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基于变步长离散随机集的风险不确定性分析方法

段永胜 赵继广 陈鹏 赵蓓蕾 吕潇磊

段永胜, 赵继广, 陈鹏, 等 . 基于变步长离散随机集的风险不确定性分析方法[J]. 北京航空航天大学学报, 2018, 44(2): 295-304. doi: 10.13700/j.bh.1001-5965.2017.0047
引用本文: 段永胜, 赵继广, 陈鹏, 等 . 基于变步长离散随机集的风险不确定性分析方法[J]. 北京航空航天大学学报, 2018, 44(2): 295-304. doi: 10.13700/j.bh.1001-5965.2017.0047
DUAN Yongsheng, ZHAO Jiguang, CHEN Peng, et al. Analysis method on risk uncertainty based on variable step discrete random set[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(2): 295-304. doi: 10.13700/j.bh.1001-5965.2017.0047(in Chinese)
Citation: DUAN Yongsheng, ZHAO Jiguang, CHEN Peng, et al. Analysis method on risk uncertainty based on variable step discrete random set[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(2): 295-304. doi: 10.13700/j.bh.1001-5965.2017.0047(in Chinese)

基于变步长离散随机集的风险不确定性分析方法

doi: 10.13700/j.bh.1001-5965.2017.0047
详细信息
    作者简介:

    段永胜  男, 博士研究生。主要研究方向:航天任务分析与设计

    赵继广  男, 博士, 教授, 博士生导师。主要研究方向:航天任务总体

    通讯作者:

    赵继广, E-mail:jiguang_zhao@aliyun.com

  • 中图分类号: V419+.9;O211.6

Analysis method on risk uncertainty based on variable step discrete random set

More Information
  • 摘要:

    针对信息不一致、不完整下的风险评估不确定性难以刻画与传播问题,提出一种基于变步长离散随机集理论的风险混合不确定性分析方法。将各类不完整、不精确信息转化为随机集刻画框架,在随机集理论框架下建立了统一的混合不确定性传播模型,利用随机扩张原理,计算出风险的不确定性包络曲线。为解决不一致冲突信息的不确定性合成,采用D-S证据合成原则实现多源不确定性的融合。为减小不确定性传播截尾相对误差,提出一种不确定性变量分布的变步长离散随机集刻画策略,并给出了基于变步长离散随机集理论的混合不确定性传播实施步骤。通过一个质量-弹簧-阻尼非线性物理与现象响应模型,验证了方法的有效性和可用性。

     

  • 图 1  p-box的离散化方法

    Figure 1.  Discretization method of p-box

    图 2  混合不确定性传播框架流程

    Figure 2.  Flowchart of hybrid uncertainty propagation

    图 3  质量-弹簧-阻尼系统

    Figure 3.  Mass-spring-damper system

    图 4  参数m的随机集刻画

    Figure 4.  Random set representation of parameter m

    图 5  参数k1的VADM法随机集刻画

    Figure 5.  Random set representation of parameter k1 based on VADM

    图 6  参数k的VADM法随机集刻画

    Figure 6.  Random set representation of parameterk based on VADM

    图 7  参数ω的VODM法随机集刻画

    Figure 7.  Random set representation of parameter ω based on VODM

    图 8  均匀步长离散策略下系统Ds响应

    Figure 8.  Response of system Ds under uniform step discretization strategy

    图 9  变步长离散策略下系统Ds响应

    Figure 9.  Response of system Ds under variable step discretization strategy

    表  1  参数x的证据区间信息

    Table  1.   Evidence interval information of parameter x

    区间信息 焦元1 焦元2 焦元3
    区间1 m([0.5, 1.0])=0.3 m([1.0, 1.4])=0.2 m([1.2, 2.0])=0.5
    区间2 m([0.6, 1.0])=0.2 m([0.5, 1.4])=0.4 m([1.0, 2.0])=0.4
    下载: 导出CSV

    表  2  参数x的联合证据区间信息

    Table  2.   Combination of evidence interval information of parameter x

    焦元A [0.6, 1.0] [0.5, 1.0] [1.0, 1.4] [1.2, 1.4] [1.2, 2.0]
    m(A) 0.081 1 0.162 2 0.216 2 0.270 3 0.270 3
    下载: 导出CSV

    表  3  不确定性参数k

    Table  3.   Uncertainty parameter k

    参数 min mod max
    k1 [100,110] [160,170] [210,220]
    k2 [90,110] [150,180] [210,220]
    k3 [80,120] [130,180] [200,230]
    下载: 导出CSV

    表  4  参数m的焦元及其BPA

    Table  4.   Focal elements and BPA of parameter m

    参数 Am, i Mm(Am, i)
    1 [10, 10.2] 0.01
    2 [10.2, 10.4] 0.05
    3 [10.4, 10.6] 0.11
    4 [10.6, 10.8] 0.15
    5 [10.8, 11] 0.17
    6 [11, 11.2] 0.18
    7 [11.2, 11.4] 0.16
    8 [11.4, 11.6] 0.12
    9 [11.6, 11.8] 0.08
    10 [11.8.12] 0.02
    下载: 导出CSV

    表  5  不同离散策略下期望μ及其不确定性测度d

    Table  5.   Expectation μ and uncertainty measure d under different discretization strategies

    离散策略 μ d
    ODM(n=10) [1.217 1, 2.716 9] 2.538
    VODM(n=10) [1.305 7, 2.693 4] 2.515
    ADM(n=10) [1.450 2, 2.399 6] 2.137
    VADM(n=10) [1.542 2, 2.373 2] 2.028
    ODM(n=20) [1.221 8, 2.708 5] 2.374
    VODM(n=20) [1.307 4, 2.682 1] 2.297
    ADM(n=20) [1.455 7, 2.396 2] 2.029
    VADM(n=20) [1.544 1, 2.366 8] 1.912
    下载: 导出CSV

    表  6  均匀步长离散策略下Ds的下界及其相对误差ΔEA-Binf

    Table  6.   Lowerbound of Ds and relative errors ΔEA-Binf under uniform step discretization strategy

    Ds ODM ADM
    n=10 n=20 ΔEinfA-B/% n=10 n=20 ΔEinfA-B/%
    1.3 0.033 6 0.035 2 -4.7 0.110 3 0.114 6 -3.90
    1.5 0.095 4 0.097 8 -2.52 0.140 1 0.143 1 -2.14
    2 0.312 5 0.316 6 -1.31 0.351 5 0.351 8 -0.09
    3 0.665 3 0.669 0 -0.56 0.715 4 0.717 8 -0.34
    4 0.962 1 0.961 9 0.08 0.905 0 0.904 5 0.05
    5 0.975 5 0.975 2 0.02 0.975 2 0.975 0 0.01
    下载: 导出CSV

    表  7  变步长离散策略下Ds的下界及其相对误差ΔEA-Binf

    Table  7.   Lowerbound of Ds and relative errors ΔEA-Binf under variable step discretization strategy

    Ds VODM VADM
    n=10 n=20 ΔEinfA-B/% n=10 n=20 ΔEinfA-B/%
    1.3 0.043 5 0.044 7 -2.76 0.136 5 0.138 2 -1.26
    1.5 0.112 3 0.113 3 -0.89 0.157 1 0.158 4 -0.83
    2 0.335 7 0.338 1 -0.71 0.371 5 0.373 5 -0.54
    3 0.622 8 0.626 2 -0.55 0.816 3 0.818 7 -0.29
    4 0.916 5 0.916 1 0.03 0.951 4 0.951 1 0.03
    5 0.979 4 0.979 0 0.02 0.987 2 0.987 0 0.01
    下载: 导出CSV
  • [1] GIANG P H. Decision making under uncertainty comprising complete ignorance and probability[J].International Journal of Approximate Reasoning, 2015, 62:27-45. doi: 10.1016/j.ijar.2015.05.001
    [2] SONG S, LU Z, LI W, et al.The uncertainty importance measures of the structural system in view of mixed uncertain variables[J].Fuzzy Sets & Systems, 2014, 243:25-35. https://www.sciencedirect.com/science/article/pii/B9780080999975000320
    [3] HELTON J C.Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty[J].Journal of Statistical Computation & Simulation, 2007, 57(1):3-76. doi: 10.1080/00949659708811803
    [4] FERSON S, GINZBURG L R.Different methods are needed to propagate ignorance and variability[J].Reliability Engineering & System Safety, 1996, 54(2):133-144. https://www.sciencedirect.com/science/article/pii/S0951832096000713
    [5] BAUDRIT C. Comparing methods for joint objective and subjective uncertainty propagation with an example in risk assessment[C]//Proceedings of 4th International Symposium on Imprecise Probabilities and Their Application (ISIPTA'05), 2005: 31-40.
    [6] GUYONNET D, BAUDRIT C, DUBOIS D.Postprocessing the hybrid method for addressing uncertainty in risk assessments[J].Journal of Environmental Engineering, 2005, 131(12):1750-1754. doi: 10.1061/(ASCE)0733-9372(2005)131:12(1750)
    [7] WANG C, QIU Z.Hybrid uncertain analysis for steady-state heat conduction with random and interval parameters[J].International Journal of Heat & Mass Transfer, 2015, 80(80):319-328. https://www.sciencedirect.com/science/article/pii/S0017931014008254
    [8] WALLEY P.Statistical reasoning with imprecise probabilities[M].London:Chapman and Hall, 1991:12-231.
    [9] DEMPSTER A P.Upper and lower probabilities induced by a multi-valued mapping[J].Annals of Mathematical Statistics, 1967, 38(2):325-339. doi: 10.1214/aoms/1177698950
    [10] SHAFER G.A mathematical theory of evidence[J].Technometrics, 1978, 20(1):1-242. doi: 10.1080/00401706.1978.10489609
    [11] SMETS P.The normative representation of quantified beliefs by belief functions[J].Artificial Intelligence, 1997, 92(1-2):229-242. doi: 10.1016/S0004-3702(96)00054-9
    [12] ZADEH L A.Fuzzy sets as a basis for a theory of possibility[J].Fuzzy Sets & Systems, 1978, 1(1):3-28. https://www.sciencedirect.com/science/article/pii/S0165011499800049
    [13] BAUDRIT C, COUSO I, DUBOIS D, et al.Joint propagation of probability and possibility in risk analysis:Towards a formal framework[J].International Journal of Approximate Reasoning, 2007, 45(1):82-105. doi: 10.1016/j.ijar.2006.07.001
    [14] AVEN T.On how to define, understand and describe risk[J].Reliability Engineering & System Safety, 2010, 95(6):623-631. https://www.sciencedirect.com/science/article/pii/S095183201000027X
    [15] YAGER R R.Uncertainty representation using fuzzy measures[J].IEEE Transactions on Systems Man & Cybernetics Part B (Cybernetics), 2002, 32(1):13-20. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=979955
    [16] FLAGE R, BARALDI P, ZIO E, et al.Probability and possibility-based representations of uncertainty in fault tree analysis[J].Risk Analysis, 2013, 33(1):121-133. doi: 10.1111/risk.2013.33.issue-1
    [17] HELTON J C, JOHNSON J D, OBERKAMPF W L, et al.Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty[J].Reliability Engineering & System Safety, 2006, 91(10):1414-1434. http://isiarticles.com/bundles/Article/pre/pdf/25862.pdf
    [18] GUYONNET D, BOURGINE B, DUBOIS D, et al.Hybrid approach for addressing uncertainty in risk assessments[J].Journal of Environmental Engineering, 2003, 129(1):68-78. doi: 10.1061/(ASCE)0733-9372(2003)129:1(68)
    [19] TONON F.Using random set theory to propagate epistemic uncertainty through a mechanical system[J].Reliability Engineering & System Safety, 2004, 85(1):169-181. https://www.sciencedirect.com/science/article/pii/S0951832004000584
    [20] MOLCHANOV I.Theory of random sets[M].Berlin:Springer, 2006:31-210.
    [21] BERNARDINI A.What are the random and fuzzy sets and how to use them for uncertainty modelling in engineering systems[M].Berlin:Springer, 1999:63-125.
    [22] DUBOIS D, PRADE H.Random sets and fuzzy interval analysis[J].Fuzzy Sets & Systems, 1991, 42(1):87-101. https://www.sciencedirect.com/science/article/pii/0165011491900914
    [23] ALVAREZ D A.On the calculation of the bounds of probability of events using infinite random sets[J].International Journal of Approximate Reasoning, 2006, 43(3):241-267. doi: 10.1016/j.ijar.2006.04.005
    [24] SADIQ R, NAJJARAN H, KLEINER Y.Investigating evidential reasoning for the interpretation of microbial water quality in a distribution network[J].Stochastic Environmental Research and Risk Assessment, 2006, 21(1):63-73. doi: 10.1007/s00477-006-0044-7
    [25] GRABISCH M. Dempster-Shafer and possibility theory[M].Berlin:Springer, 2016:377-437.
    [26] DUBOIS D, FOULLOY L, MAURIS G, et al.Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities[J].Reliable Computing, 2004, 10(4):273-297. doi: 10.1023/B:REOM.0000032115.22510.b5
    [27] OUSSALAH M.On the probability/possibility transformations:A comparative analysis[J].International Journal of General System, 2000, 29(5):671-718. doi: 10.1080/03081070008960969
    [28] 锁斌, 程永生, 曾超, 等.基于证据理论的异类信息统一表示与建模[J].系统仿真学报, 2013, 25(1):6-11. http://www.cnki.com.cn/Article/CJFDTOTAL-XTFZ201301004.htm

    SUO B, CHENG Y S, ZENG C, et al.Unified method of describing and modeling heterogeneous information based on evidence theory[J].Journal of System Simulation, 2013, 25(1):6-11(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-XTFZ201301004.htm
    [29] FLOREA M C, JOUSSELME A L, GRENIER D, et al.Approximation techniques for the transformation of fuzzy sets into random sets[J].Fuzzy Sets & Systems, 2008, 159(3):270-288. https://www.sciencedirect.com/science/article/pii/S0165011407004174
    [30] KOLMOGOROV A N, FOMIN S.Elements of the theory of functions and functional analysis.Vol.1, Metric and normed spaces[M].Rochester:Graylock Press, 1957:372-389.
    [31] OBERKAMPF W L, HELTON J C, JOSLYN C A, et al.Challenge problems:Uncertainty in system response given uncertain parameters[J].Reliability Engineering & System Safety, 2004, 85(1):11-19. http://proceedings.asmedigitalcollection.asme.org/article.aspx?articleid=1415001
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出版历程
  • 收稿日期:  2017-02-03
  • 录用日期:  2017-03-17
  • 网络出版日期:  2018-02-20

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