Lubricating oil deterioration modeling and remaining useful life prediction based on hidden semi-Markov modeling

Lubricating oil, which carries information about machine’s health condition, is of great importance to the performance of machines in the full life cycle. The main purpose of oil deterioration modeling and its remaining useful life prediction is to determine the exact time that the lubricating oil has degraded and it is no longer able to maintain its functions. Generally, lubricating oil deterioration can be partially detected by condition monitoring based on wear debris analysis, and thus can be categorized into three states. In our paper, vector data, which contain wear debris concentration and carry information about the state of lubricating oil, are obtained by an on-line visual ferrograph sensor from a four-ball tester at regular sampling epochs. The oil’s state process is described by a hidden semi-Markov model, and its sojourn times in each state are assumed to be Erlang distributed. A vector autoregressive method based on time series modeling is presented to obtain residual observations, which are regarded as the observable process of oil information in the hidden semi-Markov model framework. The unknown parameters of the hidden semi-Markov model are then estimated by using expectation-maximization algorithm. Afterward, a Bayesian updating approach is presented to derive the explicit formulas of the conditional reliability and mean residual life. To validate the proposed approach, a real case study of lubricating oil deterioration is demonstrated and a comparison with the hidden Markov model is given to illustrate the effectiveness of the new developed remaining useful life prediction approach for lubricating oil.