Remaining Useful Life Prediction Using Elliptical Basis Function Network and Markov Chain
Abstract:This paper presents a novel method for remaining
useful life prediction using the Elliptical Basis Function (EBF)
network and a Markov chain. The EBF structure is trained by a
modified Expectation-Maximization (EM) algorithm in order to take
into account the missing covariate set. No explicit extrapolation is
needed for internal covariates while a Markov chain is constructed to
represent the evolution of external covariates in the study. The
estimated external and the unknown internal covariates constitute an
incomplete covariate set which are then used and analyzed by the EBF
network to provide survival information of the asset. It is shown in the
case study that the method slightly underestimates the remaining
useful life of an asset which is a desirable result for early maintenance
decision and resource planning.
 H. Liao, W. Zhao, and H. Guo "Predicting remaining useful life of an
individual unit using proportional hazards model and logistic regression
model," in 2006 Annual Reliability and Maintainability Symposium.
RAMS '06., pp. 127-132.
 D. Kumar, B. Westberg, "Some reliability models for analysing the effects
of operating conditions," International Journal of Reliability, Quality and
Safety Engineering, vol. 4, pp. 133-148, 1997.
 D. R. Cox, "Regression models and life tables (with discussion),"
Journal of the Royal Statistical Society. Series B (Methodological), vol.
34, no. 2, pp. 187-220, 1972.
 D. R. Cox, D. Oakes, Analysis of survival data. Chapman & Hall/CRC,
 Y. Sun, L. Ma, J. Mathew, W. Wang, and S. Zhang, "Mechanical systems
hazard estimation using condition monitoring," Mechanical Systems and
Signal Processing, vol. 20, no. 5, pp. 1189-1201, 2006.
 Y. Shao, K. Nezu, "Prognosis of remaining bearing life using neural
networks," Proceedings of the Institution of Mechanical Engineers, Part
I: Journal of Systems and Control Engineering, vol. 214, no. 3, pp.
 P. W. Tse, D. P. Atherton, "Prediction of machine deterioration using
vibration based fault trends and recurrent neural networks," Journal of
Vibration and Acoustics, vol. 121, no. 3, pp. 355-343, 1999.
 J. D. Kalbeisch, R. L. Prentice, The statistical analysis of failure time
data. New York: Wiley, 1980.
 C. M. Bishop, Neural networks for pattern recognition. Oxford Univ Pr,
 Y. Yu, L. Ma, Y. Sun, and Y. Gu "Handling Incomplete Data In Survival
Analysis With Multiple Covariates," in 2010 Proceedings of the 5rd
World Congress on Engineering Asset Management and Intelligent
Maintenance Systems., to be published.
 M. T. Musavi, W. Ahmed, K. H. Chan, K. B. Faris, and D. M. Hummels,
"On the training of radial basis function classifiers," Neural Networks,
vol. 5, no. 4, pp. 595-603, 1992.
 M. W. Mak, C.K. Li, "Elliptical basis function networks and radial basis
function networks for speaker verification: A comparative study," in 1999
International Joint Conference on Neural Networks (IJCNN'99), pp.
 A. P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum likelihood from
incomplete data via the EM algorithm," Journal of the Royal Statistical
Society. Series B (Methodological), vol. 39, no. 1, pp. 1-38, 1977.
 G.J. McLachlan, T. Krishnan, The EM algorithm and extensions. New
York: Wiley, 1997.
 Z. Ghahramani, M. I. Jordan, "Supervised learning from incomplete data
via an EM approach," in Advances in neural information processing
systems 6, J. D. Cowan, G. Tesauro, and J. Alspector, Ed. Morgan
Kaufmann, 1995, pp. 120-127.
 W. Wang, "A model to predict the residual life of rolling element bearings
given monitored condition information to date," IMA Journal of
Management Mathematics, vol. 13, no. 1, pp. 3-16, 2002.
 B. Craig, P. Sendi, "Estimation of the transition matrix of a discrete-time
Markov chain," Health Economics, vol. 11, no. 1, pp. 33-42, 2002.
 H. Yeh, W. Chan, E. Symanski, and B. Davis, "Estimating Transition
Probabilities for Ignorable Intermittent Missing Data in a Discrete-Time
Markov Chain," Communications in Statistics-Simulation and
Computation, vol. 39, no. 2, pp. 433-448, 2010.
 R. Dybowski, "Classification of incomplete feature vectors by radial basis
function networks," Pattern Recognition Letters, vol. 19, no. 14, pp.
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