Uncertainty Quantification and Sensitivity Analysis in Subsurface Defect Detection with Sparse Models

The purpose of this paper is to conduct a thorough investigation of a stochastic eddy-current testing problem, when the geometric parameters of the system under study are characterized by uncertainty. Focusing on the case of subsurface defect detection, we devise reliable surrogates for the quantities of interest (QoI) based on the principles of the generalized polynomial chaos (PC) and using the orthogonal matching pursuit (OMP) solver to promote sparsity in the approximate models. In addition, a variance-based approach is implemented for the sequential construction of the necessary sample set, enabling more accurate estimation of the statistical metrics without imposing additional computational overhead. Apart from quantifying the inherent uncertainty, a sensitivity analysis is performed that assesses the impact of each geometric variable on the QoI, via the computation of Sobol indices. The efficiency of the OMP-PC algorithm is demonstrated in two variants of the subsurface-discontinuity problem, yielding at the same time useful conclusions regarding the properties of the stochastic outputs.