Prognostic considering missing data: An input output hidden Markov model based solution

Kamrul Islam Shahin*, Christophe Simon, Philippe Weber, Aslak Johansen, Mikkel Baun Kjaergaard

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


The remaining useful life of a system is unknown and uncertain due to the uncertainty of system failure. However, by monitoring the behaviour of the system, it is possible to predict the current health and also the near future health states. To make a correct prognostic, we need to understand the degradation process of similar systems from the historical data, which is often not easy to collect in huge amount because the degradation process is a slow progression. A complete sequence requires collecting data from the beginning of a system’s operation until its death or failure. However, in reality, most deployments will have to deal with missing data, misreading or sensor saturation. This paper works on handling the missing data for improving the model training by extracting as much information as possible even from the incomplete sequences. In this paper, we propose an IOHMM-based missing data processing method, which is shown to provide better results compared to the list deletion method. A bootstrap method is developed that resamples using replacement sequences picked by the learning algorithms. Two well-known learning algorithms: the Baum Welch and the forward-backward algorithm are adapted to handle the missing data. A numerical application is simulated to demonstrate the role of the proposed algorithm and the corresponding model performance in RUL prediction, which is the basis of the RUL management.

Original languageEnglish
JournalProceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
Issue number5
Pages (from-to)980-993
Publication statusPublished - Oct 2023


  • Degradation
  • diagnostic
  • remaining useful life
  • missing data
  • operating condition
  • PHM


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