面向高空电磁脉冲波形分布的贝叶斯优化神经网络快速求解

王锦锦; 赵墨; 井靖; 王文兵; 刘政; 李进玺; 吴伟; 刘铁铭

doi:10.11999/JEIT260877

面向高空电磁脉冲波形分布的贝叶斯优化神经网络快速求解

doi: 10.11999/JEIT260877 cstr: 32379.14.JEIT260877

王锦锦^{1, 2,},
赵墨²,
井靖¹,
王文兵²,
刘政²,
李进玺²,
吴伟²,
刘铁铭^1, ,

1.
信息工程大学郑州 410024
2.
西北核技术研究所，强脉冲辐射模拟与效应国家重点实验室西安 710024

详细信息

作者简介:
王锦锦：女，博士生，研究方向为电磁脉冲效应技术、人工智能，　wangjinjin@nint.ac.cn

赵墨：男，博士、副研究员，研究方向为电磁脉冲效应技术

井靖：女，博士、副教授，研究方向为人工智能、信息安全

王文兵：男，硕士，助理研究员，研究方向为电磁脉冲效应技术

刘政：男，博士生，助理研究员，研究方向为电磁脉冲效应技术

吴伟：男，博士，正高级工程师，研究方向为电磁脉冲效应技术

刘铁铭：男，博士，副教授，研究方向为人工智能、信息安全，　fxliutm@163.com

通讯作者:
刘铁铭　fxliutm@163.com

中图分类号: O441.4; TP183
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- 被引次数: 0
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

Bayesian-Optimized Neural Network Rapid Solver for HEMP Waveform Distribution

WANG Jinjin^{1, 2
,},
ZHAO Mo²,
JING Jing¹,
WANG Wenbing²,
LIU Zheng²,
LI Jinxi²,
WU Wei²,
LIU Tieming^{1
, ,}

1.
Information Engineering University, Zhengzhou 450001, China
2.
National Key Laboratory of Intense Pulsed Radiation Simulation and Effect, Northwest Institute of Nuclear Technology, Xi’an 710034, China

摘要

摘要: 随着高空电磁脉冲数字化实验和在线评估技术的快速发展，迫切需要对高空电磁脉冲波形分布进行实时计算。传统的高空电磁脉冲环境数值计算方法比较费时，需要2-3小时完成1次波形分布的计算，无法满足系统需要的实时在线计算需求。该文提出了一种贝叶斯优化的神经网络快速求解方法，结合数值推导，建立了不同条件下一定范围内任意爆炸高度、伽马当量和位置在地面高空电磁脉冲波形参数的预测模型。实验结果表明该方法预测波形参数与仿真计算的波形参数误差小于3.12%，计算时间从小时量级减低到了秒量级，时间复杂度从O(n⁵)减低到O(n²)。该方法为高空电磁脉冲的快速推演和依赖于环境激励的仿真计算提供了基础，支持大规模场景的快速对比分析，可在分钟内完成数百种不同场景的波形分布计算与横向对比。
- 高空电磁脉冲 /
- E1环境 /
- 波形函数分布 /
- 快速计算
Abstract: Objective High-altitude Electromagnetic Pulse (HEMP) has large area, strong fields. It is difficult for HEMP's damage of critical infrastructures which are crucial to country's electromagnetic security. Especially under E1 environment, the waveform distribution characteristic will have direct influence on the effectiveness of protection design. But for cases which need a lot of waveforms calculation like system level effects simulation and protection scheme optimization etc., traditional calculation method of waveform parameter in coverage region is time consuming, which can not realize the real-time calculation of massive ground waveforms on the field distribution. The rapidly and accurately calculation of other parameters of the waveform function is still an issue for the electromagnetic environment field, limiting the useful application of computed fast HEMP environment results for a particular type of explosion when using these results in another calculation. This approach solves a problem that conventional computations cannot be linked into software to perform on-line computation, which provides the basis for the simulation calculation as well as HEMP damage evaluation, enables a fast comparison between different large scale scenarios, enabling us to calculate waveform functions for hundreds of different cases within a few minutes and thus constitutes an efficient tool for rapid analyses as part of the HEMP robust design and evaluation. Methods In this paper, an approach based on Bayesian optimization for deciding how many nodes should be included within each hidden layer of a multilayer feed forward NN is proposed. Reducing searching times for hidden layer node and ensure model precision, in fast solution modeling of HEMP waveform function. And a neural network is firstly utilized for abstracting all of the physical calculation process as a function and builds up a multilayer feedforward neural network model between input and output. However, in such networks, the choice of hidden layer node count affects network performance. In order to achieve both high prediction accuracy and low model complexity, Bayesian optimization finds the best solution in few iterations. While building the surrogate model, an initial data set is formed, and a gaussian process is utilized for the surrogate model which represents the distribution of the objective function. Updating the acquisition function, the best fit parameters, and For the HEMP waveform function, models for E_max, $ \alpha $, $ \beta $, k, and t₀ are sequentially established to predict waveform parameters under different conditions. By calculating the waveforms along the north south axis and incorporating the angle between the burst point projection and the observation point, the HEMP waveform parameters at any location are further derived and computed. Results and Discussions The above method uses both numerical calculation and Bayesian optimization based neural network algorithm, in order to build up an artificial intelligence model of predicting the ground HEMP waveform parameters, covering arbitrary height of bursts, yield of gammas, position in a certain range. Bayesian optimization neural network method reduces searching times on the number of nodes in hidden layers and improve the predicting precision. In Bayesian optimization process, the searching space of hidden layer as [8, 50] is defined to avoid model over fitting, and gives a best network structure of quite small number of hidden layer nodes. To control algorithm training time, the maximum number of Bayesian evaluations is set to 20, approximately half the search space. Through Bayesian optimization, the optimal hidden layer node counts for E_max, $ \alpha $, $ \beta $, k, and t₀ are found to be 19, 16, 11, 13, and 10, respectively. The simulation results indicate that the error of waveform parameter predicted by this method compared to the calculation result of simulation is lower than 3.12%, which has a better performance in comparison with several other methods. It works best on each metric. Experimental comparisons show the stability and generalization ability of the proposed algorithm for predicting different parameters. Analysis shows that Bayesian optimization, using a probabilistic surrogate model and an acquisition function, defines a probabilistic map between the number of nodes and the error on the validation set, to guide the following sampling steps with uncertainty estimation on predictions, which reduces the original calculation time from hours to seconds and the time complexity from O(n⁵) to O(n²), supporting large scale real time computation for the parameters in a HEMP waveform, given different scenarios. Conclusions This paper proposes a Bayesian optimization based multilayer feedforward neural network method to model the simulation computation process of HEMP ground waveforms, enabling rapid calculation of standard waveform functions for all points within the ground field distribution of HEMP over a certain range. The method uses Bayesian optimization to optimize the number of hidden layer nodes in the multilayer feedforward neural network, reducing search iterations and improving model prediction accuracy. Compared with five other artificial intelligence methods, the FBEMP method performs best in terms of all metrics. By combining the neural network with numerical derivation, all waveform functions within the field distribution coverage area can be calculated for different burst heights, gamma yields, longitudes and latitudes. This approach lowers the order of operation count from O(n⁵) in conventional numerical computation to O(n²), and reduces the calculation time of waveform functions for a given field distribution from hour scale to second scale, with errors on each parameter less than 3.12%. It realizes real time calculation of waveform function in HEMP field distribution, and had become applied to large-scale real-time HEMP waveform function calculations, solving the longstanding technical challenge of time-consuming HEMP environment computations that previously prevented real-time calculation, thereby providing an online computational environmental foundation for digital simulation and assessment in HEMP experiments.
- High-altitude electromagnetic pulse /
- E1 environment /
- Waveform distribution /
- Rapid calculation

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图 1 场分布归一化图

下载: 全尺寸图片幻灯片

图 2 不同位置处的波形

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图 3 面向HEMP的贝叶斯优化快速求解方法结构图

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图 4 测试集上的对比结果

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图 5 不同场景下场分布和不同位置处的波形参数

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1 FB算法描述

输入：训练数据集X，搜索空间H，初始采样点数k，观测集D，　模型记录M
输出：训练好的5个参数模型和每个模型对应的最优隐藏层节点　数和模型results
(1) for i = 1 to 5 do
(2) 　for j = 1 to r do
(3) 　　h ← 从H中随机采样
(4) 　　[model(h(j)), L(h(j))] ← train(h(j), X)
(5) 　　D ← D ∪ {(h(j), L(j))}
(6) 　　M ← M ∪ {(h(j), L(j), model(j))}
(7) 　end for
(8) 　for t = 1 to T-r do
(9) 　　GP ← fitgp(D)
(10) 　 for each h in (H−D) do
(11) 　 ($ \mu $,$ \delta $) ← GP(h)
(12) 　 a(h) ← LCD($ \mu $, $ \delta $)
(13) 　 end for
(14) 　 h(t) ← argmin{h ∈ (H-D)} a(h)
(15) 　 [model(t), L(t)] ← train(h(t))
(16) 　 D ← D ∪ {(h(t), L(t))}
(17) M ← M ∪ {(h(t), L(t), model(t))}
(18) end for
(19) (h, model) ← argmin{(h, L(h), model) ∈ M} L(h)
(20) results[i] ← (h, model)
(21) end for

下载: 导出CSV

2 FBEMP算法描述

输入：5个波形参数训练好的模型results，预测数据的输入U
输出：场分布下的波形参数p
(1) for i =1 to 5 do
(2) 　p{i}= predict(results[i], U);
(3) 　for j = 1 to m do
(4) 　　for k =1 to l do
(5) 　　　p{i}(j,k) = p(j,1)×A(j,k);
(6) 　　end for
(7) 　end for
(8) end for

下载: 导出CSV

表 1 各参数的预测对比结果

参数	指标	FBEMP	LSTM	KNN	RBF	CNN	RF
E_max	MAPE(%)	2.21	16.56	33.62	18.84	7.7	8.12
	RMSE(×10³)	0.34	2.66	6.12	2.4	1.12	1.5
	MAE(×10³)	0.25	2.35	5.21	1.87	0.84	1.16
α	MAPE(%)	2.83	11.17	22.19	28.9	7.96	20.61
	RMSE(×10⁷)	0.98	4.78	3.65	9.97	2.73	7.15
	MAE(×10⁷)	0.79	3.2	7.32	8.14	2.16	5.57
β	MAPE(%)	5.45	11.59	28.07	50.61	13.83	9.14
	RMSE(×10⁶)	1.03	2.68	5.6	10.7	2.27	1.83
	MAE(×10⁶)	0.83	1.8	4.82	8.4	1.78	1.39
k	MAPE(%)	0.51	0.91	1.45	1.69	0.45	0.61
	RMSE(×10^–2)	0.81	1.35	2.33	2.51	0.73	0.96
	MAE(×10^–2)	0.62	1.11	1.78	2.05	0.55	0.74
t₀	MAPE(%)	2.94	9.02	25.29	17.55	4.52	6.52
	RMSE(×10^–9)	0.54	1.73	5.36	3.16	0.9	1.15
	MAE(×10^–9)	0.4	1.32	3.89	2.5	0.64	0.89

下载: 导出CSV

参考文献(21)

[1]	ZHONG Haizhe, LIANG Jiantao, LI Hanlin, et al. Environment analysis of high-altitude electromagnetic pulse coupling field in cavity with aperture shielding[J]. IEICE Electronics Express, 2024, 21(24): 20240556. doi: 10.1587/elex.21.20240556.
[2]	LEHMAN C A, ROBINETT III R D, WEAVER W W, et al. Bounding case requirements for power grid protection against high-altitude electromagnetic pulses[J]. Energies, 2025, 18(10): 2614. doi: 10.3390/en18102614.
[3]	XIE Haiyan, LIU Yu, LI Yong, et al. A prediction model based on artificial neural network for E1 hemp coupling with distribution power lines[J]. IEEE Transactions on Power Delivery, 2022, 37(6): 5337–5344. doi: 10.1109/TPWRD.2022.3176118.
[4]	LIU Zheng, WANG Jinjin, MAO Congguang, et al. An efficient way to calculate the conducted environment with the consideration of radiated distribution[C]. 2023 Photonics & Electromagnetics Research Symposium, Prague, Czech Republic, 2023: 1225–1230. doi: 10.1109/PIERS59004.2023.10221431.
[5]	程引会, 李进玺, 马良, 等. 高空电磁脉冲环境计算中的自洽方法[J]. 计算物理, 2017, 34(4): 403–408. doi: 10.19596/j.cnki.1001-246x.2017.04.004. CHENG Yinhui, LI Jinxi, MA Liang, et al. Self-consistent method in calculation of high-altitude electromagnetic pulse environment[J]. Chinese Journal of Computational Physics, 2017, 34(4): 403–408. doi: 10.19596/j.cnki.1001-246x.2017.04.004.
[6]	DONG Ning and XIE Yanzhao. On the self-consistent simulation of high-altitude electromagnetic pulse[J]. IEEE Transactions on Nuclear Science, 2022, 69(9): 2074–2082. doi: 10.1109/TNS.2022.3193586.
[7]	程引会, 马良, 李进玺, 等. 确定高空电磁脉冲标准波形参数的频域方法[J]. 现代应用物理, 2014, 5(2): 135–139. doi: 10.3969/j.issn.2095-6223.2014.02.009. CHENG Yinhui, MA Liang, LI Jinxi, et al. Frequency-domain method for determining HEMP standard waveform parameters[J]. Modern Applied Physics, 2014, 5(2): 135–139. doi: 10.3969/j.issn.2095-6223.2014.02.009.
[8]	王建国. 核爆炸早中期电磁脉冲产生的数值模拟方法[J]. 电波科学学报, 2024, 39(5): 787–796. doi: 10.12265/j.cjors.2024143. WANG Jianguo. Numerical simulation method of early-time and intermediate-time electromagnetic pulses generated by nuclear explosions[J]. Chinese Journal of Radio Science, 2024, 39(5): 787–796. doi: 10.12265/j.cjors.2024143.
[9]	XIAO Donghai, YANG Chao, YANG Jingcong, et al. Parameter estimation of high-altitude electromagnetic pulse based on physics and data co-supervised neural network[J]. Optics Express, 2025, 33(5): 11800–11818. doi: 10.1364/OE.553410.
[10]	XIE Haiyan, DU Taijiao, ZHANG Maoyu, et al. Theoretical and experimental study of effective coupling length for transmission lines illuminated by HEMP[J]. IEEE Transactions on Electromagnetic Compatibility, 2015, 57(6): 1529–1538. doi: 10.1109/TEMC.2015.2463814.
[11]	CARCIAGHI F, MAGISTRI S, MANSUETO P, et al. A Bi-objective optimization based acquisition strategy for batch Bayesian global optimization[J]. Computational Optimization and Applications, 2025, 92(1): 81–123. doi: 10.1007/s10589-025-00696-7.
[12]	蒋丹萍, 戴紫彬, 刘燕江, 等. 贝叶斯优化驱动的粗粒度可重构密码逻辑阵列设计空间探索方法[J]. 电子与信息学报, 2025, 47(11): 4482–4492. doi: 10.11999/JEIT250624. JIANG Danping, DAI Zibin, LIU Yanjiang, et al. Bayesian optimization-driven design space exploration method for coarse-grained reconfigurable cipher logic array[J]. Journal of Electronics & Information Technology, 2025, 47(11): 4482–4492. doi: 10.11999/JEIT250624.
[13]	GHRITLAHRE H K and VERMA M. Solar air heaters performance prediction using multi-layer perceptron neural network – a systematic review[J]. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2025, 47(1): 7682–7699. doi: 10.1080/15567036.2021.1923869.
[14]	LONGMIRE C L. On the electromagnetic pulse produced by nuclear explosions[J]. IEEE Transactions on Electromagnetic Compatibility, 1978, EMC-20(1): 3–13. doi: 10.1109/TEMC.1978.303688.
[15]	KARZAS W J and LATTER R. Detection of the electromagnetic radiation from nuclear explosions in space[J]. Physical Review, 1965, 137(5B): B1369–B1378. doi: 10.1103/PhysRev.137.B1369.
[16]	周维新, 高肇岗, 肖宛昂. 面向可穿戴式的基于LSTM神经网络的智能心音异常诊断芯片[J]. 电子与信息学报, 2024, 46(2): 555–563. doi: 10.11999/JEIT230934. ZHOU Weixin, GAO Zhaogang, and XIAO Wanang. Intelligent heart sound abnormal diagnosis chip based on LSTM for wearable applications[J]. Journal of Electronics & Information Technology, 2024, 46(2): 555–563. doi: 10.11999/JEIT230934.
[17]	杨孟欣, 张青婷, 曾令昕, 等. 面向低轨卫星的时空特征融合LSTM松弛测量方法[J]. 电子与信息学报, 2025, 47(12): 4995–5004. doi: 10.11999/JEIT251146. YANG Mengxin, ZHANG Qingting, ZENG Lingxin, et al. A spatio-temporal feature fusion LSTM relaxation measurement method for LEO satellites[J]. Journal of Electronics & Information Technology, 2025, 47(12): 4995–5004. doi: 10.11999/JEIT251146.
[18]	WANG Jue and INO F. A general-purpose K-nearest neighbor method with an efficient pruning strategy for GPUs[J]. Journal of Parallel and Distributed Computing, 2026, 207: 105187. doi: 10.1016/j.jpdc.2025.105187.
[19]	GE Qiang, XU Dingli, CAI Qiannan, et al. Double filter noise reduction algorithm optimized by RBF neural network for laser absorption spectroscopy[J]. Infrared Physics & Technology, 2025, 145: 105718. doi: 10.1016/j.infrared.2025.105718.
[20]	李伟, 陈億, 陈韬, 等. 面向边缘计算的可重构CNN协处理器研究与设计[J]. 电子与信息学报, 2024, 46(4): 1499–1512. doi: 10.11999/JEIT230509. LI Wei, CHEN Yi, CHEN Tao, et al. A research and design of reconfigurable CNN co-processor for edge computing[J]. Journal of Electronics & Information Technology, 2024, 46(4): 1499–1512. doi: 10.11999/JEIT230509.
[21]	KHRAISAT A, TALUKDER A, UDDIN A, et al. RF-FedAvg: Federated learning-based random forest model for intrusion detection in wireless sensor networks[J]. Cluster Computing, 2025, 28(13): 873. doi: 10.1007/s10586-025-05591-8.