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基于可能性矩的混合不确定性全局灵敏度分析

成凯 吕震宙 石岩

成凯, 吕震宙, 石岩等 . 基于可能性矩的混合不确定性全局灵敏度分析[J]. 北京航空航天大学学报, 2017, 43(8): 1705-1712. doi: 10.13700/j.bh.1001-5965.2016.0626
引用本文: 成凯, 吕震宙, 石岩等 . 基于可能性矩的混合不确定性全局灵敏度分析[J]. 北京航空航天大学学报, 2017, 43(8): 1705-1712. doi: 10.13700/j.bh.1001-5965.2016.0626
CHENG Kai, LYU Zhenzhou, SHI Yanet al. Global sensitivity analysis under mixed uncertainty based on possibilistic moments[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(8): 1705-1712. doi: 10.13700/j.bh.1001-5965.2016.0626(in Chinese)
Citation: CHENG Kai, LYU Zhenzhou, SHI Yanet al. Global sensitivity analysis under mixed uncertainty based on possibilistic moments[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(8): 1705-1712. doi: 10.13700/j.bh.1001-5965.2016.0626(in Chinese)

基于可能性矩的混合不确定性全局灵敏度分析

doi: 10.13700/j.bh.1001-5965.2016.0626
基金项目: 

中央高校基本科研业务费专项资金 3102015BJ(Ⅱ) CG009

详细信息
    作者简介:

    成凯  男, 硕士研究生。主要研究方向:可靠性工程、灵敏度分析

    吕震宙  女, 博士, 教授, 博士生导师。主要研究方向:飞行器设计及可靠性工程

    通讯作者:

    吕震宙, E-mail: zhenzhoulu@nwpu.edu.cn

  • 中图分类号: TB114

Global sensitivity analysis under mixed uncertainty based on possibilistic moments

Funds: 

Fundamental Research Funds for the Central Universities 3102015BJ(Ⅱ) CG009

More Information
  • 摘要:

    在同时包含随机不确定性和模糊不确定性结构系统中,为了分别度量随机输入变量和模糊输入变量对输出响应的统计特征的影响,提出了随机输入变量和模糊输入变量的全局灵敏度新指标。在模糊变量可能性矩定义的基础上,分析了混合不确定性下输出响应的特征。从输出响应可能性矩的角度出发,以输出响应的可能性期望为例,通过比较输出响应有条件和无条件可能性期望的概率密度函数(PDF)的平均差异,分别建立了随机输入变量和模糊输入变量关于输出响应的可能性期望的灵敏度指标。讨论了所提指标的性质,并采用Kriging代理模型来提高混合不确定性全局灵敏度指标的计算效率。最后通过算例验证了本文所提方法的准确性和高效性。

     

  • 图 1  流体管道系统示意图

    Figure 1.  Schematic diagram of a sewer pipe system

    图 2  屋架结构的简单示意图

    Figure 2.  Schematic diagram of a roof truss structure

    表  1  算例1各输入变量的灵敏度指标值

    Table  1.   Sensitivity index values of input variables in Example 1

    随机变量灵敏度指标值
    一般方法Kriging法
    x10.211 30.211 3
    x20.408 70.408 7
    x30.048 20.048 2
    x40.094 70.094 8
    下载: 导出CSV

    表  2  算例2各模糊变量参数值

    Table  2.   Parameter values of fuzzy variables in Example 2

    随机变量模糊变量cσ
    x1C10.8250.070
    x2C20.8250.070
    x3C30.9000.050
    下载: 导出CSV

    表  3  算例2各输入变量的灵敏度指标值

    Table  3.   Sensitivity index values of input variables in Example 2

    参数灵敏度指标值
    一般方法Kriging法
    C10.004 90.004 9
    C20.004 90.004 9
    C30.004 30.004 3
    Y0.764 20.764 2
    W0.053 70.053 7
    下载: 导出CSV

    表  4  屋架结构随机变量的数值特征

    Table  4.   Numerical characteristics of random variables in roof truss structure

    随机变量分布类型均值标准差
    q/(N·m-1)正态20 0001 400
    l/m正态120.12
    As/m2正态9.82×10-45.982×10-5
    Ac/ m2正态0.040.004 8
    下载: 导出CSV

    表  5  算例3各输入变量基于输出可能性期望的灵敏度指标值

    Table  5.   Sensitivity index values of input variables based on output possibilistic expectation in Example 3

    参数灵敏度指标值
    一般方法Kriging法
    q0.339 40.339 1
    l0.673 90.673 6
    Ac0.144 40.144 3
    Ec0.012 00.011 9
    As0.158 50.158 4
    Es0.029 10.029 0
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-07-27
  • 录用日期:  2016-09-02
  • 网络出版日期:  2017-08-20

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