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

Wavelet analysis has been extensively used in damage detection due to its inherent merits over traditional Fourier transforms, and it has been applied to identify abnormality from vibration mode shapes in structural damage identification. However, most related studies have only demonstrated its ability to identify the abnormality of retrieved mode shapes with a relatively higher signal-to-noise ratio, and its incapability of identifying slight abnormality usually corrupted by noise is still a challenge. In this paper, a new technique (so-called 'integrated wavelet transform (IWT)') of taking synergistic advantages of the stationary wavelet transform (SWT) and the continuous wavelet transform (CWT) is proposed to improve the robustness of abnormality analysis of mode shapes in damage detection. Two progressive wavelet analysis steps are considered, in which SWT-based multiresolution analysis (MRA) is first employed to refine the retrieved mode shapes, followed by CWT-based multiscale analysis (MSA) to magnify the effect of slight abnormality. The SWT-MRA is utilized to separate the multicomponent modal signal, eliminate random noise and regular interferences, and thus extract purer damage information, while the CWT-MSA is employed to smoothen, differentiate or suppress polynomials of mode shapes to magnify the effect of abnormality. The choice of the optimal mother wavelet in damage detection is also elaborately addressed. The proposed methodology of the IWT is evaluated using the mode shape data from the numerical finite element analysis and experimental testing of a cantilever beam with a through-width crack. The methodology presented provides a robust and viable technique to identify minor damage in a relatively lower signal-to-noise ratio environment.