  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.
