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.




Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
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)
Li, T., Zhang, Y.: Fault detection and diagnosis for stochastic systems via output PDFs. J. Frankl. Inst. 348(6), 1140–1152 (2011)
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)
Berger, T.: Fault tolerant funnel control. PAMM 18(1), 1–2 (2018)
Schenk, K., Gulbitti, B., Lunze, J.: Cooperative fault-tolerant control of networked control system. IFAC-Pap. OnLine 18(1), 571–577 (2018)
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)
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)
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)
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)
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)
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)
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)
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)
Forrai, A.: System identification and fault diagnosis of an electromagnetic actuator. IEEE Trans. Control Syst. Technol. 25(3), 1028–1035 (2017)
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)
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)
Liu, J., Li, H.: Approximation of generalized fuzzy system to function. Sci. China (Series E) 30(5), 413–423 (2000)
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)
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)
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)
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)
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)
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)
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)
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)
Liu, B., Tang, W.S.: Modern Control Theory, pp. 204–205. China Machine Press, Beijing (2006)
Konatowski, S., Kaniewski, P.: Comparison of estimation accuracy of EKF, UKF and PF filters. Ann. Navig. 23, 69–87 (2016)
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
Corresponding author
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-019-00750-7