Generalized SSPRT for Fault Identification and Estimation of Linear Dynamic Systems Based on Multiple Model Algorithm

 

Ji Zhang¹, Yu Liu*² and Xuguang Li³

 

¹ Department of Computer, North China Electric Power University, Baoding, Hebei 071003, China.

² Department of Electrical Engineering, University of New Orleans, New Orleans, LA 70148, USA. lyu2@uno.edu

³ Clinical Laboratory, 323 Hospital Xi'an, Shaanxi 710054, China.

 

ABSTRACT

The generalized Shiryayev sequential probability ratio test (SSPRT) is applied to linear dynamic systems for single fault isolation and estimation. The algorithm turns out to be the multiple model (MM) algorithm considering all the possible model trajectories. In real application, this algorithm must be approximated due to its increasing computation complexity and the unknown parameters of the fault severeness. The Gaussian mixture reduction is employed to address the problem of computation complexity. The unknown parameters are estimated in real time by model augmentation based on maximum likelihood estimation (MLE) or expectation. Hence, the system state estimation, fault identification and estimation can be fulfilled simultaneously by a multiple model algorithm incorporating these two techniques. The performance of the proposed algorithm is demonstrated by Monte Carlo simulation. Although our algorithm is developed under the assumption of single fault, it can be generalized to deal with the case of (infrequent) sequential multiple faults. The case of simultaneous faults is more complicated and will be considered in future work.

Keywords: Generalized SSPRT, state estimation, fault isolation and estimation, multiple model, Gaussian mixture reduction, model augmentation.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

Research was supported by the Fundamental Research Funds for the Central Universities (China), project No. 12QN41.

 

References

[1] D. Middleton and R. Esposito, "Simultaneous optimum detection and estimation of signals in noise," lEEE Transactions on Information Theory, vol. 14, no. 3, pp. 434-444, May 1968.         [ Links ]

[2] H.L.V. Trees, Detection, Estimation, and Modulation Theory, Part I: Detection, Estimation, and Linear Modulation Theory. New York: Wiley, 1971.         [ Links ]

[3] A.S. Willsky, "A survey of design methods for failure detection in dynamic systems," Automatica, vol. 12, no. 6, pp. 601-611, November 1976.         [ Links ]

[4] P.M. Frank, "Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy — asurvey and some new results," Automatica, vol. 26, no. 3, pp. 459-474, May 1990.         [ Links ]

[5] M. Basseville and I. Nikiforov, Detection of Abrupt Changes: Theory and Application. Englewood Cliffs, NJ: Prentice Hall, 1993.         [ Links ]

[6] I.V. Nikiforov, "A generalized change detection problem," IEEE Journal of Oceanic Engineering Transactions on Information Theory, vol. 41, no. 1, pp. 171-187, January 1995.         [ Links ]

[7] Y. Zhang and X.R. Li, "Detection and diagnosis of sensor and actuator failures using IMM estimator," IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 4, pp. 1293-1313, October 1998.         [ Links ]

[8] D.P. Malladi and J.L. Speyer, "A generalized Shiryayev sequential probability ratio test for change detection and isolation," IEEE Transactions on Automatic Control, vol. 44, no. 8, pp. 1522-1534, August 1999.         [ Links ]

[9] T.L. Lai, "Sequential multiple hypothesis testing and efficient fault detection-isolation in stochastic systems," IEEE Transactions on Information Theory, vol. 46, no. 2, pp. 595-608, March 2000.         [ Links ]

[10] J. Ru and X. R. Li, "Variable-structure multiple-model approach to fault detection, identification, and estimation," IEEE Transactions on Control Systems Technology, vol. 16, no. 5, pp. 1029-1038, September 2008.         [ Links ]

[11] E.S. Page, "Continuous inspection schemes," Biometrika, vol. 41, pp. 100-115, 1954.         [ Links ]

[12] G. Lorden, "Procedures for reacting to a change in distribution," The Annals of Mathematical Statistics, vol. 42, no. 6, pp. 1897-1908, 1971.         [ Links ]

[13] G.V. Moustakides, "Optimal stopping times for detecting changes in distributions," The Annals of Statistic, vol. 14, no. 4, pp. 1379-1387, December1986.         [ Links ]

[14] A.N. Shiryayev, Optimal Stopping Rules. New York: Springer-Verlag, 1977.         [ Links ]

[15] X.R. Li and V.P. Jilkov, "Survey of maneuvering target tracking — part V: multiple-model methods," IEEE Transaction on Aerospace and Electronic Systems, vol. 41, no. 4, pp. 1255-1321, Oct. 2005.         [ Links ]

[16] P.S. Maybeck and R. D. Stevens, "Reconfigurable flight control via multiple model adaptive control method," IEEE Transactions on Aerospace and Electronic Systems, vol. 27, no. 3, pp. 470-480, May 1991.         [ Links ]

[17] P.S. Maybeck, "Application of multiple model adaptive algorithms to reconfigurable flight control," Control and Dynamic Systems, vol. 52, pp.291-320, 1992.         [ Links ]

[18] T.E. Menke and P.S. Maybeck, "Sensor/actuator failure detection in the Vista F-16 by multiple model adaptive estimation," IEEE Transactions on Aerospace and Electronic Systems, vol. 31, no. 4, pp. 1218-1229, October1995.         [ Links ]

[19] H.A.P. Blom and Y. Bar-Shalom, "The interacting multiple model algorithm for systems with Markovian switching coefficients," IEEE Transactions on Automatic Control, vol. 33, no. 8, pp. 780-783, August 1988.         [ Links ]

[20] J. Ru and X.R. Li, "Interacting multiple model algorithm with maximum likelihood estimation for FDI," in IEEE International Symposium on Intelligent Control, Houston, TX, October 2003, pp. 661-666.         [ Links ]

[21] J.F. Ru, "Adaptive estimation and detection techniques with applications," Ph.D. dissertation, University of New Orleans, New Orleans, LA, August 2005.         [ Links ]

[22] J.F. Ru, X.R. Li, and V.P. Jilkov, "Multiple model detection of target maneuvers," in Proceedings of Signal and Data Processing of Small Target, vol. 5913, 2005, pp. 100-108.         [ Links ]

[23] J.L. Williams and P.S. Mayback, "Cost-function-based Gaussian mixture reduction for target tracking," in Proceedings of the 6th International Conference on Information Fusion, Cairns, Australia, July 2003.         [ Links ]

[24] J.L. Williams, "Gaussian mixture reduction for tracking multiple maneuvering targets in clutter," M.S.E.E, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH, 2003.         [ Links ]

[25] X.R. Li, V. P. Jilkov, and J. Ru, "Multiple-model estimation with variable structure - part VI: expected-mode augmentation," IEEE Transactions on Aerospace and Electronic Systems, vol. 41, no. 3, pp. 853-867, July 2005.         [ Links ]

[26] R.E. Kalman, "A new approach to linear filtering and prediction problems," Journal of Basic Engineering, vol. 82, no. 1, pp. 35-45, 1960.         [ Links ]

[27] D.J. Salmond, "Mixture reduction algorithms for target tracking in clutter," in Proceedings of SPIE Signal and Data Processing of Small Targets, vol. 1305, October 1990, pp. 434-445.         [ Links ]

[28] M. West, "Approximating posterior distributions by mixtures," Journal of the Royal Statistical Society Series B Methodological, vol. 55, no. 2, pp. 409-422, 1993.         [ Links ]

[29] P.S. Mayback and B.D. Smith, "Multiple model tracker based on Gaussian mixture reduction for maneuvering targets in clutter," in Proceedings of 8th International Conference on Information Fusion, vol. 1, 2005, pp. 40-47.         [ Links ]

[30] A.R. Runnalls, "Kullback-Leibler approach to Gaussian mixture reduction," IEEE Transactions on Aerospace and Electronic Systems, vol. 43,no. 3, pp. 989-999, July 2007.         [ Links ]

[31] M. Huber, P. Krauthausen, and U.D. Hanebeck, "Superficial Gaussian mixture reduction," in Proceedings of the IEEE ISIF Workshop on Sensor Data Fusion Trends Solutions Applications SDF, 2011.         [ Links ]

[32] J. Zhang and Y. Liu, "Single maneuvering target tracking in clutter based on multiple model algorithm with Gaussian mixture reduction," Journal of Applied Research and Technology, vol. 11, no. 5, pp. 641-652, 2013.         [ Links ]

[33] J.R. Hershey and P.A. Olsen, "Approximating the Kullback-Leibler divergence between Gaussian mixture models," in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Honolulu, HI, April 2007, pp. IV-317 - IV-320.         [ Links ]

[34] Y. Zhu, "Efficient recursive state estimator for dynamic systems without knowledge of noise covariances," IEEE Transactions on Aerospace and Electronic Systems, vol. 35, no. 1, pp. 102-114, January 1999.         [ Links ]

[35] Y. Zhu, K. Zhang, and X.R. Li, "Fusion of distributed extended forgetting factor RLS state estimators," IEEE Transactions on Aerospace and Electronic Systems, vol. 44, no. 2, pp. 457-467, April 2008.         [ Links ]