Grey Relational Analysis of Measure for Uncertainty of Rolling Bearing Friction Torque as Time Series

摘要

Based on the grey system theory, the friction torque time series of the rolling bearing at different rotational speeds is studied. These four measures are the mean of the fluctuant ranges (MFR), the information entropy, the correlation dimension, and the box dimension. By defining two new concepts, viz., the optimal distinguishing coefficient and the grey confidence level, an optimal grey relational space is constructed. And the grey relations between these measures are investigated in this space. The results show that in the given range of the rotational speed of the rolling bearing, this space can be applied to unify the uncertainty of a stochastic process, the uncertainty of an information source, and the nonlinearly dynamical features of a chaotic time series.