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The structures under fatigue loading are fault prone. The damage reduces the local stiffness. This local stiffness leads to a slope discontinuity in the structure's elastic line. Localizing the local discontinuity reveals the location of the damage. Wavelet transform is a powerful tool to localize a local slope discontinuity in a signal. The major challenges in the localization of damage in a beam are obtaining the high spatial resolution beam deflection and eliminating the border distortion. The high spatial resolution shrinks the border distortion as well as gives more localized crack detection. The reduced border distortion leads to the detection of cracks very close to the ends of the beam. In the present work, finite element analysis is used for getting the simulated beam deflection. The lifting wavelet is used for the localization of cracks in the beam. The lifting wavelet has certain advantages over the classical wavelet. The lifting wavelet possesses perfect reconstruction and a narrower border distortion zone. A comparative study is presented between the discrete wavelet transform and the lifting wavelet transform for localizing the crack. The ability of lifting wavelet is tested for different noise conditions and multiple crack localization. A photographic method is used to get the high-resolution of experimental beam deflection of stainless-steel material.
Nigam et al. (Fri,) studied this question.