Damage Identification in Beams by Post-processing Modal Displacements and Rotations with Haar Wavelet

A study on the post-processing of modal displacements and modal rotations with the Haar wavelet is presented in this paper. A free-free aluminum beam is chosen as a structure to be analyzed and its modal displacements and rotations in both undamaged and multiple damaged states are computed with the finite element method. Three sets of damage indicators are proposed: (1) wavelet transform of damaged modal displacements or modal rotations, (2) wavelet transform of differences in modal displacements or modal rotations, and (3) ratio of wavelet transform of differences in modal displacements or modal rotations to wavelet transform of undamaged modal displacements or modal rotations. The study shows that post-processing modal displacements with the Haar wavelet leads to poor damage identifications. On the other hand, if one applies the same type of wavelet to modal rotations, the damage indicators (2) and (3) clearly pinpoints the location of the damage. Although the set of damage indicators (1) and (2) are prone to the boundary effect, where high values of wavelets coefficients are present, the third set of damage indicators does not present this problem. Furthermore, for large values of damage, this damage indicators shows the presence of damage in all scales of the wavelet scalogram. The present study clearly shows that by post-processing modal rotations with the simplest wavelet one can obtain reliable identifications of multiple damage.