Differential imaging of evolution in elastic backgrounds with unknown microstructure
Major components of nuclear power plants e.g., reactors, fuel cells and containment vessels are comprised of highly heterogeneous composites that (a) their topology and properties at micro- and meso- scales are uncertain or in most cases unknown, and (b) their deterioration due to various chemo-physical processes such ascorrosion, irradiation, thermal cycling, etc. are not yet fully understood. These processes are responsible for the continuous microstructural evolution, leading to an inevitable development of micro/macro cracks and other anomalies, that will gradually result in the loss of structural integrity and diminished functional performance such as radiation shielding.
This talk is focused on timely detection of degradation in such materials — i.e., anomalies at the microstructure scale, and active spatiotemporal tracking of their evolution. In this vein, a fast waveform tomography solution will be introduced for 3D reconstruction of evolving regions in a complex elastic background by way of ultrasonic waves. To this end, sequential sets of boundary measurements are leveraged within the framework of active sensing to carefully design a non-iterative indicator functional that is insensitive to the (unknown) stationary scatterers of the background domain e.g., its time-invariant interfaces and inhomogeneities. This differential imaging functional is rooted in the recently developed generalized linear sampling method whose affiliated cost functional is rigorously revised so that it’s minimizer carries pertinent invariant properties. The performance of this new damage indicator will be illustrated through a set of numerical experiments.