基于截断型自适应交叉近似和奇异值分解的涡流无损检测模型  

An Adaptive Cross Approximation and Singular Value Decomposition Algorithm with Kernel Truncations for Accelerating Solving Eddy Current Nondestructive Testing

作　　者：包扬[1,2] 徐旻宣 BAO Yang;XU Minxuan(College of Electronic and Optical Engineering,Nanjing University of Posts and Telecommunications,Nanjing 210023,China;College of Flexible Electronics(Future Technology),Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学电子与光学工程学院,南京210003 [2]南京邮电大学柔性电子(未来技术)学院,南京210003

出　　处：《南京航空航天大学学报》2023年第6期1126-1132,共7页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：国家自然科学基金(GZ220034)。

摘　　要：探讨了一种高效的三维涡流无损检测求解模型。该模型首次使用截断型自适应交叉算法和奇异值分解算法加速基于边界元法的涡流无损检测模型。该模型使用没有低频崩溃问题的Stratton‐Chu方程作为边界积分方程,然后使用Rao‐Wilton‐Glisson矢量基函数和脉冲基函数分别将等效面电流、磁流和磁场法向分量展开,通过Galerkin方法测试,得到阻抗矩阵。借助八叉树结构,根据块与块之间的距离关系将阻抗矩阵分为对角块、近区块和远区块,其中对角块和近区块使用边界元法直接计算存储,远区块通过综合运用自适应交叉算法、奇异值分解算法和截断核函数算法进行压缩存储。最后,以涡流无损检测基准问题为例,将运用该方法预测的结果与其他模型预测的结果以及实验结果相比较,验证了所提求解模型的准确性和有效性。A 3D numerical model of eddy current nondestructive testing(ECNDT)based on the kernel truncated(KT),adaptive cross approximation(ACA)and singular value decomposition(SVD)algorithms is proposed.It is the first time to apply the KT-ACA-SVD algorithm to accelerate the boundary element method(BEM)‐based ECNDT model.The Stratton-Chu formulation is selected,which has no low frequency breakdown issue,as the boundary integral equation.The equivalent surface electric and magnetic field currents,and normal component of the magnetic field are expended by the Rao-Wilton-Glisson(RWG)vector basis functions,and pulse basis functions,respectively.The Galerkin’s method is chosen as the testing method,then the impedance matrix can be achieved.With the help of octree structure,the impedance matrix can be partitioned into diagonal,near and far block interactions which is decided by the distances between them.The diagonal and near block interactions are computed directly by the full matrix method,while the far block interactions are compressed by the KT-ACA-SVD algorithm.Finally,several nondestructive testing(NDT)tests are conducted to compare the impedance variations predicted by the proposed model with the ones achieved by other methods,including analytical,semi-analytical methods,and the experiment.The results demonstrate both the accuracy and efficiency of the proposed model.

关 键 词：无损检测 边界元法 自适应交叉近似 奇异值分解 截断核函数 

分 类 号：TN98[电子电信—信息与通信工程]