Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
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DOI：
10.1002/mma.5387
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发表时间：
2018-09
影响因子：
2.9
通讯作者：
P. Ledger;W. Lionheart;A. A. S. Amad-A.
中科院分区：
文献类型：
--
作者：
P. Ledger;W. Lionheart;A. A. S. Amad-A.
金属探测中的实际应用涉及多个非均匀导电的可渗透物体，本文的目的是用极化张量来表征这类物体。结果表明，对于涡流模型，由于N个细小的导电性均匀夹杂的存在，磁场中微扰的先导阶项由N个项之和组成，每个项包含一个复对称阶2极化率张量。每个张量包含关于其中一个对象的形状和材料属性的信息，并且与其位置无关。我们得到的渐近展开式推广了已知的单个孤立目标的结果，并适用于目标大小较小且目标间隔足够好的情况。我们还得到了描述非均匀和近距离物体的扰动磁场的第二个展开式，该展开式再次用复对称阶2张量来表征物体。张量的系数可以通过求解一个向量值传输问题来计算，我们用数值例子来说明描述扰动场的渐近公式与数值预测之间的一致性。我们还包括用于定位和识别多个非均匀对象的算法。
Realistic applications in metal detection involve multiple inhomogeneous‐conducting permeable objects, and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading order terms for the perturbation in the magnetic field, due to the presence of N small conducting permeable homogeneous inclusions, comprises of a sum of N terms with each containing a complex symmetric rank 2 polarizability tensor. Each tensor contains information about the shape and material properties of one of the objects and is independent of its position. The asymptotic expansion we obtain extends a previously known result for a single isolated object and applies in situations where the object sizes are small and the objects are sufficiently well separated. We also obtain a second expansion that describes the perturbed magnetic field for inhomogeneous and closely spaced objects, which again characterises the objects by a complex symmetric rank 2 tensor. The tensor's coefficients can be computed by solving a vector valued transmission problem, and we include numerical examples to illustrate the agreement between the asymptotic formula describing the perturbed fields and the numerical prediction. We also include algorithms for the localisation and identification of multiple inhomogeneous objects.