A transdimensional Bayesian approach to ultrasonic travel-time tomography for non-destructive testing

Tant, K M M and Galetti, E and Mulholland, A J and Curtis, A and Gachagan, A (2018) A transdimensional Bayesian approach to ultrasonic travel-time tomography for non-destructive testing. Inverse Problems, 34 (9). 095002. ISSN 0266-5611 (https://doi.org/10.1088/1361-6420/aaca8f)

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Traditional imaging algorithms within the ultrasonic non-destructive testing community typically assume that the material being inspected is primarily homogeneous, with heterogeneities only at sub-wavelength scales. When the medium is of a more generally heterogeneous nature, this assumption can contribute to the poor detection, sizing and characterisation of any defects. Prior knowledge of the varying velocity fields within the component would allow more accurate imaging of defects, leading to better decisions about how to treat the damaged component. This work endeavours to reconstruct the inhomogeneous velocity fields of random media from simulated ultrasonic phased array data. This is achieved via application of the reversible-jump Markov chain Monte Carlo method: a sampling-based approach within a Bayesian framework. The inverted maps are then used in conjunction with an imaging algorithm to correct for deviations in the wave speed, and the reconstructed flaw images are then used to quantitatively measure the success of this methodology. Using full matrix capture data arising from a finite element simulation of a phased array inspection of a heterogeneous component, a six-fold improvement in flaw location is achieved by taking into account the reconstructed velocity map which exploits almost no \textit{a priori} knowledge of the material's internal structure. Receiver operating characteristic curves are then calculated to demonstrate the enhanced probability of detection achieved when the material map is accounted for.