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Fault detection for nonlinear discrete-time systems via deterministic learning

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Abstract

Recently, an approach for the rapid detection of small oscillation faults based on deterministic learning theory was proposed for continuous-time systems. In this paper, a fault detection scheme is proposed for a class of nonlinear discrete-time systems via deterministic learning. By using a discrete-time extension of deterministic learning algorithm, the general fault functions (i.e., the internal dynamics) underlying normal and fault modes of nonlinear discrete-time systems are locally-accurately approximated by discrete-time dynamical radial basis function (RBF) networks. Then, a bank of estimators with the obtained knowledge of system dynamics embedded is constructed, and a set of residuals are obtained and used to measure the differences between the dynamics of the monitored system and the dynamics of the trained systems. A fault detection decision scheme is presented according to the smallest residual principle, i.e., the occurrence of a fault can be detected in a discrete-time setting by comparing the magnitude of residuals. The fault detectability analysis is carried out and the upper bound of detection time is derived. A simulation example is given to illustrate the effectiveness of the proposed scheme.

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References

  1. J. Chen, R. J. Patton. Robust Model-based Fault Diagnosis for Dynamic Systems. Boston: Kluwer, 1999.

    Book  MATH  Google Scholar 

  2. S. Simani, C. Fantuzzi, R. J. Patton. Model-based Fault Diagnosis in Dynamic Systems Using Identification Techniques. London: Springer, 2003.

    Book  Google Scholar 

  3. H. Hammouri, M. Kinnaert, E. H. Yaagoubi. Observer-based approach to fault detection and isolation for nonlinear systems. IEEE Transactions on Automatic Control, 1999, 44(10): 1879–1884.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Edwards, S. K. Spurgeon, R. J. Patton. Sliding mode observers for fault detection and isolation. Automatica, 2000, 36(4): 541–553.

    Article  MATH  MathSciNet  Google Scholar 

  5. C. D. Persis, A. Isidori. A geometric approach to nonlinear fault detection and isolation. IEEE Transactions on Automatic Control, 2001, 46(6): 853–865.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. Jiang, M. Staroswiecki, V. Cocquempot. Fault diagnosis based on adaptive observer for a class of nonlinear systems with unknown parameters. International Journal of Control, 2004, 77(4): 415–426.

    Article  MATH  MathSciNet  Google Scholar 

  7. F. Caccavale, P. Cilibrizzi, F. Pierri, et al. Actuators fault diagnosis for robot manipulators with uncertain model. Control Engineering Practice, 2009, 17(1): 146–157.

    Article  Google Scholar 

  8. Q. Shen, B. Jiang, V. Cocquempot. Fault tolerant control for T-S fuzzy systems with application to near space hypersonic vehicle with actuator faults. IEEE Transaction on Fuzzy Systems, 2012, 20(4): 652–665.

    Article  Google Scholar 

  9. L. Yao, J. Qin, H. Wang, et al. Design of new fault diagnosis and fault tolerant control scheme for non-Gaussian singular stochastic distribution systems. Automatica, 2012, 48(9): 2305–2313.

    Article  MATH  MathSciNet  Google Scholar 

  10. H. Wang, Z. Huang, S. Daley. On the use of adaptive updating rules for actuator and sensor fault diagnosis. Automatica, 1997, 33(2): 217–225.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. M. Polycarpou, P. A. Ioannou. Modelling, identification and stable adaptive control of continuous-time nonlinear dynamical systems using neural networks. Proceedings of the American Control Conference, Evanston: American Automatic Control Council, 1992: 36–40.

    Google Scholar 

  12. M. A. Demetriou, M. M. Polycarpou. Incipient fault diagnosis of dynamical systems using online approximators. IEEE Transactions on Automatic Control, 1998, 43(11): 1612–1617.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. M. Polycarpou, A. B. Trunov. Learning approach to nonlinear fault diagnosis: detectability analysis. IEEE Transactions on Automatic Control, 2000, 45(4): 806–812.

    Article  MATH  MathSciNet  Google Scholar 

  14. X. Zhang, M. M. Polycarpou, T. Parisini. A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems. IEEE Transactions on Automatic Control, 2002, 47(4): 576–593.

    Article  MATH  MathSciNet  Google Scholar 

  15. Z. Mao, B. Jiang, P. Shi. Fault-tolerant control for a class of nonlinear sampled-data systems via a Euler approximate observer. Automatica, 2010, 46(11): 1852–1859.

    Article  MATH  MathSciNet  Google Scholar 

  16. F. Caccavale, F. Pierri, L. Villani. Adaptive observer for fault diagnosis in nonlinear discrete-time systems. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 2008, 130(2): DOI 10.1115/1.2837310.

    Google Scholar 

  17. T. T. Balaje, S. Jagannathan. An online approximator-based fault detection framework for nonlinear discrete-time systems. Proceedings of the 46th IEEE Conference on Decision and Control, Piscataway: IEEE, 2007: 2608–2613.

    Google Scholar 

  18. T. T. Balaje, S. Jagannathan. A model-based fault-detection and prediction scheme for nonlinear multivariable discrete-time systems with asymptotic stability guarantees. IEEE Transactions on Neural Networks, 2010, 21(3): 404–423.

    Article  Google Scholar 

  19. M. G. Riccardo, G. Ferrari, T. Parisini, et al. Distributed fault detection and isolation of large-scale discrete-time nonlinear systems: an adaptive approximation approach. IEEE Transactions on Automatic Control, 2012, 57(2): 275–290.

    Article  MathSciNet  Google Scholar 

  20. C. Wang, D. J. Hill. Learning from neural control. IEEE Transactions on Neural Networks, 2006, 17(1): 30–46.

    Article  Google Scholar 

  21. C. Wang, D. J. Hill. Deterministic learning and rapid dynamical pattern recognition. IEEE Transactions on Neural Networks, 2007, 18(3): 617–630.

    Article  Google Scholar 

  22. C. Wang, D. J. Hill. Deterministic Learning Theory for Identification, Recognition and Control. Boca Raton: CRC Press, 2009.

    Google Scholar 

  23. C. Wang, T. Chen. Rapid detection of small oscillation faults via deterministic learning. IEEE Transactions on Neural Networks, 2011, 22(8): 1284–1296.

    Article  Google Scholar 

  24. C. Wang, B. Wen, W. Si, et al. Modeling and detection of rotating stall in axial flow compressors–Part I: Investigation on high-order M-G models via deterministic learning. Acta Automatica Sinica, 2014, 40(7): 1265–1277.

    Article  Google Scholar 

  25. W. Zeng, C. Wang. Gait recognition across different walking speeds via deterministic learning. Neurocomputing, 2015, 152: 139–150.

    Article  Google Scholar 

  26. W. Zeng, C. Wang. Classification of neurodegenerative diseases using gait dynamics via deterministic learning. Information Sciences, 2015, 317: 246–258.

    Article  Google Scholar 

  27. X. Dong, C. Wang, J Hu. Electrocardiogram (ECG) pattern modeling and recognition via deterministic learning. Control Theory and Technology, 2014, 12(4): 333–344.

    Article  Google Scholar 

  28. E. W. Bai, S. S. Sastry. Persistency of excitation, sufficient richness and parameter convergence in discrete time adaptive control. Systems & Control Letters, 1985, 6(3): 153–163.

    Article  MATH  MathSciNet  Google Scholar 

  29. T. Liu, C. Wang, D. J. Hill. Deterministic learning and rapid dynamical pattern recognition of discrete-time systems. Proceedings of the IEEE International Symposium on Intelligent Control, Piscataway: IEEE, 2008: 1091–1096.

    Google Scholar 

  30. C. Wang, T. R. Chen, T. Liu. Deterministic learning and databased modeling and control. Acta Automatica Sinica (Chinese), 2009, 35(6): 693–706.

    Article  MATH  MathSciNet  Google Scholar 

  31. C. Yuan, C. Wang. Design and performance analysis of deterministic learning of sampled-data nonlinear systems. Science China Information Sciences, 2014, 57(18): DOI 10.1007/s11432-012-4731-3.

    Google Scholar 

  32. L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, et al. Methods of Qualitative Theory in Nonlinear Dynamics–Part II. Singapore: World Scientific, 2001.

    MATH  Google Scholar 

  33. C. Wang, T. Chen, G. Chen, et al. Deterministic learning of nonlinear dynamical systems. International Journal of Bifurcation and Chaos, 2009, 19(4): 1307–1328.

    Article  MATH  MathSciNet  Google Scholar 

  34. V. H. Garnier, A. H. Epstein, E. M. Greitzer. Rotating wave as a stall inception indiccation in axial compressors. ASME Journal of Turbomachinery, 1991, 113(2): 1–9.

    Google Scholar 

  35. J. H. Deane, D. C. Hamill. Instability, subharmonics, and chaos in power electronic systems. IEEE Transactions on Power Electronics, 1990, 5(3): 260–268.

    Article  Google Scholar 

  36. S. R. Samantaray, P. K. Dash, S. K. Upadhyay. Adaptive Kalman fiter and neural network based high impedance fault detection in power distribution networks. Electrical Power and Energy Systems, 2009, 31(3): 167–172.

    Article  Google Scholar 

  37. A. R. Messina. Inter-area Oscillations in Power Systems. New York: Springer, 2009.

    Book  Google Scholar 

  38. H. Yin, P. Wang, T. Alpcan, et al. Hopf bifurcation and oscillations in a communication network with heterogeneous delays. Automatica, 2009, 45(10): 2358–2367.

    Article  MATH  MathSciNet  Google Scholar 

  39. H. G. Hosseini, D. Luo, K. J. Reynolds. The comparison of different feed forward neural network architectures for ECG signal diagnosis. Medical Engineering & Physics, 2006, 28(4): 372–378.

    Article  Google Scholar 

  40. C. Yuan, C. Wang. Pesistency of excitation and performance of deterministic learning. Systems & Control Letters, 2011, 60(12): 952–959.

    Article  MATH  MathSciNet  Google Scholar 

  41. U. Altinisik, M. Yildirim. A new fault tolerant control approach for the three-tank system using data mining. Computers & Electrical Engineering, 2012, 38(6): 1627–1635.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Automation Science and Engineering, South China University of Technology, Guangzhou Guangdong, 510640, China

    Junmin Hu, Cong Wang & Xunde Dong

Authors
  1. Junmin Hu
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  2. Cong Wang
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  3. Xunde Dong
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Corresponding author

Correspondence to Cong Wang.

Additional information

This work was supported by the National Science Fund for Distinguished Young Scholars (No. 61225014), the National Major Scientific Instruments Development Project (No. 61527811), the National Natural Science Foundation of China (Nos. 61304084, 61374119), the Guangdong Natural Science Foundation (No. 2014A030312005), and the Space Intelligent Control Key Laboratory of Science and Technology for National Defense.

Junmin HU is a Ph.D. candidate at the Center for Control and Optimization, School of Automation Science and Engineering, South China University of Technology. Her research interest covers adaptive NN control/identification, deterministic learning theory and oscillation fault diagnosis.

Cong WANG received the B.E. and M.E. degrees from Beijing University of Aeronautic & Astronautics in 1989 and 1997, respectively, and the Ph.D. degree from the Department of Electrical&Computer Engineering, The National University of Singapore in 2002. From 2001 to 2004, he did his postdoctoral research at the Department of Electronic Engineering, City University of Hong Kong. He has been with the School of Automation Science and Engineering, South China University of Technology, Guangzhou, China, since 2004, where he is currently a professor. He has authored and co-authored over 60 international journal and conference papers and the book Deterministic Learning Theory for Identification, Recognition and Control. He serves as an Associate Editor of the IEEE Transactions on Neural Networks and Learning Systems since 2012, and as an Associate Editor for Control Theory and Technology, and ACTA AUTOMATICA SINICA (two best journals in systems and control area in China) since 2008 and 2011, respectively. He is a member of the Technical Committee on Intelligent Control of the IEEE CSS. His research interest includes intelligent control, neural networks, nonlinear systems and control, dynamical pattern recognition, pattern-based control, dynamical systems, and oscillation fault diagnosis.

Xunde DONG is a Ph.D. candidate at the Center for Control and Optimization, School of Automation Science and Engineering, South China University of Technology. His research interest covers adaptive NN control/identification, deterministic learning theory and distributed parameter system.

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Hu, J., Wang, C. & Dong, X. Fault detection for nonlinear discrete-time systems via deterministic learning. Control Theory Technol. 14, 159–175 (2016). https://doi.org/10.1007/s11768-016-4140-z

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