Similarity learning hidden semi-Markov model for adaptive prognostics of composite structures

Nick Eleftheroglou*, Georgios Galanopoulos, Theodoros Loutas

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Data-driven methodologies have found increasing usage in the last decade for remaining useful life (RUL) prognostics of composite materials utilizing structural health monitoring (SHM) data. Of particular interest is the reliable RUL prediction in cases where the end-of-life is not in between the extreme values within the testing dataset. For example, when unexpected phenomena that severely compromise the structural integrity occur during the service life. Such cases are often referred as outliers and the RUL prognosis based on a data-driven model that learns from past data is often erroneous. This study addresses this challenge by proposing a new stochastic model; the Similarity Learning Hidden Semi Markov Model (SLHSMM), an extension of the Non-Homogenous Hidden Semi Markov Model (NHHSMM). Through the utilization of a nonparametric discrete distribution, which characterizes the similarity between the testing structure and the training structures, a dynamic re-estimation process is employed. This process assigns higher importance to the training structures that display greater similarity to the testing one. As a result, the estimated parameters effectively capture the specific characteristics of the testing structure. The training and testing SHM data sets consist of strain measurements collected from a case study where carbon–epoxy single-stringered panels, are subjected to constant, variable, and random amplitude fatigue loading until failure. RUL estimations from the SLHSMM, the NHHSMM, and the Gaussian Process Regression (GPR) are compared. The SLHSMM clearly outperforms its classical counterpart and GPR providing more accurate outlier and inlier prognostics, demonstrating its capability to adapt to unexpected phenomena and integrate unforeseen data into a prognostic platform.

Original languageEnglish
Article number109808
Number of pages17
JournalReliability Engineering and System Safety
Publication statusPublished - 2024


The research work was supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “First Call for H.F.R.I. Research Projects to support Faculty members and Researchers and the procurement of high-cost research equipment grant” (Project Number: 2573).


  • Adaptive prognostics
  • Composites
  • HSMM
  • Markov models
  • PHM
  • Prognostics
  • Remaining useful life


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