基于卷积神经网络的双站雷达散射截面减缩超表面设计

朱顺凯; 袁方; 胡凯; 皮涛涛; 朱熙铖; 李程

doi:10.7498/aps.74.20250109

摘要

随着雷达组网技术的发展成熟, 未来电磁隐身对抗中双站雷达散射截面(radar cross section, RCS)减缩将比单站更为重要. 人工电磁超表面为双站RCS减缩提供了全新的技术途径. 然而, 受制于大规模阵列优化耗时及双站RCS减缩全空间最值特性, 目前的双站 RCS 减缩超表面设计还存在效率不高、性能较差的问题. 鉴于此, 本文提出了一种小样本条件下的卷积神经网络(convolutional neural network, CNN)方法, 通过定向优化超表面相位分布, 实现雷达回波全空间均匀散射, 从而达到双站 RCS 减缩效果. 本方法结合了卷积特征提取、残差增强与全连接优化模块, 配合自定义损失函数, 可高效捕捉漫反射相位与 RCS 全空间最值的多维度复杂关系. 理论计算、全波仿真和样品测试结果表明, 在7.26—10.74 GHz 频段内, 利用本方法设计的超表面可实现10 dB以上的双站RCS减缩, 相比传统优化算法减缩效果提升17.2%, 且优化效率显著提高, 有望为武器装备的全空间电磁隐身提供新的技术思路.

关键词:

Abstract

Radar cross section (RCS), a crucial physical quantity that characterizes the backscattering intensity of targets under radar illumination, is the primary metric for assessing stealth capabilities. With the development of radar detection technologies, RCS reduction has become a forefront research topic in radar stealth, aiming to minimize target detectability. With the maturity of radar networking technology, the bistatic radar RCS reduction is becoming increasingly important in future electromagnetic stealth countermeasures compared with the monostatic radar RCS reduction. Artificial electromagnetic metasurfaces have introduced innovative technical approaches for realizing the bistatic radar RCS reduction. However, current metasurface designs still face challenges related to inefficiency and suboptimal performance, mainly due to the time-consuming nature of large-scale array optimization and the global extremum characteristics of bistatic radar RCS reduction. To overcome these limitations, this study proposes a few-shot convolutional neural network (CNN)-based approach, which achieves uniform full-space radar echo scattering by directionally optimizing metasurface phase distributions, thereby enabling effective bistatic radar RCS reduction. This approach integrates convolutional feature extraction, residual enhancement, and fully connected optimization modules with a customized loss function to efficiently capture the complex multidimensional relationships between diffuse reflection phases and the full-space RCS extrema. Theoretical calculations, full-wave simulations, and experimental tests show that the metasurface designed with this approach can achieve over 10 dB of Bistatic Radar RCS reduction in a frequency range from 7.26 GHz to 10.74 GHz. The method also ensures uniform diffuse reflection across the full space for various incidence angles (30°, 45°, 60°). Compared with traditional optimization algorithms, this method enhances RCS reduction by 17.2% while significantly improving computational efficiency. This approach provides a promising new technical paradigm for achieving full-space electromagnetic stealth in advanced weapon systems.

Keywords:

metasurface /
bistatic radar cross section reduction /
convolutional neural network

作者及机构信息

1.
南京信息工程大学电子与信息工程学院, 南京　210044

2.
国防科技大学第六十三研究所, 南京　210007

3.
国防科技大学电子科学学院, 长沙　410073

通信作者: 袁方, 13379260913@163.com ; 李程, licheng@nudt.edu.cn

基金项目: 国家资助博士后研究人员计划(批准号: GZB20240991)和国家自然科学基金青年科学基金(批准号: 62401596)资助的课题.

Authors and contacts

1.
School of Electronics and Information Engineering, Nanjing University of Information Science andTechnology, Nanjing 210044, China

2.
The Sixty-third Research Institute, National University of Defense Technology, Nanjing 210007, China

3.
College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China

Corresponding author: YUAN Fang, 13379260913@163.com ; LI Cheng, licheng@nudt.edu.cn

Funds: Project supported by the Postdoctoral Fellowship Program of CPSF (Grant No. GZB20240991) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 62401596).

文章全文

参考文献

[1]	Rao G A, Mahulikar S P 2002 Aeronaut. J. 106 629 Google Scholar
[2]	Ball R E, Albrecht R S, Horne R L 2003 The Fundamentals of Aircraft Combat Survivability: Analysis and Design (2nd Ed.) (Reston: AIAA) pp8–56
[3]	Westwick P 2019 Stealth: The Secret Contest to Invent Invisible Aircraft (Oxford: Oxford University Press) pp5–42
[4]	Singh H, Antony S, Jha R M 2016 Plasma-based Radar Cross Section Reduction (Singapore: Springer) pp1–46
[5]	Knott E F 2012 Radar Cross Section Measurements (New York: Springer) pp12–36
[6]	Knott E F, Schaeffer J R, Tuley M T 2004 Radar Cross Section (2nd Ed.) (Reston: SciTech Publishing) pp4–22
[7]	Kim S H, Lee S Y, Zhang Y, Park S J, Gu J 2023 Adv. Sci. 10 2303104 Google Scholar
[8]	Ananth P B, Abhiram N, Krishna K H, Nisha M S 2021 Mater. Today Proc. 47 4872 Google Scholar
[9]	Ye D, Wang Z, Xu K, Li H, Huangfu J, Wang Z, Ran L 2013 Phys. Rev. Lett. 111 187402 Google Scholar
[10]	Wang J, Yang R, Ma R, Tian J, Zhang W 2020 IEEE Access 8 105815 Google Scholar
[11]	Liu Y, Zhao X 2014 IEEE Antennas Wirel. Propag. Lett. 13 1473 Google Scholar
[12]	Yu N, Genevet P, Kats Ma, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333 Google Scholar
[13]	Gao X, Han X, Cao W P, Li H O, Ma H F, Cui T J 2015 IEEE Trans. Antennas Propag. 63 3522 Google Scholar
[14]	Abdullah M, Koziel S 2022 IEEE Trans. Microwave Theory Tech. 70 264 Google Scholar
[15]	Paquay M, Iriarte J C, Ederra I, Gonzalo R, Maagt P de 2007 IEEE Trans. Antennas Propag. 55 3630 Google Scholar
[16]	Chen W, Balanis C A, Birtcher C R 2015 IEEE Trans. Antennas Propag. 63 2636 Google Scholar
[17]	Sang D, Chen Q, Ding L, Guo M, Fu Y 2019 IEEE Trans. Antennas Propag. 67 2604 Google Scholar
[18]	Cui T J, Qi M Q, Wan X, Zhao J, Cheng Q 2014 Light Sci. Appl. 3 e218 Google Scholar
[19]	Liu X, Gao J, Xu L, Cao X, Zhao Y, Li S 2016 IEEE Antennas Wirel. Propag. Lett. 16 724 Google Scholar
[20]	Fu C, Han L, Liu C, Lu X, Sun Z 2021 IEEE Trans. Antennas Propag. 70 2352 Google Scholar
[21]	Li W, Huang N, Kang Y, Zou T, Ying Y, Yu J, Zheng J, Qiao L, Li J, Che S 2024 IEICE Electron. Express 21 20240246 Google Scholar
[22]	Qi W J, Yu C, Du J L, Zhao Y J 2022 Int. J. RF Microwave Comput. Aided Eng. 32 23306 Google Scholar
[23]	Koziel S, Abdullah M 2020 IEEE Trans. Microwave Theory Tech. 69 2028 Google Scholar
[24]	Tao S, Pan X T, Li M K, Xu S H, Yang F 2020 IEEE J. Emerg. Sel. Top. Circuits Syst. 10 114 Google Scholar
[25]	杨欣雨 2023 硕士学位论文 (南京: 东南大学) Yang X Y 2023 M. S. Thesis (Nanjing: Southeast University
[26]	袁方, 毛瑞棋, 高冕, 郑月军, 陈强, 付云起 2022 物理学报 71 084102 Google Scholar Yuan F, Mao R Q, Gao M, Chen Q, Fu Q Y 2022 Acta Phys. Sin. 71 084102 Google Scholar
[27]	Yuan F, Wang G M, Xu H X, Cai T, Zou X J, Pang Z H 2017 EEE Antennas Wirel. Propag. Lett. 16 3188 Google Scholar
[28]	Han X M, Xu H J, Chang Y P, Lin M, Zhang W Y, Xin W 2020 IEEE Access 8 162313 Google Scholar
[29]	Zhou Y, Cao X Y, Gao J, Li S, Liu X 2017 Electron. Lett. 53 1381 Google Scholar
[30]	Katoch S, Chauhan S S, Kumar V 2021 Multimed. Tools Appl. 80 8091 Google Scholar
[31]	Wang D S, Tan D P, Liu L 2018 Soft Comput. 22 387 Google Scholar
[32]	Pan X, Xue L, Lu Y, Sun N 2019 Multimed. Tools Appl. 78 29921 Google Scholar
[33]	Dumoulin V, Visin F 2016 arXiv:1603.07285 [stat.ML]
[34]	Xu B, Wang N Y, Chen T Q, Li M 2015 arXiv: 1505.00853 [cs.LG]
[35]	Bjorck N, Gomes C P, Selman B, Weinberger K Q 2018 arXiv: 1806.02375 [cs.LG]
[36]	Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R 2014 J. Mach. Learn. Res. 15 1929
[37]	Dubey S R, Singh S K, Chaudhuri B B 2022 Neurocomputing 503 92 Google Scholar
[38]	Zhou P, Xie X, Lin Z, Yan S 2024 IEEE Trans. Pattern Anal. Mach. Intell. 46 6486 Google Scholar
[39]	Shi G, Zhang J, Li H, Wang C 2019 Neural Process. Lett. 50 57 Google Scholar
[40]	Al-Kababji A, Bensaali F, Dakua S P 2022 arXiv: 2202.06373 [cs.CV]
[41]	Yuan F, Xu H X, Jia X Q, Wang G M, Fu Y Q 2020 IEEE Trans. Antennas Propag. 68 2463 Google Scholar

施引文献

图 1 (a)随机相位分布; (b)随机相位3D远场图; (c)随机相位2D远场图

Fig. 1. (a) Random phase distribution; (b) 3D far-field of random phase; (c) 2D far-field of random phase

下载: 全尺寸图片幻灯片

图 2 (a)—(d) GA, PSO, PSO-GA, PSO-SA优化后的相位分布; (e)—(h) 优化相位分布后的3D远场图; (i)—(l)优化相位分布后的2D远场图

Fig. 2. (a)–(d) Phase distributions optimized by GA, PSO, PSO-GA, and PSO-SA; (e)–(h) 3D far-field patterns of the optimized phase distributions; (i)–(l) 2D far-field patterns of the optimized phase distributions

下载: 全尺寸图片幻灯片

图 3 优化算法迭代过程中RCS均值的变化趋势

Fig. 3. Variation trend of RCS mean value in the iteration process of optimization algorithms

下载: 全尺寸图片幻灯片

图 4 CNN 模型示意图

Fig. 4. Diagram of CNN model.

下载: 全尺寸图片幻灯片

图 5 全连接层结构示意图

Fig. 5. Diagram of fully connected layer structure

下载: 全尺寸图片幻灯片

图 6 (a) Leaky ReLU激活函数图; (b) Sigmoid激活函数图

Fig. 6. (a) Leaky ReLU activation function graph; (b) Sigmoid activation function graph

下载: 全尺寸图片幻灯片

图 7 (a)损失函数图; (b) RCS 值迭代曲线图; (c)模型运行 100次结果图

Fig. 7. (a) Loss function diagram; (b) RCS value iteration curve diagram; (c) results of 100 runs with model

下载: 全尺寸图片幻灯片

图 8 (a) CNN 优化后的相位分布; (b) CNN 优化相位分布后的3D远场图; (c) CNN优化相位分布后的2D远场图

Fig. 8. (a) Phase distribution optimized by CNN; (b) 3D far-field patterns after optimizing phase distribution by CNN; (c) 2D far-field patterns after optimizing phase distribution by CNN

下载: 全尺寸图片幻灯片

图 9 (a) 各类算法优化效果; (b) 各类算法运行时间

Fig. 9. (a) Optimization effect of various algorithms; (b) running time of various algorithms

下载: 全尺寸图片幻灯片

图 10 (a) 单元图; (b) 2 × 2子阵图

Fig. 10. (a) Cell diagram; (b) 2 × 2 submatrix

下载: 全尺寸图片幻灯片

图 11 (a)—(d) PEC, 随机, PSO-SA 优化, CNN 优化相位分布后的3D远场图; (e)—(h) PEC, 随机, PSO-GA优化, CNN优化相位分布后的2D远场图

Fig. 11. (a)–(d) 3D far-field patterns after phase distribution optimization by PEC, Random, PSO-SA, and CNN, respectively; (e)–(h) 2D far-field plots after phase distribution optimization by PEC, Random, PSO-SA, and CNN respectively

下载: 全尺寸图片幻灯片

图 12 入射角分别为30°, 45°, 60°时　(a)—(c) CST 全波仿真 PEC 板的3D远场图; (d)—(f) CNN优化后的相位分布; (g)—(i) CNN优化后的相位分布在CST全波仿真的3D远场图; (j)—(l) CNN优化后的相位分布在CST全波仿真的2D远场图

Fig. 12. Incident angles of 30°, 45°, 60°: (a)–(c) 3D far-field patterns of CST full-wave simulation of PEC plates; (d)–(f) phase distribution optimized by CNN; (g)–(i) 3D far-field patterns of CST full-wave simulation with CNN-optimized phase distribution; (j)–(l) 2D far-field patterns of CST full-wave simulation with CNN-optimized phase distribution

下载: 全尺寸图片幻灯片

图 13 (a) CST全波仿真中RCS值随频率变化曲线; (b)双站RCS减缩值

Fig. 13. (a) RCS vs. frequency curve in CST full-wave simulation; (b) bistatic RCS reduction

下载: 全尺寸图片幻灯片

图 14 (a)超表面加工样品示意图; (b)暗室测试环境

Fig. 14. (a) Schematic illustration of the metasurface fabrication sample; (b) darkroom testing environment

下载: 全尺寸图片幻灯片

图 15 (a), (b) PEC 板全波仿真与实测1D远场结果图; (c), (d)样品全波仿真与实测1D远场结果图

Fig. 15. (a), (b) 1D far-field results for full-wave simulation and measurement of PEC; (c), (d) 1D far-field results for full-wave simulation and measurement of sample

下载: 全尺寸图片幻灯片

图 16 双站 RCS 减缩仿真与实测值

Fig. 16. Bistatic RCS reduction simulation and measured values

下载: 全尺寸图片幻灯片

表 1 损失函数不同权重参数效果对比

Table 1. Comparison of the effects of different weight coefficients of the loss function.

权重参数	参数取值	RCS 值
$ \gamma_{{\mathrm{RCS}}} $	0.1, 0.5, 1.0, 1.5	15.5, 14.7, 14.6, 14.6 (收敛速度慢)
$ \gamma_{{\mathrm{Phase}}} $	0.1, 0.3, 0.7, 1.0	16.8, 16.3, 16.2, 16.0 (无法减缩RCS)
$ \gamma_{{\mathrm{RCS}}} $ + $ \gamma_{{\mathrm{Phase}}} $	(0.1, 0.1), (0.5, 0.1), (0.5, 0.3)···	16.3, 14.8, 15.6··· (二值化模糊)
$ \gamma_{{\mathrm{RCS}}} $ + $ \gamma_{{\mathrm{Phase}}} $ + $ \gamma_{{\mathrm{Reg}}} $	(0.5, 0.1, 0.5), (0.5, 0.1, 1), (0.5, 0.1, 1.5)···	14.8, 14.7, 14.6···

下载: 导出CSV

表 A1 实验环境配置

Table A1. Experimental environment configuration.

名称	配置信息
开发语言	Python 3.9
框架	PyTorch 1.10.0 + CUDA 12.0
CPU	Intel Core i9
GPU	GeForce RTX 4060 Laptop GPU (8G)
内存	8 G
NumPy	1.21.3
Matplotlib	3.9.2
torchvision	0.13.0
Pandas	1.3.3

下载: 导出CSV

[1]	Rao G A, Mahulikar S P 2002 Aeronaut. J. 106 629 Google Scholar
[2]	Ball R E, Albrecht R S, Horne R L 2003 The Fundamentals of Aircraft Combat Survivability: Analysis and Design (2nd Ed.) (Reston: AIAA) pp8–56
[3]	Westwick P 2019 Stealth: The Secret Contest to Invent Invisible Aircraft (Oxford: Oxford University Press) pp5–42
[4]	Singh H, Antony S, Jha R M 2016 Plasma-based Radar Cross Section Reduction (Singapore: Springer) pp1–46
[5]	Knott E F 2012 Radar Cross Section Measurements (New York: Springer) pp12–36
[6]	Knott E F, Schaeffer J R, Tuley M T 2004 Radar Cross Section (2nd Ed.) (Reston: SciTech Publishing) pp4–22
[7]	Kim S H, Lee S Y, Zhang Y, Park S J, Gu J 2023 Adv. Sci. 10 2303104 Google Scholar
[8]	Ananth P B, Abhiram N, Krishna K H, Nisha M S 2021 Mater. Today Proc. 47 4872 Google Scholar
[9]	Ye D, Wang Z, Xu K, Li H, Huangfu J, Wang Z, Ran L 2013 Phys. Rev. Lett. 111 187402 Google Scholar
[10]	Wang J, Yang R, Ma R, Tian J, Zhang W 2020 IEEE Access 8 105815 Google Scholar
[11]	Liu Y, Zhao X 2014 IEEE Antennas Wirel. Propag. Lett. 13 1473 Google Scholar
[12]	Yu N, Genevet P, Kats Ma, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333 Google Scholar
[13]	Gao X, Han X, Cao W P, Li H O, Ma H F, Cui T J 2015 IEEE Trans. Antennas Propag. 63 3522 Google Scholar
[14]	Abdullah M, Koziel S 2022 IEEE Trans. Microwave Theory Tech. 70 264 Google Scholar
[15]	Paquay M, Iriarte J C, Ederra I, Gonzalo R, Maagt P de 2007 IEEE Trans. Antennas Propag. 55 3630 Google Scholar
[16]	Chen W, Balanis C A, Birtcher C R 2015 IEEE Trans. Antennas Propag. 63 2636 Google Scholar
[17]	Sang D, Chen Q, Ding L, Guo M, Fu Y 2019 IEEE Trans. Antennas Propag. 67 2604 Google Scholar
[18]	Cui T J, Qi M Q, Wan X, Zhao J, Cheng Q 2014 Light Sci. Appl. 3 e218 Google Scholar
[19]	Liu X, Gao J, Xu L, Cao X, Zhao Y, Li S 2016 IEEE Antennas Wirel. Propag. Lett. 16 724 Google Scholar
[20]	Fu C, Han L, Liu C, Lu X, Sun Z 2021 IEEE Trans. Antennas Propag. 70 2352 Google Scholar
[21]	Li W, Huang N, Kang Y, Zou T, Ying Y, Yu J, Zheng J, Qiao L, Li J, Che S 2024 IEICE Electron. Express 21 20240246 Google Scholar
[22]	Qi W J, Yu C, Du J L, Zhao Y J 2022 Int. J. RF Microwave Comput. Aided Eng. 32 23306 Google Scholar
[23]	Koziel S, Abdullah M 2020 IEEE Trans. Microwave Theory Tech. 69 2028 Google Scholar
[24]	Tao S, Pan X T, Li M K, Xu S H, Yang F 2020 IEEE J. Emerg. Sel. Top. Circuits Syst. 10 114 Google Scholar
[25]	杨欣雨 2023 硕士学位论文 (南京: 东南大学) Yang X Y 2023 M. S. Thesis (Nanjing: Southeast University
[26]	袁方, 毛瑞棋, 高冕, 郑月军, 陈强, 付云起 2022 物理学报 71 084102 Google Scholar Yuan F, Mao R Q, Gao M, Chen Q, Fu Q Y 2022 Acta Phys. Sin. 71 084102 Google Scholar
[27]	Yuan F, Wang G M, Xu H X, Cai T, Zou X J, Pang Z H 2017 EEE Antennas Wirel. Propag. Lett. 16 3188 Google Scholar
[28]	Han X M, Xu H J, Chang Y P, Lin M, Zhang W Y, Xin W 2020 IEEE Access 8 162313 Google Scholar
[29]	Zhou Y, Cao X Y, Gao J, Li S, Liu X 2017 Electron. Lett. 53 1381 Google Scholar
[30]	Katoch S, Chauhan S S, Kumar V 2021 Multimed. Tools Appl. 80 8091 Google Scholar
[31]	Wang D S, Tan D P, Liu L 2018 Soft Comput. 22 387 Google Scholar
[32]	Pan X, Xue L, Lu Y, Sun N 2019 Multimed. Tools Appl. 78 29921 Google Scholar
[33]	Dumoulin V, Visin F 2016 arXiv:1603.07285 [stat.ML]
[34]	Xu B, Wang N Y, Chen T Q, Li M 2015 arXiv: 1505.00853 [cs.LG]
[35]	Bjorck N, Gomes C P, Selman B, Weinberger K Q 2018 arXiv: 1806.02375 [cs.LG]
[36]	Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R 2014 J. Mach. Learn. Res. 15 1929
[37]	Dubey S R, Singh S K, Chaudhuri B B 2022 Neurocomputing 503 92 Google Scholar
[38]	Zhou P, Xie X, Lin Z, Yan S 2024 IEEE Trans. Pattern Anal. Mach. Intell. 46 6486 Google Scholar
[39]	Shi G, Zhang J, Li H, Wang C 2019 Neural Process. Lett. 50 57 Google Scholar
[40]	Al-Kababji A, Bensaali F, Dakua S P 2022 arXiv: 2202.06373 [cs.CV]
[41]	Yuan F, Xu H X, Jia X Q, Wang G M, Fu Y Q 2020 IEEE Trans. Antennas Propag. 68 2463 Google Scholar

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