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**A novel approach to equipment health management based on auto-regressive hidden semi-Markov model (AR-HSMM).**
*(English)*
Zbl 1172.62332

Summary: As a new maintenance method, CBM (condition based maintenance) is becoming more and more important for the health management of complicated and costly equipments. A prerequisite to widespread deployment of CBM technology and practice in industry is effective diagnostics and prognostics. Recently, a pattern recognition technique called HMM (hidden Markov model) was widely used in many fields. However, due to some unrealistic assumptions, diagnositic results from HMM were not so good, and it was difficult to use HMM directly for prognosis. By relaxing the unrealistic assumptions in HMM, this paper presents a novel approach to equipment health management based on auto-regressive hidden semi-Markov model (AR-HSMM). Compared with HMM, AR-HSMM has three advantages: 1) It allows explicitly modeling the time duration of the hidden states and therefore is capable of prognosis. 2) It can relax observations’ independence assumption by accommodating a link between consecutive observations. 3) It does not follow the unrealistic Markov chain’s memoryless assumption and therefore provides more powerful modeling and analysis capability for real problems. To facilitate the computation in the proposed AR-HSMM-based diagnostics and prognostics, new forward-backward variables are defined and a modified forward-backward algorithm is developed. The evaluation of the proposed methodology was carried out through a real world application case study: health diagnosis and prognosis of hydraulic pumps in Caterpillar Inc. The testing results show that the proposed new approach based on AR-HSMM is effective and can provide useful support for the decision-making in equipment health management.

### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62J99 | Linear inference, regression |

62M99 | Inference from stochastic processes |

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\textit{M. Dong}, Sci. China, Ser. F 51, No. 9, 1291--1304 (2008; Zbl 1172.62332)

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### References:

[1] | Bunks C, Mccarthy D, Tarik A. Condition based maintenance of machines using hidden Markov models. Mech Syst Sig Proc, 2000, 14: 597–612 |

[2] | Rabiner L R. A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE, 1989, 77: 257–286 |

[3] | Baruah P, Chinnam R B. HMMs for diagnostics and prognostics in machining processes. In: Proceedings of the 57th Society for Machine Failure Prevention Technology Conference, 2003. 389–398 · Zbl 1068.90554 |

[4] | Ljolie A, Levinson S E. Development of an acoustic-phonetic hidden Markov model for continuous speech recognition. IEEE Trans Sig Proc, 1991, 39: 29–39 |

[5] | Ostendorf M. Stochastic segment model for phoneme-based continuous speech recognition. IEEE Trans Acous, Speech, Sig Proc, 1989, 37: 1857–1869 |

[6] | Kannan A, Ostendorf, M. Comparison of trajectory and mixture modeling in segment-based word recognition. In: IEEE International Conference on Acoustics, Speech and Signal Processing, 1993. II-327–II-330 |

[7] | Chen M Y, Kundu A, Zhou J. Off-line handwritten work recognition using a hidden Markov model type stochastic network. IEEE Trans Patt Anal Mach Intell, 1994, 16: 481–496 · Zbl 05111426 |

[8] | Chen M Y, Kundu A, Srihari S N. Variable duration hidden Markov model and morphological segmentation for handwritten word recognition. IEEE Trans Image Proc, 1995, 4: 1675–1688 |

[9] | Wang L, Mehrabi M G, Kannatey-Asibu Jr. Hidden Markov model-based tool wear monitoring in machining. ASME J Manufact Sci Eng, 2002, 124: 651–658 |

[10] | Atlas L, Ostendorf M, Bernard G D. Hidden Markov models for monitoring machining tool-wear. In: IEEE International Conference on Acoustics, Speech and Signal Processing, 2000. 3887–3890 |

[11] | Ertunc H M, Loparo K A. A decision fusion algorithm for tool wear condition monitoring in drilling. Int J Mach Tools Manufact, 2001a, 41: 1347–1362 |

[12] | Ertunc H. M, Loparo K A, Ocak H. Tool wear condition monitoring in drilling operations using hidden Markov models (HMMs). Int J Mach Tools Manufact, 2001b, 41: 1363–1384 |

[13] | Begg C D, Merdes T, Byington, C, et al. Dynamic modeling for mechanical diagnostics and prognostics. In: Proceedings of Maintenance and Reliability Conference, 1999. 2201–2213 |

[14] | Roemer M J, Kacprzynski G J. Advanced diagnostics and prognostics for gas turbine engine risk assessment. In: Proceedings of the 2000 IEEE Aerospace Conference, 2000. 345–354 |

[15] | Roemer M J, Nwadiogbu E O, Bloor G. Development of diagnostic and prognostic technologies for aerospace health management applications. In: Proceedings of the 2001 IEEE Aerospace Conference, 2001. 63139–63147 |

[16] | Dong M, He D. A segmental hidden semi-Markov model (HSMM)-based diagnostics and prognostics framework and methodology. Mech Syst Sig Proc, 2007, 21: 2248–2266 |

[17] | Dong M, He D. Hidden semi-Markov model based methodology for multi-sensor equipment health diagnosis and prognosis. Europ J Oper Res, 2007, 178: 858–878 · Zbl 1163.90784 |

[18] | Dong M, He D, Banerjee P, et al. Equipment diagnosis and prognosis using hidden semi-Markov models. Int J Adv Manufact Tech, 2006, 30: 738–749 |

[19] | Ferguson J D. Variable duration models for speech. In: Proc. of the Symposium on the Application of Hidden Markov Models to Text and Speech, 1980. 143–179 |

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