EDDY-CURRENT INTERACTION WITH AN IDEAL CRACK .2. THE INVERSE PROBLEM

Eddy-current inversion is the process whereby the geometry of a flaw i n a metal is derived from electromagnetic probe measurements. An inver sion scheme is described for finding the shape and size of cracks from eddy-current probe impedance measurements. The approach is based on a n optimization scheme that seeks to minimize a global error function q uantifying the difference between predicted and observed probe impedan ces. The error minimum is sought using a standard descent algorithm th at requires a knowledge of the gradient of the error with respect to a variation of the flaw geometry. Computation of the gradient is based on a provisional flaw estimate, then the flaw estimate is updated in a ''direction'' that reduces the error. The process continues iterative ly until a convergence criterion has been satisfied. Then the final fl aw estimate should match the shape of the real defect. An equation for the gradient has been derived using an integral formulation of the id eal crack problem. Numerical estimates of the error gradient and the p robe impedances have been calculated using approximations based on the moment method. Tests of the inversion scheme using single frequency p robe impedance measurements have been carried out by calculating the s hapes of narrow slots in aluminum alloy plates. Good agreement is foun d between the optimum profiles and the measured slot shapes.