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1. 海军航空工程学院 飞行器工程系, 烟台 264001;
2. 海军装备研究院, 上海 200436

Carrier airwake simulation methods based on improved multi-objective genetic algorithm
TAO Yang1,2, HAN Wei1
1. Department of Airborne Vehicle Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, China;
2. Naval Academy of Armament, Shanghai 200436, China
Abstract:A new numerical turbulence simulation method to enhance the credibility of simulation of carrier airwake free-air turbulence components has been presented. At first, the turbulence sequence of each direction was presented as the Euler forward different format with correction factors. Meanwhile, associated with the thought of intelligence algorithm, the mean squared error and correlation function error in turbulence correlation test were regarded as the optimized objective functions. And the selection of correction factors was treated as a multi-objective optimization problem. The correction factors were determined by improving multi-objective genetic algorithm. At last, the validity and rationality of this method were verified by simulation cases. The calculation results show that the required turbulence sequences can be generated flexibly with different sampling steps. Especially in case of some small sampling step, the simulated turbulence sequences fit the theoretical values very well, and the method can meet the requirement of virtual flight test.
Key words: carrier airwake     free-air random turbulence     multi-objective optimization     genetic algorithm     error functions

1 自由大气紊流生成方法

1.1 第1类频谱函数

Φu(Ω)Φw(Ω)之间存在线性关系,故以Φw(Ω)为例说明进行.Φw(Ω)共轭分解后得到的传递函数Gw(s)=8.461+100s,由Euler前向差分格式可得紊流速度:

ξ=nh,有

1.2 第2类频谱函数

ξ=nh,总的相关函数:

Δ=[abB1B22221)]2+4abc2B21B22σ21σ22

2 待修正系数确定方法

f2(x)=maxRx(ξ)－Rx,th(ξ),待修正系数为通过寻优最终得到的决策变量.

2.1 改进的NSGA2算法

2.1.1 基于序值的交叉、变异操作

2.1.2 基于拥挤距离的修剪方法

NSGA2中,采用的是精英选择的策略,低序值的个体会被优先保留.这样做存在一定的不足,一旦算法陷入了局部最优,因为修剪掉的都是高序值的个体,而自身种群没有新个体更新,因此很难跳出.为了保持种群的多样性,避免算法早熟现象,这里对修剪方法进行改进.假设每一前端的个体由两部分构成,其中原前端按拥挤距离保留一定比例的个体,其余的由下一前端的个体补上,候补的个体同样遵循按拥挤距离从大到小的选取方法.

2.2 基于改进NSGA2算法的参数选择

 图 1 修正系数选择流程图Fig. 1 Flow chart of correction coefficient selection

3 计算结果及分析

 图 2 x,y,z向Pareto解分布图Fig. 2 Distribution image of Pareto solution in x,y,z direction

 参数 原始目标函数误差 优化后目标函数误差 对应的修正系数 u (1.557×10－1,7.216×10－3) (1.113×10－2,7.433×10－5) (0.989,1.974) v (3.031×10－2,2.134×10－1) (1.012×10－3,5.576×10－3) (1.002,0.993,0.982,2.402) w (5.573×10－2,4.318×10－3) (3.772×10－3,2.613×10－4) (0.989,1.958)
 图 3 x,y,z向相关性检验Fig. 3 Correlation tests in x,y,z direction
 图 4 x,y,z向紊流序列Fig. 4 changeswiththeinputangle
4 结 论

1) 本文算法得到的Pareto非劣解集在解空间的分布均匀且连续,算法的分布性较好.

2) 仿真得到的舰尾紊流序列的均方差误差和相关函数误差均在要求误差范围之内,满足该模型频谱函数的理论表达式,表明通过该方法生成的舰尾流紊流序列的准确性高,而且在小步长情况下也能够得到较精确的修正系数,验证了本文方法的正确性和合理性.

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#### 文章信息

TAO Yang, HAN Wei

Carrier airwake simulation methods based on improved multi-objective genetic algorithm

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(3): 443-448.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0198