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

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 Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.

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

“…Once the arrival times have been obtained, they are stored in a time of flight (ToF) matrix T 0 , where each element t s,r represents the time taken for the wave to travel from transmitting element s to receiving element r. In a homogeneous, globally isotropic medium, the time taken is dependent only on distance and so we obtain symmetric, banded ToF matrices. However, as soon as an element of heterogeneity is introduced, these bands are distorted [5] and it is this distortion that we exploit to obtain information on the material's underlying structure.…”

“…Using mathematical algorithms to decipher the resulting data sets, an image of the component's interior can be constructed and, in scenarios where the component is composed of a homogeneous material, defects can be reliably detected and characterized [1,2]. However, when the material exhibits inhomogeneous and/or anisotropic behaviour, its inspection becomes challenging [3][4][5]: the ultrasonic wave paths are distorted and their expected arrival times (on which many existing imaging algorithms are based) are usually no longer reliable.…”

“…It has already been shown that a priori knowledge of a material's spatially variant properties can be used to construct more accurate and reliable images of embedded defects [3][4][5]. Although the microstructural maps required for this correction can be obtained experimentally [6,10], such techniques are not considered to be strictly non-destructive and thus cannot be deployed in situ.…”

“…The inverse problem of recovering information about the spatially varying material properties of a component from ultrasonic phased array data has yet to be solved satisfactorily, and is attracting increased attention within the NDT community. In recent years, some work has been carried out on the determination of crystallographic orientation in single crystal materials [15] and mapping the velocity field in locally isotropic random media [5]. In the case of locally anisotropic polycrystalline materials (for example, steel welds [4,8,16]), the wave speed through the material is dependent on the angle of incidence of the wave, and so a single map of the velocity field cannot fully represent the complexity of the wave's journey.…”

“…Building upon this existing body of work, the work presented in this paper presents the reversible-jump Markov chain Monte Carlo (rj-MCMC) method [22] as an alternative means for inverting ultrasonic phased array data to obtain information on the distribution of crystal orientations in polycrystalline materials. The authors have already applied this inversion method to reconstruct the varying velocity field in locally isotropic, random media [5,23,24] and in this paper, the method is extended to map the locally anisotropic grain structure of austenitic steel welds. Similar to the methodology presented in [4], and in contrast to the work carried out in [8,16,17,19,20], this methodology is not weld-specific and may be applied to any environment in which waves propagate through heterogeneous and locally anisotropic media (for example, it may be easily adapted for application by the seismic community where isotropic assumptions are often made in materials known to be anisotropic, negatively impacting the fidelity of the resulting reconstructions).…”