On partially supervised learning and inference in dynamic Bayesian networks for prognostics with uncertain factual evidence: Illustration with Markov switching models



Pablo Juesas Emmanuel Ramasso Sébastien Drujont Vincent Placet


This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors’ data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in
the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

How to Cite

Juesas, P., Ramasso, E., Drujont, S., & Placet, V. (2016). On partially supervised learning and inference in dynamic Bayesian networks for prognostics with uncertain factual evidence: Illustration with Markov switching models. PHM Society European Conference, 3(1). https://doi.org/10.36001/phme.2016.v3i1.1642
Abstract 41 | PDF Downloads 29



CMAPSS datasets, Hidden Markov Model, Markov switching, Autoregressive process, Theory of Weighted Distributions

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