考虑吸波材料的雷达散射截面伴随优化方法

doi:10.7527/S1000-6893.2024.30347

Abstract

Abstract:

The development of anti-stealth technology has put forward higher requirements for the stealth performance of military aircraft. This study establishes a discrete adjoint equation of Maxwell’s equation considering the absorbing material to perform optimization design of low observable aircraft considering the absorbing material. The fast multi-layer multipole expansion form of the adjoint equation is derived， achieving efficient RCS gradient calculation with respect to shape parameters， material electrical parameters， and coating thickness. A switch function is proposed to conduct absorbing material coating position optimization. Shape parameters， material coating position， coating thickness， and electromagnetic parameters are optimized using the adjoint method. Numerical results indicate that the adjoint approach can further reduce the cavity RCS compared to the ideal conductor shape design and material coating. Also， the adjoint approach is able to optimize the design of material parameters and coating thickness， providing guidance for the selection and coating of the absorbing material. Optimization of the coating position based on the switch function can achieve optimal allocation of the absorbing material with the constraint of total material weight. The proposed RCS adjoint optimization method considering the absorbing material can provide technical support for the efficient design of coating position and absorbing material coefficients.

Key words: electromagnetic adjoint equation, radar absorbing material, impedance boundary condition, radar cross section, gradient optimization

CLC Number:

V218

Lin ZHOU, Jiangtao HUANG, Shidong ZHONG, Gang LIU, Jun DENG, Zhenghong GAO. Radar cross section optimization based on adjoint approach considering radar absorbing material[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(24): 130347.

Figures/Tables 20

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References 27

1	桑建华. 飞行器隐身技术［M］. 北京：航空工业出版社， 2013.
	SANG J H. Low-observable technologies of aircraft［M］. Beijing： Aviation Industry Press， 2013 （in Chinese）.
2	姬金祖. 隐身原理［M］. 北京：北京航空航天大学出版社， 2018.
	JI J Z. Stealth principle［M］. Beijing： Beijing University of Aeronautics & Astronautics Press， 2018 （in Chinese）.
3	王明亮，高正红. 吸波材料在飞行器隐身设计中的应用研究［J］. 航空计算技术， 2005， 35（4）： 45-49.
	WANG M L， GAO Z H. Research about designing stealth aircraft by using radar absorbing material［J］. Aeronautical Computing Technique， 2005， 35（4）： 45-49 （in Chinese）.
4	王龙，钟易成，张堃元. 金属/介质涂覆的S形扩压器电磁散射特性［J］. 物理学报， 2012， 61（23）： 193-201.
	WANG L， ZHONG Y C， ZHANG K Y. Electromagnetic scattering study for metal/dielectic coated inlet diffuser［J］. Acta Physica Sinica， 2012， 61（23）： 193-201 （in Chinese）.
5	陈炀，招启军，蒋相闻，等. 武装直升机雷达散射截面计算及雷达吸波材料影响分析［J］. 南京航空航天大学学报， 2019， 51（1）： 75-82.
	CHEN Y， ZHAO Q J， JIANG X W， et al. Radar cross section calculation on armed helicopter and effect analyses of radar absorbing material［J］. Journal of Nanjing University of Aeronautics & Astronautics， 2019， 51（1）： 75-82 （in Chinese）.
6	郭霄，杨青真，施永强，等. 介质涂覆位置对球面收敛喷管电磁散射特性影响［J］. 航空学报， 2017， 38（4）： 240-248.
	GUO X， YANG Q Z， SHI Y Q， et al. Electromagnetic scattering characteristics of spherical convergent vector nozzle with coating medium at different parts［J］. Acta Aeronautica et Astronautica Sinica， 2017， 38（4）： 240-248 （in Chinese）.
7	高翔，施永强，杨青真，等. 介质涂覆位置对双S弯排气系统电磁散射特性影响研究［J］. 物理学报， 2015， 64（2）： 24103.
	GAO X， SHI Y Q， YANG Q Z， et al. Electromagnetic scattering characteristics of double S-shape exhaust nozzle with different coating medium parts‍［J］. Acta Physica Sinica， 2015， 64（2）： 24103 （in Chinese）.
8	宋宇，杨青真，高翔，等. 介质涂覆位置对二元塞式喷管的电磁散射特性影响［J］. 推进技术， 2022， 43（11）： 156-163.
	SONG Y， YANG Q Z， GAO X， et al. Electromagnetic scattering characteristics of binary plug nozzle with coating medium at different part［J］. Journal of Propulsion Technology， 2022， 43（11）： 156-163 （in Chinese）.
9	徐含乐，祝小平，周洲，等. 基于左手材料的翼面隐身结构设计及优化［J］. 航空学报， 2014， 35（12）： 3331-3340.
	XU H L， ZHU X P， ZHOU Z， et al. Design and optimization of low detectable wing structure based on LHM［J］. Acta Aeronautica et Astronautica Sinica， 2014， 35（12）： 3331-3340 （in Chinese）.
10	黄爱凤. 飞行器翼面隐身结构电磁散射特性设计优化［D］. 南京：南京航空航天大学， 2005.
	HUANG A F. Optimization of the design of electromagnetic scattering characteristics of the stealth structure of the aircraft wing surface［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2005 （in Chinese）.
11	李莎莎. 基于吸波材料的隐身目标散射特性分析［D］. 西安：西安电子科技大学， 2021.
	LI S S. Study on scattering characteristics of stealth targets based on absorbing materials［D］. Xi’an： Xidian University， 2021 （in Chinese）.
12	聂毅，余雄庆. 翼面隐身结构电磁散射特性稳健优化设计研究［J］. 航空学报， 2007， 28（）： 104-108.
	NIE Y， YU X Q. Study on robust design optimization of electromagnetic scattering for stealthy wing structure［J］. Acta Aeronauticaet Astronautica Sinica， 2007， 28（）： 104-108 （in Chinese）.
13	ZHOU L， HUANG J T， GAO Z H. Radar cross section gradient calculation based on adjoint equation of method of moment［C］∥ZHANG X. Asia-Pacific International Symposium on Aerospace Technology. Singapore： Springer， 2019： 1427-1445.
14	ZHOU L， HUANG J T， GAO Z H， et al. Three-dimensional aerodynamic/stealth optimization based on adjoint sensitivity analysis for scattering problem‍［J］. AIAA Journal， 2020， 58（6）： 2702-2715.
15	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.
	ZHOU L， HUANG J T， GAO Z H. Three dimensional radar cross section geometric sensitivity calculation based on discrete adjoint equation［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（5）： 623361 （in Chinese）.
16	周琳，陈宪，黄江涛，等. 基于伴随方程和自动微分的雷达散射截面表面灵敏度计算［J］. 航空学报， 2023， 44（22）： 128508.
	ZHOU L， CHEN X， HUANG J T， et al. Radar cross section surface sensitivity calculation based on adjoint approach and automatic differentiation［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（22）： 128508 （in Chinese）.
17	LI M， CHEN J J， FENG X Y， et al. An efficient adjoint method for the aero-stealth shape optimization design［J］. Aerospace Science and Technology， 2021， 118： 107017.
18	LI M， BAI J Q， LI L， et al. A gradient-based aero-stealth optimization design method for flying wing aircraft［J］. Aerospace Science and Technology， 2019， 92： 156-169.
19	曾渊. 阻抗边界条件理论与研究应用［D］. 西安：西北工业大学， 2003.
	ZENG Y. Impedance boundary conditions theory and research applications［D］. Xi’an： Northwestern Polytechnical University， 2003 （in Chinese）.
20	WANG D S. Limits and validity of the impedance boundary condition on penetrable surfaces［J］. IEEE Transactions on Antennas and Propagation， 1987， 35（4）： 453-457.
21	HOPPE D J， RAHMAT-SAMII Y. Impedance boundary conditions in electromagnetics［M］. Washington， D.C.： Taylor & Francis， 1995.
22	李江海，阙肖峰，胡静伟，等. 基于阻抗边界条件建模的涂敷目标电磁散射分析［J］. 微波学报， 2015， 31（1）： 7-11.
	LI J H， QUE X F， HU J W， et al. Analysis of electromagnetic scattering for coated objects using the impedance boundary conditions‍［J］. Journal of Microwaves， 2015， 31（1）： 7-11 （in Chinese）.
23	YAN S， JIN J M. Self-dual integral equations for electromagnetic scattering from IBC objects［J］. IEEE Transactions on Antennas and Propagation， 2013， 61（11）： 5533-5546.
24	SONG J M， 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.
25	韩奎. 超电大目标电磁散射问题的积分方程区域分解方法研究［D］. 成都：电子科技大学， 2018.
	HAN K. Research on integral equation domain decomposition method for solving electromagnetic scattering from electrically extra large objects［D］.Chengdu： University of Electronic Science and Technology of China， 2018 （in Chinese）.
26	黄江涛，周琳，陈宪，等. 基于NS/CFIE伴随方程的飞行器气动隐身综合优化［J］. 航空学报， 2023， 44（12）： 127757.
	HUANG J T， ZHOU L， CHEN X， et al. Integrated aerodynamic and stealth optimization of aircraft based on NS/CFIE adjoint equations［J］. Acta Aeronauticaet Astronautica Sinica， 2023， 44（12）： 127757 （in Chinese）.
27	阙肖峰，聂在平. 一类基于MLFMA的分组稀疏近似逆预条件技术［C］∥2009年全国天线年会论文集. 北京：中国电子学会， 2009： 677-680.
	QUE X F， NIE Z P. A grouped sparse approximate inverse preconditioning for MLFMA ［C］∥The 2009 National Antenna Annual Conference Proceedings. Beijing： Chinese Institute of Electronics， 2009： 677-680 （in Chinese）.

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Radar cross section optimization based on adjoint approach considering radar absorbing material

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