Blind filtering is an emerging topic in various domains to recover an excitation from responses measured by sensors. In the existing literature, the minimum entropy deconvolution is often regarded as the maximum kurtosis deconvolution without providing an underlying connection between them. However, a recent progress towards sparsity measures has shown that kurtosis is actually different from negative entropy. Moreover, a generalized sparse measure, called Box-Cox sparse measures (BCSM), has been proposed to establish a connection between the kurtosis and the negative entropy. Thus, this research investigates an underlying connection between the minimum entropy deconvolution and the maximum kurtosis deconvolution by using the BCSM. After that, the BCSM is incorporated into a generalized Rayleigh quotient to form a generalized blind filter that extracts a signal with the sparsest envelope spectrum. Finally, the effectiveness of the proposed generalized filter is verified using both simulated and real experimental bearing data. Results demonstrates that the proposed method can be used to detect multiple faults using a single measurement set.

盲过滤是各个领域的新兴主题，用于从传感器测量的响应中恢复激励。在现有文献中，最小熵反卷积通常被认为是最大峰度反卷积，而没有提供它们之间的潜在联系。然而，最近在稀疏度量方面的进展表明，峰度实际上不同于负熵。此外，已经提出了一种称为 Box-Cox 稀疏度量 (BCSM) 的广义稀疏度量来建立峰度和负熵之间的联系。因此，本研究使用 BCSM 研究了最小熵解卷积和最大峰态解卷积之间的潜在联系。在那之后，BCSM 被合并到广义瑞利商中以形成广义盲滤波器，该滤波器提取具有最稀疏包络谱的信号。最后，使用模拟和真实的实验轴承数据验证了所提出的广义滤波器的有效性。结果表明，所提出的方法可用于使用单个测量集检测多个故障。