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

DOI: 10.12677/EAA.2014.32003, PP. 13-24

Keywords: 电磁层析成像，完美导体，边界元–有限元法，灵敏度，屏蔽层
Magnetic Induction Tomography, Perfect Electric Conductor, BEM-FEM, Sensitivity Map, Shield

Full-Text   Cite this paper   Add to My Lib

Abstract:

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。

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.

References

[1]	Watson, S., Williams, R.J., Gough, W.A. and Griffiths, H. (2008) A magnetic induction tomography system for samples with conductivities less than 10 S m？1. Measurement Science &Technology, 19, 045501.
[2]	Yin, W.L. and Peyton, A.J. (2004) Simultaneous measurements of thickness and distance of a thin metal plate with an electromagnetic sensor using a simplified model. IEEE Transactions on Instrumentation and Measurement, 53, 1335- 1338.
[3]	Ma, L., Wei, H.Y. and Soleimani, M. (2013) Planar magnetic induction tomography for 3D near subsurface imaging. Progress in Electromagnetics Research, 138, 65-82.
[4]	Wei, H.Y. and Soleimani, M. (2012) Three-dimensional magnetic induction tomography imaging using a matrix free Krylov subspace inversion algorithm. Progress in Electromagnetics Research, 122, 29-45.
[5]	Wei, H.Y. and Soleimani, M. (2012) Four dimensional reconstruction using magnetic induction tomography: Experimental study. Progress in Electromagnetics Research, 129, 17-32.
[6]	Ma, X., Peyton, A.J., Higson, S.R., Lyons, A. and Dickinson, S.J. (2012) Hardware and software design for an electromagnetic induction tomography (EMT) system for high contrast metal process applications. Measurement Science & Technology, 17, 111-118.
[7]	Griffiths, H. (2001) Magnetic induction tomography. Measurement Science & Technology, 12, 1126-1131.
[8]	Yin, W.L., Chen, G., Chen, L.J. and Wang, B. (2011) The design of a digital magnetic induction tomography (MIT) system for metallic object imaging based on half cycle demodulation. Sensors Journal, 11, 2233-2240.
[9]	Soleimani, M., Lionheart, W.R.B., Riedel, C.H. and Dossel, O. (2003) Forward problem in 3D magnetic induction tomography (MIT). 3rd World Congress on Industrial Process Tomography, Banff, 2-5 September 2003, 275- 280.
[10]	Wu, K.L., Delisle, G.Y., Fang, D.G. and Lecours, M. (1990) Coupled finite element and boundary element methods in electromagnetic scattering. Progress in Electromagnetics Research, 2, 113-132.
[11]	Liao, S. and Vernon, R.J. (2006) On the image approximation for electromagnetic wave propagation and PEC scattering in cylindrical harmonics. Progress in Electromagnetics Research, 66, 65-88.
[12]	Sun, K.L., O’Neill, K., Shubitidze, F., Haider, S.A. and Paulsen, K.D. (2002) Simulation of electromagnetic induction scattering from targets with negligible to moderate penetration by primary fields. IEEE Transactions on Geoscience and Remote Sensing, 40, 910-927.
[13]	Pham, M.H. and Peyton, A.J. (2008) A model for the forward problem in magnetic induction tomography using boundary integral equations. IEEE Transactions on Magnetics, 44, 2262-2267.
[14]	Zhao, Q., Hao, J.N. and Yin, W.L. (2013) A simulation study of flaw detection for rail sections based on high frequency magnetic induction sensing using the boundary element method. Progress in Electromagnetics Research, 141, 309-325.
[15]	Zhao, Q., Chen, G., Hao, J.N., Xu, K. and Yin, W.L. (2013) Numerical approach for the sensitivity of a high-frequency magnetic induction tomography system based on boundary elements and perturbation method. Measurement Science and Technology, 24, 074004.
[16]	Peyton, A., Watson, S., Williams, R., Griffiths, H., and Gough, W. (2003) Characterizing the effects of the external electromagnetic and shield on a magnetic induction tomography sensor. 3rd World Congress on Industrial Process Tomography, Banff, 2-5 September 2003, 352-357.
[17]	Morrison, J.A. (1979) Integral equations for electromagnetic scattering by perfect conductors with two-dimensional geometry. Bell System Technical Journal, 58, 409-425.
[18]	Graglia, R.D. (1987) Static and dynamic potential integrals for linearly varying source distributions in two- and three-dimensional problems. IEEE Transactions on Antennas and Propagation, 35, 662-669.
[19]	Lazic, L. and Mastorakis, N. (2008) Orthogonal array application for optimal combination of software defect detection tech-niques choices. WSEAS Transactions on Computers, 7, 1319-1333.

Full-Text