Ascertainment-adjusted parameter estimation approach to improve robustness against misspecification of health monitoring methods

Abstract

Condition monitoring aims at ensuring system safety which is a fundamental requirement for industrial applications and that has become an inescapable social demand. This objective is attained by instrumenting the system and developing data analytics methods such as statistical models able to turn data into relevant knowledge. One difficulty is to be able to correctly estimate the parameters of those methods based on time-series data. This paper suggests the use of the Weighted Distribution Theory together with the Expectation-Maximization algorithm to improve parameter estimation in statistical models with latent variables with an application to health monotonic under uncertainty. The improvement of estimates is made possible by incorporating uncertain and possibly noisy prior knowledge on latent variables in a sound manner. The latent variables are exploited to build a degradation model of dynamical system represented as a sequence of discrete states. Examples on Gaussian Mixture Models, Hidden Markov Models (HMM) with discrete and continuous outputs are presented on both simulated data and benchmarks using the turbofan engine datasets. A focus on the application of a discrete HMM to health monitoring under uncertainty allows to emphasize the interest of the proposed approach in presence of different operating conditions and fault modes. It is shown that the proposed model depicts high robustness in presence of noisy and uncertain prior.

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

“…In order to estimate the parameters of an ARPHMM in a sound manner when some prior knowledge W about the hidden states is available, we suggest an approach using the TWD described by Patil [23] and we derive the optimal solution in terms of maximum likelihood. It follows a similar reasoning to [24,27] and has connections with [22].…”

“…The integration of the prior suggested in this paper for ARHMM is based on the Theory of Weighted Distributions (TWD) [23] which is compatible with the Expectation-Maximization (EM) algorithm in the sense that the convergence properties are still satisfied. It makes use of concepts initially developed by [17,22] based on Dempster-Shafer's theory of belief functions and of [24] using the TWD to include prior in EM-based learning procedures.…”

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

“…In order to estimate the parameters of an ARPHMM in a sound manner when some prior knowledge W about the hidden states is available, we suggest an approach using the TWD described by Patil (Patil, 2002) and we derive the optimal solution in terms of maximum likelihood. It follows a similar reasoning to (Juesas & Ramasso, 2016;Ramasso, 2014) and has connections with (Denoeux, 2013).…”

“…The integration of the prior suggested in this paper for ARHMM is based on the Theory of Weighted Distributions (TWD) (Patil, 2002) which is compatible with the Expectation-Maximization (EM) algorithm in the sense that the convergence properties are still satisfied. It makes use of concepts initially developed by (Côme et al, 2009;Denoeux, 2013) based on Dempster-Shafer's theory of belief functions and of (Juesas & Ramasso, 2016) using the TWD to include prior in EM-based learning procedures.…”

Partially Hidden Markov Chain Multivariate Linear Autoregressive model: inference and forecasting—application to machine health prognostics

“…We used the regression model specific to each timestep, to estimate ĤI (i) t . Afterwards, operational states were obtained by segmenting the estimated HI, following the method presented in and used in (Juesas & Ramasso, 2016). We considered four operational states: healthy, intermediate, faulty and failure denoted by 1, 2, 3 and 4, respectively.…”