留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

可靠性全局灵敏度指标的空间分割高效方法

员婉莹 吕震宙 蒋献 杨彩琼

员婉莹, 吕震宙, 蒋献, 等 . 可靠性全局灵敏度指标的空间分割高效方法[J]. 北京航空航天大学学报, 2017, 43(6): 1199-1207. doi: 10.13700/j.bh.1001-5965.2016.0479
引用本文: 员婉莹, 吕震宙, 蒋献, 等 . 可靠性全局灵敏度指标的空间分割高效方法[J]. 北京航空航天大学学报, 2017, 43(6): 1199-1207. doi: 10.13700/j.bh.1001-5965.2016.0479
YUN Wanying, LYU Zhenzhou, JIANG Xian, et al. An efficient method for reliability global sensitivity index by space-partition[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(6): 1199-1207. doi: 10.13700/j.bh.1001-5965.2016.0479(in Chinese)
Citation: YUN Wanying, LYU Zhenzhou, JIANG Xian, et al. An efficient method for reliability global sensitivity index by space-partition[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(6): 1199-1207. doi: 10.13700/j.bh.1001-5965.2016.0479(in Chinese)

可靠性全局灵敏度指标的空间分割高效方法

doi: 10.13700/j.bh.1001-5965.2016.0479
基金项目: 

国家自然科学基金 51475370

中央高校基本科研业务费专项资金 3102015BJ (Ⅱ) CG009

西北工业大学博士论文创新基金 CX201708

详细信息
    作者简介:

    员婉莹, 女, 博士研究生。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:可靠性工程、灵敏度分析、模型确认及多学科优化

    通讯作者:

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

  • 中图分类号: TB114.3

An efficient method for reliability global sensitivity index by space-partition

Funds: 

Natural Science Foundation of China 51475370

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

Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University CX201708

More Information
  • 摘要:

    可靠性全局灵敏度指标能够有效地分析输入变量的不确定性对结构系统失效概率的影响程度,为提高该灵敏度指标求解数字模拟法的效率,提出了一种基于密度权重及连续无重叠区间全方差公式的空间分割高效方法。所提方法通过连续无重叠区间上的全方差公式来加快该指标计算的收敛速度,利用密度权重法在输入变量可能的取值区间内进行均匀抽样,并以均匀样本点的联合概率密度函数的权重来保证计算的等价性,这使得所构造的方法不需要寻找失效域的设计点,因此其可以有效解决非线性程度较高难以找到设计点及多设计点的问题。除此之外,应用空间分割技术,使得本文所提方法仅需重复利用一组样本点,就可同时得到各个输入变量的可靠性全局灵敏度指标,消除了计算量与输入变量维数的相关性,大大地提高了样本的利用率和计算效率。验证算例的计算结果,说明了本文方法对计算功能函数非线性程度较高及多设计点问题的高效性。

     

  • 图 1  α取不同值时算例2的失效面

    Figure 1.  Failure surfaces of example 2 with different values of α

    表  1  算例1的计算结果

    Table  1.   Calculation results for example 1

    样本量 Si
    X1 X2
    本文方法 S-MCS 本文方法 S-MCS
    512 0.032 9[0.011 0] N/A 0.043 4[0.013 5] N/A
    1 024 0.032 8[0.005 9] N/A 0.043 7[0.005 6] N/A
    2 048 0.033 7[0.002 7] N/A 0.044 6[0.004 3] N/A
    4 096 0.034 7[0.001 4] 0.029 0[0.013 4] 0.045 0[0.002 7] 0.043 0[0.024 1]
    8 192 0.036 0[0.001 0] 0.030 5[0.007 1] 0.044 5[0.001 3] 0.039 6[0.009 1]
    D-MCS(2×104×104) 0.036 2 0.044 7
    下载: 导出CSV

    表  2  算例2中α=0的Si计算结果

    Table  2.   Calculation results of Si when α=0 for example 2

    样本量 Si
    X1 X2 X3
    本文方法 IS S-MCS 本文方法 IS S-MCS 本文方法 IS S-MCS
    512(640) 0.612 0 0.624 0 N/A 0.003 5 0.001 8 N/A 0.003 4 0.002 3 N/A
    1 024(1 280) 0.601 2 0.614 1 N/A 0.003 0 0.002 8 N/A 0.002 9 0.002 0 N/A
    2 048(2 560) 0.656 2 0.616 1 0.624 0 0.002 6 0.002 1 0 0.002 7 0.002 1 -0.013 3
    4 096(5 120) 0.621 1 0.612 0 0.621 7 0.002 7 0.001 9 0 0.002 7 0.002 8 0.003 3
    8 192(10 240) 0.610 7 0.609 9 0.607 9 0.002 7 0.002 6 0.001 3 0.002 6 0.002 3 0.000 5
    D-MCS(3×104×104) 0.611 21 0.002 7 0.002 7
    下载: 导出CSV

    表  3  算例2中α=0时100次Si计算结果的标准差(SD)

    Table  3.   Standard deviation (SD) of calculation results of Si by 100 iterations when α=0 for example 2

    样本量 SD
    X1 X2 X3
    本文方法 IS S-MCS 本文方法 IS S-MCS 本文方法 IS S-MCS
    512(640) 0.060 3 0.118 5 N/A 0.001 1 0.006 9 N/A 0.001 5 0.007 0 N/A
    1 024(1 280) 0.043 2 0.077 4 N/A 0.000 5 0.009 8 N/A 0.000 6 0.005 0 N/A
    2 048(2 560) 0.036 3 0.052 1 0.120 8 0.000 3 0.005 1 0 0.000 3 0.003 7 0.044 7
    4 096(5 120) 0.024 0 0.038 2 0.039 1 0.000 2 0.002 8 0 0.000 2 0.007 1 0.002 8
    8 192(1 0240) 0.014 6 0.023 1 0.018 2 0.000 1 0.005 2 0.001 3 0.000 1 0.003 7 0.001 2
    下载: 导出CSV

    表  4  算例2中α=1的Si计算结果

    Table  4.   Calculation results of Si when α=1 for example 2

    样本量 Si
    X1 X2 X3
    本文方法 IS S-MCS 本文方法 IS S-MCS 本文方法 IS S-MCS
    512(640) 0.508 8 0.054 5 N/A 0.011 8 0.014 1 N/A 0.012 1 0.022 8 N/A
    1 024(1 280) 0.532 4 0.324 7 0.535 7 0.010 4 0.009 2 0.010 0 0.010 6 0.017 7 0.010 0
    2 048(2 560) 0.544 2 0.199 6 0.520 0 0.010 0 0.008 6 -0.012 0 0.009 9 0.011 2 0.014 7
    4 096(5 120) 0.545 6 0.204 5 0.506 7 0.010 0 0.006 2 0.003 1 0.009 9 0.008 0 0.010 0
    8 192(10 240) 0.548 0 0.300 8 0.485 3 0.009 6 0.006 2 0.009 6 0.009 6 0.007 8 0.011 1
    D-MCS(3×104×104) 0.542 8 0.009 6 0.009 6
    下载: 导出CSV

    表  5  算例2中α=1时100次Si计算结果的标准差

    Table  5.   Standard deviation of calculation results of Si by 100 iterations when α=1 for example 2

    样本量 SD
    X1 X2 X3
    本文方法 IS S-MCS 本文方法 IS S-MCS 本文方法 IS S-MCS
    512(640) 0.065 2 0.144 8 N/A 0.004 2 0.039 5 N/A 0.005 9 0.117 4 N/A
    1 024(1 280) 0.049 8 2.668 8 0.264 9 0.002 2 0.019 6 0.010 0 0.002 7 0.062 3 0.010 0
    2 048(2 560) 0.029 0 1.000 2 0.066 8 0.001 7 0.020 2 0.045 7 0.001 9 0.030 6 0.007 5
    4 096(5 120) 0.021 9 0.534 0 0.022 2 0.001 1 0.008 4 0.002 7 0.001 4 0.015 7 0.002 0
    8 192(10 240) 0.008 0 1.314 7 0.009 5 0.000 7 0.018 3 0.001 0 0.000 8 0.021 4 0.000 9
    下载: 导出CSV
  • [1] SALTELLI A. Sensitivity analysis for importance assessment[J].Risk Analysis, 2002, 22(3):579-590. doi: 10.1111/risk.2002.22.issue-3
    [2] BORGONOVO E, APOSTOLAKIS G E.A new importance measure for risk-informed decision-making[J].Reliability Engineering and System Safety, 2001, 72(2):193-212. doi: 10.1016/S0951-8320(00)00108-3
    [3] BORGONOVO E, APOSTOLAKIS G E, TARANTOLA S, et al.Comparison of local and global sensitivity analysis techniques in probability safety assessment[J].Reliability Engineering and System Safety, 2003, 79(2):175-185. doi: 10.1016/S0951-8320(02)00228-4
    [4] TARANTOLA S, KOPUSTINSKAS V, BOLADO-LAVIN R, et al.Sensitivity analysis using contribution to sample variance plot:Application to a water hammer model[J].Reliability Engineering and System Safety, 2012, 99(2):62-73. https://www.researchgate.net/publication/251621927_Sensitivity_analysis_using_contribution_to_sample_variance_plot_Application_to_a_water_hammer_model
    [5] WEI P F, LU Z Z, RUAN W B, et al.Regional sensitivity analysis using revised mean and variance ratio functions[J].Reliability Engineering and System Safety, 2014, 121(1):121-135. https://www.researchgate.net/publication/270814729_Regional_sensitivity_analysis_using_revised_mean_and_variance_ratio_functions
    [6] SALTELLI A, RATTO M, ANDRES T, et al.Global sensitivity analysis[M].New York:John Wiley & Sons, 2008:115-174.
    [7] SALTELLI A, MARIVOET J.Non-parametric statistics in sensitivity analysis for model output:A comparison of selected techniques[J].Reliability Engineering and System Safety, 1990, 28(2):229-253. doi: 10.1016/0951-8320(90)90065-U
    [8] ZHANG X F, PANDEY M D.An effective approximation for variance-based global sensitivity analysis[J].Reliability Engineering and System Safety, 2014, 121(4):164-174. https://www.researchgate.net/publication/275180221_An_effective_approximation_for_variance-based_global_sensitivity_analysis
    [9] WEI P, LU Z Z, SONG J W.A new variance-based global sensitivity analysis technique[J].Computation Physics Communication, 2013, 184(11):2540-2551. doi: 10.1016/j.cpc.2013.07.006
    [10] DEMAN G, KONAKLI K, SUDRET B, et al.Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in multi-layered hydrogeological model[J].Reliability Engineering and System Safety, 2016, 147:156-169. doi: 10.1016/j.ress.2015.11.005
    [11] PIANOSI F, WAGENER T.A simple and efficient method for global sensitivity analysis based on cumulative distribution functions[J].Environmental Modelling & Software, 2015, 67:1-11. https://www.researchgate.net/publication/271428340_A_simple_and_efficient_method_for_global_sensitivity_analysis_based_on_cumulative_distribution_functions
    [12] BORGONOVO E.A new uncertainty importance measure[J].Reliability Engineering and System Safety, 2007, 92(6):771-784. doi: 10.1016/j.ress.2006.04.015
    [13] LIU Q, HOMMA T.A new importance measure for sensitivity analysis[J].Journal of Nuclear Science and Technology, 2010, 47(1):53-61. doi: 10.1080/18811248.2010.9711927
    [14] CUI L J, LU Z Z, ZHAO X P.Moment-independent importance measure of basic random variable and its probability density evolution solution[J].Science China Technological Sciences, 2010, 53(4):1138-1145. doi: 10.1007/s11431-009-0386-8
    [15] LI L Y, LU Z Z, FENG J, et al.Moment-independent importance measure of basic variable and its state dependent parameter solution[J].Structural Safety, 2012, 38:40-47. doi: 10.1016/j.strusafe.2012.04.001
    [16] 张磊刚, 吕震宙, 陈军.基于失效概率的矩独立重要性测度的高效算法[J].航空学报, 2014, 35(8):2199-2206. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201408013.htm

    ZHANG L G, LYU Z Z, CHEN J.An efficient method of failure probability-based moment-independent importance measure[J].Acta Aeronautica et Astronautica Sinica, 2014, 35(8):2199-2206(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201408013.htm
    [17] WEI P F, LU Z Z, HAO W R, et al.Efficient sampling methods for global reliability sensitivity analysis[J].Computation Physics Communication, 2012, 183(8):1728-1743. doi: 10.1016/j.cpc.2012.03.014
    [18] DITLEVSEN O, MADSEN H O.Structural reliability methods[M].Chichester:Wiley, 1996:102-109.
    [19] RASHKI M, MIRI M, MOGHADDAM M A.A new efficient simulation method to approximate the probability of failure and most probability point[J].Structural Safety, 2012, 39(4):22-29. https://www.researchgate.net/publication/257006965_A_new_efficient_simulation_method_to_approximate_the_probability_of_failure_and_most_probable_point
    [20] ZHAI Q Q, YANG J, ZHAO Y.Space-partition method for the variance-based sensitivity analysis:Optimal partition scheme and comparative study[J].Reliability Engineering and System Safety, 2014, 131:66-82. doi: 10.1016/j.ress.2014.06.013
    [21] 吕召燕, 吕震宙, 李贵杰, 等.基于密度权重的可靠性灵敏度分析方法[J].航空学报, 2014, 35(1):179-186. http://www.cnki.com.cn/Article/CJFDTOTAL-ZJKN201701002.htm

    LV Z Y, LV Z Z, LI G J, et al.Reliability sensitivity analysis method based on weight index of density[J].Acta Aeronautica et Astronautica Sinica, 2014, 35(1):179-186(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-ZJKN201701002.htm
    [22] SOBOL I M.Uniformly distributed sequences with additional uniformity properties[J].USSR Computational Mathematics and Mathematical Physics, 1976, 16(5):236-242. doi: 10.1016/0041-5553(76)90154-3
  • 加载中
图(1) / 表(5)
计量
  • 文章访问数:  859
  • HTML全文浏览量:  122
  • PDF下载量:  431
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-06-04
  • 录用日期:  2016-07-07
  • 网络出版日期:  2017-06-20

目录

    /

    返回文章
    返回
    常见问答