Parameter estimation and remaining useful life prediction of lubricating oil with HMM

Lubricating oil plays a vital role in the full life-span performance of the machine. Lubricating oil deterioration, which leads to the attenuation of oil performance and severe wear afterwards, is a slow degrading process, which can be observed by condition monitoring, but the actual degree of the oil degradation is often very difficult to examine. The main purpose of lubricating oil degradation prediction is to estimate the failure time when the oil no longer fulfills its functions. We suppose that the state process evolution of lubricating oil degradation can be modeled using a hidden Markov model (HMM) with three states: healthy state, unhealthy state, and failure state. Only the failure state is observable. While the lubricating oil is in service, vector data that are stochastically related to the deterioration state are obtained through on-line condition monitoring by an OLVF (On-line Visual Ferrograph) sensor at regular sampling epochs. A method of Time Series Analysis (TSA) is applied to the healthy portions of the oil data histories to get the residuals as the observable process containing partial information to fit the hidden Markov model. The unknown parameters of the fitted hidden Markov model are estimated by the Expectation-Maximization (EM) algorithm. The remaining useful life (RUL) of lubricating oil can be evaluated through explicit formulas of the characteristics such as the conditional reliability function (CRF) and mean residual life (MRL) function in terms of the posterior probability.