基于离散伴随方程的三维雷达散射截面几何敏感度计算

doi:10.7527/S1000-6893.2019.23361

飞行器气动外形数值优化与设计专栏

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基于离散伴随方程的三维雷达散射截面几何敏感度计算

周琳¹, 黄江涛², 高正红¹

1. 西北工业大学航空学院, 西安 710072;
2. 中国空气动力研究与发展中心, 绵阳 621000

收稿日期:2019-08-09 修回日期:2019-12-11 出版日期:2020-05-15 发布日期:2020-01-02
通讯作者: 高正红 E-mail:zgao@nwpu.edu.cn
基金资助:
西北工业大学翼型、叶栅空气动力学重点实验室项目（JCKYS2019607009）

Three dimensional radar cross section geometric sensitivity calculation based on discrete adjoint equation

ZHOU Lin¹, HUANG Jiangtao², GAO Zhenghong¹

1. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. China Aerodynamics Research and Development Center, Mianyang 621000, China

Received:2019-08-09 Revised:2019-12-11 Online:2020-05-15 Published:2020-01-02
Supported by:
National Key Laboratory of Science and Technology on Aerodynamic Desigh and Research Support Project of Northwestern Polytechincal University (JCKYS2019607009)

摘要/Abstract

摘要： 针对有限差分法计算雷达散射截面（RCS）梯度效率低，采用高精度雷达散射截面评估时计算代价高的问题，提出了一种基于麦克斯韦积分方程离散伴随方程的RCS梯度高效计算方法。基于伴随方程的梯度计算可以通过一次雷达散射截面求解、一次伴随方程求解获得RCS关于所有设计变量的梯度。其中麦克斯韦积分方程离散伴随方程的形式与原方程基本一致，可以采用矩量法（MOM）及多层快速多极子算法（MLFMA）求解。伴随方程求解计算量与直接雷达散射截面评估基本一致，存储量在直接雷达散射截面评估的基础上增加不明显。通过双椎体模型、导弹模型对基于矩量法、多层快速多极子算法的伴随梯度进行验证，证明了基于伴随方法的RCS梯度计算可以实现复杂外形中RCS梯度的高效、高精度求解，为基于梯度的高精度气动/隐身一体化优化提供了基础。

关键词: 雷达散射截面, 梯度计算, 离散伴随方程, 矩量法, 多层快速多极子算法

Abstract: A Radar Cross Section (RCS) gradient calculation method based on adjoint equation of Maxwell integral equation is proposed. This method aims to overcome the high cost and low efficiency in the traditional finite difference calculation method. The adjoint method can obtain the gradients of all design variables by one radar cross-section solution and one adjoint solution. The required calculation amount of the gradient solution is basically independent of the number of design variables. The form of adjoint equation is similar to the original equation, and can be solved by the Method of Moment (MOM) and Multilevel Fast Multipole Algorithm (MLFMA). The calculation and storage amount in solving adjoint equation is basically the same as the calculation of RCS. By adopting the double ogive model and a missile model, two test cases are adopted to ve-rify the reliability and precision of the adjoint method. Gradients calculated based on the adjoint method of MOM and MLFMA are compared with the finite difference results. Numerical results prove the accuracy of the adjoint method, and demonstrate that it can be applied in complex shapes, providing a basis for the construction of gradient-based aerodynamics-stealth optimization framework.

Key words: radar cross section, gradient calculation, discrete adjoint equation, method of moment, multilevel fast multipole algorithm

中图分类号:

V218

周琳, 黄江涛, 高正红. 基于离散伴随方程的三维雷达散射截面几何敏感度计算[J]. 航空学报, 2020, 41(5): 623361-623361.

ZHOU Lin, HUANG Jiangtao, GAO Zhenghong. Three dimensional radar cross section geometric sensitivity calculation based on discrete adjoint equation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(5): 623361-623361.

参考文献 29

[1]	王荣, 闫溟, 白鹏, 等. 飞翼无人机平面外形气动隐身优化设计[J]. 航空学报, 2017, 38(S1):77-84. WANG R, YAN M, BAI P, et al. Optimization design of aerodynamics and stealth for a flying-wing UAV platf-orm[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(S1):77-84(in Chinese).
[2]	蒋相闻, 招启军, 孟晨. 直升机旋翼桨叶外形对雷达特征信号的影响[J]. 航空学报, 2014, 35(11):3123-3136. JIANG X W, ZHAO Q J, MENG C. Effect of helicopter rotor blade shape on its radar signal characteristics[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(11):3123-3136(in Chinese).
[3]	阮颖铮. 雷达截面与隐身技术[M]. 北京:国防工业出版社, 1998:115-120. RUAN Y Z. Radar cross section and stealth technol-ogy[M]. Beijing:National Defense Industry Press, 1998:115-120(in Chinese).
[4]	桑建华. 飞行器隐身技术[M]. 北京:航空工业出版社, 2012:321-334. SANG J H. Low-observable technologies of aircraft[M]. Beijing:Aviation Industry Press, 2012:321-334(in Chinese).
[5]	王明亮, 高正红, 夏露. 气动与隐身性能计算精度对飞行器设计的影响[J]. 飞行力学,2009, 27(6):14-17. WANG M L, GAO Z H, XIA L. Influence of aerodynamic and stealth performance conputation precision on aircraft optimization design[J]. Flight Dynamics, 2009, 27(6):14-17(in Chinese).
[6]	张彬乾, 罗烈, 陈真利, 等. 飞翼布局隐身翼型优化设计[J]. 航空学报, 2014, 35(4):957-967. ZHANG B Q, LUO L, CHEN Z L, et al. On stealth airfoil design for flying wing configuration[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(4):957-967(in Chinese).
[7]	HARRINGTON R F, HARRINGTON J L. Field computation by moment methods[M]. New York:Wiley-IEEE Press,1993:15-20.
[8]	COIFMAN R, ROKHLIN V, WANDZURA S. The fast multipole method for the wave equation:A pedestrian prescription[J]. IEEE Antennas and Propagation Magazine, 1993, 35(3):7-12.
[9]	高正红, 夏露, 李天, 等. 飞行器气动与隐身性能一体化优化设计方法研究[J]. 飞机设计, 2003(3):1-5. GAO Z H, XIA L, LI T, et al. Investigation into collaborative optimization design techniques of aircraft aerodynamics and stealth performances[J]. Aircraft Design, 2003(3):1-5(in Chinese).
[10]	夏露, 张欣, 杨梅花, 等. 飞翼布局翼型气动隐身综合设计[J]. 西北工业大学学报, 2017, 35(5):821-826. XIA L, ZHANG X, YANG M H, et al. Airfoil aerodynamic stealth integrated design for a flying wing configuration[J]. Journal of Northwestern Polytechnical University, 2017, 35(5):821-826(in Chinese).
[11]	ZINGG D W, NEMEC M, PULLIAM T H. A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization[J]. European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, 2008, 17(1-2):103-126.
[12]	黄江涛, 刘刚, 周铸, 等. 基于离散伴随方程求解梯度信息的若干问题研究[J]. 空气动力学学报, 2017, 35(4):554-562. HUANG J T, LIU G, ZHOU Z, et al. Investigation of gradient computation based on discrete adjoint method[J]. Acta Aerodynamica Sinica, 2017, 35(4):554-562(in Chinese).
[13]	黄江涛, 周铸, 刘刚, 等. 飞行器气动/结构多学科延迟耦合伴随系统数值研究[J]. 航空学报, 2018, 39(5):101-112. HUANG J T, ZHOU Z, LIU G, et al. Numerical study of aero-structural multidisciplinary lagged coupled adjoint system for aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(5):101-112(in Chinese).
[14]	黄江涛, 张绎典, 高正红, 等. 基于流场/声爆耦合伴随方程的超音速公务机声爆优化[J]. 航空学报, 2019, 40(5):122505. HUANG J T, ZHANG Y D, GAO Z H, et al. The supersonic jet sonicboom optimization based on flow/sonicboom coupled adjoint equations[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(5):122505(in Chinese).
[15]	BONDESON A, YANG Y, WEINERFELT P. Shape optimization for radar cross sections by a gradient method[J]. International Journal for Numerical Methods in Engineering, 2004, 61(5):687-715.
[16]	WANG L, ANDERSON W K. Adjoint-based shape optimization for electromagnetic problems using discontinuous galerkin methods[J]. AIAA Journal, 2011, 49(6):1302-1305.
[17]	ZHOU L, HUANG J T, GAO Z H. Radar cross section gradient calculation based on adjoint equation of method of moment[C]//Asia-Pacific International Symposium on Aerospace Technology. Singapore:Springer, 2018:1427-1445.
[18]	SONG J, CHEW W C. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering[J]. Microwave and Optical Technology Letters, 1995, 10(1):14-19.
[19]	RAO S M, WILTON D R, GLISSON A W. Electromagnetic scattering by surfaces of arbitrary shape[J]. IEEE Transactions on Antennas & Propagation, 1982, 30(3):409-418.
[20]	张玉, 赵勋旺, 陈岩. 计算电磁学中的超大规模并行矩量法[M]. 西安:西安电子科技大学出版社, 2016:30-45. ZHANF Y, ZHAO X W, CHEN Y. Hyper-large-scale parallel method of moment in computational electromagnetics[M]. Xi'an:Xidian University Press, 2016:30-45(in Chinese).
[21]	麻军. 矩量法及其并行计算在粗糙面和目标电磁散射中的应用[D]. 西安:西安电子科技大学, 2009:25-30. MA J. The application of the method of moment and its parallel computation in EM-scattering from the rough surface and the target[D]. Xi'an:Xidian University, 2009:25-30(in Chinese).
[22]	张玉. 电磁场并行计算[M]. 西安:西安电子科技大学出版社, 2006:37-47. ZHANG Y. Parallel computation in electromagnetics[M]. Xi'an:Xidian University Press, 2006, 37-47(in Chinese).
[23]	聂在平, 胡俊, 姚海英, 等. 用于复杂目标三维矢量散射分析的快速多极子方法[J]. 电子学报, 1999, 27(6):104-109. NIE Z P, HU J, YAO H Y, et al. The fast multipole method for vector analysis of scattering from 3-dimensional objects with complex structure[J]. Acta Electronica Sinica, 1999, 27(6):104-109(in Chinese).
[24]	KNOTT E F, SHAEFFER J F, TULEY M T. Radar cross section[M]. Raleigh:SciTech Publishing, 2004:270-274.
[25]	VAN DER VORST H A. Bi-cgstab:A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems[J]. SIAM Journal on Scientific and Statistical Computing, 1992, 13(2):631-644.
[26]	GIBSON W C. The method of moments in electromagnetics[M]. New York:Chapman and Hall/CRC, 2007:205-220.
[27]	WOO A C, WANG H T G, SCHUH M J, et al. Em programmer's notebook-benchmark radar targets for the validation of computational electromagnetics programs[J]. IEEE Antennas and Propagation Magazine, 1993; 35(1):84-89.
[28]	MORRIS A, ALLEN C S, RENDALL T. Domain-element method for aerodynamic shape optimization applied to modern transport wing[J]. AIAA Journal, 2009, 47(7):1647-1659.
[29]	RENDALL T C, ALLEN C B. Efficient mesh motion using radial basis functions with data reduction algorithms[J]. Journal of Computational Physics, 2009, 228(17):6231-6249.

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于离散伴随方程的三维雷达散射截面几何敏感度计算

Three dimensional radar cross section geometric sensitivity calculation based on discrete adjoint equation

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