Any measurement in condition monitoring applications is associated with disturbing noise. Till now, most of the diagnostic procedures have assumed the Gaussian distribution for the noise. This paper shares a novel perspective to the problem of local damage detection. The acquired vector of observations is considered as an additive mixture of signal of interest (SOI) and noise with strongly non-Gaussian, heavy-tailed properties, that masks the SOI. The distribution properties of the background noise influence the selection of tools used for the signal analysis, particularly for local damage detection. Thus, it is extremely important to recognize and identify possible non-Gaussian behavior of the noise. The problem considered here is more general than the classical goodness-of-fit testing. The paper highlights the important role of variance, as most of the methods for signal analysis are based on the assumption of the finite-variance distribution of the underlying signal. The finite variance assumption is crucial but implicit to most indicators used in condition monitoring (such as the root-mean-square value, the power spectral density, the kurtosis, the spectral correlation, etc.), in view that infinite variance implies moments higher than 2 are also infinite. The problem is demonstrated based on three popular types of non-Gaussian distributions observed for real vibration signals. We demonstrate how the properties of noise distribution in the time domain may change by its transformations to the time–frequency domain (spectrogram). Additionally, we propose a procedure to check the presence of the infinite-variance of the background noise. Our investigations are illustrated using simulation studies and real vibration signals from various machines.

状态监测应用中的任何测量都与干扰噪声有关。到目前为止，大多数诊断程序都假设噪声服从高斯分布。本文对局部损伤检测问题提出了一个新的观点。获得的观察矢量被认为是感兴趣信号 (SOI) 和具有强非高斯、重尾特性的噪声的加性混合，它掩盖了 SOI。背景噪声的分布特性影响用于信号分析的工具的选择，特别是局部损伤检测。因此，识别和识别噪声的可能非高斯行为是极其重要的。这里考虑的问题比经典的拟合优度检验更普遍。该论文强调了方差的重要作用，因为大多数信号分析方法都是基于基础信号的有限方差分布的假设。有限方差假设对于状态监测中使用的大多数指标（如均方根值、功率谱密度、峰度、谱相关性等）来说是至关重要的，但隐含在其中，因为无限方差意味着时刻更高比 2 也是无限的。该问题基于对真实振动信号观察到的三种流行类型的非高斯分布进行论证。我们演示了时域噪声分布的特性如何通过其向时频域（频谱图）的转换而改变。此外，我们提出了一个程序来检查背景噪声的无限方差的存在。