MCIVER, M., 1991. An inverse problem in electromagnetic crack detection. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 47 (2), pp.127-145.
In this work, the inverse problem of predicting the shape and size of a surfacebreaking
crack in a nonferrous metal sheet is examined. The crack is interrogated
by a uniform stream of alternating current and thin-skin electromagnetic theory is
used. The initial data is assumed to be the distribution of the normal component
of the magnetic field along the top of the crack. The inverse problem is
formulated using the potential for the surface magnetic field on one crack face
and its conjugate function as the independent variables. An application of
Green's theorem leads to a Fredholm integral equation of the first kind for the
shape of the lower edge of the crack. The behaviour of the shape function near
the crack tips is determined by examining the complex potential and its inverse
function for a circular arc shaped crack. With the use of this information, the
integral equation is solved numerically for general initial data, using a minimization
technique. In addition, an explicit solution to the equation is found for one
particular class of initial data. Finally, the numerical procedure is tested using
potential distributions from cracks of known shape.