Damage Identification in Beams via Contourlet Transform of Shearography Modal Data

This paper presents a novel method for damage identification in aluminum beams using the contourlet transform. Four aluminum beams were used in the study: one was undamaged, while the other three had different damage scenarios. The damage included middle and side slots with depth-to-thickness ratios of 7% and 28%. Damage is identified using the proposed index of contourlet transform of the modal rotations and modal curvatures of the beams for the free-free condition. The beam’s first three modal rotations are directly measured with digital shearography, and the corresponding modal curvatures are obtained through their numerical differentiation. The results indicated that to detect the exact locations and identify damage severities using the proposed damage indices, instead of modal rotations, the modal curvatures should be introduced as the input. Moreover, they revealed that the proposed damage indices need modal data of the undamaged state as a baseline to identify smaller damage. In addition, comparing the proposed contourlet-based damage indices with previously suggested wavelet-based damage detection methods revealed that, although the wavelet-based damage index is more sensitive to damage severity, it also exhibits higher noise levels in undamaged locations. The Tukey windowing process was introduced to address the boundary effect problem.