﻿ 拦截弹道快速设计方法
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Rapid design algorithm for intercept missile trajectory
WANG Bei, ZHOU Tao, DONG Changhong
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:Traditional optimization algorithm always needs iterative calculation and consumes long time when it is used to solve the problem of intercept trajectory design under the multi-constraints condition. In view of this disadvantage, a rapid trajectory design algorithm for intercept missile was proposed. The new algorithm was based on the nonlinear fit technique of artificial neural network. First, a sample was calculated offline through a general optimization algorithm. The target position and the optimized flight procedure parameters in the sample were trained to fit the input-output mapping. Then the optimal flight procedure parameters could be calculated fast in the condition that the target position was given, and the goal of improving the trajectory design efficiency was achieved. Applying this algorithm to intercept trajectory design, while ensuring good hit accuracy, the calculation time is greatly reduced compared with the traditional algorithm, and it improves the timeliness of intercept trajectory design. The numerical simulation demonstrates the effectiveness of the algorithm proposed.
Key words: intercept missiles     trajectories     optimization     design     neural networks

1 拦截弹的数学建模 1.1 动力学模型

1) 假设地球为圆球形;

2) 采用USSA76标准大气模型;

3) 忽略导弹的侧向运动,即导弹始终在发射点、预测拦截点和地心确定的大圆面内;

4) 只考虑导弹弹体的俯仰运动[12].

1.2 飞行程序设计

 图 1 程序角变化曲线Fig. 1 Program angle change curve
1.3 弹道优化模型

1) 优化目标.

2) 设计变量.

3) 约束条件.

2 基于神经网络的快速弹道设计 2.1 基于神经网络的快速弹道设计原理

 图 2 传统优化算法的弹道设计流程图Fig. 2 Trajectory design flow chart using general optimization algorithm

 图 3 应用神经网络的弹道设计流程图Fig. 3 Trajectory design flow chart using neural network
2.2 神经网络样本的生成

2.3 神经网络设计

 图 4 BP神经网络结构Fig. 4 BP neural network structure

3 算例仿真

 图 5 神经网络训练均方误差Fig. 5 Mean squared error of neural network training
 图 6 训练数据线性回归结果Fig. 6 Linear regression results of training data

 图 7 拦截弹道曲线Fig. 7 Intercept trajectory curve
 图 8 拦截弹速度曲线Fig. 8 Velocity curve of interceptor

 算法 拦截时间/s 与预测命中点偏差/m 仿真时间/s 粒子群寻优 331 84 31.7 神经网络 331 743 0.06

 图 9 不同拦截点的蒙特卡洛仿真Fig. 9 Monte Carlo simulation in different intercept points

 拦截点坐标/km 拦截 时间/s 飞行程序角/(°) 命中点偏差/m φ1 φ2 (568,577) 247 65.0526 29.6046 328 (972,677) 302 55.7570 26.9703 547 (1320,760) 354 52.2236 26.0688 551 (769,885) 312 74.3646 29.6276 144 (1180,952) 363 63.8327 28.5656 346 (630,1023) 315 75.4373 46.6856 560
4 结 论

1) 该方法相比传统算法设计的拦截弹弹道偏差稍大,但依然有良好的命中精度.

2) 该方法在设计拦截弹道时的计算时间得到极大的缩短,有效地实现了快速设计弹道.

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#### 文章信息

WANG Bei, ZHOU Tao, DONG Changhong

Rapid design algorithm for intercept missile trajectory

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(2): 358-363.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0143