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Stage-wise multidisciplinary design optimization for multi-stage solid launch vehicle
MA Shuwei, LI Jinglin, CHEN Xi, CHEN Wanchun
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-04-07; Accepted: 2015-07-03; Published online: 2015-07-17 14:48
Corresponding author. Tel.: 010-82339769 E-mail: wanchun_chen@buaa.edu.cn
Abstract: Because of the strong coupling of multi-disciplines and the complicated algorithm and the low design efficiency, the integral optimization design of solid launch vehicle is a difficult, but important problem. To solve this problem, the multidisciplinary models of a multi-stage solid launch vehicle, including geometry, mass, aerodynamic, propulsion and trajectory/guidance systems, were established. Then, the multi-stage solid launch vehicle was divided into several sub-stages which were connected by the continuous requirements of the flight states. Thus, the system-level and subsystem-level solution frameworks were constructed. Furthermore, two types of optimization processes, named parallel and serial methods, were presented to solve the multidisciplinary design optimization (MDO) problem where the objective function is to minimize the gross weight. The results show that via the stage-wise formulation, the number of iterations can be reduced and better results can be obtained,compared with the traditional multidisciplinary feasible (MDF) method, and thus we verify the feasibility and superiority of the proposed approach applied to MDO problems for multi-stage solid launch vehicles.
Key words: multi-stage     solid launch vehicle     multidisciplinary design optimization (MDO)     stage-wise     parallel     serial

1 多级运载火箭学科模型

 图 1 MINOTAUR IV运载火箭外形示意图 Fig. 1 Schematic of shape of MINOTAUR IV launch vehicle
1.1 几何外形学科建模

1.2 质量学科建模

 图 2 质量分类 Fig. 2Classification of mass

1.3 气动学科建模

 图 3 阻力系数 Fig. 3 Drag coefficients
1.4 推进学科建模

MINOTAUR IV前三级均采用固体火箭发动机,本文采用理想固体火箭发动机[14],如图 4所示。

 P1 ，T1,A1,v1—发动机燃烧室压强、温度、面积和气流速度；P2 ，T2,A2,v2—喷管出口压强、温度、面积和气流速度；P3—外部大气压强；Pt,At,vt—喉道压强、面积和气流速度。 图 4 理想火箭发动机构型 Fig. 4 Constitution of ideal rocket engine

1.5 弹道/制导学科建模

 θ—弹道倾角;α—攻角;γ—俯仰角; L—升力;D—阻力;F—推力;v—飞行速度。 图 5 运载火箭动力学模型 Fig. 5 Dynamic model of launch vehicle

 图 6 俯仰角指令曲线 Fig. 6 Profile of pitch angle command

 图 7 Hohmann转移 Fig. 7 Hohmann transfer

2 多学科分级优化

2.1 分级优化思想 2.1.1 经典多学科方法——MDF

MDF是解决MDO问题中的最普遍、最经典的方法,它包括多学科分析(MDA)与系统优化器。MDA是多学科分析的过程,它用来分析各学科之间的耦合关系。在每一次迭代过程中都需要调用一次MDA,这样如果增加该系统学科的复杂度,会使MDA过程相当地耗时,极大地增加了MDF的计算复杂度。在系统优化器中经常采用遗传算法进行优化计算。

 MGLOW—运载火箭起飞质量; Mpi—各级推进剂质量;Mengine—发动机质量。 图 8 MDF流程图 Fig. 8 Process of MDF
2.1.2 分级优化方法

1) 飞行过程分段

 图 9 多级运载火箭飞行过程分段 Fig. 9 Flight process division of multi-stage launch vehicle

2) 优化算法

2.2 MDF方法

2.3 分级优化方法

2.3.1 并行方式

 图 10 并行方式分级优化流程图 Fig. 10 Parallel stage-wise optimization process

1) 系统级

2) 第i子系统级

2.3.2 串行方式

 图 11 串行方式分级优化流程图 Fig. 11 Serial stage-wise optimization process

1) 系统级

2) 子系统级

for i=3:1

end

3 优化方法对比及结果分析 3.1 设计优化规模

 图 12 设计变量个数随运载火箭级数变化 Fig. 12 Number of design variable changing with stages of launch vehicle
 图 13 不等式约束个数随运载火箭级数变化 Fig. 13 Number of inequality constraints changing with stages of launch vehicle
 图 14 等式约束个数随运载火箭级数变化 Fig. 14 Number of equality constraints changing with stages of launch vehicle

3.2 优化结果对比

MDF和分级优化结果如表 1所示。可以看出分级优化起飞质量比MDF小,有效地降低了运载火箭的起飞质量,尤其对起飞质量较大的固体运载火箭意义重大。而且,结果中的状态变量的连续误差都在5%以内,在运载火箭设计的初级阶段是可以被接受的。

 优化方法 目标函数 达到目标函数最优迭代次数 起飞质量/kg MDF 97 87299.16 并行 47 86635.79 串行 34 86203.01

 图 15 分级优化结果弹道 Fig. 15 Trajectory results of stage-wise optimization

4 结 论

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#### 文章信息

MA Shuwei, LI Jinglin, CHEN Xi, CHEN Wanchun

Stage-wise multidisciplinary design optimization for multi-stage solid launch vehicle

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(3): 542-550.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0196