Measurement of Shape of Three-Dimensional Surface Crack by A. C. Electric Potential CT Method Using Frequency Information

将直流电势CT(计算机层析成像)方法扩展到从交流电势读数测量表面裂纹的形状。所获得的主要结果概括如下：1.对二维体在交流作用下的电磁场进行了有限元推导和程序设计，假定场量是定常的，场量采用复变量表示。交流电势分布的实测值与计算值吻合较好。建立了计算甚低频和甚高频下三维电磁场的边界元公式，并编制了边界元程序。对含表面裂纹平板的交流电势进行了计算。提出了一种基于最小残差法的表面裂纹形状反演方法，用于从多种交流电势读数中估计表面裂纹的形状。数值模拟表明，当势能读数为两位数时，估算的裂纹形状与给定值吻合较好。所估计的裂纹形状与3位有效数字的电势读数吻合得很好。测量了含表面裂纹的铁磁板和顺磁板的交流电势。根据测得的电势读数，基于反演法估计裂纹的形状。结果表明，虽然在高频下测量交流电势分布仍然存在一些技术问题，但可以很好地估计裂纹的形状。考察了基于最小残差法的优化技术在裂纹形状、位置和尺寸估计中的适用性。提出了一种分层次的评估方法，并在评估中得到了应用。研究还发现，优化变量的选择对于实现有效的估计也很重要。

The D. C. electric potential CT (computed tomography) method was extended to measurement of shape of a surface crack from A. C. potential readings. The main results obtained are summarized as follows.1. Finite element formulation and programming were made for calculating electromagnetic fields in a two-dimensional body under A. C. application, assuming that the fields were stationary and using complex variable representation of filed quantities. The measured A. C. potential distribution agreed fairly well with the calculated distribution.2. Boundary element formulations were made for calculating three-dimensional electromagnetic fields under very low frequency and very high frequency, and boundary element programming was made. A. C. electric potential in a plate with a surface crack was calculated. An inversion scheme based on the least residual method was developed for estimating the shape of surface crack from several A. C. potential readings. Numerical simulations showed that the estimated crack shape agreed fairly well with the given ones when potential readings had 2 significant digits. The estimated crack shape agreed well potential readings with 3 significant digits were used.4. Measurement of A. C. potential were made for ferromagnetic and paramagnetic plates with a surface crack. Measured potential readings were used to estimate the crack shape based on the inversion scheme. It was found that fairly good estimation of crack shape can be made, although there remained technical problems unresolved in measuring A. C. potential distribution under high frequencies.5. Applicability of the optimization techniques in estimating crack shape, location and size based on the least residual method was examined. A hierarchical procedure in the estimation was proposed and was found useful in the estimation. Selection of variables of optimization was also found to be important in attaining efficient estimation.