Variational Bayesian Inversion Approaches for Ultrasonic Tomography

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Ultrasonic non-destructive evaluation (NDE) is critical for the structural assessment of the UK's aging industrial infrastructure, as well as for the monitoring and quality control of modern additive manufacturing methods. Traditional imaging algorithms within the ultrasonic NDE community typically assume that the component being inspected is primarily homogeneous, with heterogeneities occurring at sub-wavelength scales. Unfortunately, in many materials of interest, for example carbon fibre reinforced polymers (CFRPs) or polycrystalline welds, this assumption is invalid and can significantly lower the probability of detection of embedded defects. However, prior knowledge of the spatially varying material properties within the component can allow correction of the delay laws on which time domain imaging algorithms are usually based and result in more reliable detection and imaging of defects. Ultrasonic travel time tomography presents a practicable non-destructive approach to recovering the spatially dependent material properties of a component from measurements taken on its surface. Since tomographic inversion is significantly nonlinear, Monte Carlo (MC) sampling methods are often used for this purpose, but they are generally computationally intractable for large datasets and high-dimensional parameter spaces. The aim of this project is to examine the potential of Variational Bayesian Inversion (VBI) methods in place of MC approaches. These methods formulate the Bayesian inversion problem as a deterministic optimisation problem, seeking an approximation to the posterior distribution from a pre-defined family of probability distributions through the minimisation of the Kullback-Leibler (KL) divergence. In this way, a closed form expression estimating the posterior distribution can be achieved (in contrast to the numerical approximation obtained using MC methods) at much lower computational expense. This project will apply this approach to two distinct and industrially relevant inverse problems:a) The reconstruction of velocity fields from ultrasonic travel time measurements made on the boundary of the component.b) The reconstruction of locally anisotropic stiffness maps from ultrasonic travel time measurements made on the boundary of the component.The reconstructed maps of the component's spatially varying material properties will then be used in conjunction with existing imaging algorithms to quantify the improvement achieved in flaw detection capabilities.