Model-based deep neural network inversion for ultrasonic reconstruction of thick-section welds

The interpretation of ultrasonic wave propagation in inhomogeneous materials remains a challenging task. This is a topic of particular interest in the nuclear industry, where the inspection of inhomogeneous thick-section welds is vital to meet safety standards. Such welds are characterised by columnar grains with varying preferred orientations resulting from a complex solidification process. Consequently, conventional post-processing techniques of ultrasonic data may lead to erroneous conclusions, as the ultrasonic beam is distorted and attenuated, no longer following a straight path. This issue can be resolved if material information is available. We propose a model-based deep neural network (DNN) inversion workflow to infer weld microstructure description from time-of-flight (ToF) maps. Work to date focused on grain orientations; in this contribution, we extend it to weld geometry, array position, and the elastic tensor. The workflow uses numerically generated welds and a fast ray-tracing solver based on the shortest-ray-path (SRP) principle to determine propagation times. The weld orientation configurations (weld maps) use the generalised Ogilvy description, sampled in a parameter space with up to ten variables, such as the dominant grain orientation, the rate of change of the grain orientations, the chamfer angle, the array position, and the coefficients of the transversely isotropic elastic tensor in 2D. Therefore, the characterisation considers both geometric and material properties, encompassing a broad range of welds. We develop, use, and evaluate several DNN-based metamodels to determine weld maps from ultrasonic array data and validate the approach using grain-scale finite-element simulations and experimental ToF measurements. Weld maps resulting from the inversion are used to determine the delay laws for correcting the ultrasonic images of defects, achieving a signal-to-noise ratio improvement of up to 6.4dB.