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

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.

[1]  Georg Lindgren,et al.  Recursive estimation in mixture models with Markov regime , 1991, IEEE Trans. Inf. Theory.

[2]  Xiaoyue Jiang,et al.  A condition-based maintenance model , 1998 .

[3]  C. White.  Optimal control-limit strategies for a partially observed replacement problem† , 1979 .

[4]  Ari Arapostathis,et al.  Analysis of an adaptive control scheme for a partially observed controlled Markov chain , 1990 .

[5]  Edward J. Sondik,et al.  The optimal control of par-tially observable Markov processes , 1971 .

[6]  Wolfgang Stadje,et al.  Maximal wearing-out of a deteriorating system: An optimal stopping approach , 1994 .

[7]  Iain B. Collings,et al.  A new maximum likelihood gradient algorithm for on-line hidden Markov model identification , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[8]  Jan Nygaard Nielsen,et al.  Parameter estimation in stochastic differential equations: An overview , 2000 .

[9]  Diederik J.D. Wijnmalen,et al.  Optimum condition-based maintenance policies for deteriorating systems with partial information , 1996 .

[10]  John B. Moore,et al.  On-line estimation of hidden Markov model parameters based on the Kullback-Leibler information measure , 1993, IEEE Trans. Signal Process..

[11]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[12]  Terje Aven.  Condition based replacement policiesa counting process approach , 1996 .

[13]  Subhash Challa,et al.  Nonlinear filter design using Fokker-Planck-Kolmogorov probability density evolutions , 2000, IEEE Trans. Aerosp. Electron. Syst..

[14]  John B. Moore,et al.  On-line identification of hidden Markov models via recursive prediction error techniques , 1994, IEEE Trans. Signal Process..

[15]  S. Eddy.  Hidden Markov models. , 1996, Current opinion in structural biology.

[16]  Boris Rozovskii,et al.  Recursive Nonlinear Filter for a Continuous-Discrete Time Model: Separation of Parameters and Observations , 1998 .

[17]  A. H. Christer,et al.  A state space condition monitoring model for furnace erosion prediction and replacement , 1997 .

[18]  Viliam Makis,et al.  Optimal Replacement In The Proportional Hazards Model , 1992 .

[19]  Guang-Hui Hsu,et al.  Optimal Stopping by Means of Point Process Observations with Applications in Reliability , 1993, Math. Oper. Res..

[20]  Carey Bunks,et al.  CONDITION-BASED MAINTENANCE OF MACHINES USING HIDDEN MARKOV MODELS , 2000 .

[21]  Viliam Makis,et al.  Filters and parameter estimation for a partially observable system subject to random failure with continuous-range observations , 2004, Advances in Applied Probability.

[22]  V. Makis,et al.  Recursive filters for a partially observable system subject to random failure , 2003, Advances in Applied Probability.

[23]  Shanjian Tang,et al.  General necessary conditions for partially observed optimal stochastic controls , 1995, Journal of Applied Probability.