混合方法分析电大目标附近天线受扰方向图
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摘要
电大尺寸复杂载体上各种天线和天线阵列的电磁辐射和电磁兼容问题是当今理论界与工程界中极富挑战性的课题。该课题的涉及面相当广泛，研究方法众多。随着计算机技术的不断进步，计算机辅助设计已经在工业产品的设计和生产过程中得到普及。目前，非均匀有理B样条(NURBS)曲面建模技术已经成为工业产品建模的主流方法。基于NURBS曲面建模技术的电磁计算方法是一个紧迫且具有重大理论意义和工程意义的课题。本文紧密结合支撑技术项目，综合考虑传统的高频方法和低频方法的优势，用高低频混合方法来分析这类问题，研究了基于NURBS曲面建模的MOM-PO混合方法以及高阶MOM结合UTD方法，并将其用于分析电大目标附近天线和天线阵列的受扰方向图。本文的主要工作和创新点可以概括为：
1.提出一种改进的基于NURBS建模的PO方法来分析电大散射体附近天线的受扰方向图。该方法克服了传统方法中用球面波代替真实天线，且天线必须远离散射体的局限性。本文用真实天线辐射场作为PO区域的入射场来激发感应电流，使得天线无需远离散射体，增强了算法的通用性。基于SPM的NURBS-PO方法中，使用优化方法搜索驻相点。本文利用Ludwig积分来计算感应电流的曲面积分，使得算法更加简洁易于实现。另一方面研究了基于SPM的NURBS-PO方法的加速算法，使得该算法效率大幅提高。
2.提出一种改进的基于NURBS建模的MOM-PO混合方法来分析位于散射体附近天线的受扰方向图。传统基于NURBS建模的MOM-PO方法中，采用SPM方法计算感应电流的曲面积分，天线必须远离散射体一个波长以上。本文从数值算例及理论两方面分析了SPM方法在近场计算时失效的原因。采用Ludwig积分计算有理贝齐尔曲面上的物理光学感应电流积分，克服了近场计算失效问题。数值算例验证了本文方法的有效性，且不受限于天线与散射体的距离。此外，提出了一种类似于自适应方法的积分区域剖分判定方法来提高算法效率。
3.提出Ludwig积分结合SPM技术的NURBS MOM-PO方法，用于电大平台问题的高效分析。Ludwig积分需要对一个矩形区域进行剖分，为得到较高精度的计算结果，往往剖分较细，使得计算效率不高。SPM方法不需要任何剖分。因此，先对天线单元与散射体的距离进行预判断，如果距离低于一个波长则用Ludwig积分处理，反之则使用SPM方法。利用Ludwig积分结合SPM技术计算有理贝齐尔曲面上物理光学感应电流的积分，既避免了单纯使用SPM方法时近区场计算失效的问题，又避免了单纯使用Ludwig积分时计算效率较低的缺点。
4.提出基于Ludwig积分结合SPM方法的NURBS MOM-PO快速算法。SPM方法求解过程中多次求解关键点消耗大量计算时间，本文引入两种加速技巧，通过对矩量法区域进行分组求解及计算方向图时采用插值关键点方法，极大的提高了NURBS建模MOM-PO混合方法的计算效率。数值结果与不加速的NURBSMOM-PO方法和三角形建模的MOM-PO得到的结果吻合良好。计算时间的对比说明了本文方法与传统方法相比，效率大幅度提高。
5.提出高阶MOM结合UTD分析电大平台附近复杂天线受扰方向图。使用高阶MOM计算无平台下包围复杂天线的近区封闭面上的复矢量场，根据等效原理得到封闭面上的初始电磁流。采用UTD方法计算平台的散射场，迭代封闭面上的电磁流分布。根据迭代结束后的电磁流结合UTD计算天线的受扰方向性图，通过与矩量法的计算结果对比，说明本文方法的精度高，且该方法在计算复杂天线在电大平台下受扰方向图时具有计算时间上的优势。近似方法的提出提高了计算效率，且结果与MOM吻合甚好。本文方法比以往相关文献方法的优势在于考虑了电大平台对天线的影响，使得结果更加可靠。
The study of electromagnetic scattering and electromagnetic compatibility ofsome wire antennas mounted on electrically large complicated platform is a mostlychallenging research topic both in theory and engineering. The technology ofComputer Aided Design (CAD) is widely adopted in the design process of industriesproducts. The emergence of computational electromagnetics reduces a large amountof cost for the electromagnetic analysis. Today, the most popular method forgeometrical design is the Nonuniform Rational B-spline (NURBS) surface.Numerical method based on NURBS surface is an urgent and important issue. Beinglinked with research projects, the NURBS based hybrid Method of Moments andPhysical Optics (MOM-PO) and higher order MOM with Uniform geometricalTheory of Diffraction (UTD) are thoroughly studied. The author’s major work andcontributions are as follows:
1. The Physics Optics (PO) method is used to calculate the disturbed patternof an antenna around the electrically large platform modeled with NURBS surface.The improved Ludwig integral method is applied to compute the integration ofinduced current over the surface. Compared with the existing NURBS-PO method,the new technique overcomes the limitation that the antenna must be located faraway from the scatterer. Since the true scattering field of antenna is replaced byspherical wave in conventional method. The present method also avoids thecomplicated theory and the possible invalidation in searching stationary points ofstationary phase method (SPM) method. Numerical results obtained from proposedapproach show great agreement with that obtained from pure Method of Moment(MOM). The feasibility of the proposed method is obviously demonstrated. And theapproach presented in this paper has the advantage over the MOM method in speedwhen they are used to solve high frequency problems.
2. The MOM-PO hybrid method based on Ludwig integral and modifiedimpedance matrix is used to analyze the disturbed pattern of an antenna around theelectrically large scatterer modeled with NURBS surfaces. Compared with existingiterative MOM-PO method based on SPM, the new method avoids possible problemof iterative convergence. Ludwig integral is utilized to calculate the integral of POcurrents on Bezier surfaces. It overcomes the invalidity of SPM in the traditionalmethod. The comparison of the results obtained by this method with those publishedin literatures and from pure MOM shows the feasibility and accuracy of the present method.
3. The conventional MOM-PO method based on NURBS modeling isimplemented by modifying the voltage matrix. However, the problem of iterativedivergence may occur. To solve this problem, a method of modifying the impedancematrix is presented to avoid the potential divergence. Ludwig integral combiningwith SPM is utilized to calculate the integral of PO currents on Bezier surfaces. Itovercomes the invalidity in the conventional method while keeping its efficiency.The comparison of the results obtained by this method with those published in theliterature and from pure MOM shows feasibility and accuracy of the present method.
4. An efficient and stable MOM-PO hybrid method is proposed to calculatedisturbed pattern of antenna around electrically large platform modeled with NURBSsurfaces. Modified impendence matrix is used to implement the interaction of MOMregion and PO region for avoiding the convergence issue. SPM is used to calculatethe integral of induced current. Both grouping of MOM region and interpolation ofstationary points, are used to accelerate the present approach. Results obtained bythis method agree well with that from traditional Triangle MOM-PO. Comparison ofcomputing time of each method demonstrates the present method is accuracy enoughand much more efficient.
5. The radiation pattern of the complex antenna around electrically largeplatform is analyzed by means of iterative vector fields and UTD method in thispaper. The complex field vectors produced by antenna without platform can beobtained by higher order MOM. The initial currents over the closed surface enclosingthe antenna are computed according to the equivalence theorem. Scattering fieldfrom platform is calculated by UTD method to iterate the currents over the enclosedsurface. After the electromagnetic currents are stable, the disturbed pattern can beobtained by UTD. Based on this method, an approximate method is also presented toimprove the efficiency. The results of the suggested methods show more accurate andhigher efficiency than that of MOM.
1.提出一种改进的基于NURBS建模的PO方法来分析电大散射体附近天线的受扰方向图。该方法克服了传统方法中用球面波代替真实天线，且天线必须远离散射体的局限性。本文用真实天线辐射场作为PO区域的入射场来激发感应电流，使得天线无需远离散射体，增强了算法的通用性。基于SPM的NURBS-PO方法中，使用优化方法搜索驻相点。本文利用Ludwig积分来计算感应电流的曲面积分，使得算法更加简洁易于实现。另一方面研究了基于SPM的NURBS-PO方法的加速算法，使得该算法效率大幅提高。
2.提出一种改进的基于NURBS建模的MOM-PO混合方法来分析位于散射体附近天线的受扰方向图。传统基于NURBS建模的MOM-PO方法中，采用SPM方法计算感应电流的曲面积分，天线必须远离散射体一个波长以上。本文从数值算例及理论两方面分析了SPM方法在近场计算时失效的原因。采用Ludwig积分计算有理贝齐尔曲面上的物理光学感应电流积分，克服了近场计算失效问题。数值算例验证了本文方法的有效性，且不受限于天线与散射体的距离。此外，提出了一种类似于自适应方法的积分区域剖分判定方法来提高算法效率。
3.提出Ludwig积分结合SPM技术的NURBS MOM-PO方法，用于电大平台问题的高效分析。Ludwig积分需要对一个矩形区域进行剖分，为得到较高精度的计算结果，往往剖分较细，使得计算效率不高。SPM方法不需要任何剖分。因此，先对天线单元与散射体的距离进行预判断，如果距离低于一个波长则用Ludwig积分处理，反之则使用SPM方法。利用Ludwig积分结合SPM技术计算有理贝齐尔曲面上物理光学感应电流的积分，既避免了单纯使用SPM方法时近区场计算失效的问题，又避免了单纯使用Ludwig积分时计算效率较低的缺点。
4.提出基于Ludwig积分结合SPM方法的NURBS MOM-PO快速算法。SPM方法求解过程中多次求解关键点消耗大量计算时间，本文引入两种加速技巧，通过对矩量法区域进行分组求解及计算方向图时采用插值关键点方法，极大的提高了NURBS建模MOM-PO混合方法的计算效率。数值结果与不加速的NURBSMOM-PO方法和三角形建模的MOM-PO得到的结果吻合良好。计算时间的对比说明了本文方法与传统方法相比，效率大幅度提高。
5.提出高阶MOM结合UTD分析电大平台附近复杂天线受扰方向图。使用高阶MOM计算无平台下包围复杂天线的近区封闭面上的复矢量场，根据等效原理得到封闭面上的初始电磁流。采用UTD方法计算平台的散射场，迭代封闭面上的电磁流分布。根据迭代结束后的电磁流结合UTD计算天线的受扰方向性图，通过与矩量法的计算结果对比，说明本文方法的精度高，且该方法在计算复杂天线在电大平台下受扰方向图时具有计算时间上的优势。近似方法的提出提高了计算效率，且结果与MOM吻合甚好。本文方法比以往相关文献方法的优势在于考虑了电大平台对天线的影响，使得结果更加可靠。
The study of electromagnetic scattering and electromagnetic compatibility ofsome wire antennas mounted on electrically large complicated platform is a mostlychallenging research topic both in theory and engineering. The technology ofComputer Aided Design (CAD) is widely adopted in the design process of industriesproducts. The emergence of computational electromagnetics reduces a large amountof cost for the electromagnetic analysis. Today, the most popular method forgeometrical design is the Nonuniform Rational B-spline (NURBS) surface.Numerical method based on NURBS surface is an urgent and important issue. Beinglinked with research projects, the NURBS based hybrid Method of Moments andPhysical Optics (MOM-PO) and higher order MOM with Uniform geometricalTheory of Diffraction (UTD) are thoroughly studied. The author’s major work andcontributions are as follows:
1. The Physics Optics (PO) method is used to calculate the disturbed patternof an antenna around the electrically large platform modeled with NURBS surface.The improved Ludwig integral method is applied to compute the integration ofinduced current over the surface. Compared with the existing NURBS-PO method,the new technique overcomes the limitation that the antenna must be located faraway from the scatterer. Since the true scattering field of antenna is replaced byspherical wave in conventional method. The present method also avoids thecomplicated theory and the possible invalidation in searching stationary points ofstationary phase method (SPM) method. Numerical results obtained from proposedapproach show great agreement with that obtained from pure Method of Moment(MOM). The feasibility of the proposed method is obviously demonstrated. And theapproach presented in this paper has the advantage over the MOM method in speedwhen they are used to solve high frequency problems.
2. The MOM-PO hybrid method based on Ludwig integral and modifiedimpedance matrix is used to analyze the disturbed pattern of an antenna around theelectrically large scatterer modeled with NURBS surfaces. Compared with existingiterative MOM-PO method based on SPM, the new method avoids possible problemof iterative convergence. Ludwig integral is utilized to calculate the integral of POcurrents on Bezier surfaces. It overcomes the invalidity of SPM in the traditionalmethod. The comparison of the results obtained by this method with those publishedin literatures and from pure MOM shows the feasibility and accuracy of the present method.
3. The conventional MOM-PO method based on NURBS modeling isimplemented by modifying the voltage matrix. However, the problem of iterativedivergence may occur. To solve this problem, a method of modifying the impedancematrix is presented to avoid the potential divergence. Ludwig integral combiningwith SPM is utilized to calculate the integral of PO currents on Bezier surfaces. Itovercomes the invalidity in the conventional method while keeping its efficiency.The comparison of the results obtained by this method with those published in theliterature and from pure MOM shows feasibility and accuracy of the present method.
4. An efficient and stable MOM-PO hybrid method is proposed to calculatedisturbed pattern of antenna around electrically large platform modeled with NURBSsurfaces. Modified impendence matrix is used to implement the interaction of MOMregion and PO region for avoiding the convergence issue. SPM is used to calculatethe integral of induced current. Both grouping of MOM region and interpolation ofstationary points, are used to accelerate the present approach. Results obtained bythis method agree well with that from traditional Triangle MOM-PO. Comparison ofcomputing time of each method demonstrates the present method is accuracy enoughand much more efficient.
5. The radiation pattern of the complex antenna around electrically largeplatform is analyzed by means of iterative vector fields and UTD method in thispaper. The complex field vectors produced by antenna without platform can beobtained by higher order MOM. The initial currents over the closed surface enclosingthe antenna are computed according to the equivalence theorem. Scattering fieldfrom platform is calculated by UTD method to iterate the currents over the enclosedsurface. After the electromagnetic currents are stable, the disturbed pattern can beobtained by UTD. Based on this method, an approximate method is also presented toimprove the efficiency. The results of the suggested methods show more accurate andhigher efficiency than that of MOM.
引文
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