Unique shape detection in transient eddy current problems
Unique shape detection in transient eddy current problems
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DOI：
10.1088/0266-5611/29/9/095004
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发表时间：
2013-09
期刊：
影响因子：
2.1
通讯作者：
L. Arnold;B. Harrach
中科院分区：
文献类型：
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作者：
L. Arnold;B. Harrach
瞬时激励电流产生电磁场，进而在近端导体中感应电流。对于缓变场，这可以通过涡流方程来描述，该方程是通过忽略麦克斯韦方程中的介电位移电流而获得的。涡流方程为抛物-椭圆型方程。在绝缘区域中，场瞬时适应激励（椭圆行为），而在导电区域中，由于感应的涡电流（抛物线行为），这种适应需要一些时间。本工作的主题是通过电磁测量来定位被非导电介质包围的导体，即，根据激励电流的知识和相应电磁场的测量。我们表明，导体是唯一确定的测量，并给出一个明确的标准，以确定是否一个给定的点是内部或外部的导电域。这个标准作为一个严格合理的非迭代数值重建策略的基础。
Transient excitation currents generate electromagnetic fields which in turn induce electric currents in proximal conductors. For slowly varying fields, this can be described by the eddy current equations, which are obtained by neglecting the dielectric displacement currents in Maxwell’s equations. The eddy current equations are of parabolic–elliptic type. In insulating regions, the field instantaneously adapts to the excitation (elliptic behavior), while in conducting regions, this adaptation takes some time due to the induced eddy currents (parabolic behavior). The subject of this work is to locate the conductor(s) surrounded by a non-conducting medium from electromagnetic measurements, i.e., from knowledge of the excitation currents and measurements of the corresponding electromagnetic fields. We show that the conductors are uniquely determined by the measurements, and give an explicit criterion to decide whether a given point is inside or outside the conducting domain. This criterion serves as a base for rigorously justified non-iterative numerical reconstruction strategies.