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On-line parameter estimation for a failure-prone system subject to condition monitoring

Part of: Stochastic processes Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Daming Lin  and
Viliam Makis
Daming Lin*
Affiliation:
University of Toronto
Viliam Makis*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
∗ Postal address: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
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Abstract

In this paper, we study the on-line parameter estimation problem for a partially observable system subject to deterioration and random failure. The state of the system evolves according to a continuous-time homogeneous Markov process with a finite state space. The state of the system is hidden except for the failure state. When the system is operating, only the information obtained by condition monitoring, which is related to the working state of the system, is available. The condition monitoring observations are assumed to be in continuous range, so that no discretization is required. A recursive maximum likelihood (RML) algorithm is proposed for the on-line parameter estimation of the model. The new RML algorithm proposed in the paper is superior to other RML algorithms in the literature in that no projection is needed and no calculation of the gradient on the surface of the constraint manifolds is required. A numerical example is provided to illustrate the algorithm.

Keywords

Partially observable systemcontinuous-discrete modelon-line parameter estimationrecursive maximum likelihoodcondition-based maintenance

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60G35: Signal detection and filtering 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 211 - 220
Copyright
Copyright © Applied Probability Trust 2004 

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References

Aven, T. (1996). Condition based replacement policies—a counting process approach. Reliability Eng. System Safety 51, 275–281.Google Scholar
Bunks, C., McCarthy, D., and Al-Ani, T. (2000). Condition-based maintenance of machines using hidden Markov models. Mechanical Systems Signal Process. 14, 597–612.Google Scholar
Challa, S., and Bar-Shalom, Y. (2000). Nonlinear filter design using Fokker–Planck–Kolmogorov probability density evolutions. IEEE Trans. Aerospace Electron. Systems 36, 309–315.Google Scholar
Christer, A. H., Wang, W., and Sharp, J. M. (1997). A state space condition monitoring model for furnace erosion prediction and replacement. Europ. J. Operat. Res. 101, 1–14.Google Scholar
Collings, I. B. and Rydén, T. (1998). A new maximum likelihood gradient algorithm for on-line hidden Markov model identification. In Proc. 1998 IEEE Internat. Conf. Acoustics, Speech Signal Processing, IEEE, New York, pp. 2261–2264.Google Scholar
Collings, I. B., Krishnamurthy, V., and Moore, J. B. (1994). On-line identification of hidden Markov models via recursive prediction error techniques. IEEE Trans. Signal Process. 42, 3535–3539.CrossRefGoogle Scholar
Elliott, R. J., Aggoun, L., and Moore, J. B. (1995). Hidden Markov Models (Appl. Math 29). Springer, New York.Google Scholar
Fernández-Gaucherand, E., Arapostathis, A., and Marcus, S. I. (1993). Analysis of an adaptive control scheme for a partially observed controlled Markov chain. IEEE Trans. Automatic Control 38, 987–993.Google Scholar
Holst, U., and Lindgren, G. (1991). Recursive estimation in mixture models with Markov regime. IEEE Trans. Inf. Theory 37, 1683–1690.Google Scholar
Hontelez, J. A. M., Burger, H. H., and Wijnmalen, J. D. (1996). Optimum condition-based maintenance policies for deteriorating systems with partial information. Reliability Eng. System Safety 51, 267–274.Google Scholar
Jensen, U., and Hsu, G. H. (1993). Optimal stopping by means of point process observations with applications in reliability. Math. Operat. Res. 18, 645–657.CrossRefGoogle Scholar
Krishnamurthy, V., and Moore, J. B. (1993). On-line estimation of hidden Markov model parameters based on the Kullback–Leibler Information measure. IEEE Trans. Signal Process. 41, 2557–2573.Google Scholar
Li, X., and Tang, S. (1995). General necessary conditions for partially observed optimal stochastic controls. J. Appl. Prob. 32, 1118–1137.CrossRefGoogle Scholar
Lin, D., and Makis, V. (2003). Recursive filters for a partially observable system subject to random failure. Adv. Appl. Prob. 35, 207–227.Google Scholar
Lin, D., and Makis, V. (2003). Filters and parameter estimation for a partially observable system subject to random failure with continuous-range observations. Submitted.Google Scholar
Ljung, L. and Söderström, T. (1983). Theory and Practice of Recursive Identification. MIT Press, Cambridge, MA.Google Scholar
Lototsky, S. V., and Rozovskii, B. L. (1998). Recursive nonlinear filter for a continuous discrete-time model: separation of parameters and observations. IEEE Trans. Automatic Control 43, 1154–1158.Google Scholar
Makis, V., and Jardine, A. K. S. (1992). Optimal replacement in the proportional hazards model. INFOR 30, 172–183.Google Scholar
Makis, V., Jiang, X., and Jardine, A. K. S. (1998). A condition-based maintenance model. IMA J. Math. Appl. Business Industry 9, 201–210.Google Scholar
Miller, A. J. (1999). A new wavelet basis for the decomposition of gear motion error signals and its application to gearbox diagnostics. Masters Thesis, Pennsylvania State University.Google Scholar
Nielsen, J. N., Madsen, H., and Young, P. C. (2000). Parameter estimation in stochastic differential equations: an overview. Ann. Rev. Control 24, 83–94.Google Scholar
Sondik, E. J. (1971). The optimal control of partially observable Markov processes. Doctoral Thesis, Stanford University.Google Scholar
Stadje, W. (1994). Maximal wearing-out of a deteriorating system. Europ. J. Operat. Res. 73, 472–479.Google Scholar
White, C. C. (1979). Optimal control-limit strategies for a partially observed replacement problem. Internat. J. System Sci. 10, 321–331.Google Scholar