| Summary: | Non-negative matrix factorization (NMF) has been used in various applications, including local damage detection in rotating machines. Recent studies highlight the limitations of diagnostic techniques in the presence of non-Gaussian noise. The authors examine the impact of non-Gaussianity levels on the extraction of the signal of interest (SOI). The simple additive model of the signal is proposed: SOI and non-Gaussian noise. As a model of the random component, i.e., noise, a heavy-tailed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-stable distribution with two important parameters (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>) was proposed. If SOI is masked by noise (controlled by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>), the influence of non-Gaussianity level (controlled by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>) is more critical. We performed an empirical analysis of how these parameters affect SOI extraction effectiveness using NMF. Finally, we applied two NMF algorithms to several (both vibration and acoustic) signals from a machine with faulty bearings at different levels of non-Gaussian disturbances and the obtained results align with the simulations. The main conclusion of this study is that NMF is a very powerful tool for analyzing non-Gaussian data and can provide satisfactory results in a wide range of a non-Gaussian noise levels.
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