To improve the reconstruction image spatial resolutions of ultrasonic guided wave ray tomography, a sparse model, based on the differences between the inspected and original slowness of the ultrasonic guided waves propagating in the plate-like or pipe-like materials, is first proposed in this paper. Unlike the conventional ultrasonic guided wave tomography whose reconstruction image resolutions are limited by an underdetermined linear model, analyses show that our new model, although it is also underdetermined, can give the optimal solution of the reconstruction image when the constraints on the sparsity of the slowness difference distribution are valid. The reason for the validation of the sparse constraints on the corrosions of the materials is explained. Based on our new model, a least absolute shrinkage and selection operator (LASSO) approach to do the thickness change mapping of a structure health monitoring (SHM) application is then formulated. Analyses also show that the visible artifacts can be avoided using our method, and the spatial resolutions of reconstruction image by our approach can further be improved by increasing the number of grids in the calculation. The approach is validated by experimental work on an aluminum plate. It is also shown that compared to the conventional ray tomography, the presented method can achieve a relatively high spatial resolution, with good suppression of artifacts.
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