Reconstruction of round cracks in the three-dimensional ultrasonic NDT

  • M. Brigante
  • M.A. Sumbatyan

Abstract

We propose a direct numerical algorithm applied to reconstruct a round (penny-shaped) crack in the 3d acoustic medium. The geometry of the crack is defined by three parameters, its radius and orientation. The input data is based on the back-scattered far-field diagram which is assumed to be known at a fixed frequency for all directions of scattering. We firstly study respective direct problem by reducing this to some 2d integral equations over the face of the crack. This is developed both for acoustically soft and acoustically hard boundary conditions. In both the cases the equation is of the first kind. For acoustically soft crack the kernel possesses a weak singularity, but in the case of acoustically hard boundary conditions we have a first-kind equation with a hyper-singular kernel. Then we develop appropriate algorithms to solve numerically the arising integral equations. Further, the inverse problem on crack reconstruction is reduced to a minimization of a certain non-quadratic functional. This optimization problem is solved numerically by a global random search.
Published
2010-11-25
Section
Articles