利用BEM-FEM混合法对高频电磁层析成像系统中金属屏蔽层的优化分析

A Hybrid BEM and FEM Numerical Approach for the Optimization of Metallic Shield in a High Frequency Magnetic Induction Tomography

摘要: 电磁层析成像技术是一种基于电磁感应原理的成像技术。外加激励电源在导电物体中产生涡流，进而生成二次磁场，该磁场反过来会影响到原有磁场的分布。当激励频率非常高时，导电物体可以看作是完美导体。此时，磁场对物体的渗透深度非常浅，从而基于边界积分方程的边界元法便成为一种有效的分析方法。但是如果电磁层析成像系统中存在一个无法忽略尺寸的屏蔽层时，边界元法就失去了它的优势。针对这种情况，我们提出了一种边界元–有限元混合法。其中，有限元法用于计算屏蔽层对主磁场的影响，边界元法用于计算完美导体在被测区域内移动时接收线圈上的感应电压。通过这种方法，可以计算出在不同参数的屏蔽层的影响下，电磁层析成像系统的灵敏度分布，进而通过合适的灵敏度评估参数对屏蔽层进行优化设置。

Abstract: Magnetic induction tomography (MIT) is an imaging technique based on the measurement of the magnetic field perturbation due to eddy currents induced in conducting objects exposed to an external magnetic excitation field. When the driving frequency is significantly high relative to the frequency range that MIT normally operates, a highly conducting and permeable metallic target between the coils can be treated as perfect electric conductors (PEC). In this scenario, the penetration depth of the magnetic field into the target is extremely small and Boundary Element Method (BEM) based on integral formulations becomes an effective way to analyze this kind of scattering problems. However, BEM is most efficient when the scatter object is small rather than distributed. This is not suitable for the case when a surrounding shield of significant size and surface area is incorporated in the BEM model, which negates any benefits due to the BEM formulation. For this reason, we proposed a hybrid method in this paper, which combines the BEM and the Finite Element Method (FEM). FEM is used to calculate the shield effect while BEM is used to calculate the perturbation due to a small PEC inside the sensing space. In this way, we are able to compute sensitivity maps for MIT due to the effect of different shield configurations. An appropriate index related to the sensitivity maps was proposed to obtain the optimal parameters of the shield.