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.

在本文中，基于共轭梯度（CG）优化方法和作者开发的快速MIECT正向模拟器，提出了一种从运动感应涡流检测（MIECT）信号重建钢轨疲劳裂纹轮廓的反演方案. 为了计算 MIECT 信号相对于裂纹参数的梯度，推导了一个简化的解析梯度公式，这使得能够从 MIECT 信号对铁磁材料中的裂纹进行高效的裂纹重建。反演方案的有效性首先通过用斜椭圆裂纹模型的铁磁材料的数值模拟信号重建裂纹来证明。良好的重建结果表明，新的信号梯度公式对于用CG算法重建铁磁材料中的裂纹是有效的。最后，由于非磁性和铁磁材料板中的裂纹，使用测量的 MIECT 信号进行人工裂纹的尺寸测量。重构的裂纹参数与真实值吻合较好，实验证明了所提出的反演方案和新的信号梯度公式用于MIECT反演的有效性和有效性。