Crack detection using electrostatic measurements

Abstract

Abstract. In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation of our algorithm more computationally demanding.Mathematics Subject Classification. 35R30, 31A25.

Imaging Schemes for Perfectly Conducting Cracks

“…The paper extends several recent results, concepts, and methods for imaging cracks. Crack detection algorithms using electrostatic measurements have been derived in [11,10,17]. In [5] a continuous model was considered and an asymptotic expansion of the boundary perturbations that are due to the presence of a small crack was derived.…”

Crack reconstruction using a level-set strategy

“…To compute the corresponding physical measurements given by (10) and corresponding to the applied potential c j , we employ a straightforward finite difference scheme.…”

Crack identification for transient heat operator by using domain decomposition method

“…These methods does not allow the recovring the crack, they give only qualitative results (information on the shape and the location of the crack). Further more, they are usually based on the essential assumption that the over determined boundary data are 'complete', which means that they are known on the whole outer boundary of the body (Andrieux and Ben Abda 1996 [4]; Brühl et al 2001 [14]; Baratchart et al 1999 [7]). …”