Effective grain orientation mapping of complex and locally anisotropic media for improved imaging in ultrasonic non-destructive testing

Abstract

Imaging defects in austenitic welds presents a significant challenge for the ultrasonic non-destructive testing community. Due to the heating process during their manufacture, a dendritic structure develops, exhibiting large grains with locally anisotropic properties which cause the ultrasonic waves to scatter and refract. When basic imaging algorithms, which typically make constant wave speed assumptions, are applied to datasets arising from the inspection of these welds, the resulting defect reconstructions are often distorted and difficult to interpret correctly. However, knowledge of the underlying spatially varying material properties allows correction of the expected wave travel times and thus results in more reliable defect reconstructions. In this paper, an approximation to the underlying, locally anisotropic structure of the weld is constructed from ultrasonic time of flight data. A new forward model of wave front propagation in locally anisotropic media is presented and used within the reversible-jump Markov chain Monte Carlo method to invert for the map of effective grain orientations across different regions of the weld. This forward model and estimated map are then used as the basis for an advanced imaging algorithm and the resulting defect reconstructions exhibit a significant improvement across multiple flaw characterization metrics.

An inverse problem for Voronoi diagrams: A simplified model of non‐destructive testing with ultrasonic arrays

“…In this section, we derive the inverse problems (), () from the more general setting of travel time tomography in anisotropic media. Our physical motivation is the determination of metal microstructure and defects from the travel times of ultrasonic waves 5,8,9,19 …”

“…This can be done for the isotropic case (where ξ ( x , ν ) is independent of ν ) using for example the supergradient marching algorithm of Benmansour et al, 20 which applies automatic differentiation to a fast‐marching algorithm 21 . One approach to the anisotropic case could be to generalise Benmansour et al 20 to anisotropic metrics, using an anisotropic fast‐marching algorithm such as those presented in other studies, 8,22,23 but we do not pursue this here.…”

“…In the ultrasonic non‐destructive evaluation (NDE) community, inspections are often carried out using a single transducer (as opposed to the arrays of sensors available in seismic and medical imaging), and so until recently, development of tomographic capabilities has been somewhat neglected. However, with the rapid uptake of ultrasonic phased arrays (which are capable of simultaneously transmitting and receiving ultrasound across multiple elements 5 ), tomographic inversion is now becoming feasible 6‐9 and presents a potential solution to the challenge of imaging defects embedded in complex media. There are many cases in industry where, due to manufacturing conditions or design, heterogeneous and locally anisotropic microstructures can arise 10‐12 and defect detection can prove difficult.…”

“…This results in a highly scattering, refractive and locally anisotropic medium where contributions to the scattered field by small defects are often obscured. However, it has been shown that a priori knowledge of such microstructures can be used to compensate for these effects and better focus the defect scattering energy to produce more reliable flaw reconstructions 7‐9,15 …”

“…Inspired by this particular problem in the ultrasonic NDE community, we propose a new approach to extracting information on the spatially varying material properties of this class of locally anisotropic media from travel time information collected on the boundary of the object. This specific problem has previously been tackled using Markov chain Monte Carlo (MCMC) methods, 7‐9 where an ensemble of samples estimating the posterior probability density function is produced and its associated moments are used to describe the probability distribution of the model given the observed data. These MCMC methods are generally applicable to most high‐dimensional inverse problems but are usually associated with prohibitive computational costs from the iterative runs of forward models over large and complex parameter spaces, which are in some cases inefficiently sampled 16 .…”