基于改进CPSO-BPNN的再入飞行器四维可达区在线预测

doi:10.12305/j.issn.1001-506X.2026.09.27

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (9): 3146-3158.doi: 10.12305/j.issn.1001-506X.2026.09.27

• 制导、导航与控制 • 上一篇

基于改进CPSO-BPNN的再入飞行器四维可达区在线预测

邢晓露¹^,²^,³, 王铮¹^,²^,³, 白云飞⁴, 王时雨⁴, 宁昕⁵

1. 西北工业大学无人系统技术研究院，陕西西安 710072
2. 西北工业大学无人机技术集成攻关大平台，陕西西安 710072
3. 西北工业大学无人飞行器技术全国重点实验室，陕西西安 710072
4. 中国运载火箭技术研究院，北京 100076
5. 西北工业大学航天学院，陕西西安 710072

收稿日期:2025-07-07 修回日期:2025-08-19 出版日期:2025-11-25 发布日期:2025-11-25
通讯作者: 王铮
作者简介:邢晓露（1999—），女，博士研究生，主要研究方向为多飞行器协同弹道规划
白云飞（1989—），男，工程师，硕士，主要研究方向为飞行器动力学与仿真
王时雨（1996—），男，工程师，硕士，主要研究方向为飞行器动力学与仿真
宁昕（1982—），男，教授，博士，主要研究方向为航天器飞行动力学与控制
基金资助:
国家自然科学基金（62303378）；上海航天科技创新基金（SAST2022-114）资助课题

Online prediction of four-dimensional reachable zones for reentry vehicles based on improved CPSO-BPNN

Xiaolu Xing¹^,²^,³, Zheng Wang¹^,²^,³, Yunfei Bai⁴, Shiyu Wang⁴, Xin Ning⁵

1. Unmanned System Research Institute，Northwestern Polytechnical University，Xi’an 710072，China
2. Integrated Research and Development Platform of Unmanned Aerial Vehicle Technology，Northwestern Polytechnical University，Xi’an 710072，China
3. National Key Laboratory of Unmanned Aerial Vehicle Technology，Northwestern Polytechnical University，Xi’an 710072，China
4. China Academy of Launch Vehicle Technology，Beijing 100076，China
5. School of Astronautics，Northwestern Polytechnical University，Xi’an 710072，China

Received:2025-07-07 Revised:2025-08-19 Online:2025-11-25 Published:2025-11-25
Contact: Zheng Wang

摘要/Abstract

摘要：

针对再入飞行器四维可达区的在线预测问题，提出一种基于改进混沌粒子群优化（chaos particle swarm optimization, CPSO）算法和反向传播神经网络（back propagation neural network, BPNN）的智能预测模型。首先，基于飞行器动力学特性，构建融合初始飞行状态、有限控制约束及复杂空域限制的时间-纵程-横程-高度四维可达域数学表征模型。其次，提出基于几何特征解析的高维可达域表征方法，采用非对称三维中心曲面与二维边界曲线联合表征策略实现特征参数提取。最后，引入改进CPSO对BPNN进行模型参数协同优化，建立四维可达区的智能预测模型。仿真表明，所提方法对可达区覆盖率超过95%，单次预测耗时不超过100 ms，较传统数值仿真方法提升3个数量级，可以实现对再入飞行器四维可达区的高精度实时预测。

关键词: 再入飞行器, 四维可达区, 几何特征解析, 混沌粒子群优化, 实时预测

Abstract:

In view of the problems of the online prediction of four-dimensional reachable zones for reentry vehicles, an intelligent prediction model based on enhanced chaos particle swarm optimization （CPSO） algorithm and back propagation neural network （BPNN） is proposed. Firstly, a mathematical characterization model integrating initial flight states, finite control constraints, and complex airspace limitations is established based on vehicle dynamic characteristic, describing the time-longitudinal range-lateral range-altitude four-dimensional reachable zones. Secondly, a geometric feature-based characterization method is proposed for high-dimensional reachable zones, employing a joint representation strategy of asymmetric three-dimensional medial surfaces and two-dimensional boundary curves to extract feature parameters. Finally, an improved CPSO algorithm is introduced to collaboratively optimize parameters of BPNN, establishing an intelligent prediction model for four-dimensional reachable zones. Simulations demonstrate that the proposed method achieves over 95% coverage of reachable zones with single prediction run time below 100 ms, outperforming traditional numerical simulation methods by three orders of magnitude, enabling high-precision real-time prediction of four-dimensional reachable zones for reentry vehicles.

Key words: reentry vehicle, four-dimensional reachable zones, geometric feature analysis, chaotic particle swarm optimization, real-time prediction

中图分类号:

V 448

邢晓露, 王铮, 白云飞, 王时雨, 宁昕. 基于改进CPSO-BPNN的再入飞行器四维可达区在线预测[J]. 系统工程与电子技术, 2026, 48(9): 3146-3158.

Xiaolu Xing, Zheng Wang, Yunfei Bai, Shiyu Wang, Xin Ning. Online prediction of four-dimensional reachable zones for reentry vehicles based on improved CPSO-BPNN[J]. Systems Engineering and Electronics, 2026, 48(9): 3146-3158.

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参考文献 31

1	王鹏, 赵石磊, 陈万春. 基于可达区在线预测的GPI中制导协同拦截策略[J]. 北京航空航天大学学报, 2024, 50 (11): 3463.
2	Pan L, Peng S C, Xie Y, et al. 3D guidance for hypersonic reentry gliders based on analytical prediction[J]. Acta Astronautica, 2020, 167, 42. doi: 10.1016/j.actaastro.2019.07.039
3	Diao Y, Mu R J, Guan Y Z, et al. Boost-phase trajectory planning with the nonregular reachable area constraints[J]. International Journal of Aerospace Engineering, 2022, 2022 (1): 9443050.
4	Li M J, Zhou C J, Shao L, et al. A trajectory generation algorithm for a reentry gliding vehicle based on convex optimization in the flight range domain and distributed grid points adjustment[J]. Applied Sciences, 2023, 13 (3): 1988. doi: 10.3390/app13031988
5	Patel J, Kamesh S. Reachability analysis for atmospheric reentry vehicle[J]. Journal of Guidance, Control, and Dynamics, 2024, 47 (1): 133.
6	Chai R Q, Savvaris A, Tsourdos A. Violation learning differential evolution-based hp-adaptive pseudospectral method for trajectory optimization of space maneuver vehicle[J]. IEEE Trans. on Aerospace and Electronic Systems, 2017, 53 (4): 2031. doi: 10.1109/TAES.2017.2680698
7	Han F, Wang Z L, He L, et al. Trajectory plan for an ultra-short distance on-orbit service based on the Gaussian pseudo-spectral method[J]. IEEE/CAA Journal of Automatica Sinica, 2018, 5(6): 1089.
8	Liu Y, Heiligers J, Ceriotti M. Loosely-displaced geostationary orbits with hybrid sail propulsion[J]. Aerospace Science and Technology, 2018, 79, 105. doi: 10.1016/j.ast.2018.05.034
9	Tian B L, Fan W R, Su R, et al. Real-time trajectory and attitude coordination control for reusable launch vehicle in reentry phase[J]. IEEE Trans. on Industrial Electronics, 2014, 62 (3): 1639.
10	Liu X F, Shen Z J, Lu P. Solving the maximum-crossrange problem via successive second-order cone programming with a line search[J]. Aerospace Science and Technology, 2015, 47, 10. doi: 10.1016/j.ast.2015.09.008
11	Lu P. Asymptotic analysis of quasi-equilibrium glide in lifting entry flight[J]. Journal of Guidance, Control, and Dynamics, 2006, 29 (3): 662.
12	Lu P, Xue S B. Rapid generation of accurate entry landing footprints[J]. Journal of Guidance, Control, and Dynamics, 2010, 33 (3): 756.
13	Wang T, Zhang H B, Li Y G, et al. An improved footprint generation method for entry vehicles[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2017, 231 (10): 1951. doi: 10.1177/0954410016662060
14	Li H F, Zhang R, Li Z Y, et al. Footprint problem with angle of attack optimization for high lifting reentry vehicle[J]. Chinese Journal of Aeronautics, 2012, 25 (2): 243. doi: 10.1016/S1000-9361(11)60384-1
15	Zhang R, Li Z Y, Shi L N. A general footprint generation approach for lifting reentry vehicle[C]//2012 28th International Congress of the Aeronautical Sciences, 2012: 23.
16	冉云霆, 泮斌峰. 多约束下升力式再入飞行器可达域计算方法[J]. 北京航空航天大学学报, 2025, 51 (3): 904.
17	Fu S N, Lu T Y, Yin J, et al. Rapid algorithm for generating entry landing footprints satisfying the no-fly zone constraint[J]. International Journal of Aerospace Engineering, 2021, 2021
18	He R Z, Zhang Y L, Liu L L, et al. Feasible footprint generation with uncertainty effects[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2019, 233 (1): 138. doi: 10.1177/0954410017728971
19	吴楠, 王锋, 赵敏, 等. 高超声速滑翔再入飞行器的可达区快速预测[J]. 国防科技大学学报, 2021, 43 (1): 1.
20	Huang Q W, Deng Z X, Liu L H. A fast prediction method for the target reachable zone of boosting gliding vehicle based on database[J]. Applied Sciences, 2023, 13 (3): 1848. doi: 10.3390/app13031848
21	Xu J J, Dong C H, Cheng L. Deep neural network-based footprint prediction and attack intention inference of hypersonic glide vehicles[J]. Mathematics, 2022, 11 (1): 185. doi: 10.3390/math11010185
22	Liu Q G, Liu X X, Wu J, et al. A fast computational method for the landing footprints of space-to-ground vehicles[J]. Journal of Systems Engineering and Electronics, 2020, 31 (5): 1062. doi: 10.23919/JSEE.2020.000080
23	Feng S R, Liu L, Wang Y J. Onboard reentry landing footprints generation based on neural network[C]//Chinese Automation Congress, 2017: 579 .
24	Cheng Z W, Ge Y X, Yuan J, et al. Gliding footprint calculation method for aircraft with thrust failure based on six-degree-of-freedom flight envelope and back-propagation artificial neural network[J]. Aerospace, 2024, 11 (2): 160. doi: 10.3390/aerospace11020160
25	Mitiku M H, Salau A O, Sharew E A. Design of an artificial neural network and proportional-integral-derivative controller using particle swarm optimization for Boeing 747-400 aircraft pitch control[J]. Advanced Control for Applications: Engineering and Industrial Systems, 2024, 6 (3): e224. doi: 10.1002/adc2.224
26	Wang Z L, Liang X H. Fault diagnosis method of morphing aircraft based on particle swarm optimization and convolutional neural network[C]//International Annual Conference on Complex Systems and Intelligent Science, 2024: 716 .
27	Li H, Si Y K, Zhang Q, et al. 4D track prediction based on BP neural network optimized by improved sparrow algorithm[J]. Electronics, 2025, 14 (6): 1097. doi: 10.3390/electronics14061097
28	葛鲁亲, 孙旺, 南英. 对空导弹射后动态可攻击区的快速高精度拟合方法研究[J]. 航空兵器, 2019, 26 (5): 41.
29	Xie Y, Liu L H, Liu J, et al. Rapid generation of entry trajectories with waypoint and no-fly zone constraints[J]. Acta Astronautica, 2012, 77, 167. doi: 10.1016/j.actaastro.2012.04.006
30	钟宇亮. 离散点云模型曲面重构三种方式的研究及扩展[D]. 杭州: 浙江大学, 2008.
31	王铮, 邢晓露, 晁鲁静, 等. 一种基于模糊神经网络的飞行器打击区预测系统和方法[P]. 中国: CN202210800667.4, 2024-09-20.

飞行器编号	速度$\rm /({m} \cdot {{s}^{ - 1}})$	高度$\rm /km$	弹道偏角$\rm{/(^\circ) }$	弹道倾角$\rm{/(^\circ)} $
1	4910	113	65.6	−0.092
2	4980	196	12.8	−0.049
3	4750	140	60.8	−0.066
4	4040	128	56.8	−0.005

角标符号	飞行器编号
角标符号	1	2	3	4	5
$ \iota $	−0.11	5.55×10 ⁻⁴	−4.4×10⁻⁸	−1.36×10⁻¹¹	1.44×10⁻¹⁵
$ \varsigma $	−4.7	0.006	−3.687×10⁻⁶	1.1×10⁻⁹	−1.27×10⁻¹³
$ \xi $	2.7×10⁻⁴	−2.35×10⁻⁷	8.89 ×10⁻¹¹	−1.24 ×10⁻¹⁴	−
$ \zeta $	1395.8	−7.9 ×10⁻⁷	4.7 ×10⁻¹¹	−2.27 × 10⁻¹⁵	−
$ \varpi $	3.8 ×10⁻¹⁰	−1.33 ×10⁻¹⁴	−6.2 ×10⁻¹⁴	−	−
$ g $	514356.09	−1069.0708	0.4117	−	−
$ a $	15.3451	0.6073	−0.0045	−	−
$ q $	937173.39	−1541.0164	0.4964	−	−
$ b $	−70.0443	0.50447	0.034	−	−

参数	取值范围
初始弹道偏角$/(^ \circ )$	（0.8，80）
飞行时间$/{{\mathrm{s}}}$	（501，600）
初始高度$/{{\mathrm{km}}}$	（101，200）
初始飞行速度$/({{\mathrm{m}}} \cdot {{{\mathrm{s}}}^{ - 1}})$	（4010，5000）
初始弹道倾角${/(^ \circ) }$	（−0.001，−0.1）

序号	输入数据					输出数据
序号	初始弹道偏角${/(^\circ) }$	飞行时间$/{{\mathrm{s}}}$	初始高度$/{{\mathrm{km}}}$	初始速度$/({{\mathrm{m}}} \cdot {{{\mathrm{s}}}^{ - 1}})$	初始弹道倾角${/(^\circ) }$	$ {\zeta _1} $
1	65.6	564	113	4910	−0.092	3343.18
2	8	597	155	4280	−0.096	1057.35
3	12.8	581	196	4980	−0.049	−5586.5
4	12	596	192	4430	−0.08	3809.22
5	52.8	568	185	4040	−0.094	2106.8
6	66.4	504	132	4700	−0.096	−181.15
7	39.2	576	165	4450	−0.071	3206.59

参数	数值
种群规模$n$	30
最大迭代次数$M$	140
阈值${\delta _m}$	10
步长缩放因子${a_m}$	0.5
惯性权重最大值${w_1}$，最小值${w_2}$	0.7，0.3

基于改进CPSO-BPNN的再入飞行器四维可达区在线预测

Online prediction of four-dimensional reachable zones for reentry vehicles based on improved CPSO-BPNN

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飞行编号	最大热流$ /({{\mathrm{kJ}}} \cdot {{{\mathrm{m}}}^{ - 2}} \cdot {{{\mathrm{s}}}^{ - 1}}) $	最大动压$/{{\mathrm{kpa}}}$	最大过载$ /{{\mathrm{g}}} $
1	1000	100	5
2	1000	100	5
3	1000	100	5
4	1000	100	5

飞行器编号	初始速度$/({{\mathrm{m}}} \cdot {{{\mathrm{s}}}^{ - 1}})$	初始高度$/{{\mathrm{km}}}$	初始弹道偏角${/(^\circ) }$	初始弹道倾角${/(^\circ) }$	飞行时间$/{{\mathrm{s}}}$
1	4680	166	22.4	−0.017	512
2	4550	114	76.8	−0.015	526
3	4760	176	23.2	−0.039	557
4	4060	154	6.4	−0.078	594
5	4040	185	52.8	−0.094	568
6	4700	132	66.4	−0.096	504
7	4450	165	39.2	−0.071	576
8	4750	140	60.8	−0.066	518

参数	CPSO-反向传播网络	弹道解算模型
四维可达区预测所需时间	0.035 6	134.7

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