Fractional Long-Range Dependence Model for Remaining Useful Life Estimation of Roller Bearings

Estimation of remaining useful life (RUL) of roller bearings is a prevalent problem for predictive maintenance in manufacturing. However, roller bearings are subject to a variety of factors during their operation. As a result, we deal with a slow nonlinear degradation process, which is long-range dependent, self-similar and has non-Gaussian characteristics. Proper data pre-processing enables us to use Pareto’s probability density function (PDF), Generalized Pareto motion (GPm) and its fractional-order extension (fGPm) as the degradation predictive model. Estimation of the Hurst exponent shows that this model has a long-range correlation and self-similarity. Through the analysis of the uncertainty of the end point of the bearing’s RUL and the prediction process, not only did it verify the high adaptability of fGPm in simulating complex degradation processes but also the criteria for judging self-similarity, and LRD characteristics were established. The case study mainly proves the validity of the theory, providing an effective analytical tool for a deeper understanding of the degradation mechanism.