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首页> 外文期刊>Mechanical systems and signal processing >Spectral L2/L1 norm: A new perspective for spectral kurtosis for characterizing non-stationary signals
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Spectral L2/L1 norm: A new perspective for spectral kurtosis for characterizing non-stationary signals

机译：频谱L2 / L1范数：频谱峰度用于表征非平稳信号的新观点

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Thanks to the great efforts made by Antoni (2006), spectral kurtosis has been recognized as a milestone for characterizing non-stationary signals, especially bearing fault signals. The main idea of spectral kurtosis is to use the fourth standardized moment, namely kurtosis, as a function of spectral frequency so as to indicate how repetitive transients caused by a bearing defect vary with frequency. Moreover, spectral kurtosis is defined based on an analytic bearing fault signal constructed from either a complex filter or Hilbert transform. On the other hand, another attractive work was reported by Borghesani et al. (2014) to mathematically reveal the relationship between the kurtosis of an analytical bearing fault signal and the square of the squared envelope spectrum of the analytical bearing fault signal for explaining spectral correlation for quantification of bearing fault signals. More interestingly, it was discovered that the sum of peaks at cyclic frequencies in the square of the squared envelope spectrum corresponds to the raw 4th order moment. Inspired by the aforementioned works, in this paper, we mathematically show that: (1) spectral kurtosis can be decomposed into squared envelope and squared L2/L1 norm so that spectral kurtosis can be explained as spectral squared L2/L1 norm; (2) spectral L2/L1 norm is formally defined for characterizing bearing fault signals and its two geometrical explanations are made; (3) spectral L2/L1 norm is proportional to the square root of the sum of peaks at cyclic frequencies in the square of the squared envelope spectrum; (4) some extensions of spectral L2/L1 norm for characterizing bearing fault signals are pointed out.
机译：由于Antoni（2006）的不懈努力，频谱峰度已被认为是表征非平稳信号，尤其是轴承故障信号的里程碑。频谱峰度的主要思想是使用第四标准化矩（即峰度）作为频谱频率的函数，以指示由轴承缺陷引起的重复瞬态如何随频率变化。此外，基于从复杂滤波器或希尔伯特变换构造的分析方位故障信号来定义频谱峰度。另一方面，Borghesani等报道了另一项有吸引力的工作。 （2014）用数学方法揭示了分析轴承故障信号的峰度与分析轴承故障信号平方包络谱平方的平方之间的关系，从而解释了量化轴承故障信号的频谱相关性。更有趣的是，发现平方包络谱的平方中的循环频率处的峰值之和对应于原始的四阶矩。受上述工作的启发，本文从数学上证明：（1）频谱峰度可以分解为平方包络和平方L2 / L1范数，从而可以将频谱峰度解释为频谱平方L2 / L1范数； （2）正式定义了频谱L2 / L1范数以表征轴承故障信号，并作了两种几何解释； （3）频谱L2 / L1范数与平方包络频谱的平方中的循环频率处的峰值之和的平方根成比例； （4）指出了用于表征轴承故障信号的频谱L2 / L1范数的一些扩展。

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