基于改进二阶优化器并行学习的弹道导弹神经网络落点预测方法

doi:10.7527/S1000-6893.2022.27964

Abstract

Abstract:

To address the requirement for Impact Point Prediction （IPP） in precision guidance for the ballistic missile after high maneuver penetration， an IPP Neural Network （NN） model is proposed based on an improved second-order optimizer. The IPP of the current flight state is predicted based on the elliptical trajectory theory， and the impact deviation is decoupled. Furthermore， a sample set with flight state as input and impact deviation of elliptical trajectory as output is constructed， which greatly reduces the difficulty of NN learning. To improve the prediction accuracy， three NNs are applied to predict the three components of the impact deviation. An improved Levenberg-Marquardt optimizer for multi-GPU parallel learning is established by using the matrix block algorithm， which shortens the network learning time and reduces the demand for GPU memory. A simulation experiment is designed to analyze the advantages and computational complexity of the proposed method. Simulation results show that the proposed method has low learning difficulty， high prediction accuracy and good real-time performance. Among the 869 320 samples contained in the training set and the test set， the $3 σ$ prediction error is 4.97 m. In the learning environment with 2 GPUs， the learning time is reduced by about 49.18%. On the STM32F407 single-chip microcomputer， IPP takes 2.585 ms. The proposed method can provide support for the design of guidance algorithm， and is applicable for engineering practice.

Key words: ballistic missile, high maneuver penetration, impact point prediction, neural network, parallel learning, elliptical trajectory, single-chip microcomputer

CLC Number:

V448.131

Leliang REN, Yong XIAN, Shaopeng LI, Gang LEI, Wei WU, Bing LI. A neural network model for impact point prediction of ballistic missile based on improved second-order optimizer with parallel learning[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(14): 327964.

Figures/Tables 23

Fig.1

Fig.2

Fig.3

Fig.4

Fig. 5

Table 1

Range of simulation parameters

参数	下界	上界	离散间隔
$H 0,1$ /km	100.0	200.0	10.0
$H m$ /km	0	5.0	1.0
$φ s$ /（°）	20.0	36.0	4.0
$V s$ $/ (m ⋅ s - 1)$	6 650.0	7 850.0	40.0
$σ s$ /（°）	0	360.0	30.0
$Θ s$ /（°）	-18.5	-12.5	1.0

Table 1

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Table 2

Network architecture of the proposed method

模型	隐藏层1	隐藏层2
$f x N N ·$	11	6
$f y N N ·$	6	5
$f z N N ·$	5	2

Table 2

Fig.12

Fig.13

Table 3

Network architecture of Ref. ［5］

模型	隐藏层1	隐藏层2
$f x, D T N N ·$	16	9
$f y, D T N N ·$	11	8
$f z, D T N N ·$	8	5

Table 3

Table 4

Computational complexity of the proposed method and Ref. ［5］

模型	激活函数个数		乘法量
$f x, D T N N ·$	25	共57	8×16+16×9+9×1=281	共582
$f y, D T N N ·$	19		8×11+11×8+8×1=184
$f z, D T N N ·$	13		9×8+8×5+5×1=117
$f x N N ·$	17	共35	8×11+11×6+6×1=160	共300
$f y N N ·$	11		8×6+6×5+5×1=83
$f z N N ·$	7		9×5+5×2+2×1=57

Table 4

Fig.14

Fig. 15

Fig.16

Fig.17

Table 5

Training runtime and GPU memory consumption

网络模型	网络节点数		$N G P U$	1 000代训练平均耗时/s	耗时降低率/%	$ϑ 1 = ϑ 2 = 1$ 时的显存占用量/MB		$ϑ 1 = ϑ 2 = 2$ 时的显存占用量/MB
网络模型	隐藏层1	隐藏层2	$N G P U$	1 000代训练平均耗时/s	耗时降低率/%	GPU1	GPU2	GPU1	GPU2
$f z N N ·$	5	2	2	59.97	32.30	2 105	2 003	1 563	1 461
$f z N N ·$	5	2	1	88.58	32.30	3 233		2 127
$f y N N ·$	6	5	2	62.26	36.00	2 483	2 381	1 743	1 641
$f y N N ·$	6	5	1	97.28	36.00	3 907		2 501
$f x, D T N N ·$	16	9	2	233.68	47.46	6 509	6 405	3 793	3 689
$f x, D T N N ·$	16	9	1	444.73	47.46	12 043		6 527
$f N N 1$	17	16	2	1 511.55	48.86	19 531	19 429	10 201	10 099
$f N N 1$	17	16	1	2 955.88	48.86	显存不足		19 553
$f N N 1$	20	15	2	1 875.13	49.18	21 577	21 475	11 317	11 215
$f N N 1$	20	15	1	3 689.83	49.18	显存不足		21 599

Table 5

Table 6

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模型	神经网络预测耗时/ms	椭圆弹道预测耗时/ms	其他耗时/ms	总耗时/ms
本文方法	1.250	0.634	0.696	2.585
文献［5］方法	2.299		0.696	2.995

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A neural network model for impact point prediction of ballistic missile based on improved second-order optimizer with parallel learning

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