The entropy-based method has been demonstrated to be an effective approach to extract the fault features by estimating the complexity of signals, but how to remove the strong background noises in analyzing early weak impulsive signal remains unexplored. To solve this problem, this paper proposes symbolic fuzzy entropy (SFE) based on symbolic dynamic filtering and fuzzy entropy to eliminate the noises and improve the calculation efficiency. The main idea of SFE is to use symbolic dynamic filtering to remove the noise-related fluctuations while significantly simplifying the circulation calculation, thereby, generating better performance in resisting the background noises and high computation efficiency. The superiority of SFE is verified via two simulated signals and other three entropy methods. For comprehensive feature description, we further extend SFE into multiscale analysis by incorporating with the coarse gaining process, called MSFE. Experimental results demonstrate that the proposed MSFE method has the best performance in extracting weak fault characteristics compared with three existing MSE, MFE, and MPE methods.

已经证明基于熵的方法是一种通过估计信号的复杂度来提取故障特征的有效方法，但是在分析早期的弱脉冲信号中如何去除强烈的背景噪声仍待探索。为了解决这个问题，本文提出了一种基于符号动态滤波和模糊熵的符号模糊熵（SFE），以消除噪声并提高计算效率。SFE的主要思想是使用符号动态滤波来消除与噪声有关的波动，同时显着简化循环计算，从而在抵御背景噪声和更高的计算效率方面产生更好的性能。通过两个模拟信号和其他三种熵方法验证了SFE的优越性。要获得全面的功能描述，我们通过结合称为MSFE的粗略增益过程，将SFE进一步扩展到多尺度分析中。实验结果表明，与现有的三种MSE，MFE和MPE方法相比，所提出的MSFE方法在提取弱故障特征方面具有最佳性能。