﻿ 基于遗传算法的飞行管理系统余度配置优化方法<sup>*</sup>
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1. 沈阳航空航天大学 安全工程学院, 沈阳 110136;
2. 沈阳飞机设计研究所, 沈阳 110031

Flight management system redundancy optimization method based on genetic algorithm
HUO Lin1, FEI Simiao2
1. School of Safety Engineering, Shenyang Aerospace University, Shenyang 110136, China;
2. Shenyang Aircraft Design and Research Institute, Shenyang 110031, China
Received: 2016-06-14; Accepted: 2016-06-20; Published online: 2016-09-01 11:42
Corresponding author. HUO Lin, E-mail: helen0404@icloud.com
Abstract: Aircraft management system is an important part to guarantee flight safety, and redundancy design is the main method to improve the safety of the system. The redundancy design, however, is constrained by the budget (economy) in the design and manufacture and the consumption of the maintenance support resources (reliability). According to the safety, basic reliability and economy models of aircraft management system, a redundancy configuration optimization method was proposed by using the improved integer optimal genetic algorithm, with safety as the objective, and basic reliability and economy as the constraint. Then an example was taken to show its effectiveness to the complex system redundancy optimization. The sensitivity analysis shows that the safety optimal value declines with the increase of the basic reliability lower bound, and rises with the increase of the economy upper bound. For two constraints on the optimization of the objective competitive constraints, at the same time only one constraint condition plays a major constraint role. These two constraint conditions play a role in the competition, and at the same time there is only one main constraint.
Key words: redundancy optimization     safety optimization     genetic algorithm     flight management system     basic reliability

1 飞管系统组成

 图 1 飞管系统组成 Fig. 1 Composition of flight management system
2 飞管系统建模 2.1 飞管系统基本可靠性模型

 (1)

2.2 飞管系统安全性模型

 (2)

2.3 飞管系统经济性模型

 (3)

3 余度配置优化方法

 图 2 遗传算法流程图 Fig. 2 Flowchart of genetic algorithm

3.1 交叉算子

 (4)

 (5)
3.2 变异算子

 (6)

4 以安全性为目标的飞管系统余度优化配置

 (7)

 设备名称 MTBF/(106h) MTBCF/(106h) 单价/万元 余度范围 大气数据传感器 3.0 3.8 3 1~4 速率陀螺组 1.2 2.9 5 1~4 加速度计组 2.7 7.6 2 1~4 激光惯导 3.3 8.7 8 1~4 无线电高度表 0.6 4.6 1 1~4 飞管计算机 0.9 5.7 98 1 模拟接口设备 12.9 72.7 0.8 1 数字接口设备 8.9 56.6 0.9 1 作动器远程控制终端 1.2 22.8 3.2 1~4 舵机1 2.3 12.4 1.2 1~4 作动筒1 0.8 6.3 0.5 1~4 舵机2 2.3 12.4 1.2 1~4 作动筒2 0.8 6.3 0.5 1~4

R0=0.99，C0=150万元，若不满足约束条件，适应度函数取值为1，若满足约束条件，适应度函数取值为-S (N)。图 3显示了通过本文所述遗传算法进行余度配置优化的过程。如图 3(a)所示，随着优化的进展，目标函数最优值与种群目标函数均值逐渐收敛，种群在进化70代左右时，目标函数均值趋于稳定，目标函数均值在-0.5~-1.0之间波动，整个过程不同代种群的目标函数最优值较为稳定，且收敛较快。种群分散性的变化也呈现出类似规律，如图 3(c)所示，种群间目标函数平均距离逐渐缩小，在70代左右时种群分散性趋于稳定。最终决策变量结果在图 3(b)中显示。

 图 3 余度优化结果 Fig. 3 Redundancy optimization results

 设备名称 余度 本文遗传算法 编码改进遗传算法[8] 贪婪搜索规划算法[22] 大气数据传感器 3 3 3 速率陀螺组 2 2 2 加速度计组 2 2 2 激光惯导 1 1 1 无线电高度表 2 2 2 作动器远程控制终端 2 1 1 舵机1 3 3 3 作动筒1 3 3 3 舵机2 3 3 3 作动筒2 3 3 3 安全性最优值 0.999 936 0.999 927 0.999 936 时间消耗 6 min 3 min 53 h

5 余度敏感性分析

 图 4 基本可靠性和经济性约束下敏感性分析 Fig. 4 Sensitivity analysis of basic reliability and economy constraints

 基本可靠性约束下限 余度 大气数据传感器 速率陀螺组 加速度计组 激光惯导 无线电高度表 作动器远程控制终端 舵机1 作动筒1 舵机2 作动筒2 0.990 0 2 2 2 2 2 1 2 3 2 2 0.996 0 2 2 2 2 2 1 2 3 2 2 0.996 1 2 2 2 2 2 1 3 2 2 2 0.996 5 2 2 3 2 2 1 2 2 2 2 0.996 6 2 2 3 2 2 1 2 2 2 2 0.996 7 2 2 3 2 2 1 2 2 2 2 0.996 8 2 2 2 2 2 1 2 2 2 2 0.997 0 3 2 2 2 1 1 2 2 3 2 0.997 3 2 2 2 2 1 2 2 1 2 2 0.997 5 2 2 2 1 1 1 2 1 2 2 0.997 7 3 2 2 2 1 1 1 1 3 2 0.997 9 2 2 1 2 1 1 1 1 2 2 0.998 0 2 1 2 1 1 1 1 1 2 1 0.998 1 1 1 1 1 1 1 1 1 1 1

 经济性约束上限/万元 余度 大气数据传感器 速率陀螺组 加速度计组 激光惯导 无线电高度表 作动器远程控制终端 舵机1 作动筒1 舵机2 作动筒2 140 2 2 2 1 2 1 2 2 2 2 150 3 2 2 1 2 2 3 3 3 3 160 3 3 2 2 3 2 2 2 2 2 170 3 3 3 2 4 3 3 3 3 3 180 3 3 3 3 3 3 4 4 4 4

6 结论

1) 本文提出了一种基于遗传算法的余度配置优化方法，并利用改进后适用于整数优化的遗传算法对飞管系统展开了以安全性为目标、基本可靠性与经济性为约束的余度配置优化研究。

2) 进行了多约束条件对优化目标的敏感性分析。结果表明了该遗传算法可以有效求出满足基本可靠性和经济性约束下的安全性指标最优解及相对应的余度配置策略，且该方法具有良好的精度与收敛速度。

3) 通过敏感性分析发现，安全性指标的最优值随着基本可靠性约束下限的提高而降低，随着经济性约束上限的增加而增加。且这2种约束条件对优化目标竞争约束，在同一时刻只有一种约束条件起主要约束作用，说明了提高产品安全性的手段，除了需要增加前期预算投入外，还需要增加后期维修资源的投入。

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#### 文章信息

HUO Lin, FEI Simiao

Flight management system redundancy optimization method based on genetic algorithm

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(7): 1306-1312
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0512