Refinements of damage detection methods based on wavelet analysis of dynamical shapes

This manuscript aims at illustrating significant refinements concerning the use of wavelets, when these latter are used in the guise of continuous wavelet transforms (CWT) for identifying damage on transversally vibrating structural components (e.g. beams, plates and shells). The refinements regard the presentation of wavelet-algorithms which are aimed at significantly reducing those border distortions normally arising during a wavelet-damage detection procedure. The main advantage of the algorithms is that they are self-contained, namely: (i) the wavelet transforms do not undergo any own variation and their application follows the convolution laws established in the past; (ii) it is not necessary to design a specific boundary wavelet; (iii) no significant analytical treatment neither of the wavelets nor of the signal is required and, finally, (iv) the algorithms can be adapted to different boundary conditions and different physical situations. Besides all the specified advantages, the wavelet-damage detection procedure is still carried out by excluding historical data. The effectiveness of the algorithms is shown through numerical and experimental examples. These latter are illustrated along with reduced outliers of experimental estimation through a related consistent statistical procedure.