A regularization method based on level-sets for the problem of crack detection from electrical measurements

Abstract

We investigate regularization methods for solving the problem of crack detection in bounded planar domains from electrical measurements on the boundary. Based on the multiple level-set approach introduced in [Dorn, et al., J.Comput.Phys.2009] and on the regularization strategy devised in [DeCezaro, et al., Inv.Probl.2009], we propose a Tikhonov type method for stabilizing the inverse problem. Convergence and stability results for this Tikhonov method are proven. An iterative method of (multiple) level-set type is derived from the optimality conditions for the Tikhonov functional, and a relation between this method and the iterated Tikhonov method is established. The proposed level-set method is tested on the same benchmark problem considered in [Dorn, et al., J.Comput.Phys.2009]. The numerical experiments demonstrate its ability to identify cracks in different scenarios with high accuracy even in the presence of noise.

A combination of extended finite element method and the Kriging model based crack identification method

“…In the forward analysis problem, part of the physical properties of the structure are generally known, and the response values of the structure, such as stress and displacement are obtained by solving the control differential equation. For the inversion analysis problem [44], some unknown physical characteristics of the structure are retrieved by obtaining the response value of the response point. The inversion of structural internal defects is a kind of classical inversion analysis problem.…”