{"title":"Remaining Useful Life Prediction Using Elliptical Basis Function Network and Markov Chain","authors":"Yi Yu, Lin Ma, Yong Sun, Yuantong Gu","volume":47,"journal":"International Journal of Computer and Information Engineering","pagesStart":1741,"pagesEnd":1746,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/5372","abstract":"This paper presents a novel method for remaining\nuseful life prediction using the Elliptical Basis Function (EBF)\nnetwork and a Markov chain. The EBF structure is trained by a\nmodified Expectation-Maximization (EM) algorithm in order to take\ninto account the missing covariate set. No explicit extrapolation is\nneeded for internal covariates while a Markov chain is constructed to\nrepresent the evolution of external covariates in the study. The\nestimated external and the unknown internal covariates constitute an\nincomplete covariate set which are then used and analyzed by the EBF\nnetwork to provide survival information of the asset. It is shown in the\ncase study that the method slightly underestimates the remaining\nuseful life of an asset which is a desirable result for early maintenance\ndecision and resource planning.","references":"[1] H. Liao, W. Zhao, and H. Guo \"Predicting remaining useful life of an\nindividual unit using proportional hazards model and logistic regression\nmodel,\" in 2006 Annual Reliability and Maintainability Symposium.\nRAMS '06., pp. 127-132.\n[2] D. Kumar, B. Westberg, \"Some reliability models for analysing the effects\nof operating conditions,\" International Journal of Reliability, Quality and\nSafety Engineering, vol. 4, pp. 133-148, 1997.\n[3] D. R. Cox, \"Regression models and life tables (with discussion),\"\nJournal of the Royal Statistical Society. Series B (Methodological), vol.\n34, no. 2, pp. 187-220, 1972.\n[4] D. R. Cox, D. Oakes, Analysis of survival data. Chapman & Hall\/CRC,\n1984.\n[5] Y. Sun, L. Ma, J. Mathew, W. Wang, and S. Zhang, \"Mechanical systems\nhazard estimation using condition monitoring,\" Mechanical Systems and\nSignal Processing, vol. 20, no. 5, pp. 1189-1201, 2006.\n[6] Y. Shao, K. Nezu, \"Prognosis of remaining bearing life using neural\nnetworks,\" Proceedings of the Institution of Mechanical Engineers, Part\nI: Journal of Systems and Control Engineering, vol. 214, no. 3, pp.\n217-230, 2000.\n[7] P. W. Tse, D. P. Atherton, \"Prediction of machine deterioration using\nvibration based fault trends and recurrent neural networks,\" Journal of\nVibration and Acoustics, vol. 121, no. 3, pp. 355-343, 1999.\n[8] J. D. Kalbeisch, R. L. Prentice, The statistical analysis of failure time\ndata. New York: Wiley, 1980.\n[9] C. M. Bishop, Neural networks for pattern recognition. Oxford Univ Pr,\n2005.\n[10] Y. Yu, L. Ma, Y. Sun, and Y. Gu \"Handling Incomplete Data In Survival\nAnalysis With Multiple Covariates,\" in 2010 Proceedings of the 5rd\nWorld Congress on Engineering Asset Management and Intelligent\nMaintenance Systems., to be published.\n[11] M. T. Musavi, W. Ahmed, K. H. Chan, K. B. Faris, and D. M. Hummels,\n\"On the training of radial basis function classifiers,\" Neural Networks,\nvol. 5, no. 4, pp. 595-603, 1992.\n[12] M. W. Mak, C.K. Li, \"Elliptical basis function networks and radial basis\nfunction networks for speaker verification: A comparative study,\" in 1999\nInternational Joint Conference on Neural Networks (IJCNN'99), pp.\n3034-3039.\n[13] A. P. Dempster, N.M. Laird, and D.B. Rubin, \"Maximum likelihood from\nincomplete data via the EM algorithm,\" Journal of the Royal Statistical\nSociety. Series B (Methodological), vol. 39, no. 1, pp. 1-38, 1977.\n[14] G.J. McLachlan, T. Krishnan, The EM algorithm and extensions. New\nYork: Wiley, 1997.\n[15] Z. Ghahramani, M. I. Jordan, \"Supervised learning from incomplete data\nvia an EM approach,\" in Advances in neural information processing\nsystems 6, J. D. Cowan, G. Tesauro, and J. Alspector, Ed. Morgan\nKaufmann, 1995, pp. 120-127.\n[16] W. Wang, \"A model to predict the residual life of rolling element bearings\ngiven monitored condition information to date,\" IMA Journal of\nManagement Mathematics, vol. 13, no. 1, pp. 3-16, 2002.\n[17] B. Craig, P. Sendi, \"Estimation of the transition matrix of a discrete-time\nMarkov chain,\" Health Economics, vol. 11, no. 1, pp. 33-42, 2002.\n[18] H. Yeh, W. Chan, E. Symanski, and B. Davis, \"Estimating Transition\nProbabilities for Ignorable Intermittent Missing Data in a Discrete-Time\nMarkov Chain,\" Communications in Statistics-Simulation and\nComputation, vol. 39, no. 2, pp. 433-448, 2010.\n[19] R. Dybowski, \"Classification of incomplete feature vectors by radial basis\nfunction networks,\" Pattern Recognition Letters, vol. 19, no. 14, pp.\n1257-1264, 1998.\n[20] PHM, Available from:\nhttp:\/\/www.phmconf.org\/jOCS\/index.php\/phm\/2008\/challenge.2008.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 47, 2010"}