基于竞争博弈的多目标可靠性优化设计方法

冯嘉珍; 张建国; 邱继伟

doi:10.13700/j.bh.1001-5965.2017.0367

基于竞争博弈的多目标可靠性优化设计方法

doi: 10.13700/j.bh.1001-5965.2017.0367

冯嘉珍^{1, 2},
张建国^{1, 2, ,},
邱继伟^{1, 2}

1.
北京航空航天大学可靠性与系统工程学院, 北京 100083
2.
北京航空航天大学可靠性与环境工程技术重点实验室, 北京 100083

基金项目:

国家重点研发计划 2013CB733000

国家自然科学基金 51675026

国家自然科学基金 71671009

详细信息

作者简介:
冯嘉珍男, 博士研究生。主要研究方向:机械可靠性

张建国男, 博士, 教授, 博士生导师。主要研究方向:机械/机构/结构可靠性

通讯作者:
张建国, E-mail: zjg@buaa.edu.cn

中图分类号: TB114.3
计量
- 文章访问数: 750
- HTML全文浏览量: 171
- PDF下载量: 349
- 被引次数: 0
出版历程
- 收稿日期: 2017-05-31
- 录用日期: 2017-08-01
- 网络出版日期: 2018-04-20

Multi-objective reliability design optimization approach based on competition game

FENG Jiazhen^{1, 2},
ZHANG Jianguo^{1, 2
, ,},
QIU Jiwei^{1, 2}

1.
School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
2.
Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Funds:

National Key R&D Program of China 2013CB733000

National Natural Science Foundation of China 51675026

National Natural Science Foundation of China 71671009

More Information

Corresponding author: ZHANG Jianguo, E-mail: zjg@buaa.edu.cn

摘要

摘要:
针对目标权重选取的主观性问题，提出基于竞争博弈进行多目标可靠性优化设计的方法。首先，将各设计目标视为不同的博弈方，通过随机设计变量集映射（RDVSM）技术，将优化模型中的随机设计变量集分解为各博弈方所拥有的策略集；然后，各博弈方以自身收益为目标，结合性能测量方法在各自的策略集中进行单目标可靠性优化设计，并由所有的优化设计结果形成一轮博弈的策略组合；经过多轮博弈之后得博弈均衡解。压力容器和齿轮减速器2个案例的分析表明，所提方法有效避免了目标权重的选择，设计结果具有较高客观性。
- 多目标 /
- 可靠性优化设计 /
- 竞争博弈 /
- 随机设计变量集映射(RDVSM) /
- 博弈均衡解
Abstract:
Aimed at the subjectivity of the selection of target weights, multi-objective reliability design optimization approach based on competition game is proposed. In this approach, every design objective is treated as the corresponding game player, and the random design variable set is decomposed into multiple strategy sets that are allocated to the corresponding player through the random design variable set mapping (RDVSM) technology. Then, combined with the performance measurement analysis method, every player takes its payoff as the single objective function for the reliability design optimization in its own strategy set, and the optimal results of all players form a group of strategies in this game round. After multi-round games, the equilibrium solution of the game is acquired. The study of a pressure vessel case and a gear reducer case shows that the proposed approach avoids the selection of target weights, and the design results have high objectivity.
- multi-objective /
- reliability design optimization /
- competition game /
- random design variable set mapping (RDVSM) /
- game equilibrium solution

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图 1 压力容器示意图^[16]

Figure 1. Schematic diagram of pressure vessel^[16]

下载: 全尺寸图片幻灯片

图 2 减速器传动原理示意图^[17]

Figure 2. Schematic diagram of drive principle of reducer^[17]

下载: 全尺寸图片幻灯片

表 1 压力容器随机变量的概率分布

Table 1. Probability distribution of random variables of pressure vessel

变量	均值	变异系数	均值范围
r/mm	595.8611	0.05	[2.54, 914.4]
l/mm	999.7745	0.05	[2.54, 3556]
t/mm	62.4510	0.05	[12.7, 152.4]

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表 2 基于NSGA-Ⅱ的压力容器部分优化结果

Table 2. Part optimization results of pressure vessel based on NSGA-Ⅱ

变量	非劣解1	非劣解2	非劣解3
μ_t^N/mm	107.554 0	108.746 8	106.403 1
μ_l^N/mm	1 059.278 0	1 509.354 4	1 601.394 3
μ_r^N/mm	795.133 5	815.710 1	827.923 2
μ_w^N/kg	12 393.860 9	15 135.898 9	15 523.401 2
μ_v^N/m³	4.207 6	5.425 9	5.822 7

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表 3 基于加权法的压力容器优化结果

Table 3. Optimization results of pressure vessel based on weighted method

变量	权重组合1(ω₁=0.01，ω₂= 0.99)	权重组合2(ω₁=0.1，ω₂= 0.9)	权重组合3(ω₁= ω₂= 0.5)	权重组合4(ω₁=0.9，ω₂=0.1)	权重组合5(ω₁=0.99，ω₂= 0.01)
μ_t^W/mm	105.092 8	105.099 4	105.096 6	83.953 1	12.7
μ_l^W/mm	1 719.527 4	1 713.351 9	1 721.302 9	2 093.012 8	962.011 8
μ_r^W/mm	840.228 2	841.113 6	837.490 1	672.022 5	71.356 5
μ_w^W/kg	16 187.338 1	16 184.143 9	16 121.364 6	10 387.539 0	54.265 2
μ_v^W/m³	6.295 3	6.297 5	6.250 2	4.238 7	0.016 9

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表 4 减速器随机变量的概率分布

Table 4. Probability distribution of random variables of reducer

cm
变量	均值	标准差	均值范围
齿面宽度x₁	3.58	0.05	[2.6, 3.6]
齿轮模数x₂	0.72	0.01	[0.7, 0.8]
轴1轴承间距x₄	7.48	0.05	[7.3, 8.3]
轴2轴承间距x₅	7.83	0.05	[7.3, 8.3]
轴1直径x₆	3.37	0.05	[2.9, 3.9]
轴2直径x₇	5.26	0.05	[5.0, 5.5]
注：齿轮1齿数x₃(取整数)均值范围为[17, 28]。

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表 5 基于NSGA-Ⅱ的减速器部分优化结果

Table 5. Part optimization results of reducer based on NSGA-Ⅱ

变量	非劣解1	非劣解2	非劣解3
μ_x₁^N/cm	3.579 8	3.588 4	3.582 3
μ_x₂^N/cm	0.701 7	0.700 9	0.701 1
μ_x₃^N	17	17	17
μ_x₄^N/cm	8.042 3	8.043 8	8.039 6
μ_x₅^N/cm	7.927 6	7.962 3	8.046 0
μ_x₆^N/cm	3.537 9	3.456 1	3.509 1
μ_x₇^N/cm	5.379 2	5.390 5	5.395 9
μ_f₁^N/cm³	3 194.976 0	3 195.355 4	3 210.576 2
μ_f₂^N/MPa	93.504 2	100.295 7	95.823 8
μ_f₃^N/MPa	80.688 1	80.183 7	79.944 4

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表 6 基于加权法的减速器优化结果

Table 6. Optimization results of reducer based on weighted method

变量	权重组合1(ω₁=0.02, ω₂=ω₃=0.49)	权重组合2(ω₁=0.2, ω₂=ω₃=0.4)	权重组合3(ω₁=ω₂=ω₃=1/3)	权重组合4(ω₁=0.8, ω₂=ω₃=0.1)	权重组合5(ω₁=0.98, ω₂=ω₃=0.01)
μ_x₁^W/cm	3.50	3.50	3.50	3.50	3.50
μ_x₂^W/cm	0.7	0.7	0.7	0.7	0.7
μ_x₃^W	17	17	17	17	17
μ_x₄^W/cm	7.986 8	7.750 1	7.750 6	7.475 1	7.476 4
μ_x₅^W/cm	7.950 1	7.952 0	8.112 9	7.995 9	7.995 3
μ_x₆^W/cm	3.9	3.9	3.9	3.434 2	3.434 0
μ_x₇^W/cm	5.5	5.5	5.369 0	5.369 2	5.369 2
μ_f₁^W/cm³	3 313.345 3	3 310.516 3	3 226.071 3	3 077.533 3	3 077.463 2
μ_f₂^W/MPa	69.813 3	69.783 6	69.783 7	102.155 3	102.177 7
μ_f₃^W/MPa	75.490 7	75.493 9	81.153 4	81.143 2	81.143 2

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