﻿ 战术导弹气动隐身快速多目标优化方法
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Effective multi-objective optimization for aerodynamic and stealthy performance of tactical missiles
Liu Li, Jiang Menglong, Long Teng, Wu Di, Huang Bo
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Abstract:A new effective multi-objective optimization method was employed to solve the aerodynamic and stealthy performance optimization of tactical missile problem. Physical programming was selected to translate the multi-objective problem into the single objective problem. Genetic algorithm (GA) was applied to carrying on the design space search. Variable selection and radial basis function (RBF) were contributed to reducing the design variable space dimension and the number of high fidelity model evaluations. Then, the aerodynamic and stealthy performance optimization of a quasi BGM-109 model was chosen as an example to deliver the whole optimization steps and verify the correctness of the method. The optimization task is to minimize the drag coefficient and the heading radar cross section (RCS) subject to the aerodynamic performance constraint, namely the lift coefficient has to be no less than the initial value. Through application to engineering case, the computational cost of the proposed method decreases by 83% compared to that of GA, while two methods has nearly identical performance.
Key words: tactical missile design     aerodynamic and stealthy performance     multi-objective optimization     physical programming     surrogate model     variable selection

1 战术导弹气动隐身性能分析方法 1.1 气动分析模型

 图 1 法向力系数的DATCOM计算数据与实验数据对比Fig. 1 Comparison of normal force coefficient from DATCOM and experiment
1.2 隐身分析模型

 图 2 NASA杏仁体RCS的FEKO计算结果与实验数据对比Fig. 2 Comparison of RCS between NASA almond’s results from FEKO and experiment
2 战术导弹多目标优化方法 2.1 战术导弹气动隐身多目标优化

2.2 物理规划方法

 Δy1~Δy5—穿越该区域时偏好函数的变化值.区域划分应遵循均分原则，即保证每个目标函数在穿越该区间内造成的偏好函数变化值相等.图 3 偏好函数区域划分图Fig. 3 Preference function regions for ith generic criterion

SIB和LIB偏好函数方程的构造,需要给定5个边界值,利用边界值可以准确地描述各偏好函数,进而求解出多目标问题的总偏好,最后将总偏好代入优化函数中进行优化,得到相应的非劣解.物理规划优化方法的流程如图 4所示.

 图 4 物理规划流程Fig. 4 Flowchart of physical programming

2.3 变量筛选

 图 5 变量筛选流程Fig. 5 Flowchart of variable selection

2.4 代理模型

3 算 例 3.1 类BGM-109外形参数化及问题描述

 图 6 类BGM-109模型与真实模型对比图Fig. 6 Quasi/real BGM-109 model geometry differences

3.2 基于方差分析的变量筛选

 设计变量 参数名称 重要度/% 偏好函数 约束条件 c1 弹头长度 0.00 0.00 c2 钝头半径 2.01 0.00 c3 弹身直径 71.35 18.05 c4 弹身长度 0.00 0.00 c5 弹尾长度 0.00 0.00 c6 尾部直径 10.62 1.83 c7 主翼安装位置 1.00 0.00 c8 主翼翼展 6.09 61.75 c9 主翼根弦长 0.00 0.00 c10 主翼稍弦长 1.40 7.89 c11 主翼前缘后掠角 0.19 2.47 c12 尾翼安装位置 0.49 0.00 c13 尾翼翼展 5.46 6.63 c14 尾翼根弦长 0.00 0.00 c15 尾翼稍弦长 1.32 1.11 c16 尾翼后缘后掠角 0.00 0.11 注:c3,c6,c8,c10和c13为筛选后的设计变量，加粗显示.
3.3 优化流程

 图 7 战术导弹气动隐身多目标优化流程Fig. 7 Flowchart of aerodynamic stealthy coupled multi-objective optimization for tactical missile
3.4 构建代理模型及优化

 评价参数 相对误差均值 复相关系数 数值 0.016 8 0.943 4

 方案 Cd σ/(dB·m2) Cl 初始方案 初始数据 0.055 -10.859 0.477 遗传算法 优化结果 0.046 -15.946 0.481 变化量 -16.4% -46.8% +1% 本文方法 优化结果 0.048 -15.358 0.548 变化量 -12.7% -41.4% +15.3%

 项目 c3 c6 c8 c10 c13 初值 0.520 0.240 1.055 0.300 0.270 最优值 0.416 0.192 1.266 0.320 0.284
 径向数据表征前向散射的RCS，dB·m2;周向数据表征入射角度. 图 8 RCS前向散射特性对比Fig. 8 Change of heading RCS

4 结 论

1) 经过变量筛选,设计者能直观地获得几何外形参数对气动隐身性能影响的重要度排序,即给出了改善气动隐身性能的努力方向;

2) 本文算法将参考模型的阻力系数降低了12.7%,前向RCS降低了41.4%,与遗传算法相比,在优化结果相差小于6%的情况下,减少了83%的计算量;

3) 筛选出的5个设计变量中有3个设计变量取到了边界值,可预计若适当放宽约束条件,得到的优化结果会更好.

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#### 文章信息

Liu Li, Jiang Menglong, Long Teng, Wu Di, Huang Bo

Effective multi-objective optimization for aerodynamic and stealthy performance of tactical missiles

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(12): 1654-1659.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0753