot, D.: On the observer design in discrete-time. Syst. Control Lett. 49(4), 255–266 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Chadli, M., Karimi, H.: Robust observer design for unknown inputs Takagi-Sugeno models. IEEE Trans. Fuzzy Syst. 21(1), 158–164 (2013)

    Article  Google Scholar 

  15. Chen, J., Patton, R.J.: Robust Model-Based Fault Diagnosis for Dynamic Systems. Kluwer Academic Publishers, London (1999)

    Book  MATH  Google Scholar 

  16. Chen, J., Patton, R.J.: Robust Model Based Fault Diagnosis for Dynamic Systems. Kluwer Academic Publishers, London (1999)

    Google Scholar 

  17. Chen, J., Patton, R.J., Zhang, H.: Design of unknown input observers and fault detection filters. Int. J. Control 63(1), 85–105 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ichalal, D., Marx, B., Ragot, J., Maquin, D.: Fault detection, isolation and estimation for Takagi-Sugeno nonlinear systems. J. Franklin Inst. 351(7), 3651–3676 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Darouach, M., Zasadzinski, M.: Unbiased minimum variance estimation for systems with unknown exogenous inputs. Automatica 33(4), 717–719 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  20. Deng, S., Yang, L.: Reliable control design of discrete-time takagi-sugeno fuzzy systems with actuator faults. Neurocomputing 173, Part 3, 1784–1788 (2016). https://doi.org/10.1016/j.neucom.2015.09.053

    Article  Google Scholar 

  21. Ding, S.: Model-Based Fault Diagnosis Techniques: Design Schemes. Algorithms and Tools. Springer, Berlin (2008)

    Google Scholar 

  22. Gertler, J.: Fault Detection and Diagnosis in Engineering Systems. Marcel Dekker, New York (1998)

    Google Scholar 

  23. Gillijns, S., De Moor, B.: Unbiased minimum-variance input and state estimation for linear discrete-time systems. Automatica 43, 111–116 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Guernez, C., Cassar, J.P., Staroswiecki, M.: Extension of parity space to non-linear polynomial dynamic systems. In: Proceedings of 3rd IFAC Symposium Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS’97, vol. 2, pp. 861–866. Hull, UK (1997)

    Google Scholar 

  25. Hac, A.: Design of disturbance decoupled observers for bilinear systems. ASME J. Dyn. Syst. Meas. Control 114, 556–562 (1992)

    Article  MATH  Google Scholar 

  26. Hammouri, H., Kabore, P., Othman, S., Biston, J.: Observer-based approach to fault detection and isolation for nonlinear systems. IEEE Trans. Autom. Control 44(10), 1879–1884 (1999)

    Article  MathSciNet  Google Scholar 

  27. Hammouri, H., Kinnaert, M., Yaagoubi, E.H.E.: Observer-based approach to fault detection and isolation for nonlinear systems. IEEE Trans. Autom. Control 44, 1879–1884 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  28. Hou, M., Mueller, P.C.: Design of observers for linear systems with unknown inputs. IEEE Trans. Autom. Control 37(6), 871–875 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  29. Hou, M., Patton, R.: Optimal filtering for systems with unknown inputs. IEEE Trans. Autom. Control 43(3), 445–449 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hou, M., Pugh, A.C.: Observing state in bilinear systems: an \(\text{ UIO }\) approach. In: Proceedings of IFAC Symposium Fault Detection, Supervision and Safety of Technical Processes: SAFEPROCESS’97, vol. 2, pp. 783–788. Hull, UK (1997)

    Google Scholar 

  31. Hui, S., Zak, S.: Observer design for systems with unknown input. Int. J. Appl. Math. Comput. Sci. 15(4), 431–446 (2005)

    MathSciNet  MATH  Google Scholar 

  32. Iserman, R.: Fault Diagnosis Systems. An Introduction from Fault Detection to Fault Tolerance. Springer, New York (2006)

    Book  Google Scholar 

  33. Isermann, R.: Fault Diagnosis Applications: Model Based Condition Monitoring, Actuators, Drives, Machinery, Plants, Sensors, and Fault-tolerant Systems. Springer, Berlin (2011)

    Google Scholar 

  34. Keller, J.Y., Darouach, M.: Two-stage \(\text{ Kalman }\) estimator with unknown exogenous inputs. Automatica 35(2), 339–342 (1999)

    MATH  Google Scholar 

  35. Kemir, K., Ben Hmida, F., Ragot, J., Gossa, M.: Novel optimal recursive filter for state and fault estimation of linear systems with unknown disturbances. Int. J. Appl. Math. Comput. Sci. 21(4), 629–638 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  36. Kinneart, M.: Robust fault detection based on observers for bilinear systems. Automatica 35(11), 1829–1842 (1999)

    Article  MathSciNet  Google Scholar 

  37. Kobayashi, N., Nakamizo, R.: An observer design for linear systems with unknown inputs. Int. J. Control 17(3), 471–479 (1982)

    Google Scholar 

  38. Koenig, D., Mammar, S.: Desing of a class of reduced unknown inputs non-linear observer for fault diagnosis. In: Proceedings of American Control Conference, ACC. Arlington, USA (2002)

    Google Scholar 

  39. Korbicz, J., Kościelny, J., Kowalczuk, Z., Cholewa, W. (eds.): Fault Diagnosis. Models, Artificial Intelligence, Applications. Springer, Berlin (2004)

    Google Scholar 

  40. Kowalczuk, Z., Gunawickrama, K.: Leak detection and isolation for transission pipelines via non-linear state estimation. In: Proceedings of 4th IFAC Symposium Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS 2000, vol. 2, pp. 943–948. Budapest, Hungary (2000)

    Google Scholar 

  41. Krishnaswami, V., Rizzoni, G.: Non-linear parity equation residual generation for fault detection and isolation. In: Proceedings of 2nd IFAC Symposium Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS’94, vol. 1, pp. 317–322. Espoo, Finland (1994)

    Article  Google Scholar 

  42. Kroll, A., DÃijrrbaum, A.: On control-specific derivation of affine takagi-sugeno models from physical models: assessment criteria and modeling procedure. In: Computational Intelligence in Control and Automation (CICA), pp. 23–30 (2011). https://doi.org/10.1109/CICA.2011.5945746

  43. Li, L., Ding, S.X., Yang, Y., Zhang, Y.: Robust fuzzy observer-based fault detection for nonlinear systems with disturbances. Neurocomputing 174, Part B, 767–772 (2016). https://doi.org/10.1016/j.neucom.2015.09.102

    Article  Google Scholar 

  44. Mattei, M., Gaetano, P., Valerio, S.: Nonlinear observers with \(\cal{H}_{\infty }\) performance for sensor fault detection and isolation: a linear matrix inequality design procedure. Control Eng. Pract. 13, 1271–1281 (2006)

    Google Scholar 

  45. Mahmoud, M., Jiang, J., Zhang, Y.: Active Fault Tolerant Control Systems: Stochastic Analysis and Synthesis. Springer, Berlin (2003)

    Google Scholar 

  46. Maksarow, D., Norton, J.: State bounding with ellipsoidal set description of the uncertainty. Int. J. Control 65(5), 847–866 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  47. Marquez, H.: Nonlinear Control Systems. Analysis and Design. Wiley, New Jersey (2003)

    Google Scholar 

  48. Milanese, M., Norton, J., Piet-Lahanier, H., Walter, E.: Bounding Approaches to System Identification. Plenum Press, New York (1996)

    Google Scholar 

  49. Mrugalski, M.: An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection. Int. J. Appl. Math. Comput. Sci. 23(1), 157–169 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  50. Nobrega, E., Abdalla, M., Grigoriadis, K.: Robust fault estimation of unceratain systems using an LMI-based approach. Int. J. Robust Nonlinear Control 18(7), 1657–1680 (2008)

    Article  MATH  Google Scholar 

  51. Noura, H., Theilliol, D., Ponsart, J., Chamseddine, A.: Fault-tolerant Control Systems: Design and Practical Applications. Springer, Berlin (2003)

    Google Scholar 

  52. Parisini, T., Polycarpou, M., Sanguineti, M., Vemuri, A.: Robust parametric and non-parametric fault diagnosis in nonlinear input-output systems. In: Proceedings of 36th Conference Decision and Control, pp. 4481–4482. San Diego, USA (1997)

    Google Scholar 

  53. Patton, R.J., Frank, P.M., Clark, R.N.: Issues of Fault Diagnosis for Dynamic Systems. Springer, Berlin (2000)

    Google Scholar 

  54. Pazera, M., Korbicz, J.: A process fault estimation strategy for non-linear dynamic systems. In: Journal of Physics: Conference Series, vol. 783, p. 012003. IOP Publishing (2017)

    Google Scholar 

  55. Pazera, M., Witczak, M., Buciakowski, M., Mrugalski, M.: Simultaneous estimation of multiple actuator anc sensor faults for takagi-sugeno fuzzy systems. In: 2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 939–944. IEEE (2017)

    Google Scholar 

  56. Persis, C.D., Isidori, A.: A geometric approach to nonlinear fault detection and isolation. IEEE Trans. Autom. Control 46(6), 853–865 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  57. Persis, C.D., Santis, R.D., Isidori, A.: An \(\cal{H}_{\infty }\)-suboptimal fault detection filter for bilinear systems. Proc. Nonlinear Control Year 2000, 331–339 (2000)

    MATH  Google Scholar 

  58. Persis, C.D., Santis, R.D., Isidori, A.: Nonlinear actuator fault detection and isolation for a vtol aircraft. In: Proceedings of the 2001 American Control Conference. Accessed from 25–27 June 2001

    Google Scholar 

  59. Pertew, A.M., Marquez, H.J., Zhao, Q.: \(\cal{H}_{\infty }\) synthesis of unknown input observers for non-linear lipschitz systems. Int. J. Control 78(15), 1155–1165 (2005)

    MathSciNet  MATH  Google Scholar 

  60. Rajamani, R.: Observers for \(\text{ Lipschitz }\) non-linear systems. IEEE Trans. Autom. Control 43(3), 397–401 (1998)

    MATH  Google Scholar 

  61. Rajamani, R., Cho, Y.M.: Existence and design of observers for nonlinear systems: relation to distance to unobservability. Int. J. Control 69(5), 717–731 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  62. Rotondo, D., Nejjari, F., Puig, V.: A virtual actuator and sensor approach for fault tolerant control of lpv systems. J. Process Control 24(3), 203–222 (2014)

    Article  Google Scholar 

  63. Schreier, G., Ragot, J., Patton, R.J., Frank, P.M.: Observer design for a class of non-linear systems. In: Proceedings of 3rd IFAC Symposium Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS’97, vol. 1, pp. 483–488. Hull, UK (1997)

    Google Scholar 

  64. Seliger, R., Frank, P.: Robust observer-based fault diagnosis in non-linear uncertain systems. In: Patton, F., Clark (eds.) Issues of Fault Diagnosis for Dynamic Systems. Springer, Berlin (2000)

    Chapter  Google Scholar 

  65. Seron, M.M., Doná, J.A.D.: Robust fault estimation and compensation for LPV systems under actuator and sensor faults. Automatica 52, 294–301 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  66. Shields, D.N., Ashton, S.: A fault detection observer method for non-linear systems. In: Proceedings of 4th IFAC Symp. Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS 2000, vol. 1, pp. 226–231. Budapest, Hungary (2000)

    Google Scholar 

  67. Shumsky, A.: Robust residual generation for diagnosis of non-linear systems: parity relation approach. In: Proceedings of 3rd IFAC Symposium Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS’97, vol. 2, pp. 867–872. Hull, UK (1997)

    Google Scholar 

  68. Stipanovic, D., Siljak, D.: Robust stability and stabilization of discrete-time non-linear: the LMI approach. Int. J. Control 74(5), 873–879 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  69. Tabatabaeipour, S.M., Bak, T.: Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems. J. Frankl. Inst. 351(1), 277–295 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  70. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC-15(1), 116–132 (1985)

    Article  MATH  Google Scholar 

  71. Thau, F.E.: Observing the state of nonlinear dynamic systems. Int. J. Control 17(3), 471–479 (1973)

    Article  MATH  Google Scholar 

  72. Veluvolu, K., Kim, M., Lee, D.: Nonlinear sliding mode high-gain observers for fault estimation. Int. J. Syst. Sci. 42(7), 1065–1074 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  73. Walker, B., Kuang-Yang, H.: \(\text{ FDI }\) by extended \(\text{ Kalman }\) filter parameter estimation for an industrial actuator benchmark. Control Eng. Pract. 3(12), 1769–1774 (1995)

    Google Scholar 

  74. Walter, E., Pronzato, L.: Identification of Parametric Models from Experimental Data. Springer, London (1996)

    Google Scholar 

  75. Wang, S.H., Davison, E.J., Dorato, P.: Observing the states of systems with unmeasurable disturbances. IEEE Trans. Autom. Control 20(5), 716–717 (1975)

    Article  MATH  Google Scholar 

  76. Wang, Z., Unbehauen, H.: A class of non-linear observers for discrete-time systems with parametric uncertainty. Int. J. Syst. Sci. 31(1), 19–26 (2000)

    Article  MATH  Google Scholar 

  77. Watkins, J., Yurkovich, S.: Set-membership strategies for fault detection and isolation. In: Proceedings of IEEE–SMC Symposium on Modelling, Analysis and Simulation, CESA, pp. 824–830. Lille, France (1996)

    Google Scholar 

  78. Witczak, M.: Identification and Fault Detection of Non-linear Dynamic Systems. Lecture Notes in Control and Computer Science, vol. 1. University of Zielona Góra Press, Zielona Góra (2003)

    Google Scholar 

  79. Witczak, M.: Modelling and Estimation Strategies for Fault Diagnosis of Non-linear Systems. Springer, Berlin (2007)

    Google Scholar 

  80. Witczak, M.: Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear Systems: Analytical and Soft Computing approaches. Springer International Publishing, Heidelberg (2014)

    Book  MATH  Google Scholar 

  81. Witczak, M., Buciakowski, M., Puig, V., Rotondo, D., Nejjari, F.: An lmi approach to robust fault estimation for a class of nonlinear systems. Int. J. Robust Nonlinear Control 26(7), 1530–1548 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  82. Witczak, M., Obuchowicz, A., Korbicz, J.: Genetic programming based approaches to identification and fault diagnosis of non-linear dynamic systems. Int. J. Control 75(13), 1012–1031 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  83. Yu, D., Shileds, D.N.: Bilinear fault detection observer and its application to a hydraulic system. Int. J. Control 64, 1023–1047 (1996)

    Article  MathSciNet  Google Scholar 

  84. Zemouche, A., Boutayeb, M.: Observer design for \(\text{ Lipschitz }\) non-linear systems: the discrete time case. IEEE Trans. Circuits Syst. - II: Express Briefs 53(8), 777–781 (2006)

    Google Scholar 

  85. Zemouche, A., Boutayeb, M., Iulia Bara, G.: Observer for a class of \(\text{ Lipschitz }\) systems with extension to \(\cal{H}_{\infty }\) performance analysis. Syst. Control Lett. 57(1), 18–27 (2008)

    MathSciNet  MATH  Google Scholar 

  86. Zhang, H.Y., Chan, C.W., Cheung, K.C., J., H.: Nonlinear adaptive observer design based on b-spline neural network. In: 14-th IFAC World Congress, pp. 213–217. Beijing, P.R. China (1999)

    Google Scholar 

  87. Zhang, X., Polycarpou, M., Prisini, T.: Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation. Automatica 46(2), 290–299 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  88. Zhao, Y., Tao, J., Shi, N.: A note on observer design for one-sided lipschitz nonlinear systems. Syst. Control Lett. 59(1), 66–71 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The work was supported by the National Science Centre of Poland under grant: UMO-2017/27/B/ST7/00620.

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  1. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Marcin Witczak & Marcin Pazera

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  1. Research Center for Supervision, Safety and Automatic Control (CS2AC), Universitat Politècnica de Catalunya (UPC), Terrassa, Spain

    Teresa Escobet

  2. Department of Computer Science, University of Valladolid, Segovia, Spain

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  3. Department of Computer Science, University of Valladolid, Valladolid, Spain

    Belarmino Pulido

  4. Research Center for Supervision, Safety and Automatic Control (CS2AC), Universitat Politècnica de Catalunya (UPC), Terrassa, Spain

    Vicenç Puig

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Witczak, M., Pazera, M. (2019). Selected Estimation Strategies for Fault Diagnosis of Nonlinear Systems. In: Escobet, T., Bregon, A., Pulido, B., Puig, V. (eds) Fault Diagnosis of Dynamic Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-17728-7_11

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