Periodically impulsive behavior detection in noisy observation based on generalized fractional order dependency map

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In this paper a novel procedure for the detection of periodically impulsive behavior is presented. It is a basis for local damage detection in gears/bearings. Signals acquired from the machines working in heavy industry environment often contain high level of noise (Gaussian or non-Gaussian) which makes diagnosis difficult. Complex structure of the signal requires time-frequency decomposition for advanced analysis. Proposed method relies on the heavy-tailed distribution based modeling of the time-frequency decomposed signal. The α-stable distribution used for the modeling of the sub-signals utilizes the impulsivity property of the signal of interest (SOI). When impulses are cyclic it is reasonable to apply methods allowing for the cyclicity detection. However, considering that we model them with the α-stable distribution it is needed for the methods to be appropriate for the α-stable distribution. As such, one should not use correlation or covariance as they are not consistent with the proposed distribution. We propose to use fractional lower-order covariance as it is specifically defined for the aforementioned distribution. Furthermore, it allows one to use the cyclicity and impulsivity property of the SOI. Measures calculated for each band form the novel lag-frequency map. In the next step it is possible to apply denoising by application of the Local Maxima method. This method is applied to simulated and real data which was acquired from the two-stage gearbox working in mining environment.