平板导体涡流场并矢格林函数的快速计算  

Fast Calculation of Dyadic Green’s Function of Eddy Current Field in a Conductive Plate

作　　者：幸玲玲[1] 

机构地区：[1]南京师范大学电气与自动化工程学院,江苏省南京市210042

出　　处：《中国电机工程学报》2007年第36期57-62,共6页Proceedings of the CSEE

基　　金：江苏省高校自然科学研究资助项目(05KJB470060)。

摘　　要：用积分方程法求解平板导体中含有裂缝的涡流场时,需要大量计算并矢格林函数中包含的广义Sommerfeld积分(generalized Sommerfeld integrals,GSI)。将矩阵束方法推广应用于涡流场中广义Sommerfeld积分的计算,将极点的求解转变为矩阵广义特征值问题的求解,分别用奇异值分解方法和最小二乘法确定极点和留数,讨论了不同采样间隔和矩阵束参数对极点分布的影响。该方法将GSI转化为有限项级数之和,极大地加速了并矢格林函数的计算。根据涡流无损检测中的几组典型数据,比较了用该文方法和直接数值积分法计算并矢格林函数的精度和求解速度。大量计算表明,在场点与源点距离小于5倍透入深度时,该文方法计算误差均在2%以下,计算速度较之数值积分法提高100倍以上,为用积分方程法快速计算涡流场奠定了基础。The paper deals with evaluation of dyadic Green＇s functions that arise in eddy current testing for a conductive plate. The matrix pencil method（MPM） is extended to evaluate generalized Sommerfeld integrals （GSI） in dyadic Green＇s function. The computations of poles are transformed into solving generalized eigenvalue problems. The poles and residues are found by singular-value decomposition and least-square method. The effects of sampling periods and pencil parameter on distribution of poles are discussed. By present method, the Sommerfeld integrals can be evaluated in terms of their closed-form representations quickly. The accuracy and cost time of calculating the Sommerfeld integrals by the present method are compared with those obtained by numerical integration. It is found that the present technique can give an error of less than two percent at the field-to-source point distance less than 5 skin depths, and can give a computing speed over 100 times faster than numerical integration. With the present technique, the perturbed eddy current fields in terms of integral equation can be computed more rapidly.

关 键 词：涡流无损检测 并矢格林函数 Sommerfeld积分 矩阵束方法 

分 类 号：TM154[电气工程—电工理论与新技术]