Hidden semi-markov models for predictive maintenance

Mathematical Problems in Engineering

Volumn 2015, Issue , 2015, Pages

  Cartella, Francesco ^a   Lemeire, Jan ^a   Dimiccoli, Luca ^a   Sahli, Hichem ^a,b  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b IMEC   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONDITION MONITORING; INFERENCE ENGINES; MAINTENANCE; MARKOV PROCESSES; STATISTICAL TESTS;

AKAIKE INFORMATION CRITERION; AUTOMATIC MODEL SELECTION; AVERAGE ABSOLUTE ERROR; DISCRETE OBSERVATIONS; HIDDEN SEMI-MARKOV MODELS; INDUSTRIAL MACHINES; PREDICTION ALGORITHMS; PREDICTIVE MAINTENANCE;

HIDDEN MARKOV MODELS;

EID: 84924567461     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2015/278120     Document Type: Article

References (118)

1. L. Solomon, "Essential elements of maintenance improvement programs," in Proceedings of the IFAC Workshopon Production Control in the Process Industry, Osaka, Japan and Kariya, Japan, October-November 1989, E. Oshima and C. van Rijn, Eds., pp. 195-198, Pergamon Press, Oxford, UK, 1989.
2. T. Honkanen, Modelling industrial maintenance systems and the effects of automatic condition monitoring [Ph.D. dissertation], Helsinki University of Technology, Information and Computer Systems in Automation, 2004.
3. R. Dekker, "Applications of maintenance optimization models: a review and analysis," Reliability Engineering & System Safety, Vol. 51, no. 3, pp. 229-240, 1996.
4. H. Wang, "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Vol. 139, no. 3, pp. 469-489, 2002.
5. AFNOR, "Condition monitoring and diagnostics of machines-prognostics-part 1: generalguidelines," Tech. Rep. NF ISO 13381-1, 2005.
6. F. Salfner, Event-based failure prediction: an extended hidden markov model approach [Ph.D. thesis], Humboldt-Universität zu, Berlin, Germany, 2008.
7. C. Domeniconi, C.-S. Perng, R. Vilalta, and S. Ma, "A classification approach for prediction of target events in temporal sequences," in Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD '02), pp. 125-137, Springer, London, UK, 2002, http://dl.acm.org/citation.cfm?id=645806.670309.
8. K. Medjaher, J.-Y. Moya, and N. Zerhouni, "Failure prognostic by using dynamic Bayesian networks," in Dependable Control of Discrete Systems: 2nd IFAC Workshop on Dependable Control of Discrete Systems (DCDS '09), June 2009, Bari, Italy, M. P. Fanti and M. Dotoli, Eds., Vol. 1, pp. 291-296, International Federation of Accountants, New York, NY, USA, 2009, http://hal.archives-ouvertes.fr/hal-00402938/en/.
9. A. Sfetsos, "Short-term load forecasting with a hybrid clustering algorithm," IEE Proceedings: Generation, Transmission and Distribution, Vol. 150, no. 3, pp. 257-262, 2003.
10. R. Vilalta and S. Ma, "Predicting rare events in temporal domains," in Proceedings of the 2nd IEEE International Conference on Data Mining (ICDM '02), pp. 474-481, December 2002.
11. E. Sutrisno, H. Oh, A. S. S. Vasan, and M. Pecht, "Estimation of remaining useful life of ball bearings using data driven methodologies," in Proceedings of the IEEE Conference on Prognostics and Health Management (PHM '12), pp. 1-7, Denver, Colo, USA, June 2012.
12. K. Goebel, B. Saha, and A. Saxena, "A comparison of three data-driven techniques for prognostics," in Proceedings of the 62nd Meeting of the Society for Machinery Failure Prevention Technology, April 2008.
13. L. R. Rabiner, "Tutorial on hidden Markov models and selected applications in speech recognition," Proceedings of the IEEE, Vol. 77, no. 2, pp. 257-286, 1989.
14. F. Cartella, T. Liu, S. Meganck, J. Lemeire, and H. Sahli, "Online adaptive learning of lef-right continuous HMM for bearings condition assessment," Journal of Physics: Conference Series, Vol. 364, Article ID 012031, 2012, http://iopscience.iop.org/1742-6596/364/1/012031.
15. S. Lee, L. Li, and J. Ni, "Online degradation assessment and adaptive fault detection usingmodified hidden markov model," Journal of Manufacturing Science and Engineering, Vol. 132, no. 2, Article ID 021010, 11 pages, 2010.
16. D. A. Tobon-Mejia, K. Medjaher, N. Zerhouni, and G. Tripot, "A mixture of gaussians hiddenmarkov model for failure diagnostic and prognostic," in Proceedings of the IEEE International Conference on Automation Science and Engineering (CASE '10), pp. 338-343, Toronto, Canada, August 2010.
17. D. A. Tobon-Mejia, K. Medjaher, N. Zerhouni, and G. Tripot, "Estimation of the remaining useful life by using wavelet packet decomposition and HMMs," in Proceedings of the IEEE Aerospace Conference (AERO '11), pp. 1-10, IEEE Computer Society, AIAA, Big Sky, Mont, USA, March 2011.
18. D. A. Tobon-Mejia, K. Medjaher, N. Zerhouni, and G. Tripot, "A data-driven failure prognostics method based on mixture of gaussians hidden markov models," IEEE Transactions on Reliability, Vol. 61, no. 2, pp. 491-503, 2012.
19. K. Medjaher, D. A. Tobon-Mejia, and N. Zerhouni, "Remaining useful life estimation of critical components with application to bearings," IEEE Transactions on Reliability, Vol. 61, no. 2, pp. 292-302, 2012.
20. J. Ferguson, "Variable duration models for speech," in Proceedings of the Symposium on the Application of Hidden Markov Models to Text and Speech, pp. 143-179, October 1980.
21. K. P. Murphy, "Hidden semi-Markov models (hsmms)," Tech. Rep., University of British Columbia, 2002, http://www.cs.ubc.ca/~murphyk.
22. A. Kundu, T. Hines, J. Phillips, B. D. Huyck, and L. C. Van Guilder, "Arabic handwriting recognition using variable duration HMM," in Proceedings of the 9th International Conference on Document Analysis and Recognition (ICDAR '07), Vol. 2, pp. 644-648, IEEE, Washington, DC, USA, September 2007.
23. M. T. Johnson, "Capacity and complexity of HMM duration modeling techniques," IEEE Signal Processing Letters, Vol. 12, no. 5, pp. 407-410, 2005.
24. J.-T. Chien and C.-H. Huang, "Bayesian learning of speech duration models," IEEE Transactions on Speech and Audio Processing, Vol. 11, no. 6, pp. 558-567, 2003.
25. K. Laurila, "Noise robust speech recognition with state duration constraints," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97), Vol. 2, pp. 871-874, IEEE Computer Society, Munich, Germany, April 1997.
26. S.-Z. Yu, "Hidden semi-Markov models," Artificial Intelligence, Vol. 174, no. 2, pp. 215-243, 2010.
27. S.-Z. Yu and H. Kobayashi, "An eficient forward-backward algorithm for an explicit-duration hidden Markov model," IEEE Signal Processing Letters, Vol. 10, no. 1, pp. 11-14, 2003.
28. S.-Z. Yu and H. Kobayashi, "Practical implementation of an eficient forward-backward algorithm for an explicit-duration hidden Markov model," IEEE Transactions on Signal Processing, Vol. 54, no. 5, pp. 1947-1951, 2006.
29. N. Wang, S.-D. Sun, Z.-Q. Cai, S. Zhang, and C. Saygin, "A hidden semi-markov model with duration-dependent state transition probabilities for prognostics," Mathematical Problems in Engineering, Vol. 2014, Article ID 632702, 10 pages, 2014.
30. M. Azimi, P. Nasiopoulos, and R. K. Ward, "Online identification of hidden semi-Markov models," in Proceedings of the 3rd International Symposium on Image and Signal Processing and Analysis (ISPA '03), Vol. 2, pp. 991-996, Rome, Italy, September 2003.
31. M. Azimi, Data transmission schemes for a new generation of interactive digital television [Ph.D. dissertation], Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, Canada, 2008.
32. M. Azimi, P. Nasiopoulos, and R. K. Ward, "Offline and online identification of hidden semi-Markov models," IEEE Transactions on Signal Processing, Vol. 53, no. 8, pp. 2658-2663, 2005.
33. J. Q. Li and A. R. Barron, "Mixture density estimation," in Advances in Neural Information Processing Systems 12, pp. 279-285, MIT Press, Boston, Mass, USA, 1999.
34. M. Dong and D. He, "A segmental hidden semi-Markov model (HSMM)-based diagnostics and prognostics framework and methodology," Mechanical Systems and Signal Processing, Vol. 21, no. 5, pp. 2248-2266, 2007.
35. T. Liu, J. Chen, and G. Dong, "Application of continuous hide markov model to bearing performance degradation assessment," in Proceedings of the 24th International Congress on Condition Monitoring and Diagnostics Engineering Management (COMADEM '11), pp. 166-172, 2011.
36. H. Ocak and K. A. Loparo, "A new bearing fault detection and diagnosis scheme based onhidden markov modeling of vibration signals," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 3141-3144, IEEE Computer Society, Washington, DC, USA, 2001.
37. C. Fraley and A. E. Raftery, "Model-based clustering, discriminant analysis, and density estimation," Journal of the American Statistical Association, Vol. 97, no. 458, pp. 611-631, 2002.
38. K. L. Nylund, T. Asparouhov, and B. O. Muthén, "Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study," Structural Equation Modeling, Vol. 14, no. 4, pp. 535-569, 2007.
39. T. H. Lin and C. M. Dayton, "Model selection information criteria for non-nested latent class models," Journal of Educational and Behavioral Statistics, Vol. 22, no. 3, pp. 249-264, 1997.
40. O. Lukociene and J. K. Vermunt, "Determining the number of components in mixture models for hierarchical data," in Advances in Data Analysis, Data Handling and Business Intelligence, Studies in Classification, Data Analysis, and Knowledge Organization, pp. 241-249, Springer, New York, NY, USA, 2008.
41. O. Cappé, E. Moulines, and T. Ryden, Inference in Hidden Markov Models, Springer Series in Statistics, Springer, New York, NY, USA, 2005.
42. I. L. MacDonald and W. Zucchini, Hidden Markov and Other Models for Discrete-Valued Time Series, Chapman & Hall/CRC, 1997.
43. R. J. MacKay, "Estimating the order of a hidden Markov model," The Canadian Journal of Statistics, Vol. 30, no. 4, pp. 573-589, 2002.
44. S. E. Levinson, "Continuously variable duration hidden Markov models for automatic speechrecognition," Computer Speech and Language, Vol. 1, no. 1, pp. 29-45, 1986.
45. C. D. Mitchell and L. H. Jamieson, "Modeling duration in a hidden Markov model with the exponential family," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '93), Vol. 2, pp. 331-334, Minneapolis, Minn, USA, April 1993.
46. A. Viterbi, "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm," IEEE Transactions on Information Theory, Vol. 13, no. 2, pp. 260-269, 2006.
47. G. D. Forney Jr., "The viterbi algorithm," Proceedings of the IEEE, Vol. 61, no. 3, pp. 268-278, 1973.
48. 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, Vol. 39, no. 1, pp. 1-38, 1977.
49. P. Nectoux, R. Gouriveau, K. Medjaher et al., "Pronostia: an experimental platform for bearings accelerated life test," in Proceedings of the IEEE International Conference on Prognostics and Health Management, Denver, Colo, USA, 2012.
50. P. O'Donnell, "Report of large motor reliability survey of industrial and commercial installations, part I and II," IEEE Transactions on Industry Applications, Vol. 21, no. 4, pp. 853-872, 1985.
51. P. Boškoski, M. Gašperin, D. Petelin, and D. Juričić, "Bearing fault prognostics using Rényi entropy based features and Gaussian process models," Mechanical Systems and Signal Processing, Vol. 52-53, pp. 327-337, 2015.
52. B. Chouri, F. Montero, M. Tabaa, and A. Dandache, "Residual useful life estimation based on stable distribution feature extraction and SVM classifier," Journal of Theoretical and Applied Information Technology, Vol. 55, no. 3, pp. 299-306, 2013.
53. K. Javed, R. Gouriveau, N. Zerhouni, and P. Nectoux, "A feature extraction procedure basedon trigonometric functions and cumulative descriptors to enhance prognostics modeling," in Proceedings of the IEEE Conference on Prognostics and Health Management (PHM '13), pp. 1-7, June 2013.
54. K. Medjaher, N. Zerhouni, and J. Baklouti, "Data-driven prognostics based on health indicatorconstruction: application to pronostia's data," in Proceedings of the 12th European Control Conference (ECC '13), pp. 1451-1456, Zürich, Switzerland, July 2013.
55. A. Mosallam, K. Medjaher, and N. Zerhouni, "Nonparametric time series modelling for industrial prognostics and health management," International Journal of Advanced Manufacturing Technology, Vol. 69, no. 5-8, pp. 1685-1699, 2013.
56. S. Porotsky and Z. Bluvband, "Remaining useful life estimation for systems with non-trendability behaviour," in Proceedings of the IEEE Conference on Prognostics and Health Management (PHM '12), pp. 1-6, Denver, Colo, USA, June 2012.
57. L. Serir, E. Ramasso, and N. Zerhouni, "An evidential evolving prognostic approach and itsapplication to pronostias data streams," in Annual Conference of the Prognostics and Health Management Society, p. 9, 2012.
58. F. Sloukia, M. El Aroussi, H. Medromi, and M. Wahbi, "Bearings prognostic using mixture of gaussians hidden Markov model and support vector machine," in Proceedings of the ACS International Conference on Computer Systems and Applications (AICCSA '13), pp. 1-4, May 2013.
59. B. Zhang, L. Zhang, and J. Xu, "Remaining useful life prediction for rolling element bearing based on ensemble learning," Chemical Engineering Transactions, Vol. 33, pp. 157-162, 2013.
60. L. Solomon, "Essential elements of maintenance improvement programs," in Proceedings of the IFAC Workshopon Production Control in the Process Industry, Osaka, Japan and Kariya, Japan, October-November 1989, E. Oshima and C. van Rijn, Eds., pp. 195-198, Pergamon Press, Oxford, UK, 1989.
61. T. Honkanen, Modelling industrial maintenance systems and the effects of automatic condition monitoring [Ph.D. dissertation], Helsinki University of Technology, Information and Computer Systems in Automation, 2004.
62. R. Dekker, "Applications of maintenance optimization models: a review and analysis," Reliability Engineering & System Safety, Vol. 51, no. 3, pp. 229-240, 1996.
63. H. Wang, "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Vol. 139, no. 3, pp. 469-489, 2002.
64. AFNOR, "Condition monitoring and diagnostics of machines-prognostics-part 1: generalguidelines," Tech. Rep. NF ISO 13381-1, 2005.
65. F. Salfner, Event-based failure prediction: an extended hidden markov model approach [Ph.D. thesis], Humboldt-Universität zu, Berlin, Germany, 2008.
66. C. Domeniconi, C.-S. Perng, R. Vilalta, and S. Ma, "A classification approach for prediction of target events in temporal sequences," in Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD '02), pp. 125-137, Springer, London, UK, 2002, http://dl.acm.org/citation.cfm?id=645806.670309.
67. K. Medjaher, J.-Y. Moya, and N. Zerhouni, "Failure prognostic by using dynamic Bayesian networks," in Dependable Control of Discrete Systems: 2nd IFAC Workshop on Dependable Control of Discrete Systems (DCDS '09), June 2009, Bari, Italy, M. P. Fanti and M. Dotoli, Eds., Vol. 1, pp. 291-296, International Federation of Accountants, New York, NY, USA, 2009, http://hal.archives-ouvertes.fr/hal-00402938/en/.
68. A. Sfetsos, "Short-term load forecasting with a hybrid clustering algorithm," IEE Proceedings: Generation, Transmission and Distribution, Vol. 150, no. 3, pp. 257-262, 2003.
69. R. Vilalta and S. Ma, "Predicting rare events in temporal domains," in Proceedings of the 2nd IEEE International Conference on Data Mining (ICDM '02), pp. 474-481, December 2002.
70. E. Sutrisno, H. Oh, A. S. S. Vasan, and M. Pecht, "Estimation of remaining useful life of ball bearings using data driven methodologies," in Proceedings of the IEEE Conference on Prognostics and Health Management (PHM '12), pp. 1-7, Denver, Colo, USA, June 2012.
71. K. Goebel, B. Saha, and A. Saxena, "A comparison of three data-driven techniques for prognostics," in Proceedings of the 62nd Meeting of the Society for Machinery Failure Prevention Technology, April 2008.
72. L. R. Rabiner, "Tutorial on hidden Markov models and selected applications in speech recognition," Proceedings of the IEEE, Vol. 77, no. 2, pp. 257-286, 1989.
73. F. Cartella, T. Liu, S. Meganck, J. Lemeire, and H. Sahli, "Online adaptive learning of lef-right continuous HMM for bearings condition assessment," Journal of Physics: Conference Series, Vol. 364, Article ID 012031, 2012, http://iopscience.iop.org/1742-6596/364/1/012031.
74. S. Lee, L. Li, and J. Ni, "Online degradation assessment and adaptive fault detection usingmodified hidden markov model," Journal of Manufacturing Science and Engineering, Vol. 132, no. 2, Article ID 021010, 11 pages, 2010.
75. D. A. Tobon-Mejia, K. Medjaher, N. Zerhouni, and G. Tripot, "A mixture of gaussians hiddenmarkov model for failure diagnostic and prognostic," in Proceedings of the IEEE International Conference on Automation Science and Engineering (CASE '10), pp. 338-343, Toronto, Canada, August 2010.
76. D. A. Tobon-Mejia, K. Medjaher, N. Zerhouni, and G. Tripot, "Estimation of the remaining useful life by using wavelet packet decomposition and HMMs," in Proceedings of the IEEE Aerospace Conference (AERO '11), pp. 1-10, IEEE Computer Society, AIAA, Big Sky, Mont, USA, March 2011.
77. D. A. Tobon-Mejia, K. Medjaher, N. Zerhouni, and G. Tripot, "A data-driven failure prognostics method based on mixture of gaussians hidden markov models," IEEE Transactions on Reliability, Vol. 61, no. 2, pp. 491-503, 2012.
78. K. Medjaher, D. A. Tobon-Mejia, and N. Zerhouni, "Remaining useful life estimation of critical components with application to bearings," IEEE Transactions on Reliability, Vol. 61, no. 2, pp. 292-302, 2012.
79. J. Ferguson, "Variable duration models for speech," in Proceedings of the Symposium on the Application of Hidden Markov Models to Text and Speech, pp. 143-179, October 1980.
80. K. P. Murphy, "Hidden semi-Markov models (hsmms)," Tech. Rep., University of British Columbia, 2002, http://www.cs.ubc.ca/~murphyk.
81. A. Kundu, T. Hines, J. Phillips, B. D. Huyck, and L. C. Van Guilder, "Arabic handwriting recognition using variable duration HMM," in Proceedings of the 9th International Conference on Document Analysis and Recognition (ICDAR '07), Vol. 2, pp. 644-648, IEEE, Washington, DC, USA, September 2007.
82. M. T. Johnson, "Capacity and complexity of HMM duration modeling techniques," IEEE Signal Processing Letters, Vol. 12, no. 5, pp. 407-410, 2005.
83. J.-T. Chien and C.-H. Huang, "Bayesian learning of speech duration models," IEEE Transactions on Speech and Audio Processing, Vol. 11, no. 6, pp. 558-567, 2003.
84. K. Laurila, "Noise robust speech recognition with state duration constraints," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97), Vol. 2, pp. 871-874, IEEE Computer Society, Munich, Germany, April 1997.
85. S.-Z. Yu, "Hidden semi-Markov models," Artificial Intelligence, Vol. 174, no. 2, pp. 215-243, 2010.
86. S.-Z. Yu and H. Kobayashi, "An eficient forward-backward algorithm for an explicit-duration hidden Markov model," IEEE Signal Processing Letters, Vol. 10, no. 1, pp. 11-14, 2003.
87. S.-Z. Yu and H. Kobayashi, "Practical implementation of an eficient forward-backward algorithm for an explicit-duration hidden Markov model," IEEE Transactions on Signal Processing, Vol. 54, no. 5, pp. 1947-1951, 2006.
88. N. Wang, S.-D. Sun, Z.-Q. Cai, S. Zhang, and C. Saygin, "A hidden semi-markov model with duration-dependent state transition probabilities for prognostics," Mathematical Problems in Engineering, Vol. 2014, Article ID 632702, 10 pages, 2014.
89. M. Azimi, P. Nasiopoulos, and R. K. Ward, "Online identification of hidden semi-Markov models," in Proceedings of the 3rd International Symposium on Image and Signal Processing and Analysis (ISPA '03), Vol. 2, pp. 991-996, Rome, Italy, September 2003.
90. M. Azimi, Data transmission schemes for a new generation of interactive digital television [Ph.D. dissertation], Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, Canada, 2008.
91. M. Azimi, P. Nasiopoulos, and R. K. Ward, "Offline and online identification of hidden semi-Markov models," IEEE Transactions on Signal Processing, Vol. 53, no. 8, pp. 2658-2663, 2005.
92. J. Q. Li and A. R. Barron, "Mixture density estimation," in Advances in Neural Information Processing Systems 12, pp. 279-285, MIT Press, Boston, Mass, USA, 1999.
93. M. Dong and D. He, "A segmental hidden semi-Markov model (HSMM)-based diagnostics and prognostics framework and methodology," Mechanical Systems and Signal Processing, Vol. 21, no. 5, pp. 2248-2266, 2007.
94. T. Liu, J. Chen, and G. Dong, "Application of continuous hide markov model to bearing performance degradation assessment," in Proceedings of the 24th International Congress on Condition Monitoring and Diagnostics Engineering Management (COMADEM '11), pp. 166-172, 2011.
95. H. Ocak and K. A. Loparo, "A new bearing fault detection and diagnosis scheme based onhidden markov modeling of vibration signals," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 3141-3144, IEEE Computer Society, Washington, DC, USA, 2001.
96. C. Fraley and A. E. Raftery, "Model-based clustering, discriminant analysis, and density estimation," Journal of the American Statistical Association, Vol. 97, no. 458, pp. 611-631, 2002.
97. K. L. Nylund, T. Asparouhov, and B. O. Muthén, "Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study," Structural Equation Modeling, Vol. 14, no. 4, pp. 535-569, 2007.
98. T. H. Lin and C. M. Dayton, "Model selection information criteria for non-nested latent class models," Journal of Educational and Behavioral Statistics, Vol. 22, no. 3, pp. 249-264, 1997.
99. O. Lukociene and J. K. Vermunt, "Determining the number of components in mixture models for hierarchical data," in Advances in Data Analysis, Data Handling and Business Intelligence, Studies in Classification, Data Analysis, and Knowledge Organization, pp. 241-249, Springer, New York, NY, USA, 2008.
100. O. Cappé, E. Moulines, and T. Ryden, Inference in Hidden Markov Models, Springer Series in Statistics, Springer, New York, NY, USA, 2005.
101. I. L. MacDonald and W. Zucchini, Hidden Markov and Other Models for Discrete-Valued Time Series, Chapman & Hall/CRC, 1997.
102. R. J. MacKay, "Estimating the order of a hidden Markov model," The Canadian Journal of Statistics, Vol. 30, no. 4, pp. 573-589, 2002.
103. S. E. Levinson, "Continuously variable duration hidden Markov models for automatic speechrecognition," Computer Speech and Language, Vol. 1, no. 1, pp. 29-45, 1986.
104. C. D. Mitchell and L. H. Jamieson, "Modeling duration in a hidden Markov model with the exponential family," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '93), Vol. 2, pp. 331-334, Minneapolis, Minn, USA, April 1993.
105. A. Viterbi, "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm," IEEE Transactions on Information Theory, Vol. 13, no. 2, pp. 260-269, 2006.
106. G. D. Forney Jr., "The viterbi algorithm," Proceedings of the IEEE, Vol. 61, no. 3, pp. 268-278, 1973.
107. 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, Vol. 39, no. 1, pp. 1-38, 1977.
108. P. Nectoux, R. Gouriveau, K. Medjaher et al., "Pronostia: an experimental platform for bearings accelerated life test," in Proceedings of the IEEE International Conference on Prognostics and Health Management, Denver, Colo, USA, 2012.
109. P. O'Donnell, "Report of large motor reliability survey of industrial and commercial installations, part I and II," IEEE Transactions on Industry Applications, Vol. 21, no. 4, pp. 853-872, 1985.
110. P. Boškoski, M. Gašperin, D. Petelin, and D. Juričić, "Bearing fault prognostics using Rényi entropy based features and Gaussian process models," Mechanical Systems and Signal Processing, Vol. 52-53, pp. 327-337, 2015.
111. B. Chouri, F. Montero, M. Tabaa, and A. Dandache, "Residual useful life estimation based on stable distribution feature extraction and SVM classifier," Journal of Theoretical and Applied Information Technology, Vol. 55, no. 3, pp. 299-306, 2013.
112. K. Javed, R. Gouriveau, N. Zerhouni, and P. Nectoux, "A feature extraction procedure basedon trigonometric functions and cumulative descriptors to enhance prognostics modeling," in Proceedings of the IEEE Conference on Prognostics and Health Management (PHM '13), pp. 1-7, June 2013.
113. K. Medjaher, N. Zerhouni, and J. Baklouti, "Data-driven prognostics based on health indicatorconstruction: application to pronostia's data," in Proceedings of the 12th European Control Conference (ECC '13), pp. 1451-1456, Zürich, Switzerland, July 2013.
114. A. Mosallam, K. Medjaher, and N. Zerhouni, "Nonparametric time series modelling for industrial prognostics and health management," International Journal of Advanced Manufacturing Technology, Vol. 69, no. 5-8, pp. 1685-1699, 2013.
115. S. Porotsky and Z. Bluvband, "Remaining useful life estimation for systems with non-trendability behaviour," in Proceedings of the IEEE Conference on Prognostics and Health Management (PHM '12), pp. 1-6, Denver, Colo, USA, June 2012.
116. L. Serir, E. Ramasso, and N. Zerhouni, "An evidential evolving prognostic approach and itsapplication to pronostias data streams," in Annual Conference of the Prognostics and Health Management Society, p. 9, 2012.
117. F. Sloukia, M. El Aroussi, H. Medromi, and M. Wahbi, "Bearings prognostic using mixture of gaussians hidden Markov model and support vector machine," in Proceedings of the ACS International Conference on Computer Systems and Applications (AICCSA '13), pp. 1-4, May 2013.
118. B. Zhang, L. Zhang, and J. Xu, "Remaining useful life prediction for rolling element bearing based on ensemble learning," Chemical Engineering Transactions, Vol. 33, pp. 157-162, 2013.