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In order to detect the incipient fault of rolling bearings and to effectively identify fault characteristics, based on amplitude-aware permutation entropy (<i>AAPE</i>), an enhanced method named hierarchical amplitude-aware permutation entropy (<i>HAAPE</i>) is proposed in this paper to solve complex time series in a new dynamic change analysis. Firstly, hierarchical analysis and <i>AAPE</i> are combined to excavate multilevel fault information, both low-frequency and high-frequency components of the abnormal bearing vibration signal. Secondly, from the experimental analysis, it is found that <i>HAAPE</i> is sensitive to the early failure of rolling bearings, which makes it suitable to evaluate the performance degradation of a bearing in its run-to-failure life cycle. Finally, a fault feature selection strategy based on <i>HAAPE</i> is put forward to select the bearing fault characteristics after the application of the least common multiple in singular value decomposition (LCM-SVD) method to the fault vibration signal. Moreover, several other entropy-based methods are also introduced for a comparative analysis of the experimental data, and the results demonstrate that <i>HAAPE</i> can extract fault features more effectively and with a higher accuracy.