钢筋混凝土结构的微波成像正问题研究
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摘要
随着电磁学理论的发展和计算机性能的不断提高,计算电磁学在最近几年得到了长足的发展。时域有限差分方法是计算电磁学里重要的研究方法,它将电场和磁场在时间顺序上交替抽样,将电磁场在空间上划分为Yee元胞,即将麦克斯韦方程离散以后构成显式差分方程,然后在时间上迭代求解。因而,由给定响应电磁问题的初始值,时域有限差分方法就可以逐步推进地求得以后各个时刻空间电磁场的分布。所以本文将采用时域有限差分方法解决实际问题。
本文以微波在钢筋混凝土中的传播为研究对象开展正问题计算研究。依照时域有限并分法的基本思想,结合钢筋混凝土结构的微波检测原理,给出了具体的解题步骤。其中包括:计算测量钢筋混凝土结构的微波频段;对模型进行网格剖分;由麦克斯韦方程得到描述高频电磁场的差分方程对每个Yee氏单元进行差分计算;再根据入射平面波的加入条件,设定以0°角加载到总场边界;在空气的最外层用完全匹配层(PML)截断仿真区间来模拟无限大自由空间中钢筋混凝土的散射问题。本文在吸收边界的选取中,用MATLAB编写了两种吸收边界的程序来模拟波在自由空间中的传播,从理论比较到数值仿真的比较发现PML吸收边界法优于Mur吸收边界法。
最后,建立了多个不同规格的钢筋混凝土模型。用3.0GHz频率的微波进行仿真,用Fortran语言编写程序,得到场强-位置关系图象,形象直观的显示了在混凝土内存在钢筋的情况。把该仿真结果与ANSYS的仿真结果进行归一化比较,曲线趋势比较一致。结果表明,整个问题的设计思路是正确的。用时域有限差分法实现钢筋混凝土中的微波场数值计算是可行的,而且方便快捷的。
With the development of the electromagnetic theory and the improvement of the computer performance, the computational electromagnetism has been developed fatherly in recent years. Finite Difference Time Domain (FDTD) method is an important method of computational electromagnetic research. It alternately samples chronological electric and magnetic fields, meshes the electric field into Yee unit, that is to say, disperses Maxwell's equations into the explicit differential equations, and gets the iterative solution. Therefore, with the initial value of given reply electromagnetic problem, the FDTD method is able to get the electromagnetic field distribution in space at anytime step by step. Here will take the FDTD method to solve practical problems.
In this paper, microwave dissemination in the reinforced concrete as research subjects for questions compute and research. The specific problem-solving steps are given according to basic idea of FDTD and the microwave detection principle of the reinforced concrete structure. Including calculating the microwave frequency band of measuring reinforced concrete structure, meshing the model, differential equations describing high-frequency electromagnetic fields from Maxwell's equations to difference calculate for each Yee unit, loading the plane wave to the boundary of the total field with 0 degree according to the condition of its accession, and in the outer layer truncating the simulation region with PML, using this model to simulate the scatting of reinforced concrete in infinite space. In the selection of the absorbing boundary, this paper programming two absorbing boundaries to simulate propagation of wave in free space with MATLAB. From the theoretical comparison to the numerical simulation, it is found that the PML absorbing boundary condition is superior to Mur absorbing boundary condition.
Finally, Variable specification reinforced concrete models are built and simulation is made on 3.0GHz microwave frequency by using Fortran programming language. By this way, electric field intensity-location relation image is received. It displays steel bar distributing situation in concrete intuitively. Compare with the normalized simulation result of ANSYS, the curves superposition degree is satisfying with small error. The results indicate that the whole design is reasonable. It is feasible and convenient to realize nondestructive testing for reinforced concrete structure by using FDTD method.
本文以微波在钢筋混凝土中的传播为研究对象开展正问题计算研究。依照时域有限并分法的基本思想,结合钢筋混凝土结构的微波检测原理,给出了具体的解题步骤。其中包括:计算测量钢筋混凝土结构的微波频段;对模型进行网格剖分;由麦克斯韦方程得到描述高频电磁场的差分方程对每个Yee氏单元进行差分计算;再根据入射平面波的加入条件,设定以0°角加载到总场边界;在空气的最外层用完全匹配层(PML)截断仿真区间来模拟无限大自由空间中钢筋混凝土的散射问题。本文在吸收边界的选取中,用MATLAB编写了两种吸收边界的程序来模拟波在自由空间中的传播,从理论比较到数值仿真的比较发现PML吸收边界法优于Mur吸收边界法。
最后,建立了多个不同规格的钢筋混凝土模型。用3.0GHz频率的微波进行仿真,用Fortran语言编写程序,得到场强-位置关系图象,形象直观的显示了在混凝土内存在钢筋的情况。把该仿真结果与ANSYS的仿真结果进行归一化比较,曲线趋势比较一致。结果表明,整个问题的设计思路是正确的。用时域有限差分法实现钢筋混凝土中的微波场数值计算是可行的,而且方便快捷的。
With the development of the electromagnetic theory and the improvement of the computer performance, the computational electromagnetism has been developed fatherly in recent years. Finite Difference Time Domain (FDTD) method is an important method of computational electromagnetic research. It alternately samples chronological electric and magnetic fields, meshes the electric field into Yee unit, that is to say, disperses Maxwell's equations into the explicit differential equations, and gets the iterative solution. Therefore, with the initial value of given reply electromagnetic problem, the FDTD method is able to get the electromagnetic field distribution in space at anytime step by step. Here will take the FDTD method to solve practical problems.
In this paper, microwave dissemination in the reinforced concrete as research subjects for questions compute and research. The specific problem-solving steps are given according to basic idea of FDTD and the microwave detection principle of the reinforced concrete structure. Including calculating the microwave frequency band of measuring reinforced concrete structure, meshing the model, differential equations describing high-frequency electromagnetic fields from Maxwell's equations to difference calculate for each Yee unit, loading the plane wave to the boundary of the total field with 0 degree according to the condition of its accession, and in the outer layer truncating the simulation region with PML, using this model to simulate the scatting of reinforced concrete in infinite space. In the selection of the absorbing boundary, this paper programming two absorbing boundaries to simulate propagation of wave in free space with MATLAB. From the theoretical comparison to the numerical simulation, it is found that the PML absorbing boundary condition is superior to Mur absorbing boundary condition.
Finally, Variable specification reinforced concrete models are built and simulation is made on 3.0GHz microwave frequency by using Fortran programming language. By this way, electric field intensity-location relation image is received. It displays steel bar distributing situation in concrete intuitively. Compare with the normalized simulation result of ANSYS, the curves superposition degree is satisfying with small error. The results indicate that the whole design is reasonable. It is feasible and convenient to realize nondestructive testing for reinforced concrete structure by using FDTD method.
引文
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[10]Weedon W H,Chew W C,Mayes P E.A step frequency radar imaging system for microwave nondestructive evaluation,Progress in Electromagnetics Research.2000,18:121-146.
[11]Ghodgaonkar Deepak K,et al.Microwave nondestructive testing of Malaysian timber for grading applications,Proceedings of the 14th WCNDT,New Delhi,1996.
[12]张丽霞.电磁场有限元分析中并行计算的研究:(硕士学位论文).天津:河北工业大学 2006.
[13]曾新,苏杰.微波无损检测技术及应用.仪器仪表用户,2003,2.
[14]龚杏.微波断层成像重建算法研究:(博士学位论文).杭州:浙江大学 2001.
[15]李志平,何国瑜.基于STOLT插值聚焦的二维近场微波成像.电波科学学报,2007,22(1):12-17
[16]李杰.微波成像算法研究:(硕士学位论文).西北工业大学,2002,1.
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[19]倪光正.工程电磁场原理.北京:高等教育出版社,2004.
[20]杜平安,甘娥忠,于亚婷.有限元法-原理、建模及应用.北京:国防工业出版社,2006.
[21]何红雨.电磁场数值计算法与MATLAB实现:(硕士学位论文).上海:华北师范大学,2004.
[22]魏学旺.电磁波在钢筋混凝土墙中的反射与透射研究:(硕士学位论文).汕头:汕头大学,2007.
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[24]Elodie Richalot,Matthieu Bonilla,Man-Fai Wong,"Electromagnetic propagateion into Reinforced-Concrete Walls",IEEE Transations on Microwave Theory and Techniques,2000,48(3):121-124.
[25]R.Paknys,"Reflection and transmitsion by reinforced concrete-numerical and asymptotic analysis",IEEE Trans.Antennas Propagat,2003,51(10):489-494.
[26]Daniel Pena,Rodolfo Feict,"Measurement and modeling of propagateion losses in brick and concrete walls for the 900-MHz band",IEEE Trans.Antennas Propagat,2003,51(1):1521-1527.
[27]秦卫平,丁胜高,张业荣.时域分析钢筋混凝土砖墙对电磁脉冲短径传播的影响,南京邮电学院学报,2005,25(6),12-16.
[28]倪光正,杨仕友,钱秀英.工程电磁场数值计算.机械工业出版社,2006.
[29]苏俊宏.屯磁场数值分析方法讨论.西安工业学院学报,1994,14(3):191-197.
[30]Nannapaneni Narayana Rao(著),周建华游佰强(译).工程电磁学基础.北京:机械工业出版社 2006,459-483.
[31]何红雨.电磁场数值计算法与MATLAB实现.武汉:华中科技大学出版社,2004.
[32]贺昌辉.矩量法分析目标的近场电磁散射:(硕士学位论文).武汉:华中师范大学,2006.
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