Damage identification in plates under uncertain boundary conditions

Abstract Nondestructive damage identification is a central task in industrial applications in, for example, aeronautical, civil and naval engineering. The identification approaches based on (physical) models rely on the accuracy of the model predictions, and typically suffer from effects caused by ubiquitous modeling errors and uncertainties. The identification problems are typically unstable inverse problems but may also be (apparently) stable when considering low dimensional parametrizations for the defects. The present paper considers the identification of defects in plates under uncertain boundary conditions. To partially compensate for the boundary uncertainties, we adopt the Bayesian framework for inverse problems and use approximate marginalization over the model uncertainties: the process of marginalization propagates the model uncertainties to the uncertainties in the estimated parameters. We employ a low dimensional parametrization for the defects, which would, in principle, allow for least squares or the more general maximum likelihood estimation approaches. We will show, however, that under uncertain boundary conditions, maximum likelihood estimates can yield unfeasible estimates while the approximate marginalization over uncertainties provides feasible ones.