Incorporating expected sparsity of damage into ultrasonic guided wave imaging algorithms

Abstract

Many imaging methods employing ultrasonic guided waves are based upon delay-and-sum algorithms whereby echoes scattered from sites of damage are constructively reinforced after signal addition. Resolution of the resulting images depends upon such factors as the underlying array geometry, spectral content, knowledge of the propagation environment, and incorporation of phase information. For plate-like structures of engineering interest, geometrical features such as edges, cut-outs and fastener holes contribute to signal complexity and can cause significant image artifacts, which hinders detection and localization of actual damage. However, it is reasonable to make the a priori assumption that damage is spatially sparse. If this assumption is properly incorporated into imaging algorithms, then the resulting images should also be sparse and thus be easier to interpret. Several algorithms are developed and implemented that are based upon sparse reconstruction methods, and their performance on both numerical and experimental data is evaluated in terms of image quality and computational efficiency.