Selected Applications of the Wavelet Transform

The wavelet transform is used to analyze: (1) the strain respons e signal in a resonant mechanical spectrometer, (2) the signal from a magnetic inspec tion of wire ropes, and (3) the Barkhausen noise signal. The wavelet transform of the analyzed signal yields a three-dimensional representation (the time-scale joint representation), that is, s pace (time), frequency (scale), and amplitude. The time-dependent strain signals measured by a mecha nical spectrometer, represented in the time-scale joint representation, are called “Identifie d Strain Response Signal” (ISRS) to emphasize that not only frequency content of the strain response signal but lso time is clearly revealed. The wavelet transform is applied to on-line analysis of the strain signal during mechanical loss measurements. The wavelet transform of the strain response s ig al can also be used to identify fine irregularities in a very low frequency strain response sig nal and to denoise this signal in order to obtain better signal to noise ratio of the strain signal recor d d in a subresonant mechanical spectrometer. For these reasons the wavelet analysis has proved t o b a useful tool to analyze the strain and the stress signals and thereby to improve the quali ty of oscillations in both a resonant and a subresonant mechanical spectrometer. It is concluded that the wave let transform can be successfully used in spectroscopic techniques. Nonstationary Barkhausen noi (BN) signals and signals obtained during magnetic inspection of twisted and lay ropes are also investigated by the wavelet analysis. The wavelet transform is used in the magnet ic i spection of wire ropes and in the decomposition of signals from induction sensors, that is, in non-destructive testing (NDT) techniques of wire ropes. Appropriate levels of signal decomposition provi de both reliable detection of various forms of rope wear and supplementary information about wear-of f forms in twisted and lay ropes. The wavelet transform of nonstationary magnetic signal is a promising and powerful tool for wire rope inspection and investigation of ferromagnetic materials. Introduction This paper reports results on the application of wavelet analysis: (1) to nearly stationary harmonic signals recorded in a mechanical spectrometer, (2) to nonstationary signals obtained in the investigation of the magnetic Barkhausen noise (BN), and (3) to nonstationa ry signals obtained in the non-destructive magnetic inspection of wire ropes. Solid State Phenomena Online: 2003-02-13 ISSN: 1662-9779, Vol. 89, pp 355-0 doi:10.4028/www.scientific. net/SSP.89. 355 © 2003 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific. net. (Semanticscholar.org-18/03/20,14:08:25) The wavelet transform is used to show how the frequency content of the strain response signal in a mechanical spectrometer slightly varies with time. The wavelet analysis is successfully used to examine both free decaying signals in a resonant mechanical spec trom ter and forced oscillations in a subresonant mechanical spectrometer. This paper recommends the u e of the fast Fourier transform (FFT) and the wavelet transform for performing the so -called signal quality test [1, 2] of the strain response signal in mechanical loss measurements. Nonstationary characterization of signals obtained during magnetic i spection of twisted and lay ropes and during Barkhausen noise measurements can reveal dist inctive features of the inspected objects. The nonstationary character of these signals s a erious impediment to studies that determine how the wear of the rope impacts structure weakeni ng a d how to interpret BN signals. Standard spectral analysis of nonstationary signals wa s usu lly based on short-time Fourier transform (STFT) [3, 4]. For the signals collected from inspected ropes and Barkhausen noise measurements this technique provides only general information about the s ignal’s stationary and nonstationary characteristics while some information in the timeand frequency-domain is always lost. Standard spectral analysis is used, however, to obtain the power spect a of the signal from the inspected rope (STFT is usually applied to obtain the signal spectra based on the analysis of timewindowed signal sections.) However, the precision of the STFT is still limited and is strongly dependent on the size of the window. STFT yields the frequency-based de composition of the analyzed signal enabling, in some specific cases, the observation of time vari ations of the spectrum. This paper describes a new method for the non-destructive testing of a rope. It is demonstrated that the wavelet analysis of nonstationary magnetic signals is more than adequate tool for the nondestructive inspection of a rope. The advantage of using wavelet anal ysis is that local features in a magnetic signal can be revealed with high resolution. In addition, pow er spectra of signal decomposition allow the quantification of the degree of rope wear. Det ermination of the levels at which decomposition is apparent may be further used in the design of new flaw detect ors. The Wavelet Transform and Analysis of Nonstationary Signals The wavelet transform of a signal ( ) t x is defined as the sum over all time of the signal ( ) t x multiplied by scaled and shifted version of the wavelet function ( ) t ψ , which always has a zero mean. The coefficients ( ) b a C , of the wavelet transform of the signal ( ) t x are defined as [5 12]: ( ) ( ) t a b t t x a b a C p d , − = +∞