Automatic parameter selection for Tikhonov regularization in ECT Inverse problem

Abstract

This paper presents 2D images of the eddy current distribution in an aluminium plate by inverting the corresponding magnetic field. Three linear defects with different lengths (5mm, 8mm, 12mm) were machined in a 4mm thick aluminium plate. The magnetic field maps were obtained experimentally using an eddy current measurement setup to scan the defect regions. The probe included in the system contains a planar coil to excite a sinusoidal current with spatially uniform current distribution, and a GMR sensor to measure one magnetic field component. The magnetic field maps were inverted using Tikhonov regularization. A proper choice of the regularization parameter value is essential for the success of the inversion method. In the present paper the determination of the regularization parameter was automated by careful analysis of the energy evolution of the current density data as a function of the regularization parameter. The validation of the resulting regularization parameters was obtained comparing this method with the well-known L-curve. The advantages and disadvantages of the two methods are discussed. Finally, the inversion method with parameter selection was tested with an experimental magnetic field map containing information about an L-shaped defect with length equal to 10mm to estimate the performance of the proposed method in non-linear cracks.