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Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model

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Abstract

The task of robust fault detection and diagnosis of stochastic distribution control (SDC) systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Convergency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demonstrate the effectiveness of the proposed algorithm.

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References

  1. Basseville M. On-board component fault detection and isolation using the statistical local approach. Automatica, 1998, 34(11): 1391–1415

    Article  MATH  Google Scholar 

  2. Charalambous C D, Logothetis A. Maximum likehood parameter estimation from incomplete data via the sensitivity equations: the continuous-time case. IEEE Trans Automat Contr, 2000, 45(5): 928–934

    Article  MATH  MathSciNet  Google Scholar 

  3. Kadirkamanathan V, Li P, Particle filtering based likehood ratio approach to fault diagnosis in nonlinear stochastic systems. IEEE Trans Syst Man and Cybernetics-Part C, 2001, 31(3): 337–343

    Article  Google Scholar 

  4. Fouladirad M, Nikiforov I. Optimal statistical fault detection with nuisance parameters. Automatica, 2005, 41(7):1157–1171

    Article  MATH  MathSciNet  Google Scholar 

  5. Antory D, Krager U, Irwin G, et al. Fault diagnosis in internal combustion engines using non-linear multivariate statistics. Proc Inst Mech Eng Part I J Syst Contr Eng, 2005, 219(4): 243–258

    Article  Google Scholar 

  6. Tafazoli S, Sun X H. Hybrid system state tracking and fault detection using particle filters. IEEE Trans Control Syst Tech, 2006, 14(6): 1078–1087

    Article  Google Scholar 

  7. Zhou D H, Sun Y X, Xi Y G, et al. Real-time detection and diagnosis of “parameter bias” faults for nonlinear systems. Acta Automat Sin (in Chinese), 1993, 19(2): 184–189

    MATH  MathSciNet  Google Scholar 

  8. Li J, Zhang H Y. Analysis of fault detection method based on predictive filter approach. Sci China Ser F-Inf Sci, 2005, 48(3): 335–353

    Article  MATH  Google Scholar 

  9. Patton R J, Frank P R, Clark R. Fault Diagnosis in Dynamic Systems: Theory and Application. Englewood Cliff, NJ: Prentice-Hall, 1989

    Google Scholar 

  10. Chen R H, Mingori D L, Speyer J L. Optimal stochastic fault detection filter. Automatica, 2003, 39(3): 337–390

    Article  MathSciNet  Google Scholar 

  11. Wang H, Lin W. Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions. Int J Contr, 2000, 73(15): 1424–1436

    Article  MATH  MathSciNet  Google Scholar 

  12. Guo L, Zhang Y M, Wang H, et al. Observer-based optimal fault detection and diagnosis using conditional probability distributions. IEEE Trans Signal Proc, 2006, 54(10): 3712–3719

    Article  Google Scholar 

  13. Wang H. Bounded Dynamic Stochastic Systems: Modeling and Control. London: Springer-Verlag, 2000

    Google Scholar 

  14. Wang H, Baki H, Kabore P. Control of bounded dynamic stochastic distributions using square root models: An applicability study in papermaking system. Trans Institute of Measure Contr, 2001, 23(1): 51–68

    Google Scholar 

  15. Zhou J L, Yue H, Wang H. Shaping of output PDFs based on the rational square-root B-spline model. Acta Automatic Sinica, 2005, 31(3): 343–351

    MathSciNet  Google Scholar 

  16. Guo L, Wang H. PID controller design for output PDFs of stochastic systems using linear matrix inequalities. IEEE Trans Syst, Man, and Cybernetics-Part B: Cybernetics, 2005, 35(1): 65–71

    Article  MathSciNet  Google Scholar 

  17. Guo L, Wang H. Generalized discrete-time PI control of output PDFs using square-root B-spline expansion. Automatica, 2005, 41(1): 159–162

    Article  MATH  MathSciNet  Google Scholar 

  18. Guo L, Wang H. Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters. IEEE Trans Circ Syst, 2005, 52(8): 1644–1652

    Article  MathSciNet  Google Scholar 

  19. Yao L N, Wang H. Fault diagnosis and tolerant control for non-Gaussian stochastic distribution control systems based on the rational square-root approximation model. Cont Theory Appl (in Chinese), 2006, 23(4): 561–568

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering, Zhengzhou University, Zhengzhou, 450001, China

    LiNa Yao

  2. Control Systems Centre, University of Manchester, Manchester, M60 1QD, UK

    Hong Wang

  3. Institute of Automation, Chinese Academy of Sciences, Beijing, 100080, China

    Hong Wang

Authors
  1. LiNa Yao
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  2. Hong Wang
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Corresponding author

Correspondence to LiNa Yao.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60534010) and the Outstanding Overseas Chinese Scholars Fund of CAS (Grant No. 2004-1-4)

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Yao, L., Wang, H. Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model. Sci. China Ser. F-Inf. Sci. 51, 1281–1290 (2008). https://doi.org/10.1007/s11432-008-0088-z

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  • DOI: https://doi.org/10.1007/s11432-008-0088-z

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