基于BP神经网络的超空泡射弹优化设计方法

doi:10.12382/bgxb.2024.0496

摘要/Abstract

摘要：

有效射程是超空泡射弹最重要的性能指标之一,受到外形和衡重参数的耦合影响。为了增加超空泡射弹的有效射程,建立计算超空泡射弹有效射程的数值模型,根据正交试验设计原则设计四因素五水平工况组合,通过仿真计算获得外形及衡重参数影响下的超空泡射弹有效射程数据集,结合反向传播 (Back Propagation,BP)神经网络方法和遗传算法,建立超空泡射弹设计参数优化方法,获得全域最大有效射程及其对应的外形和衡重参数设计结果。研究结果表明:超空泡射弹的水下弹道具有稳定的尾拍特性,通过极差分析,质量对有效射程的影响最大;在没有精确数学模型的情况下,运用BP神经网络,基于有限个数据点训练出的有效射程预测模型精度高,平均误差为0.735%;通过遗传算法获得了四因素耦合影响下的全域最优射程,较数据集中的最好结果提高了5.01%,较正交优化结果提升了1.95%。所得研究结果可为超空泡射弹总体设计工作提供参考。

关键词: 超空泡射弹, 正交试验, BP神经网络, 遗传算法

Abstract:

Effective range is one of the most important performance indexes of supercavitating projectiles, which is influenced by the coupling of shape and weight parameters. In order to increase the effective range of supercavitating projectile, a numerical model for calculating the effective range of supercavitating projectiles is established, and a combination of four factors and five levels is designed according to the principle of orthogonal test design. The effective range data set of supercavitating projectiles under the influence of shape and weight parameters is obtained by simulation calculation, and an optimization method of design parameters of supercavitating projectiles is established by using BP(back propagation) neural network method and genetic algorithm, and the maximum effective range of supercavitating projectile and its corresponding shape and weight parameters are obtained. The results show that the underwater trajectory of supercavitating projectile has a stable tail beat characteristic. The mass has the greatest impact on the effective range through range analysis In the absence of precise mathematical model, the accuracy of the effective range prediction model trained by BP neural network based on limited data points is high with the average error of 0.735%. The optimal range of the whole domain under the influence of four-factors coupling is obtained by genetic algorithm. The range is improved by 5.01% compared with the best result of data set, and by 1.95% compared with the result of orthogonal optimization. The research results can providereference for the overall design of supercavitating projectile.

Key words: supercavitating projectile, orthogonal test, BP neural network, genetic algorithm

中图分类号:

巩世龙, 党建军, 李少星, 黄闯. 基于BP神经网络的超空泡射弹优化设计方法[J]. 兵工学报, 2025, 46(5): 240496-.

GONG Shilong, DANG Jianjun, LI Shaoxing, HUANG Chuang. Optimization Design Method of the Supercavitating Projectile Based on BP Neural Network[J]. Acta Armamentarii, 2025, 46(5): 240496-.

图/表 18

图1 超空泡射弹外形

Fig.1 Supercavitating projectile shape

图2 计算域及边界条件

Fig.2 Computational domain and boundary conditions

图3 射弹网格模型

Fig.3 Mesh model of projectile

图4 数值计算结果与试验数据点对比

Fig.4 Comparison of numerically calculated results with test data points

图5 射弹速度衰减结果对比

Fig.5 Comparison of projectile velocity attenuation results

图6 不同网格量结果对比

Fig.6 Comparison of the results of different mesh amounts

表1 射弹参数及其水平

Table 1 Projectile parameters and level

水平	D_n/mm	L_t/mm	G/kg	J_z/(kg·mm²)
1	5.00	30	0.753	3364.1
2	5.25	27	0.828	3700.5
3	5.50	33	0.903	4036.9
4	5.75	36	0.668	3027.7
5	6.00	39	0.593	2691.3

图7 尾拍运动中的俯仰角变化曲线

Fig.7 Changing curve of attitude angle of projectile in tail-beat motion

图8 尾拍运动中的剩余动能和速度衰减曲线

Fig.8 Attenuation curves of of residual kinetic energy and velocity in tail-beat motion

图9 射弹一个周期内泡体和弹体位置关系变化

Fig.9 Change of cavity shape of projectile during tail-beating

表2 正交试验结果

Table 2 Orthogonal test results

编号	序列	初始速度 v₀/(m·s^-1)	剩余速度 v_r/(m·s^-1)	有效射程 L_r/m
1	A1B1C1D1	320	200	49.73
2	A1B2C2D2	305	191	51.27
3	A1B3C3D3	292	182	53.30
4	A1B4C4D4	340	212	47.23
5	A1B5C5D5	360	225	44.19
6	A2B1C2D3	305	191	52.99
7	A2B2C3D4	292	182	51.67
8	A2B3C4D5	340	212	45.49
9	A2B4C5D1	360	225	44.88
10	A2B5C1D2	320	200	53.75
11	A3B1C3D5	292	182	54.26
12	A3B2C4D1	340	212	45.38
13	A3B3C5D2	360	225	44.35
14	A3B4C1D3	320	200	48.26
15	A3B5C2D4	305	191	51.64
16	A4B1C4D2	340	212	44.86
17	A4B2C5D3	360	225	40.96
18	A4B3C1D4	320	200	47.05
19	A4B4C2D5	305	191	49.68
20	A4B5C3D1	292	182	53.62
21	A5B1C5D4	360	225	37.49
22	A5B2C1D5	320	200	43.25
23	A5B3C2D1	305	191	49.59
24	A5B4C3D2	292	182	52.33
25	A5B5C4D3	340	212	45.38

表3 正交试验结果分析

Table 3 Analysis of orthogonal test results

影响参数	K_i₁	K_i₂	K_i₃	K_i₄	K_i₅	R_i
D_n	49.14	49.56	49.50	47.64	46.01	3.55
L_t	46.47	46.31	47.96	50.80	50.32	4.49
G	48.21	51.23	53.16	45.67	42.37	10.79
J_z	49.00	49.71	50.10	47.02	45.97	4.13

图10 预测射弹有效射程的BP神经网络模型

Fig.10 BP neural network model for predicting the projectile effective range

表4 不同隐含层节点数对应的平均错误率

Table 4 The average error rate corresponding to the number of nodes in different hidden layers

隐含层节点数	平均错误率/%	隐含层节点数	平均错误率/%
2	3.554	8	0.761
3	1.916	9	0.795
4	1.275	10	0.823
5	0.872	11	0.816
6	0.745	12	0.779
7	0.758	13	0.805

图11 网络预测值和真实值的比较

Fig.11 Comparison of network perdictions and true values

图12 适应度函数的最佳值和平均值变化

Fig.12 Changes in the optimal and mean values of fitness function

图13 不同射弹剩余动能变化曲线

Fig.13 Changing curves of residual kinetic energy for different projectiles

表5 预测模型对比验证

Table 5 Comparative validation of predictive models

结果及误差	正交优化射弹	遗传优化射弹
数值计算结果/m	55.89	56.98
BP神经网络结果/m	55.63	57.21
误差/%	0.48	0.40

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