基于卷积神经网络与支持向量机的适配器落点预测方法

doi:10.12382/bgxb.2024.0016

摘要/Abstract

摘要：

针对发射过程适配器落点预测算法存在的求解时间长、耗费资源多等问题,提出一种基于卷积神经网络(Convolutional Neural Network,CNN)与支持向量机(Support Vector Machine,SVM)算法的适配器落点预测模型。基于欧拉角描述建立发射过程适配器动力学运动模型,并通过四阶龙格库塔法对适配器运动轨迹进行数值求解,获得大量的适配器运动状态参数和落点信息;提出CNN-SVM的适配器落点预测模型,采用Adam优化器优化CNN网络性能,并通过网格搜索法获得SVM最佳的超参数。研究结果表明:CNN-SVM模型对适配器落点预测具有较好的求解精度和较强的泛化性能,其训练集和测试集的R²值均大于0.99,同时该模型的平均绝对误差均小于0.1m;在相同的计算资源且满足任务预测精度的条件下,其求解时间仅为传统数值积分方法的8.5%。该模型在实际应用中具备显著的优势,为发射过程中适配器分离落点快速预测提供了一种有效的解决方案。

关键词: 落点预测, 适配器, 卷积神经网络, 支持向量机

Abstract:

To address the prolonged processing and resource consumption challenges in the launch process adapter drop point prediction algorithm,a adapter drop point prediction model with convolutional neural network and support vector machine (CNN-SVM) is proposed.The adapter dynamics and motion models are established by utilizing Euler angle representation,and the fourth-order Runge-Kutta method is used to numerically solve the motion trajectory of adapter to provide the extensive motion state parameters and drop point information.The CNN-SVM-based adapter drop point prediction model uses the Adam optimizer to optimize CNN network performance,and determines optimal SVM hyperparameters through mesh searching.Simulated results show that the proposed model has high solution accuracy and robust generalization performance for adapter drop prediction,achieving R² values exceeding 0.99 for both training and test sets and the mean absolute error (MAE) less than 0.1m.The solution time of the proposed method is only 8.5% compared to that of the traditional numerical integration method under the conditions of equivalent resources and the required prediction accuracy.The proposed model offers an efficient solution for rapidly predicting the adapter separation drop point during the launch process.

Key words: drop point prediction, adapter, convolutional neural network, support vector machine

中图分类号:

TJ760.9

苏政宇, 杨宝生, 杨婧, 唐静楠, 姜毅, 邓月光. 基于卷积神经网络与支持向量机的适配器落点预测方法[J]. 兵工学报, 2025, 46(2): 240016-.

SU Zhengyu, YANG Baosheng, YANG Jing, TANG Jingnan, JIANG Yi, DENG Yueguang. A CNN-SVM-based Adapter Drop Point Prediction Algorithm[J]. Acta Armamentarii, 2025, 46(2): 240016-.

图/表 22

图1 爱国者导弹发射过程适配器分离[2]

Fig.1 Patriot missile launch process adapter separation[2]

图2 CNN结构

Fig.2 CNN structure

图3 SVM示意图

Fig.3 Schematic diagram of SVM

图4 基于CNN-SVM发射过程适配器落点预测流程图

Fig.4 Flowchart of CNN-SVM-based adapter drop point prediction

图5 发射过程适配器分离示意图

Fig.5 Schematic diagram of adapter separation durimgr launching

图6 坐标系变化示意图

Fig.6 Illustration of coordinate system transformation

图7 不同攻角下适配器风洞实验

Fig.7 Adapter wind tunnel experiment under different angles of attack

图8 适配器分离实验[25]

Fig.8 Adapter separation experiment[25]

图9 实验落点分布对比

Fig.9 Comparison of experimental drop point distributions

图10 适配器落点分布密度

Fig.10 Distribution density map of adapter drop points

表1 CNN模型结构参数

Table 1 CNN model structural parameters

结构	卷积核	特征数	输出尺寸
输入层			7×1×1
卷积层1	2×1	32	6×1×32
池化层1	2×1	32	3×1×32
卷积层2	2×1	64	2×1×64
池化层2	2×1	64	1×1×64
全连接层			2×1×192

图11 X轴方向训练集预测结果(R2=0.9968)

Fig.11 Predicted results of X-direction training set (R2=0.9968)

图12 Y轴方向训练集预测结果(R2=0.9977)

Fig.12 Predicted results of Y-direction training set (R2=0.9977)

图13 训练集误差分析图

Fig.13 Training set error analysis chart

图14 X轴方向测试集预测结果(R2=0.9972)

Fig.14 Predicted results of X-direction training set (R2=0.9972)

图15 Y轴方向测试集预测结果(R2=0.9973)

Fig.15 Predicted results of Y-direction training set (R2=0.9973)

图16 测试集误差分析

Fig.16 Test set error analysis chart

表2 蒙特卡洛实验初始条件

Table 2 Initial conditions for Monte Carlo experiment

参数	数值
初始X轴方向分离速度/(m·s^-1)	(3,3)
初始Y轴方向分离速度/(m·s^-1)	(-3,3)
初始Z轴方向分离速度/(m·s^-1)	(0,40)
初始分离角速度/(rad·s^-1)	(-15,15)
外部X轴方向风速/(m·s^-1)	(-10,10)
外部Y轴方向风速/(m·s^-1)	(-10,10)
发射过程随机振动/dB	(-5,5)

图17 蒙特卡洛实验结果

Fig.17 Result of Monte Carlo experiment

图18 蒙特卡洛实验结果箱线

Fig.18 Box plot of Monte Carlo experiment

图19 求解速度对比

Fig.19 Solution speed comparison

图20 求解速度对比图

Fig.20 Solution speed comparison

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