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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 GHz—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.
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关键词:
- 超表面 /
- 双站 RCS 减缩 /
- 卷积神经网络(CNN)
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 progression of radar detection technologies, RCS reduction has become a forefront research topic in radar stealth, aiming to minimize target detectability. As radar networking technologies mature, Bistatic Radar RCS reduction is gaining increasing significance over Monostatic Radar RCS reduction in future electromagnetic stealth countermeasures. Artificial electromagnetic metasurface have introduced innovative technical pathways for Bistatic Radar RCS reduction. However, current metasurface designs still face challenges related to inefficiency and suboptimal performance, primarily 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. The approach integrates convolutional feature extraction, residual enhancement, and fully connected optimization modules, alongside 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 achieve over 10 dB of Bistatic Radar RCS reduction within the 7.26 GHz to 10.74 GHz frequency range. The method also ensures uniform diffuse reflection across the full space for various incidence angles (30°、45°、60°). Compared to traditional optimization algorithms, this method enhances RCS reduction by 17.2% while significantly improving computational efficiency. This approach offers a promising new technical paradigm for achieving full-space electromagnetic stealth in advanced weapon systems.
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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
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
图 3 优化算法迭代过程中 RCS 均值的变化趋势
Fig. 3. The Variation Trend of RCS Mean Value in the Iteration Process of Optimization Algorithms
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
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
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
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
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
图 12 入射角分别为 30°、45°、60° : (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
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
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
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
表 1 损失函数不同权重参数效果对比
Table 1. The comparison of the effects of different weight coefficients of the loss function.
权重参数 参数取值 RCS 值 $ \gamma_{RCS} $ 0.1, 0.5, 1.0, 1.5 15.5, 14.7, 14.6, 14.6 (收敛速度慢) $ \gamma_{Phase} $ 0.1, 0.3, 0.7, 1.0 16.8, 16.3, 16.2, 16.0 (无法减缩 RCS) $ \gamma_{RCS} $ + $ \gamma_{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_{RCS} $ + $ \gamma_{Phase} $ + $ \gamma_{Reg} $ (0.5, 0.1, 0.5), (0.5, 0.1, 1), (0.5, 0.1, 1.5)... 14.8, 14.7, 14.6... 
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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 8G NumPy 1.21.3 Matplotlib 3.9.2 torchvision 0.13.0 Pandas 1.3.3
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