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[This paper was initially published in PHME conference in 2016, selected forfurther publication in International Journal of Prognostics and HealthManagement.]  This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM)for fault detection and prognostics of equipments based on sensors' data. It isa particular dynamic Bayesian network that allows to represent the dynamics ofa 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 forthbetween internal states while the AR process ensures a temporal coherence onsensor measurements. A sound learning procedure of standard ARHMM based onmaximum likelihood allows to iteratively estimate all parameterssimultaneously. This paper suggests a modification of the learning procedureconsidering that one may have prior knowledge about the structure which becomespartially hidden. The integration of the prior is based on the Theory ofWeighted Distributions which is compatible with the Expectation-Maximizationalgorithm in the sense that the convergence properties are still satisfied. Weshow how to apply this model to estimate the remaining useful life based onhealth indicators. The autoregressive parameters can indeed be used forprediction while the latent structure can be used to get information about thedegradation level. The interest of the proposed method for prognostics andhealth assessment is demonstrated on CMAPSS datasets.

Autoregressive Hidden Markov Models with partial knowledge on latent space applied to aero-engines prognostics