Multi-scale entropy (MSE) is a widely recognized feature extraction approach to mechanical fault diagnosis, for it can effectively estimate the complexity of nonlinear time series. For MSE algorithm, due to the sensitivity of entropy estimation on series length, the scale factors are often required to be limited to a small range. Nevertheless, in the existing MSE methods, the scale factors can only be set to positive integers with a fixed minimum step size, which may result in insufficient analysis precision and cannot provide high-quality feature vectors with sufficient eigenvalues for intelligent diagnosis in the limited scale range. In view of the above defects, this paper subdivides the scale factors and proposes dense multi-scale entropy. In the suggested method, the number of data points in the raw sequence is expanded on the premise of guaranteeing the characteristics of the original series. Based on this, the timescale of the original series is refined and more intensive...

中文翻译：

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密集多尺度熵及其在机械故障诊断中的应用

多尺度熵（MSE）是一种广泛用于机械故障诊断的特征提取方法，因为它可以有效地估计非线性时间序列的复杂性。对于MSE算法，由于熵估计对序列长度的敏感性，通常需要将比例因子限制在较小范围内。然而，在现有的MSE方法中，比例因子只能设置为具有固定最小步长的正整数，这可能会导致分析精度不足，并且无法在有限的比例下提供具有足够特征值的高质量特征向量进行智能诊断范围。鉴于上述缺陷，本文对比例因子进行了细分，提出了稠密的多尺度熵。在建议的方法中，在保证原始序列特征的前提下，扩展原始序列中的数据点数量。在此基础上，原始影集的时间尺度得以精炼且更加密集...