Abstract
Two de-noising methods, named as the averaging method in Gabor transform domain (AMGTD) and the adaptive filtering method in Gabor transform domain (AFMGTD), are presented in this paper. These two methods are established based on the correlativity of the source signals and the background noise in time domain and Gabor transform domain, that is to say, the uncorrelated source signals and background noise in time domain would still be uncorrelated in Gabor transform domain. The construction and computation scheme of these two methods are investigated. The de-noising performances are illustrated by some simulation signals, and the wavelet transform is used to compare with these two new de-noising methods. The results show that these two methods have better de-noising performance than the wavelet transform, and could reduce the background noise in the vibration signal more effectively.
Highlights
The measured vibration signals contain important information for the prognostic and fault diagnosis purposes
We could show the configuration of averaging method in Gabor transform domain (AMGTD) by a group of signals z j (t) with equal length, which are composed of the source signal y(t) and noise N j (t), Mechatronics and Information Technology z j (t) = y(t) + N j (t), j = 1, 2, l, (6)
With the increase of noise level, the time history of the de-noised signal by wavelet transform is much different from the source one, while the time histories of the de-noised signals by AMGTD and adaptive filtering method in Gabor transform domain (AFMGTD) are similar to the source one
Summary
The measured vibration signals contain important information for the prognostic and fault diagnosis purposes. A lot of time-frequency methods suitable for non-stationary signal, such as wavelet transform, Wigner distribution, Gabor transform, etc., have been applied in fault diagnosis [3,4,5,6,7,8,9,10,11]. Shen and Yang [11] presented a novel BSS method based on Fractional Fourier Transform, which could be used to separate the mixed non-stationary signals successfully and was applied for fault diagnosis of rolling bearing in freight train successfully. In these de-noising methods based on time-frequency, an unavoidable problem is to select the appropriate threshold values in time-frequency plane. Advanced Engineering Forum Vols. 2-3 adaptive filtering method in Gabor transform domain (AFMGTD), which means that one could adaptively obtain the threshold values in Gabor transform domain by averaging many groups of measured signals
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