Rolling bearing is a key component of machinery, its fatigue failure will affect the reliability of machinery. The bearing vibration signal has strong nonlinearity, resulting in weak fault information. Multiscale sample entropy (MSE) is an effective technique for analyzing nonlinear time series. However, MSE has limitations, such as a large deviation and weak information mining abilities, and even the calculation results have no definition. To this end, a normalized balanced multiscale sample entropy (NBMSE) is proposed in this study. For NBMSE, the data are first normalized to zero mean and unit standard deviation by zero-mean normalization, which eliminates the influence of abnormal data. Secondly, the balanced multiscale approach is advanced to coarse-grain the time series, which takes into account the uniqueness of different amplitudes and the globality of the time series. The method not only avoids no-definition results, but also reduces the entropy calculation error, thus mining useful amplitude information. The comparison of synthetic signals shows that the proposed NBMSE is more robust than other methods. Furthermore, the results of two bearing cases show that NBMSE not only provides sensitive features for fatigue diagnosis but also has higher diagnostic accuracy.

滚动轴承是机械的关键部件，其疲劳失效会影响机械的可靠性。轴承振动信号具有很强的非线性，导致故障信息较弱。多尺度样本熵（MSE）是分析非线性时间序列的有效技术。但是，MSE也有局限性，如偏差大，信息挖掘能力弱，甚至计算结果没有定义。为此，本研究提出了归一化平衡多尺度样本熵（NBMSE）。对于NBMSE，首先通过零均值归一化将数据归一化为零均值和单位标准差，消除了异常数据的影响。其次，平衡多尺度方法被推进到粗粒度的时间序列，它考虑了不同振幅的唯一性和时间序列的全局性。该方法既避免了无清晰度的结果，又减少了熵的计算误差，从而挖掘出有用的振幅信息。合成信号的比较表明，所提出的 NBMSE 比其他方法更稳健。此外，两个轴承案例的结果表明，NBMSE 不仅为疲劳诊断提供了敏感的特征，而且具有更高的诊断准确性。