Skip to main content
Log in

Fault Estimator and Diagnosis for Generalized Linear Discrete-Time System via Self-constructing Fuzzy UKF Method

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This study investigated fault estimation and diagnosis using a novel approach based on an integrated fault estimator and state estimator for generalized linear discrete-time systems. The proposed scheme uses a self-constructing fuzzy unscented Kalman filter (UKF) system to simultaneously estimate the system state and approximate the fault information. To achieve this, a generalized linear discrete-time system without faults was first transformed into an equivalent standard state-space system with faults. Then, the self-constructing fuzzy UKF system was designed in order to obtain the fault information. According to fault information obtained using the proposed scheme, fault detection experiments based on fuzzy clustering were performed and the fault feature parameters required for fault isolation were determined. Finally, the scheme was applied to a direct current (DC) motor to demonstrate the effectiveness of the proposed fault estimation and diagnosis approach. Results of the simulation illustrate the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Gao, Z., Ding, S.X.: Fault estimation and fault-tolerant control for descriptor systems via proportional, multiple-integral and derivative observer design. IET Control Theory Appl. 1(5), 1208–1218 (2007)

    Article  MathSciNet  Google Scholar 

  2. Li, T., Zhang, Y.: Fault detection and diagnosis for stochastic systems via output PDFs. J. Frankl. Inst. 348(6), 1140–1152 (2011)

    Article  MathSciNet  Google Scholar 

  3. Li, X.J., Yang, G.H.: Robust adaptive fault-tolerant control for uncertain linear systems with actuator failures. IET Control Theory Appl. 6(10), 1544–1551 (2012)

    Article  MathSciNet  Google Scholar 

  4. Berger, T.: Fault tolerant funnel control. PAMM 18(1), 1–2 (2018)

    MathSciNet  Google Scholar 

  5. Schenk, K., Gulbitti, B., Lunze, J.: Cooperative fault-tolerant control of networked control system. IFAC-Pap. OnLine 18(1), 571–577 (2018)

    Google Scholar 

  6. Ben Hmida, F., Khemiri, K., Ragot, J., et al.: Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown input. J. Frankl. Inst. 349(7), 2369–2388 (2012)

    Article  MathSciNet  Google Scholar 

  7. Li, X.J., Yang, G.H.: Robust fault detection and isolation for a class of uncertain single output non-linear systems. IET Control Theory Appl. 8(7), 462–470 (2014)

    Article  MathSciNet  Google Scholar 

  8. Wang, Z., Rodrigues, M., Theilliol, D., et al.: Fault estimation filter design for discrete-time descriptor systems. IET Control Theory Appl. 9(10), 1587–1594 (2015)

    Article  MathSciNet  Google Scholar 

  9. Xiao, M.L., Zhang, Y.B., Fu, H.M.: Three-stage unscented Kalman filter for state and fault estimation of nonlinear system with unknown input. J. Frankl. Inst. 354, 8421–8443 (2017)

    Article  MathSciNet  Google Scholar 

  10. Wan, Y.M., Keviczky, T., Verhaegen, M.: Fault estimation filter design with guaranteed stability using Markov parameters. IEEE Trans. Autom. Control 63(4), 1132–1139 (2018)

    Article  MathSciNet  Google Scholar 

  11. Blázquez, L.F., de Miguel, L.J., Aller, F., Perán, J.R.: Neuro-fuzzy identification applied to fault detection in nonlinear systems. Int. J. Syst. Sci. 42(10), 1771–1787 (2011)

    Article  Google Scholar 

  12. Zhang, H.Y., Chan, C.W., Cheung, K.C., Ye, Y.J.: Fuzzy artmap neural network and its application to fault diagnosis of integrated navigation systems. Automatic 37(7), 1065–1070 (2001)

    Article  Google Scholar 

  13. Bessaoudi, T., Hmida, F.B., Hsieh, C.S.: Robust state and fault estimation for linear descriptor stochastic systems with disturbances: a DC motor application. IET Control Theory Appl. 11(5), 601–610 (2017)

    Article  MathSciNet  Google Scholar 

  14. Forrai, A.: System identification and fault diagnosis of an electromagnetic actuator. IEEE Trans. Control Syst. Technol. 25(3), 1028–1035 (2017)

    Article  Google Scholar 

  15. Chen, B., Liu, X.P., Ge, S.S., Lin, C.H.: Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 20(6), 1012–1021 (2012)

    Article  Google Scholar 

  16. Zeng, K., Zhang, N.Y., Xu, W.L.: A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators. IEEE Trans. Fuzzy Syst. 8(6), 773–780 (2000)

    Article  Google Scholar 

  17. Liu, J., Li, H.: Approximation of generalized fuzzy system to function. Sci. China (Series E) 30(5), 413–423 (2000)

    MathSciNet  Google Scholar 

  18. Ying, H., Ding, Y.S., Li, S.K., Shao, S.H.: Comparison of necessary conditions for typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximatiors. IEEE Trans. Syst. Man Cybern. Part A (S1083–4427) 29(5), 508–514 (1999)

    Article  Google Scholar 

  19. Chen, P.C.: Fuzzy and neural network control schemes with automatic structuring process for nonlinear dynamic systems. Taiwan National Chiao Tung University, Hsinchu City (2008)

    Google Scholar 

  20. Wang, G.J., Li, X.P., Sui, X.L.: Universal approximation and its realization of generalized Mamdani fuzzy system based on K-integral norms. Acta Automatica Sinica. 40(1), 143–148 (2014)

    Google Scholar 

  21. Tao, Y.J., Wang, H.Z., Wand, G.J.: Approximation ability and its realization of the generalized Mamdani fuzzy system in the sense of Kp-integral norm. Acta Electronica Sinica 43(11), 2284–2291 (2015)

    Google Scholar 

  22. Wang, L., Peng, J.J., Wang, J.Q.: A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment. J. Clean. Prod. 191(1), 105–118 (2018)

    Article  MathSciNet  Google Scholar 

  23. Song, H., Zhang, H.: Fuzzy basis function network based approach for fault information detection in unknown systems. J. Beijing Univ. Aeronaut. Astronaut. 29(7), 570–574 (2003)

    Google Scholar 

  24. Zhu, Z.Q., Jiao, X.C.: Fault detection for nonlinear networked control system based on fuzzy observer. J. Syst. Eng. Electron. 23(1), 129–136 (2012)

    Article  Google Scholar 

  25. Abid, M., Hussain, T., Khan, A.Q.: TS fuzzy approach for fault detection in nonlinear systems with immeasurable state variables. In: 2014 26th Chinese Control and Decision Conference (CCDC)

  26. Liu, B., Tang, W.S.: Modern Control Theory, pp. 204–205. China Machine Press, Beijing (2006)

    Google Scholar 

  27. Konatowski, S., Kaniewski, P.: Comparison of estimation accuracy of EKF, UKF and PF filters. Ann. Navig. 23, 69–87 (2016)

    Article  Google Scholar 

Download references

Funding

Funding was provided by National Natural Science Foundation of China (Grant No. 51675398) and National Key Basic Research Program of China (Grant No. 2015CB857100).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hong Bao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z., Bao, H., Xue, S. et al. Fault Estimator and Diagnosis for Generalized Linear Discrete-Time System via Self-constructing Fuzzy UKF Method. Int. J. Fuzzy Syst. 22, 232–241 (2020). https://doi.org/10.1007/s40815-019-00750-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00750-7

Keywords

Navigation