贴片正弦调制SSPPs漏波天线及其随机森林辅助优化设计

唐路平; 成永昊; 陈怿博; 廖晨

doi:10.11999/JEIT260651

贴片正弦调制SSPPs漏波天线及其随机森林辅助优化设计

doi: 10.11999/JEIT260651 cstr: 32379.14.JEIT260651

唐路平^{1, 2, ,},
成永昊¹,
陈怿博¹,
廖晨³

1.
南京林业大学机械电子工程学院南京 210037
2.
东南大学电子科学与工程学院南京 210037
3.
南京邮电大学电子与光学工程学院、柔性电子(未来技术)学院南京 210037

基金项目: 国家自然科学基金(52001168, 11704200)，中国博士后科学基金面上项目(2022M710668)，横向项目(028040426)

详细信息

作者简介:
唐路平：女，副教授，研究方向为人工表面等离激元漏波天线、频率扫描天线、机器学习辅助电磁优化

成永昊：男，硕士，研究方向为人工表面等离激元器件与天线设计

陈怿博：男，本科生，研究方向为天线设计与电磁仿真

廖晨：男，讲师，研究方向为电磁场理论与微波技术、人工表面等离激元

通讯作者:
唐路平　tlp@njfu.edu.cn

中图分类号: TN82
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出版历程
- 修回日期: 2026-08-26
- 录用日期: 2026-08-26
- 网络出版日期: 2026-09-01

Patch-Sinusoidally Modulated SSPPs Leaky-Wave Antenna and Its Random Forest-Assisted Optimization Design

1.
College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China
2.
School of Electronic Science and Engineering, Southeast University, Nanjing 210037, China
3.
School of Electronic and Optical Engineering, School of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210037, China

Funds: National Natural Science Foundation of China (Grant Nos. 52001168, 11704200), General Project of China Postdoctoral Science Foundation (Grant No. 2022M710668), Horizontal Project (Grant No. 028040426)

摘要

摘要: 针对人工表面等离激元(SSPPs)漏波天线多参数强耦合导致传统优化计算量大、效率低的问题，本文提出一种贴片正弦调制SSPPs漏波天线。该结构保持均匀槽深与完整接地，在传输线两侧加载宽度正弦变化的贴片阵列以灵活调控泄漏率。构建9维结构参数到6维性能指标的随机森林(RF)代理模型，平均决定系数达0.9554，并将其嵌入粒子群优化(PSO)算法中协同寻优。优化后天线增益由13.84 dBi提升至14.52 dBi，旁瓣电平由−17 dB降至−19 dB，峰值总效率由84.9% 升至92.9%，反射系数改善4.66 dB，扫描角扩展4.29°。全波仿真验证了该方法的有效性，相较于传统PSO直接调用全波仿真，全波仿真次数降低约90%。参数敏感性分析表明设计鲁棒性好。与近期同类SSPPs漏波天线相比，该天线在增益、旁瓣抑制和效率上均具明显优势，并将机器学习代理模型引入SSPPs漏波天线的优化设计。
- 人工表面等离激元 /
- 漏波天线 /
- 正弦调制 /
- 随机森林 /
- 粒子群优化
Abstract: Objective Spoof surface plasmon polaritons (SSPPs) leaky-wave antennas feature low-profile configuration and inherent frequency-scanning capability, making them promising for modern radar, communication, and intelligent sensing systems. However, strong nonlinear coupling among geometric parameters makes traditional optimization computationally costly, as full-wave simulations require thousands of evaluations and often converge to suboptimal local solutions due to landscape complexity. The leakage dynamics in SSPPs—slow-wave propagation, spatial harmonic coupling, and leakage rate distribution—adds complexity beyond conventional designs. To address this, we propose a patch-sinusoidally modulated SSPPs leaky-wave antenna and a machine learning framework integrating a random forest surrogate with particle swarm optimization (PSO) for efficient high-dimensional global optimization with reduced cost. Methods Unlike conventional groove-depth modulation, our antenna maintains uniform groove depth and a complete metal ground. Patch arrays with sinusoidally varying widths are loaded on both sides of the transmission line, with envelope functions $ Y=A\sin (Tx) $ and $ Y=A\sin (Tx+\pi ) $, enabling flexible leakage control. The antenna is fully described by a nine-dimensional continuous parameter vector: groove width g, depth s, period p, six transition lengths g₁–g₆, port dimensions l and w, and modulation A, T. Using Latin hypercube sampling, 450 parameter samples are generated to ensure uniform coverage. Full-wave frequency-domain simulations (COMSOL, 9 GHz, approximately 27 min each) extract gain, S₁₁, S₂₁, scanning angle, side lobe level (SLL), and total efficiency. Four regression models—MLP, SVR, random forest (RF), and GPR—are systematically trained. RF employs bootstrap resampling with hyperparameters optimized via random search cross-validation (trees: 500–1200, depth: 12–24, min samples per split: 2–5). The trained RF surrogate is then embedded into PSO (40 particles, 120 iterations, inertia 0.72, c₁=c₂=1.5) with a weighted fitness function (G:1.5, η:0.7, SLL:0.55, S₁₁:0.25, S₂₁:0.7, θ_scan:0.18). Results and Discussions RF achieves the highest average R² of 0.9554 across six outputs, outperforming GPR (0.9489), SVR (0.9212), and MLP (0.8952). For key radiation indicators, RF attains gain MAE of 0.032 dBi, SLL MAE of 0.168 dB, and efficiency MAE of 0.015. Scatter plots of predicted versus simulated values cluster tightly around the diagonal, and residual histograms show means near zero with no systematic bias, confirming excellent prediction accuracy and generalization. After RF-PSO optimization, full-wave simulation confirms substantial improvements: gain rises from 13.84 dBi to 14.52 dBi, SLL drops from –17 dB to –19 dB,peak total efficiency increases from 84.9% to 92.9%, S₁₁ improves from –23.26 dB to –27.92 dB (4.66 dB), and scanning range expands from 57.2° to 61.5°. The scanning angle versus frequency curve exhibits good linearity across the operating band, and the two-dimensional far-field patterns show improved symmetry. The decrease in S₂₁ (from –3.76 dB to –5.50 dB) together with the gain/efficiency increase indicates that more energy is effectively converted into radiation rather than being dissipated or reflected. Sensitivity analysis with ±2% perturbations (50 samples) shows all coefficients of variation (CV) below 1.3%: gain CV 0.21% (<±0.1 dBi), SLL CV 1.26% (±0.4 dB), efficiency CV 0.88% (±0.01), S₁₁ CV 0.97%, S₂₁ CV 0.91%, scan CV 0.37%. These fluctuations are far smaller than optimization gains, confirming excellent robustness under typical fabrication tolerances. Comparison with recent leaky-wave antennas (both SSPP-based and SIW) demonstrates superior SLL (−19 dB), competitive efficiency (89% vs. 94.95% and90% in prior SSPP work), and scanning range (61.5°) outperforming most single-port SSPP antennas (e.g., 20°, 16°, 33°, 13°). The number of full-wave simulations is reduced by approximately 90% (450 training + 1 validation vs. 4,800 simulations for conventional PSO). Conclusions This paper proposes a patch-sinusoidally modulated SSPPs leaky-wave antenna and an RF-assisted PSO framework for synergistic optimization in nine dimensions. The RF surrogate achieves an average R² of 0.9554. The optimized antenna shows significantly improved performance across all metrics: gain by 0.68 dBi, SLL by 2 dB, efficiency by 8%, S₁₁ by 4.66 dB, and scanning range by 4.29°, while maintaining compact dimensions. Sensitivity analysis confirms robustness under typical fabrication tolerances. The proposed methodology reduces the number of full-wave simulations by approximately 90%. This work marks a methodological advancement by introducing machine learning surrogate modeling into SSPPs leaky-wave antenna design for efficient high-dimensional optimization. Future work includes fabrication, experimental validation, extension to millimeter-wave bands, and reconfigurable antenna designs.
- Spoof surface plasmon polaritons /
- Leaky-wave antenna /
- Sinusoidal modulation /
- Random forest /
- Particle swarm optimization

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图 1 贴片正弦调制的SSPPs漏波天线结构

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图 2 关键参数对色散与辐射性能的影响

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图 3 预测值与仿真值散点图及残差直方图

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图 4 基于代理模型的粒子群优化流程及收敛曲线

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图 5 优化前后S参数曲线

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图 8 优化前后天线的增益与总效率随频率变化曲线

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图 6 优化前后天线二维远场辐射方向图

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图 7 优化前后天线主波束方向随频率变化曲线

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表 1 天线结构参数取值范围(mm，除注明外)

参数	范围	参数	范围	参数	范围
$ g $	6.0-9.0	$ {g}_{1} $	2.5-5.0	$ w $	2.0-5.0
$ s $	0.2-2.0	$ {g}_{6} $	5.0-9.0	$ A $	2.0-9.0(无量纲)
$ p $	4.0-8.0	$ l $	3.0-12.0	$ T $	4.0-8.0(无量纲)

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表 2 各模型的综合预测精度对比

模型	Mean MAE	Mean RMSE	Mean R²
RF	0.1834	0.2621	0.9554
GPR	0.1830	0.2397	0.9489
MLP	0.4953	0.6162	0.8952
SVR	0.1965	0.3316	0.9212

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表 3 优化前后结构参数

算法	g	s	p	g₁	g₆	l	w	A	T
原始结构	9.0	1.3	6.0	2.5	7.5	10	4	6	5.5
PSO	8.569	1.410	6.200	2.976	7.793	9.980	3.991	8.044	6.885
GA	8.592	1.199	5.765	2.934	7.314	9.980	4.019	7.609	7.832
BO	8.975	0.961	5.786	2.963	6.997	9.926	4.063	8.151	6.914
注：优化参数为连续空间解，实际加工可四舍五入至0.05 mm。

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表 4 算法优化前后性能指标对比

算法	$ G\text{(dBi)} $	$ {S}_{11}\text{(dB)} $	$ {S}_{21}\text{(dB)} $	$ {\theta }_{\text{scan}}(°) $	$ SLL\text{(dB)} $	$ \eta $
原始模型	13.84	−23.26	−3.76	57.19	−17	0.8494
PSO	14.52	−27.92	−5.50	61.48	−19	0.9291
GA	14.29	−29.94	−5.51	61.20	−19	0.9093
BO	14.43	−27.51	−5.49	60.98	−19	0.9265

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表 5 优化后结构参数

性能指标	原始值(优化后)	扰动后均值	标准差	变化范围	变异系数CV
G(dBi)	14.52	14.57	0.03	14.46～14.62	0.21%
$ SLL\text{(dB)} $	–19	–19.13	0.24	–19.32～−18.55	1.26%
$ \eta $	0.9291	0.9233	0.0082	0.9181～0.9348	0.88%
$ {S}_{11}\text{(dB)} $	–27.92	–27.44	0.27	–28.23～−26.98	0.97%
$ {S}_{21}\text{(dB)} $	–5.50	–5.41	0.05	–5.66～–5.32	0.91%
$ {\theta }_{\text{scan}}(°) $	61.48	61.22	0.23	60.86～61.58	0.37%

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表 6 本工作与近期漏波天线的性能及设计方法对比

参考文献	天线类型	工作频段(GHz)	扫描范围(°)	峰值增益(dBi)	旁瓣电平(dB)	效率(%)(类型)	端口数	尺寸(mm³)	电长度	设计/优化方法
[12]	SSPPs	7.07–10.6	20	10.7	–5	>86(min. Rad.)	单	174×38.6×0.762	5.12	参数扫描
[13]	SSPPs	10.7–12.75	16	19.6	–9	94.95(avg.Tot.)	单	369.6×35×0.813	14.45	参数扫描
[14]	SIW	13–16.5	39	12.63	−10	>66(min. Rad.)	双	262.4×13×1	12.7	传统设计
[15]	SIW	8–12	82	15.7	–15	83.6(avg.Rad.)	双	320×100×2	10.67	传统设计
[16]	SSPPs	16–24	30	11.3	–16	86(avg.Rad.)	双	189×31.5×1.5	12.60	参数扫描
[17]	SL-SSPPs	7.2-8.35	35	11.2	–7	70(avg.Rad.)	双	258×30×0.5	6.79	参数扫描
[18]	SSPPs	18.5-20	13	15.7	–15	86(Rad. @19 GHz)	双	150×33.16×1	9.63	PSO
[19]	SSPPs	4.45–6.6	180	12.51	–15	90(avg.Rad.)	双	300×60×1.43	5.53	传统设计
[20]	SSPPs	5–9	65	11	–12	>80(min. Rad.)	双	290×70×0.5	6.5	传统设计
本文	SSPPs	6.7-9.6	61.5	14.52	–19	89(avg.Tot.)	双	223.6×40.4×1	6.72	随机森林+PSO
备注：avg. Rad.为平均辐射效率；avg. Tot.为平均总效率；min. Rad. 为最低辐射效率；@f₀为该频点辐射效率

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参考文献(20)

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