An inversion scheme for sizing crack from signals of the motion-induced eddy current testing method based on a new formula of signal gradient of ferromagnetic materials

In this paper, an inversion scheme for the profile reconstruction of a fatigue crack in rails from the motion-induced eddy current testing (MIECT) signals is proposed based on the conjugate gradient (CG) optimization method and the fast MIECT forward simulator developed by authors. To calculate the gradient of MIECT signals with respect to the crack parameters, a simplified analytical gradient formula is deduced, which enables a high efficiency crack reconstruction from MIECT signals for a crack in ferromagnetic material. The validity of the inversion schemes is demonstrated at first by reconstructing cracks with numerical simulated signals for ferromagnetic materials with an oblique elliptic crack model. The good reconstruction results reveal that the new signal grandient formula is efficient for reconstructing crack in ferromagnetic material with the CG algorithm. Finally, sizing of artificial cracks are carried out with use of measured MIECT signals due to cracks in plates of both non-magnetic and ferromagnetic materials. The reconstructed crack parameters are in good agreement with the true values, which experimentally proved the validity and efficiency of the proposed inversion scheme and the new signal gradient formula for MIECT inversion.