基于Hyperband-贝叶斯优化-LSTM网络的高旋尾控修正弹修正能力研究

doi:10.12382/bgxb.2024.0651

摘要/Abstract

摘要：

为快速准确地解算出高旋尾控修正弹的修正指令,针对其能力预测问题,提出一种基于Hyperband算法-贝叶斯优化-长短期记忆网络(Hyperband algorithm-Bayesian optimization-Long Short-Term Memory network,HBBO-LSTM)的修正能力预测模型。建立高旋尾控修正弹的7自由度弹道模型,并使用龙格-库塔法进行数值仿真,生成大量样本数据;通过对数据集的分析,提出一种基于拉马努金近似公式的预处理方式,对原始数据集进行预处理,获得空间分布均匀的样本数据。构建HBBO-LSTM网络预测模型,通过训练得到模型的最佳结构参数。提出一种融合带重启机制的余弦退火衰减和指数衰减的学习率下降策略,保证训练过程的快速性和稳定性。将所述模型与长短期记忆网络模型、门控循环单元网络模型和反向传播网络模型在同一测试集下进行仿真实验,并与4自由度修正质点弹道方程数值积分法进行实验对比。研究结果表明,HBBO-LSTM网络模型的综合均方误差为0.17m²,综合平均绝对误差为0.33m,预测精度优于其他模型;且解算时间和预测精度均优于数值积分法,具有较高的可行性和参考价值。

关键词: 修正能力, 弹道修正弹, 尾控弹, 长短期记忆网络, Hyperband算法, 贝叶斯优化

Abstract:

To rapidly and accurately calculate the correction command of high-spin and tail-controlled correction projectiles,a correction capability prediction model based on hyperband algorithm-Bayesian optimization-long short-term memory (HBBO-LSTM) network is proposed for the prediction problem of correction capability.A 7DOF ballistic model of the high-spin and tail-controlled correction projectile is established.It is numerically simulated using the Runge-Kutta method to generate a large amount of sample data.By analyzing the dataset,a preprocessing method based on Ramanujan’s approximation formula is proposed to preprocess the original dataset for obtaining the sample data with uniform spatial distribution.A HBBO-LSTM network prediction model is constructed,and the optimal structural parameters are obtained through training.A learning rate decay strategy combining cosine annealing with restart mechanism and exponential decay is proposed to ensure the speed and stability of training process.The proposed model is compared with the long short-term memory network,gated recurrent unit network and back propagation network models on the same test set through simulation.It is also evaluated against the numerical integration method for 4DOF correction projectile ballistic equation.The results show that the prediction accuracy of the HBBO-LSTM network model is superior to those of other models with an overall mean squared error of 0.17m² and an overall mean absolute error of 0.33m.Additionally,the HBBO-LSTM model outperforms the numerical integration method in both computation time and prediction accuracy.This demonstrates that the HBBO-LSTM network model has high feasibility and reference value.

Key words: correction capability, ballistic correction projectile, tail-controlled projectile, long short-term memory network, hyperband algorithm, Bayesian optimization

中图分类号:

TJ012.3

周杰, 王良明, 傅健, 王彦钦, 郭首邑. 基于Hyperband-贝叶斯优化-LSTM网络的高旋尾控修正弹修正能力研究[J]. 兵工学报, 2025, 46(7): 240651-.

ZHOU Jie, WANG Liangming, FU Jian, WANG Yanqin, GUO Shouyu. Research on the Correction Capability of High-spin and Tail-controlled Correction Projectile Based on HBBO-LSTM Network[J]. Acta Armamentarii, 2025, 46(7): 240651-.

图/表 15

表1 弹丸输入特征取值范围

Table 1 Projectile input feature value range

特征名	最小值	最大值	步长
射角/(°)	45	51	1
起控时刻/s	10	89	1
滚转角/(°)	0	359.5	0.5

图1 51°射角时不同起控时刻的弹丸修正能力

Fig.1 Correction capabilities of projectiles at different control initiation times with launch angle of 51°

图2 45°射角时不同滚转角度的弹丸修正落点

Fig.2 Correction impact points of projectiles at different roll angles with launch angle of 45°

图3 LSTM单元结构

Fig.3 LSTM unit structure

图4 Hyperband算法原理

Fig.4 Principle of Hyperband algorithm

表2 超参数搜索空间

Table 2 Hyperparameter search space

超参数名称	范围	步长
高斯噪层的标准差	[0,0.003]	0.0002
LSTM层1神经元数量	[100,2000]	20
LSTM层1正则化系数	[0,0.002]	0.0002
Dropout层1丢弃率	[0,0.5]	0.1
LSTM层2神经元数量	[100,1500]	20
LSTM层2正则化系数	[0,0.002]	0.0002
Dropout层2丢弃率	[0,0.5]	0.1
初始全局学习率	[0.0001,0.01]	对数采样
批量大小	[32,256]	32

图5 测试集的修正能力

Fig.5 Correction capability of the test set

表3 HBBO-LSTM模型参数

Table 3 HBBO-LSTM Model parameters

层类型	层参数	层输出形状
高斯噪声层	标准差0.0002	(64,1,7)
LSTM层1	神经元数量1500	(64,1,1500)
激活层1	激活函数Leaky ReLU	(64,1,1500)
LSTM层2	神经元数量740	(64,740)
激活层2	激活函数Leaky ReLU	(64,740)
全连接层	神经元数量2	(64,2)

图6 学习率衰减曲线

Fig.6 Learning rate decay curve

图7 各组的最大误差

Fig.7 Maximum error of each group

图8 各组的MAE指标

Fig.8 MAE index of each group

图9 射程修正量预测误差

Fig.9 Prediction error of range correction

图10 横偏修正量预测误差

Fig.10 Prediction error of lateral deviation correction

表4 模型评估结果

Table 4 Model evaluation results

评估指标	HBBO-LSTM	LSTM	GRU	BP
射程最大误差/m	1.684	2.679	4.540	3.615
横偏最大误差/m	1.911	2.683	4.730	5.194
MSE/m²	0.172	0.352	0.677	0.781
MAE/m	0.328	0.465	0.634	0.682
MAPE/%	0.356	0.356	0.644	0.710

表5 解算时间与预测精度

Table 5 Computation time and prediction accuracy

预测点编号	数值积分法		HBBO-LSTM
预测点编号	解算时间/s	MAE/m	解算时间/s	MAE/m
1	3.15	8.85	0.61	0.26
2	5.48	13.49	0.77	0.29
3	10.35	15.62	0.79	0.34
4	2.25	6.16	0.76	0.30
5	16.80	21.23	0.81	0.34

参考文献 25

[1]	谢浩怡, 杨国伟, 王全伟, 等. 2维弹道修正技术研究综述[J]. 兵工自动化, 2018, 37(9):66-69.
	XIE H Y, YANG G W, WANG Q W, et al. Summarize of two-dimensional trajectory correction technology[J]. Ordnance Automation, 2018, 37(9):66-69. (in Chinese)
[2]	邢炳楠, 杜忠华, 杜成鑫. 二维弹道修正弹及其制导控制技术综述[J]. 国防科技大学学报, 2021, 43(4):53-68.
	XING B N, DU Z H, DU C X. Review on two-dimensional trajectory correction projectile and its guidance and control technology[J]. Journal of National University of Defense Technology, 2021, 43(4):53-68. (in Chinese)
[3]	李红云, 申强, 邓子龙. 鸭式布局二维修正双旋弹角运动及转向响应特性分析[J]. 兵工学报, 2024, 45(6):1866-1876. doi: 10.12382/bgxb.2023.0057
	LI H Y, SHEN Q, DENG Z L. Analysis of angular motion and swerving response characteristics of dual-spinning two-dimensional correction projectile with canard layout[J]. Acta Armamentarii, 2024, 45(6):1866-1876. (in Chinese) doi: 10.12382/bgxb.2023.0057
[4]	申强, 仇李良, 蒲文洋, 等. 高旋弹二维修正引信双旋结构气动特性及气动力表征[J]. 北京理工大学学报, 2024, 44(4):359-368.
	SHEN Q, QIU L L, PU W Y, et al. Aerodynamic characteristics and characterization of the double spin structure of two-dimensional correction high-spin projectile[J]. Transactions of Beijing Institute of Technology, 2024, 44(4):359-368. (in Chinese)
[5]	WANG C, DING L B, FENG Y, et al. Research on angular motion characteristics and stability of trajectory-corrected rocket projectile with Isolated rotating tail rudder[J]. Mathematical Problems in Engineering, 2023,2023:5880706.
[6]	WANG C, DING L B, ZHANG H, et al. Research on control force aerodynamic model of a guided rocket with an isolated-rotating tail rudder[J]. International Journal of Aeronautical and Space Sciences, 2022, 23(1):1-18.
[7]	郭首邑, 王良明, 傅健, 等. 一种新型后舵尾控修正弹的弹道控制仿真[J]. 兵工学报, 2024, 45(7):2209-2217. doi: 10.12382/bgxb.2023.0178
	GUO S Y, WANG L M, FU J, et al. Simulation research on ballistic control of a new tail rudder controlled correction projectile[J]. Acta Armamentarii, 2024, 45(7):2209-2217. (in Chinese)
[8]	LEI X, FU J, WANG L M, et al. Research on fractional order unidirectional sliding mode control for fixed-rudder two-dimensional correction projectile[C]//Proceedings of 2023 Chinese Intelligent Systems Conference.Belin, Germany:Springer,2023:747-759.
[9]	王中原, 史金光, 常思江, 等. 弹道修正弹技术发展综述[J]. 弹道学报, 2021, 33(2):1-12. doi: 10.12115/j.issn.1004-499X(2021)02-001
	WANG Z Y, SHI J G, CHANG S J, et al. Review on development of technology of trajectory correction projectile[J]. Journal of Ballistics, 2021, 33(2):1-12. (in Chinese)
[10]	HAO Y P, CHEN C. Research on aerodynamic characteristics and correction ability of two-dimension trajectory correction projectile of different canard rudder profile shape[C]//Proceedings of 2017 Chinese Automation Congress.Jinan, China:IEEE,2017:750-763.
[11]	宋谢恩, 王伟鹏, 丁锋, 等. 某型弹道修正弹落点散布规律研究[J]. 弹道学报, 2021, 33(2):40-46. doi: 10.12115/j.issn.1004-499X(2021)02-006
	SONG X E, WANG W P, DING F, et al. Dispersion law of impact points of a certain type of trajectory correction projectile[J]. Journal of Ballistics, 2021, 33(2):40-46. (in Chinese)
[12]	柯知非, 高敏, 王毅, 等. 旋转弹二维弹道修正组件修正能力影响因素仿真分析[J]. 弹箭与制导学报, 2019, 39(3):21-26. doi: 10.15892/j.cnki.djzdxb.2019.03.006
	KE Z F, GAO M, WANG Y, et al. Simulation analysis of influence factors on correction ability of 2-D trajectory correction fuze of spin stabilized projectile[J]. Journal of Projectiles,Rockets,Missiles and Guidance, 2019, 39(3):21-26. (in Chinese)
[13]	王磊, 马景权, 张嘉易, 等. 二维修正弹修正能力建模与仿真分析[J]. 弹箭与制导学报, 2021, 41(6):127-131. doi: 10.15892/j.cnki.djzdxb.2021.06.026
	WANG L, MA J Q, ZHANG J Y, et al. Modeling and simulation analysis of correction capability of two-dimensional correction projectile[J]. Journal of Projectiles,Rockets,Missiles and Guidance, 2021, 41(6):127-131. (in Chinese)
[14]	CUI S L, LIU X, JIANG S S, et al. Design and parameter optimization of trajectory correction control strategy for air duct structure projectile[J]. International Journal of Aerospace Engineering, 2023,2023:4448592.
[15]	刘颖, 杨鹏飞, 张立军, 等. 前馈神经网络和循环神经网络的鲁棒性验证综述[J]. 软件学报, 2023, 34(7):3134-3166.
	LIU Y, YANG P F, ZHANG L J, et al. Survey on robustness verification of feedforward neural networks and recurrent neural networks[J]. Journal of Software, 2023, 34(7):3134-3166. (in Chinese)
[16]	YONG X, LE L R, YA J X, et al. Impact point prediction guidance of ballistic missile in high maneuver penetration condition[J]. Defence Technology, 2023,26:213-230.
[17]	任济寰, 吴祥, 薄煜明, 等. 基于增强上下文信息长短期记忆网络的弹道轨迹预测[J]. 兵工学报, 2023, 44(2):462-471. doi: 10.12382/bgxb.2021.0489
	REN J H, WU X, BO Y M, et al. Ballistic trajectory prediction based on context-enhanced long short-term memory network[J]. Acta Armamentarii, 2023, 44(2):462-471. (in Chinese) doi: 10.12382/bgxb.2021.0489
[18]	ZHANG Y J, WANG G, DANG Y J, et al. Prediction technology of uncontrolled ammunition landing point based on Bi-LSTM[C]//Journal of Physics: Conference Series. Bristol,UK: IOP Publishing, 2022:012084.
[19]	韩子鹏, 常思江, 赵子华. 弹箭外弹道学[M]. 北京: 北京理工大学出版社, 2022.
	HAN Z P, CHANG S J, ZHAO Z H, et al. Exterior ballistics of projectiles and rockets[M]. Beijing: Beijing Institute of Technology Press, 2022. (in Chinese)
[20]	BISCHL B, BINDER M, LANG M, et al. Hyperparameter optimization:foundations,algorithms,best practices,and open challenges[J]. WIREs Data Mining and Knowledge Discovery, 2023, 13(2):e1484.
[21]	LI L S, JAMIESON K, DESALVO G, et al. Hyperband:a novel bandit-based approach to hyperparameter optimization[J]. Journal of Machine Learning Research, 2018, 18(1):6765-6816.
[22]	崔佳旭, 杨博. 贝叶斯优化方法和应用综述[J]. 软件学报, 2018, 29(10):3068-3090.
	CUI J X, YANG B. Survey on Bayesian optimization methodology and applications[J]. Journal of Software, 2018, 29(10):3068-3090. (in Chinese)
[23]	张颖. 深度学习模型超参数优化的研究[D]. 北京: 首都经济贸易大学, 2020.
	ZHANG Y. Research on hyperparameter optimization for deep learning models[D]. Beijing: Capital University of Economics and Business, 2020. (in Chinese)
[24]	WANG J Z, XU J S, WANG X J. Combination of hyperband and Bayesian optimization for hyperparameter optimization in deep learning[J]. arXiv, 2018, cs.CV:1801.01596.
[25]	杨泗智, 龚春林, 郝波, 等. 基于落点预测的高旋火箭弹弹道修正算法[J]. 航空学报, 2020, 41(2):323421. doi: 10.7527/S1000-6893.2019.23421
	YANG S Z, GONG C L, HAO B, et al. Trajectory correction algorithm for high-spin rockets based on impact point prediction[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(2):332421. (in Chinese)