New Look at Bayesian Prognostic Methods

Online remaining useful life (RUL) prediction is a core function of prognostics and health management (PHM), which provides solutions for comprehensive and personalised system management. RUL is realised by extrapolating timely updated prognostic models to reach a user-defined failure threshold. As of today, there are mainly two kinds of Bayesian prognostic methods. The first kind of Bayesian prognostic methods are Bayesian regression prognostic methods that directly use Bayes’ theorem to update degradation model parameters. The second kind of Bayesian prognostic methods is Bayesian state-space prognostic methods that firstly reformulate a degradation model by using state-space representation and consequently update state-space model parameters with Bayes’ theorem. However, comparisons of these two kinds of Bayesian prognostic methods have not been actively explored and discussed in a unified paper. In this study, similarities and differences between Bayesian regression prognostic methods and Bayesian state-space prognostic methods under the assumptions of additive Gaussian and Brownian motion errors were explored to enrich the PHM domain. A significant difference was observed between Bayesian regression prognostic methods and Bayesian state-space prognostic methods under different error assumptions. Experimental results showed that Bayesian state-space prognostic methods have greater RUL prediction uncertainties in two run-to-failure cases with different fluctuation strengths. However, under the assumption of Gaussian errors, because of the good ability of degradation tracking, Bayesian state-space prognostic methods may predict worse than Bayesian regression prognostic methods in a strong fluctuation dataset, which is not evident in the situation of Brownian motion errors. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i>—The Bayesian update of model parameters considering online condition monitoring data is of great practical significance for describing individual degradation and RUL prediction. Practitioners need to know the similarities and differences between different Bayesian prognostic methods, as well as how to choose an appropriate Bayesian prognostic method for a specific predicted objective that practitioners care about. This paper introduces the similarities and differences between several classic Bayesian prognostic methods, and provides their performance comparisons in different RUL prediction scenarios, providing a reference for practitioners to use Bayesian model parameters updating to predict individual RUL.