Degradation Trend Prognostics for Rolling Bearing Using Improved R/S Statistic Model and Fractional Brownian Motion Approach

Fractional order characteristics (FOCs) have been shown to be useful in the predict degradation trend of rotating machinery. In this paper, a novel prognostics methodology based on improved R/S statistic and fractional Brownian motion (FBM) for rolling bearing degradation process is proposed. Due to the fact that bearing health indicators, such as equivalent vibration intensity (EVI), often exhibit non-stationary and non-Gaussian traits, the FOC methodology normally involves the estimation of a parameter Hurst H; the improved R/S statistic technique with auto-covariance estimator was introduced to address the issue that the calculation of the Hurst exponent by classical R/S methods is sensitive to heteroskedasticity and short-range dependence. Furthermore, a slow degrading process of a rolling bearing can be predicted by a common FOC model, but the actual sharp transition points (STPs) of the degradation are often very difficult to track. The main purpose of a rolling bearing degradation prediction is to prognosticate and track the STP's trend when the failure occurs between the normal phase and the incipient degradation phase. A method that combined FBM and Brownian motion is presented when the forecasted points contaminated with STPs, in which the predicting operator, driven by a new stochastic differential equation and its computationally efficient algorithm, are explored. The experimental results show that the proposed approach can better predict the EVI degradation trend than traditional FOC and other time series models.