This paper presents a novel multi-time scale approach to bearing defect tracking and remaining useful life (RUL) prediction, which integrates enhanced phase space warping (PSW) with a modified Paris crack growth model. As a data-driven method, PSW describes the dynamical behavior of the bearing being tested on a fast-time scale, whereas the Paris crack growth model, as a physics-based model, characterizes the bearing's defect propagation on a slow-time scale. Theoretically, PSW constructs a tracking metric by evaluating the phase space trajectory warping of the bearing vibration data, and establishes a correlation between measurement on a fast-time scale and defect growth variables on a slow-time scale. Furthermore, PSW is enhanced by a multi-dimensional auto-regression (AR) model for improved accuracy in defect tracking. Also, the Paris crack growth model is modified by a time-piecewise algorithm for real-time RUL prediction. Case studies performed on two run-to-failure experiments indicate that the developed technique is effective in tracking the

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