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.

翻译：状态监测中的任何测量都伴随着干扰噪声。迄今为止，大多数诊断方法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新的视角。观测向量被视为目标信号与具有强非高斯、重尾特性的噪声的加性混合，这种噪声掩盖了目标信号。背景噪声的分布特性会影响信号分析工具的选择，尤其是局部损伤检测。因此，识别和确认噪声可能的非高斯行为至关重要。本文考虑的问题比经典的拟合优度检验更具一般性。论文强调了方差的重要作用，因为大多数信号分析方法都基于底层信号具有有限方差分布的假设。有限方差假设对状态监测中常用的大多数指标（如均方根值、功率谱密度、峭度、谱相关等）至关重要但往往暗含其中，因为无穷方差意味着高于2的矩也是无穷的。基于实际振动信号中观察到的三种典型非高斯分布类型，我们演示了问题特性。我们展示了噪声分布在时域中的特性如何通过向时频域（谱图）变换而改变。此外，我们提出了一种检验背景噪声是否存在无穷方差的方法。通过仿真研究和来自不同机器的实际振动信号，我们的研究得到了验证。