Eddy-current evaluation of three-dimensional flaws in flat conductive materialsusing a Bayesian approach

Abstract

This paper deals with quantitative eddy-current non-destructive evaluation ofvolumetric flaws. The inversion of eddy-current data leads to detection,localization, sizing and shape reconstruction of a flaw. The eddy-current probe isconstituted by a driving coil which is placed at an adapted fixed position and apick-up coil which scans the surface above the flawed region in order to collect thedata. The eddy-current probe response is linked to the local variations of theelectrical conductivity of the inhomogeneous material. A numerical model followsfrom the discretization of the coupled integral equations by using a method ofmoments. To solve the resulting nonlinear inverse problem, an inversionscheme is proposed within a Bayesian estimation framework. Lack ofinformation due to the band-pass behaviour of the forward operator iscompensated by introducing prior knowledge. The advantages of thisapproach result from combining the information contained in the data andthe a priori knowledge on the solution to be estimated. The inversionproblem is transformed into an optimization problem which is dealt withusing a sequence of local minimizations performed via a standard descentalgorithm. In order to illustrate the behaviour and the efficiency of theproposed approach, several reconstructions from simulated data are presented.