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一种新的矩独立重要性测度分析方法及高效算法

巩祥瑞 吕震宙 孙天宇 张雷雷 封雷

巩祥瑞, 吕震宙, 孙天宇, 等 . 一种新的矩独立重要性测度分析方法及高效算法[J]. 北京航空航天大学学报, 2019, 45(2): 283-290. doi: 10.13700/j.bh.1001-5965.2018.0130
引用本文: 巩祥瑞, 吕震宙, 孙天宇, 等 . 一种新的矩独立重要性测度分析方法及高效算法[J]. 北京航空航天大学学报, 2019, 45(2): 283-290. doi: 10.13700/j.bh.1001-5965.2018.0130
GONG Xiangrui, LYU Zhenzhou, SUN Tianyu, et al. A new moment-independent importance measure analysis method and its efficient algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(2): 283-290. doi: 10.13700/j.bh.1001-5965.2018.0130(in Chinese)
Citation: GONG Xiangrui, LYU Zhenzhou, SUN Tianyu, et al. A new moment-independent importance measure analysis method and its efficient algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(2): 283-290. doi: 10.13700/j.bh.1001-5965.2018.0130(in Chinese)

一种新的矩独立重要性测度分析方法及高效算法

doi: 10.13700/j.bh.1001-5965.2018.0130
详细信息
    作者简介:

    巩祥瑞  男,硕士研究生。主要研究方向:可靠性工程

    吕震宙  女,博士,教授,博士生导师。主要研究方向:飞行器可靠性工程、安全工程

    通讯作者:

    巩祥瑞, E-mail: gxrui1991@126.com

  • 中图分类号: V215.7;TB114.3

A new moment-independent importance measure analysis method and its efficient algorithm

More Information
  • 摘要:

    为了更加合理地分析输入随机变量对结构系统失效概率的影响,提出了一种新的矩独立重要性测度分析方法。传统的重要性测度指标只能估计输入随机变量在固定点时对结构系统输出响应的影响,而所提新指标能够充分反映输入随机变量在其分布区域的所有缩减区间上变化时对结构系统输出响应的平均影响程度,更加符合工程实际。为了求解新指标,给出了2种算法:传统的双层重复抽样蒙特卡罗(DLRS MC)方法和自适应超球重要抽样(ARBIS)方法。双层重复抽样蒙特卡罗方法计算结果可以作为对比参照解,但求解效率较低,计算量很大;自适应超球重要抽样方法在满足新指标求解精度的前提下,计算效率得到很大提高。应用数值算例和工程算例证明了所提新指标的意义和所提新算法的高效性。

     

  • 图 1  自适应策略获取最优化半径

    Figure 1.  Adaptive strategy for obtaining optimal radius

    图 2  DLRS MC方法和ARBIS方法计算的新的矩独立重要性测度指标的收敛曲线

    Figure 2.  Convergence curves of new moment-independent importance measure indices of numerical example computed by DLRS MC and ARBIS methods

    图 3  汽车前轴结构示意图

    Figure 3.  Schematic of automobile front axle structure

    图 4  DLRS MC方法和ARBIS方法计算汽车前轴的收敛曲线

    Figure 4.  Convergence curves of automobile front axle computed by DLRS MC and ARBIS methods

    表  1  DLRS MC方法和ARBIS方法计算的新的矩独立重要性测度指标值

    Table  1.   New moment-independent importance measure indices of numerical example computed by DLRS MC and ARBIS methods

    随机变量 DLRS MC方法 ARBIS方法
    δiP/10-2 SD/10-2 δiP/10-2 SD/10-2
    X1 0.061 0 0.010 0.058 2 0.048
    X2 0.226 4 0.007 0.216 7 0.013
    X3 1.257 2 0.035 1.217 4 0.039
    计算量 446 000 2 619
    下载: 导出CSV

    表  2  汽车前轴结构各输入变量分布参数

    Table  2.   Distribution parameters of input variables of automobile front axle structure

    随机变量 均值 标准差
    a/mm 12 0.60
    b/mm 65 3.25
    t/mm 14 0.70
    h/mm 85 4.25
    M/(N·mm) 3.5×106 7.5×105
    T/(N·mm) 3.1×106 1.5×105
    下载: 导出CSV

    表  3  DLRS MC方法和ARBIS方法计算汽车前轴指标结果

    Table  3.   Results of indices of automobile front axle computed by DLRS MC and ARBIS methods

    随机变量 DLRS MC方法 ARBIS方法
    δiP SD/10-3 δiP SD/10-3
    a 0.004 9 0.276 0.004 7 0.249
    b 0.006 4 0.394 0.006 2 0.333
    t 0.016 3 0.546 0.015 7 0.608
    h 0.001 4 0.173 0.001 3 0.149
    M 6.49×10-5 0.092 1.95×10-5 0.012
    T 0.009 5 0.426 0.009 2 0.321
    计算量 446 000 4 475
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-03-15
  • 录用日期:  2018-09-14
  • 刊出日期:  2019-02-20

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