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

K M M Tant,E Galetti,A Gachagan,A Curtis,A J Mulholland

doi:10.1088/1361-6420/aaca8f

K M M Tant, E Galetti + Show 3 more

Open Access

https://doi.org/10.1088/1361-6420/aaca8f

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Abstract

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 defects. Prior knowledge of the varying wave speeds 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 wave speed maps 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 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 assess 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 wave speed map which exploits almost no 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 speed map is accounted for.

Highlights

The oil and gas, nuclear, power and aerospace industries are only a subset of the sectors dependent on the routine maintenance of safety-critical structures [1]
It is important to note that the PZFlex software models many of the physical phenomena present in the ultrasonic phased array inspection, for example mode conversion and diffraction, and it has previously been validated against experimental data [53]
The number of grid cells which meet this threshold but do not lie within ΩF is denoted by n−. (3) The probability of detection (PoD) value is calculated as n+/n p and the false positive rate (FPR) value is given by n−/n f . (4) These calculations are repeated at decreasing thresholds to produce the receiver operating characteristic (ROC) curve which plots the probability of detection against the false positive rate over the range of selected thresholds

Summary

Introduction

The oil and gas, nuclear, power and aerospace industries are only a subset of the sectors dependent on the routine maintenance of safety-critical structures [1]. When commonly used imaging algorithms (which assume a constant wave speed throughout the inspection domain) are applied to these ultrasonic datasets, the resulting images typically display poorly characterised and mislocated flaws [6, 7]. Ultrasonic wave propagation through inhomogeneous media has previously been studied using models [8,9,10] and simulations within finite element packages [5, 11] and it has been shown that some prior knowledge of how the material properties vary spatially can be used to correct for the deviation in wave speed and path, producing improved reconstructions or images of any internal defects [6, 7, 12]

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