Detecting damage in beams through digital differentiator filters and continuous wavelet transforms

Several papers that have recently appeared in the literature have shown the potential offered by certain mathematical tools (wavelets) for detecting damage in systems such as transversally vibrating beams. However, although the applications shown by different authors suggest that the tools show promise, the literature lacks a clear and concise collocation of the wavelets with respect to these previous methods that show similar (if not identical in certain circumstances) performances. In this paper, the continuous wavelet transforms (cwts) are discussed and compared, from a theoretical and numerical point of view, with those methods known as differentiator operators. Such differentiator operators adopted as filters are also able (similarly to the cwts) to reduce unwanted high frequency noise. Therefore, literature concerning differentiator filters in the digital signal processing area is investigated and several digital filters, known and modified, are analyzed and compared with the cwts in the presence of Gaussian noise. The theoretical aspects are discussed in both the non-transformed and Fourier transformed domain. This study results in an attempt to provide an elucidation on the effectiveness and the need to use the considered methods (differentiator filters and/or cwts) for detecting damage in transversally vibrating beams.