Ultrasonic flaw sizing inverse problems

Abstract

A review is given of model-based methods that have been used to solve ultrasonic nondestructive evaluation (NDE) flaw sizing problems. The focus of the review is on those challenging NDE flaw sizing problems where the flaw is small and the amount of scattering data that can be collected is limited. Various approaches for solving these inverse problems are described, with emphasis on methods based on the Born and Kirchhoff approximations. We discuss the sensitivity of these methods to noise, bandwidth limitations, and other issues that are important to the success or failure of these inverse approaches. As an alternative to these existing methods we discuss an approach based on the early-time flaw response. Finally, we describe some open issues that prevent a number of these methods from routinely being used in practice and describe some potential solutions.

Inverse problems in elasticity

“…are now functions of both s and t. Note that the last integral in (122), which is unaffected by whether time-harmonic or transient conditions are assumed, has been omitted in (136) for the sake of brevity. To take it into account in a time-domain cost function of the form (136), one has simply to append the last term of formulae (129), (131) and (135) to (138), (139) and (140), respectively. The sensitivity formula (140) is applied in [25,33] to 2D crack identification problems formulated by means of a time-domain BEM approach, with the 2D frequency-domain situation is considered in [128].…”

XFEM‐based crack detection scheme using a genetic algorithm

“…*u *n = 0 on c (3) and u is allowed to be discontinuous across c . For given , S , D , N , k, S and the crack c , the forward or direct problem consists of finding the values u of u on some given manifold (typically part of the external boundary), subject to (1)- (3).…”

“…For given , S , D , N , k, S and the crack c , the forward or direct problem consists of finding the values u of u on some given manifold (typically part of the external boundary), subject to (1)- (3). However, the identification problem which is the subject of this investigation is an inverse problem: Given , S , D , N , k, S as well as the manifold and u , one has to find the crack boundary c such that u satisfies (1)-(3) as well as u = u on .…”

An ultrasonic inverse scattering imaging technique for defect located at an arbitrary position in the cylindrical material

“…5,6 So, the challenge of defect reconstruction can be considered as a typical inverse problem. 7,8 Some linearlized elastodynamic inversion methods to reconstruct the shape of defect have been investigated. 9,10 These methods are all based on the elastodynamic Born and Kirchhoff inverse scattering methods, and the amplitude of the scattering wave in the frequency domain plays key roles in these methods.…”