Integrated wavelet transform and its application to vibration mode shapes for the damagedetection of beam-type structures

Abstract

Wavelet analysis has been extensively used in damage detection due to its inherent meritsover traditional Fourier transforms, and it has been applied to identify abnormality fromvibration mode shapes in structural damage identification. However, most related studieshave only demonstrated its ability to identify the abnormality of retrieved mode shapeswith a relatively higher signal-to-noise ratio, and its incapability of identifying slightabnormality usually corrupted by noise is still a challenge. In this paper, a newtechnique (so-called ‘integrated wavelet transform (IWT)’) of taking synergisticadvantages of the stationary wavelet transform (SWT) and the continuous wavelettransform (CWT) is proposed to improve the robustness of abnormality analysis ofmode shapes in damage detection. Two progressive wavelet analysis steps areconsidered, in which SWT-based multiresolution analysis (MRA) is first employed torefine the retrieved mode shapes, followed by CWT-based multiscale analysis(MSA) to magnify the effect of slight abnormality. The SWT-MRA is utilized toseparate the multicomponent modal signal, eliminate random noise and regularinterferences, and thus extract purer damage information, while the CWT-MSA isemployed to smoothen, differentiate or suppress polynomials of mode shapes tomagnify the effect of abnormality. The choice of the optimal mother wavelet indamage detection is also elaborately addressed. The proposed methodology of theIWT is evaluated using the mode shape data from the numerical finite elementanalysis and experimental testing of a cantilever beam with a through-widthcrack. The methodology presented provides a robust and viable technique toidentify minor damage in a relatively lower signal-to-noise ratio environment.