Multistate Diagnosis and Prognosis of Lubricating Oil Degradation Using Sticky Hierarchical Dirichlet Process–Hidden Markov Model Framework

Abstract

In this study, we present a state-based diagnostic and prognostic methodology for lubricating oil degradation based on a nonparametric Bayesian approach, i.e., sticky hierarchical Dirichlet process–hidden Markov model (HDP-HMM). An accurate health state-space assessment for diagnostics and prognostics has always been unobservable and hypothetical in the past. The lubrication condition monitoring (LCM) data is generally segregated as “healthy or unhealthy”, representing a binary state-based perspective to the problem. This two-state performance-based formulation poses limitations to the precision and accuracy of the diagnosis and prognosis for real data wherein there may be multiple states of discrete performance that are characteristic of the system functionality. In particular, the reversible and nonlinear time-series trends of degradation data increase the complexity of state-based modeling. We propose a multistate diagnostic and prognostic framework for LCM data in the wear-out phase (i.e., the unhealthy portion of degradation data), accounting for irregular oil replenishment and oil change effects (i.e., nonlinearity in the degradation signal). The LCM data is simulated for an elementary mechanical system with four components. The sticky HDP sets the prior for the HMM parameters. The unsupervised learning over infinite observations and emission reveals four discrete health states and helps estimate the associated state transition probabilities. The inferred state sequence provides information relating to the state dynamics, which provides further guidance to maintenance decision making. The decision making is further backed by prognostics based on the conditional reliability function and mean residual life estimation.