Stochastic prognostics for rolling element bearings

The capability to accurately predict the remaining life of a rolling element bearing is prerequisite to the optimal maintenance of rotating machinery performance in terms of cost and productivity. Due to the probabilistic nature of bearing integrity and operation condition, reliable estimation of a bearing's remaining life presents a challenging aspect in the area of maintenance optimisation and catastrophic failure avoidance. Previous study has developed an adaptive prognostic methodology to estimate the rate of bearing defect growth based on a deterministic defect-propagation model. However, deterministic models are inadequate in addressing the stochastic nature of defect-propagation. In this paper, a stochastic defect-propagation model is established by instituting a lognormal random variable in a deterministic defect-propagation rate model. The resulting stochastic model is calibrated on-line by a recursive least-squares (RLS) approach without the requirement of a priori knowledge on bearing characteristics. An augmented stochastic differential equation vector is developed with the consideration of model uncertainties, parameter estimation errors, and diagnostic model inaccuracies. It involves two ordinary differential equations for the first and second moments of its random variables. Solving the two equations gives the mean path of defect propagation and its dispersion at any instance. This approach is suitable for on-line monitoring, remaining life prediction, and decision making for optimal maintenance scheduling. The methodology has been verified by numerical simulations and the experimental testing of bearing fatigue life. (C) 2000 Academic Press.