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Edge based finite element simulation of eddy current phenomenon and its application to defect characterization.

机译:基于边缘的涡流现象的有限元模拟及其在缺陷表征中的应用。

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摘要

Edge based finite elements are finite elements whose degrees of freedom are assigned to edges of finite elements rather than nodes. Compared with conventional node based counterparts, they offer many useful properties. For example, they enforce tangential continuity only on inter-element boundaries but no normal continuity; they allow a vector field separated as the sum of the gradient of a scalar function and the remaining part. This dissertation presents a magnetic vector potential formulation implemented with edge elements to simulate eddy current phenomenon. The additional degree of freedom associated with the magnetic vector potential is fixed with the help of tree and co-tree separation from graph theory. The validity of the method is verified using well-known benchmark problems.; A phenomenological signal inversion scheme is proposed to characterize defect profiles from eddy current probe signals. The method relies on the edge element based forward model to predict probe responses and a minimization algorithm to minimize an objective function representing the squared error between the modal prediction and the observed signal. A gradient-based minimization algorithm is first investigated. The long computation time associated with the gradient calculation is reduced using the adjoint equation based method. However, gradient-based methods tend to converge to a poorer local minimum. A genetic algorithm and a simulated annealing algorithm are employed to improve performance. The performance of these stochastic methods in the context of the defect characterization problem is studied. The preliminary results show the effectiveness of the stochastic methods.
机译:基于边缘的有限元是其自由度分配给有限元的边缘而不是节点的有限元。与常规的基于节点的副本相比,它们提供了许多有用的属性。例如,它们仅在元素间边界上执行切向连续性,而没有法向连续性;它们允许将矢量场分隔为标量函数和其余部分的梯度之和。本文提出了一种利用边缘元素模拟涡流现象的磁矢量势公式。借助图论中的树和共树分离,可以确定与磁矢量电势相关的附加自由度。使用已知的基准问题验证了该方法的有效性。提出了一种现象学信号反演方案,以从涡流探查信号中表征缺陷轮廓。该方法依赖于基于边缘元素的正向模型来预测探针响应,并且依赖于最小化算法来最小化表示模态预测和观测信号之间平方误差的目标函数。首先研究了基于梯度的最小化算法。使用基于伴随方程的方法可以减少与梯度计算相关的较长计算时间。但是,基于梯度的方法趋于收敛到较差的局部最小值。遗传算法和模拟退火算法被用来提高性能。研究了这些随机方法在缺陷表征问题中的性能。初步结果表明了随机方法的有效性。

著录项

  • 作者

    Li, Yue.;

  • 作者单位

    Iowa State University.;

  • 授予单位 Iowa State University.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 2002
  • 页码 133 p.
  • 总页数 133
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 无线电电子学、电信技术;
  • 关键词

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