A natural way for improving the accuracy of the continuous wavelet transforms

作者:Yang Wen Xian*
来源:Journal of Sound and Vibration, 2007, 306(3-5): 928-939.
DOI:10.1016/j.jsv.2007.07.001

摘要

Aiming at further increasing the accuracy of the continuous wavelet transforms (CWTs) of transient vibration signals, a new coefficient trimming technique is proposed in this paper. Different from the conventional CWT analysis, which treats different scales of daughter wavelets equally and without using any discrimination, the proposed technique takes the role of the daughter wavelet into account in the CWT calculations. In the concept of this new technique, not only different scales of daughter wavelets play different roles in the calculations, but also the daughter wavelet at the same scale also plays a different role at different time instants. The role of the daughter wavelet is numerically evaluated through the approach of the correlation between the daughter wavelet and the instant signal within the time-sliding window, which window length is predefined by using a compromise strategy. Once the correlation coefficient indicating the role of a daughter wavelet at certain time instant is obtained, it will be applied to trim the corresponding CWT coefficient that is derived at the corresponding wavelet scale and the current time instant. The details of this operation are given in the following context of the paper. Extensive experiments show that with the aid of this proposed technique, the false information in the CWT map is successfully removed, while the true information of the vibration signal is retained sufficiently. Moreover, different from the threshold-based purification methods, the continuity and the smoothness of the wavelet coefficients are maintained perfectly in the whole process. So the results obtained by using the proposed technique are more explicit and reliable, from which the signal features may be identified more easily and correctly. This is very helpful for promoting understanding of the dynamic behaviour of the machines and furthermore giving a more reliable assessment of their running condition.