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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

冯嘉珍, 张建国, 邱继伟等 . 基于竞争博弈的多目标可靠性优化设计方法[J]. 北京航空航天大学学报, 2018, 44(4): 887-894. doi: 10.13700/j.bh.1001-5965.2017.0367
引用本文: 冯嘉珍, 张建国, 邱继伟等 . 基于竞争博弈的多目标可靠性优化设计方法[J]. 北京航空航天大学学报, 2018, 44(4): 887-894. doi: 10.13700/j.bh.1001-5965.2017.0367
FENG Jiazhen, ZHANG Jianguo, QIU Jiweiet al. Multi-objective reliability design optimization approach based on competition game[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(4): 887-894. doi: 10.13700/j.bh.1001-5965.2017.0367(in Chinese)
Citation: FENG Jiazhen, ZHANG Jianguo, QIU Jiweiet al. Multi-objective reliability design optimization approach based on competition game[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(4): 887-894. doi: 10.13700/j.bh.1001-5965.2017.0367(in Chinese)

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
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

Multi-objective reliability design optimization approach based on competition game

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
  • 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。

     

  • 图 1  压力容器示意图[16]

    Figure 1.  Schematic diagram of pressure vessel[16]

    图 2  减速器传动原理示意图[17]

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

    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]
    下载: 导出CSV

    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
    μtN/mm 107.554 0 108.746 8 106.403 1
    μlN/mm 1 059.278 0 1 509.354 4 1 601.394 3
    μrN/mm 795.133 5 815.710 1 827.923 2
    μwN/kg 12 393.860 9 15 135.898 9 15 523.401 2
    μvN/m3 4.207 6 5.425 9 5.822 7
    下载: 导出CSV

    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)
    μtW/mm 105.092 8 105.099 4 105.096 6 83.953 1 12.7
    μlW/mm 1 719.527 4 1 713.351 9 1 721.302 9 2 093.012 8 962.011 8
    μrW/mm 840.228 2 841.113 6 837.490 1 672.022 5 71.356 5
    μwW/kg 16 187.338 1 16 184.143 9 16 121.364 6 10 387.539 0 54.265 2
    μvW/m3 6.295 3 6.297 5 6.250 2 4.238 7 0.016 9
    下载: 导出CSV

    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]。
    下载: 导出CSV

    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
    μx1N/cm 3.579 8 3.588 4 3.582 3
    μx2N/cm 0.701 7 0.700 9 0.701 1
    μx3N 17 17 17
    μx4N/cm 8.042 3 8.043 8 8.039 6
    μx5N/cm 7.927 6 7.962 3 8.046 0
    μx6N/cm 3.537 9 3.456 1 3.509 1
    μx7N/cm 5.379 2 5.390 5 5.395 9
    μf1N/cm3 3 194.976 0 3 195.355 4 3 210.576 2
    μf2N/MPa 93.504 2 100.295 7 95.823 8
    μf3N/MPa 80.688 1 80.183 7 79.944 4
    下载: 导出CSV

    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)
    μx1W/cm 3.50 3.50 3.50 3.50 3.50
    μx2W/cm 0.7 0.7 0.7 0.7 0.7
    μx3W 17 17 17 17 17
    μx4W/cm 7.986 8 7.750 1 7.750 6 7.475 1 7.476 4
    μx5W/cm 7.950 1 7.952 0 8.112 9 7.995 9 7.995 3
    μx6W/cm 3.9 3.9 3.9 3.434 2 3.434 0
    μx7W/cm 5.5 5.5 5.369 0 5.369 2 5.369 2
    μf1W/cm3 3 313.345 3 3 310.516 3 3 226.071 3 3 077.533 3 3 077.463 2
    μf2W/MPa 69.813 3 69.783 6 69.783 7 102.155 3 102.177 7
    μf3W/MPa 75.490 7 75.493 9 81.153 4 81.143 2 81.143 2
    下载: 导出CSV
  • [1] 许孟辉, 邱志平.结构模糊非概率混合可靠性分析方法[J].北京航空航天大学学报, 2014, 40(2):222-228. http://bhxb.buaa.edu.cn/CN/abstract/abstract12852.shtml

    XU M H, QIU Z P.Reliability analysis of structures with fuzzy and non-probabilistic hybrid variables[J].Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(2):222-228(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract12852.shtml
    [2] 孟广伟, 冯昕宇, 李锋, 等.基于降维算法和Edgeworth级数的结构可靠性分析[J].北京航空航天大学学报, 2016, 42(3):421-425. http://bhxb.buaa.edu.cn/CN/abstract/abstract13451.shtml

    MENG G W, FENG X Y, LI F, et al.Structural reliability analysis based on dimensionality reduction and Edgeworth series[J].Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(3):421-425(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract13451.shtml
    [3] GARG H, RANI M, SHARMA S P, et al.Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment[J].Expert Systems with Applications, 2014, 41(7):3157-3167. doi: 10.1016/j.eswa.2013.11.014
    [4] KOGISO N, KODAMA R, TOYODA M.Reliability-based multi-objective optimization using the satisficing trade-off method[J].Mechanical Engineering Journal, 2014, 1(6):1-12. http://cn.bing.com/academic/profile?id=524d70f0be5c7241450dbede356a557b&encoded=0&v=paper_preview&mkt=zh-cn
    [5] 张瑞军, 邱继伟, 贾庆轩.灰色系统理论的多目标可靠性稳健设计[J].北京邮电大学学报, 2014, 37(3):23-26.

    ZHANG R J, QIU J W, JIA Q X.Multi-objective robust design for reliability based on grey system theory[J].Journal of Beijing University of Posts and Telecommunications, 2014, 37(3):23-26(in Chinese).
    [6] 王若冰, 谷良贤, 龚春林.随机-区间混合不确定性分层序列化多学科可靠性分析方法[J].西北工业大学学报, 2016, 34(1):139-146. http://www.cnki.com.cn/Article/CJFDTOTAL-XBGD201601022.htm

    WANG R B, GU L X, GONG C L.A stratified sequencing multi-disciplinary reliability analysis method under random and interval uncertainty[J].Journal of Northwestern Polytechnical University, 2016, 34(1):139-146(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-XBGD201601022.htm
    [7] 于淼, 石博强, 姜勇.基于物理规划的湿式多盘制动器不确定性优化设计[J].农业机械学报, 2011, 42(4):22-26. http://industry.wanfangdata.com.cn/yj/Detail/Periodical?id=Periodical_nyjxxb201104005

    YU M, SHI B Q, JIANG Y.Application of physical programming in uncertainty optimization design of multi-disc wet brake[J].Transactions of the Chinese Society of Agricultural Machinery, 2011, 42(4):22-26(in Chinese). http://industry.wanfangdata.com.cn/yj/Detail/Periodical?id=Periodical_nyjxxb201104005
    [8] JUANG C H, WANG L.Reliability-based robust geotechnical design of spread foundations using multi-objective genetic algorithm[J].Computers and Geotechnics, 2013, 48(4):96-106. http://isiarticles.com/bundles/Article/pre/pdf/8129.pdf
    [9] 张干清, 龚宪生, 王欢欢, 等.基于可靠灰色粒子群算法的盾构机行星减速器轮系的多目标优化设计[J].机械工程学报, 2010, 46(23):135-145. http://www.docin.com/p-523673068.html

    ZHANG G Q, GONG X S, WANG H H, et al.Multi-objective optimization design on gear train of planetary reducer in shield tunneling machine based on reliably grey particle swarm optimization[J].Journal of Mechanical Engineering, 2010, 46(23):135-145(in Chinese). http://www.docin.com/p-523673068.html
    [10] 龙腾, 李学亮, 黄波, 等.基于自适应代理模型的翼型气动隐身多目标优化[J].机械工程学报, 2016, 52(22):101-111. http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201622014

    LONG T, LI X L, HUANG B, et al.Aerodynamic and stealthy performance optimization of airfoil based on adaptive surrogate model[J].Journal of Mechanical Engineering, 2016, 52(22):101-111(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201622014
    [11] SONG C Z, ZHAO Y Q, WANG L.Tri-objective co-evolutionary algorithm and application of suspension parameter design based on lizard behavior bionics[J].Journal of Mechanical Science and Technology, 2014, 28(12):4857-4867. doi: 10.1007/s12206-014-1106-2
    [12] DESIDERI J A.Cooperation and competition in multidisciplinary optimization application to the aero-structural aircraft wing shape optimization[J].Computational Optimization and Applications, 2012, 52(1):29-68. doi: 10.1007/s10589-011-9395-1
    [13] XIAO M, SHAO X Y, GAO L, et al.A new methodology for multi-objective multidisciplinary design optimization problems based on game theory[J].Expert Systems with Applications, 2015, 42(3):1602-1612. doi: 10.1016/j.eswa.2014.09.047
    [14] YAO W, CHEN X Q, OUYANG Q, et al.A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory[J].Structural and Multidisciplinary Optimization, 2013, 48(2):339-354. doi: 10.1007/s00158-013-0901-1
    [15] 曲福恒, 崔广才, 李岩芳, 等.模糊聚类算法及应用[M].北京:国防工业出版社, 2011:57-66.

    QU F H, CUI G C, LI Y F, et al.Fuzzy clustering algorithm and its application[M].Beijing:National Defense Industry Press, 2011:57-66(in Chinese).
    [16] RAO J R J, BADHRINATH K, PAKALA R, et al.A study of optimal design under conflict using models of multi-player games[J].Engineering Optimization, 1997, 28(1-2):63-94. doi: 10.1080/03052159708941127
    [17] GOLINSKI J.Optimal synthesis problems solved by means of nonlinear programming and random methods[J].Journal of Mechanisms, 1970, 5(3):287-309. doi: 10.1016/0022-2569(70)90064-9
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出版历程
  • 收稿日期:  2017-05-31
  • 录用日期:  2017-08-01
  • 刊出日期:  2018-04-20

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