A Particle Filtering Based Approach for Gear Prognostics

Introduction

Recently, applications of particle filtering to prognostics have been reported in the literature, for example, remaining useful life (RUL) predication of a mechanical component subject to fatigue crack growth (Zio and Peloni, 2011), on-line failure prognosis of UH-60 planetary carrier plate subject to axial crack growth (Orchard and Vachtsevanos, 2011), degradation prediction of thermal processing unit in semiconductor manufacturing (Butler and Ringwood, 2010), and prediction of lithium-ion battery capacity depletion (Saba et al., 2009). The reported application results have shown that particle filtering represents a potentially powerful prognostics tool due to its capability in handling non-linear dynamic systems and non-Gaussian noises using efficient sequential importance sampling to approximate the future state probability distributions. Particle filtering was developed as an effective on-line state estimation tool (see Doucet et al., 2000; Arulampalam et al., 2002). In order to apply particle filtering to RUL prediction of a mechanical component such as gears, a few practical implementation problems have to be solved: (1) define a state transition function that represents the degradation evolution in time of the component; (2) select the most sensitive health monitoring measures or condition indicators (CIs) and define a measurement function that represents the relationship between the degradation state of the component and the CIs; (3) define an effective l-step ahead RUL estimator. In solving the first problem, research on using particle filtering for mechanical component RUL prognostics has used Paris’ law to define the state transition function (Zio and Peloni, 2011; Orchard and Vachtsevanos, 2011). As an empirical model, Paris’ law can be effective for defining a state transition function that represents a degradation state subject to fatigue crack growth. For other type of failure modes such as pitting and corrosion, effective alternatives for defining the state transition function should be explored. Regarding the second problem, on the surface, it doesn’t seem to be a problem to use multiple CIs to define a measurement function for particle filtering as it allows information from multiple measurement sources to be fused in a logical manner (Zio and Peloni, 2011). In particle filtering, measurements are collected and used to update the prior state distribution via Bayes rule so as to obtain the required posterior state distribution. Subsequently, various kinds of uncertainties arise from different sources that are correlated. In most real applications, no single CI is sensitive to every failure mode of a component. This suggests that defining the measurement function will have some form of de-correlated sensor fusion. In order to apply particle filtering to estimate the RUL, an l-step ahead estimator has to be defined. Both biased and unbiased l-step ahead estimators have been reported by Zio and Peloni (2011) and Orchard and Vachtsevanos (2011). However, as pointed out by Zio and Peloni (2011), one issue related to these estimators is that state estimation and prediction must be accompanied by a measure of the associated error.