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

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