Data-driven vibration signal filtering procedure based on the α-stable distribution

Abstract

A novel procedure for data-driven enhancement of informative signal is presented in this paper. The introduced methodology covers decomposition of the signal via time-frequency spectrogram into set of narrowband sub-signals. Furthermore, each of the sub-signals is considered as a sample of independent identically distributed random variables and we model the distribution of the sample, in contrast to the classical methodology where the simple statistics, for example kurtosis, for each sub-signal was calculated. This approach provides a new perspective in the signal processing techniques for local damage detection. Using our methodology one can eliminate potential risk related to high sensitivity towards single outlier. In the proposed procedure we model each sub-signal in time-frequency representation by α-stable distribution. This distribution is a generalization of standard Gaussian one and allows us for modeling sub-signals related to both informative and non-informative frequencies. As a result, we obtain distribution of stability parameter vs. frequencies that is analogy to spectral kurtosis approach well known in the literature. Such characteristic is basis for filter design used for raw signal enhancement. To evaluate efficiency of our method we compare raw and filtered signal in time, time-frequency and frequency (envelope spectrum) domains. Moreover, we present comparison to the spectral kurtosis approach. The presented methodology we applied to simulated signal and real vibration signal from two stage heavy duty gearbox used in mining industry.