Characterizing the shape and material properties of hidden targets from magnetic induction data
Characterizing the shape and material properties of hidden targets from magnetic induction data
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DOI：
10.1093/imamat/hxv015
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发表时间：
2015-12
影响因子：
1.2
通讯作者：
P. Ledger;W. Lionheart
中科院分区：
文献类型：
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作者：
P. Ledger;W. Lionheart
本文的目的是澄清金属探测中的一个主要谜团，并证实HT .M.HM的工程预测，对于扰动磁场测量对置于低频背景场中的一般导电物体的存在的灵敏度，是正确的。解释一下，HT是由发射器线圈生成的背景场，HM是由接收线圈生成的背景场，就好像它被用作发射器一样，并且Mind是秩2偏振张量，其描述了对象的形状和材料属性。为了证明这一点，我们应用最近推导的渐近公式的扰动磁场由于存在的导电物体，这是表示在一类新的秩4极化张量（H。Ammari，J. Chen，Z. Chen，J. Garnier和D. Volkov Target detection and characterization from electromagnetic induction data，Journal de Mathe Iématiques Pures et Escherque Iées（2013）http：//dx.doi.org/10.1016/j.matpur.2013.05.002）.乍一看，这似乎与工程预测相矛盾，然而，与此相反，我们表明，在最多9个，而不是81个系数需要描述的秩4张量的导电对象和进一步的9个，如果该对象是磁性的。然后，我们证明了秩4张量实际上减少到秩2张量，从而为工程预测提供了坚实的理论基础。此外，通过结合约化的电导率和磁导率张量，我们得到了一个对称的秩2张量，它描述了一个一般的导电物体在只有6个复杂的独立系数。对于旋转和镜像对称的对象，我们表明，系数的数量仍然较小。我们包括数值例子来证明，新的极化张量可以通过求解向量值传输问题的hp有限元精确计算，并包括证据来确认，描述扰动场的渐近公式与数值预测一致。
The purpose of this paper is to clear up a major mystery in metal detection and confirm that the engineering prediction of HT .M.HM, for the sensitivity of measurements of the perturbed magnetic field to the presence of a general conducting object placed in a low frequency background field, is correct. Explicitly, HT is the background field generated by the transmitter coil, HM is the background field generated by the receiving coil as if it were used as a transmitter and Mind is a rank 2 polarisation tensor, which describes the shape and material properties of the object. To show this, we apply a recently derived asymptotic formula for the perturbed magnetic field due to the presence of a conducting object, which is expressed in terms of a new class of rank 4 polarisation tensors (H. Ammari, J. Chen, Z. Chen, J. Garnier and D. Volkov Target detection and characterization from electromagnetic induction data, Journal de Mathe I�matiques Pures et Applique I�es (2013) http://dx.doi.org/10.1016/j.matpur.2013.05.002). At first sight this appears to contradict the engineering prediction, however, contrary to this, we show that at most 9 rather than 81 coefficients are required to describe the rank 4 tensor for a conducting object and a further 9 are required if the object is magnetic. We then show that the rank 4 tensor does in fact reduce to a rank 2 tensor, thus providing a solid theoretical foundation for the engineering prediction. Furthermore, by combining the reduced conductivity and permeability tensors, we obtain a symmetric rank 2 tensor, which describes a general conducting object in terms of just 6 complex independent coefficients. For objects with rotational and mirror symmetries we show that the number of coefficients is still smaller. We include numerical examples to demonstrate that the new polarisation tensors can be accurately computed by solving a vector valued transmission problem by hp�finite elements and include evidence to confirm that the asymptotic formula describing the perturbed fields agrees with the numerically predictions.