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

地方C.本文将电位CT法推广应用于A. C.潜在的读数。主要研究结果如下：1.本文提出了一种计算二维物体在A。C.应用，假设场是静止的，并使用场量的复变量表示。测得的A. C.电位分布与计算值吻合较好.建立了计算甚低频和甚高频三维电磁场的边界元公式，并编制了边界元程序。A. C.计算了带有表面裂纹的平板中的电势。提出了一种基于最小残差法的表面裂纹形状反演方法。C.潜在的读数。数值模拟表明，当电位读数为2位有效数字时，估算的裂纹形状与给定的裂纹形状吻合得相当好。估计的裂纹形状与3位有效数字的电位读数一致。测量A。C.对具有表面裂纹的铁磁和顺磁平板进行了电势分析。测量的电位读数被用来估计基于反演方案的裂纹形状。结果表明，尽管在测量A时仍有一些技术问题没有解决，但可以对裂纹形状作出相当好的估计。C.高频下的电位分布.基于最小残差法，研究了优化技术在裂纹形状、位置和尺寸估计中的适用性。提出了一种分层的估计方法，并发现在估计中是有用的。优化变量的选择也被认为是重要的，在实现有效的估计。

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.