Evaluation of inversion approaches for guided wave thickness mapping

Abstract

Accurate inversion is vital for quantitative imaging, including ultrasonic guided wave tomography, where thickness maps of plate-like structures are reconstructed to quantify corrosion damage. The dispersive properties of guided waves are often exploited to enable thickness maps to be produced from wave speed reconstructions. Ray tomography, diffraction tomography and a hybrid algorithm combining their features were investigated to reconstruct wave speed. Test data produced from simple defects of different sizes using a realistic full elastic guided wave model and the equivalent idealized acoustic model were passed to the imaging algorithms, generating wave speed maps, and, from these, thickness maps. For both datasets, ray tomography exhibited poor resolution. Diffraction tomography performed better, but was limited to shallow, small defects. The hybrid algorithm achieved the best results, giving a resolution around 1.5-2 wavelengths from the realistic test data compared to half wavelength from the idealized case. These results were validated with experimental data, and also extended to a realistic corrosion patch confirming the trends demonstrated with simple defects. The resolution loss with realistic data compared with idealized data indicates the acoustic model cannot accurately capture guided wave scattering and an alternative approach is necessary for better resolution reconstructions.

Guided wave tomography performance analysis

“…Although more complex defects are likely to result from surface corrosion, it should be noted from other work [8] that the behaviour for these complex shapes is likely to be very similar to a superposition of simpler defects. The plate thickness, in the presence of this defect is described mathematically by where is the background thickness, is the defect depth, is the defect width.…”

“…In this, it is important that the full physics of the guided wave scattering from varying thickness is modelled appropriately. The finite element method is a good choice to do this, and has been validated [8]. Here, the Pogo software package (available from www.pogo-fea.com, [9]) was used; this is a high speed explicit time-domain solver running on graphics cards.…”

“…This was initially developed for breast imaging, and combines the complementary strengths of bentray tomography and diffraction tomography to determine low-and high-spatial frequency components of the image respectively. Based on this, the technique is shown to reconstruct velocity maps down to a resolution of around halfa-wavelength [8], matching the standard Born approximation limitation. However, the resolution when reconstructing thickness maps was significantly lower than this, which is a result of inaccuracies in the underlying assumption that guided waves scatter from thickness variations in the same way that acoustic waves scatter from velocity variations [8].…”

“…Based on this, the technique is shown to reconstruct velocity maps down to a resolution of around halfa-wavelength [8], matching the standard Born approximation limitation. However, the resolution when reconstructing thickness maps was significantly lower than this, which is a result of inaccuracies in the underlying assumption that guided waves scatter from thickness variations in the same way that acoustic waves scatter from velocity variations [8]. It is this assumption which is primarily investigated through this paper.…”

“…In guided wave tomography, resolution is one of the most important elements to achieving accurate reconstructions, yet the limit is typically of similar order to most defects [8]. Prior to analysing the performance, therefore, a study of how a particular resolution limit is likely to affect the accuracy of the reconstruction is undertaken.…”