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面向冲突证据的改进DS证据理论算法

张欢 陆见光 唐向红

张欢, 陆见光, 唐向红等 . 面向冲突证据的改进DS证据理论算法[J]. 北京航空航天大学学报, 2020, 46(3): 616-623. doi: 10.13700/j.bh.1001-5965.2019.0264
引用本文: 张欢, 陆见光, 唐向红等 . 面向冲突证据的改进DS证据理论算法[J]. 北京航空航天大学学报, 2020, 46(3): 616-623. doi: 10.13700/j.bh.1001-5965.2019.0264
ZHANG Huan, LU Jianguang, TANG Xianghonget al. An improved DS evidence theory algorithm for conflict evidence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 616-623. doi: 10.13700/j.bh.1001-5965.2019.0264(in Chinese)
Citation: ZHANG Huan, LU Jianguang, TANG Xianghonget al. An improved DS evidence theory algorithm for conflict evidence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 616-623. doi: 10.13700/j.bh.1001-5965.2019.0264(in Chinese)

面向冲突证据的改进DS证据理论算法

doi: 10.13700/j.bh.1001-5965.2019.0264
基金项目: 

贵州省重大基础研究项目 [2013]6019

贵州省留学回国人员科技活动择优资助项目 2018.0002

国家留学基金委项目v 201806675013

贵州省公共大数据重点实验室开放基金 2017BDKFJJ019

贵州大学引进人才基金 (2016) No. 13

详细信息
    作者简介:

    张欢  男, 硕士研究生。主要研究方向:多源数据融合与故障诊断

    陆见光  男, 博士, 副教授, 硕士生导师。主要研究方向:机器学习与智能制造

    唐向红  男, 博士, 教授, 硕士生导师。主要研究方向:数据挖掘与故障诊断

    通讯作者:

    陆见光, E-mail: jglu@gzu.edu.cn

  • 中图分类号: TP391

An improved DS evidence theory algorithm for conflict evidence

Funds: 

Science and Technology Major Project of Guizhou Province [2013]6019

Project of Guizhou High-Level Study Abroad Talents Innovation and Entrepreneurship 2018.0002

Project of China Scholarship Council 201806675013

Open Fund of Guizhou Provincial Public Big Data Key Laboratory 2017BDKFJJ019

Guizhou University Foundation for the Introduction of Talent (2016) No. 13

More Information
  • 摘要:

    DS证据理论在处理不确定信息上的优势在各个领域得到广泛应用。针对传统DS(Dempster-Shafer)存在的证据冲突问题,提出了一种改进的DS证据理论算法。首先,结合皮尔逊相关系数的相关性限制和融合过程零因子的修正,较大程度上减少分配与整体非相关证据体的权值,修正证据体的整体重要程度;然后,按照修正后的基本概率分布(BPA)进行DS组合规则计算,得到融合结果。在解决常见冲突证据和证据体融合数量等方面与其他改进DS证据理论算法进行比较,所提算法收敛速度更快,融合的可信命题基本概率结果更高,因而验证了算法的有效性。

     

  • 图 1  改进DS证据理论算法流程图

    Figure 1.  Improved DS evidence theory algorithm flowchart

    图 2  不同数量证据体下合理命题的融合BPA比较

    Figure 2.  Comparison of fusion BPA of reasonable propositions under different quantitative evidence body

    表  1  四种常见冲突证据的BPA [11]

    Table  1.   BPA of four common conflict evidences [11]

    冲突类型 证据体 命题
    A B C D E
    完全冲突 m1 1 0 0
    m2 0 1 0
    m3 0.8 0.1 0.1
    m4 0.8 0.1 0.1
    0置信冲突 m1 0.5 0.2 0.3
    m2 0.5 0.2 0.3
    m3 0 0.9 0.1
    m4 0.5 0.2 0.3
    1置信冲突 m1 0.9 0.1 0
    m2 0 0.1 0.9
    m3 0.1 0.15 0.75
    m4 0.1 0.15 0.75
    高冲突 m1 0.7 0.1 0.1 0 0.1
    m2 0 0.5 0.2 0.1 0.2
    m3 0.6 0.1 0.15 0 0.15
    m4 0.55 0.1 0.1 0.15 0.1
    m5 0.6 0.1 0.2 0 0.1
    下载: 导出CSV

    表  2  DS证据理论冲突证据融合结果

    Table  2.   DS evidence theory fusion results of conflict evidences

    冲突类型 k 融合后命题BPA DS 常理
    A B C D E
    完全冲突 1 无效 A
    0置信冲突 0.99 0 0.727 0.273 B A
    1置信冲突 0.9998 0 1 0 B C
    高冲突 0.9999 0 0.3571 0.4286 0 0.2143 C A
    下载: 导出CSV

    表  3  四种常见冲突类型融合结果

    Table  3.   Fusion results of four common conflict types

    冲突类型 算法 命题 Θ
    A B C D E
    完全冲突 文献[12] 0 0 0 1
    文献[13] 0.0917 0.0423 0.0071 0.8589
    文献[14] 0.8204 0.1748 0.0048 0
    文献[15] 0.8166 0.1164 0.0670 0
    本文算法 0.99994 0.00001 0.00005 0
    0置信冲突 文献[12] 0 0.7273 0.2727 0
    文献[13] 0.0525 0.0597 0.0377 0.8501
    文献[14] 0.4091 0.4091 0.1818 0
    文献[15] 0.4318 0.2955 0.2727 0
    本文算法 0.97815 0.01589 0.00596 0
    1置信冲突 文献[12] 0 1 0 0
    文献[13] 0.0388 0.0179 0.0846 0.8587
    文献[14] 0.1676 0.0346 0.7978 0
    文献[15] 0.1388 0.1318 0.7294 0
    本文算法 0.00001 0.00011 0.99988 0
    高冲突 文献[12] 0 0.3571 0.4286 0 0.2143 0
    文献[13] 0.0443 0.0163 0.0163 0.0045 0.0118 0.9094
    文献[14] 0.7637 0.1031 0.0716 0.0080 0.0538 0
    文献[15] 0.5324 0.1521 0.1462 0.0451 0.1241 0
    本文算法 0.99884 0.00053 0.00032 0 0.00031 0
    注:表中加粗数字表示最优结果。
    下载: 导出CSV

    表  4  不同数量证据体的融合结果

    Table  4.   Fusion results of different quantitative evidence body

    算法 m1, m2 m1, m2, m3 m1, m2, m3, m4 m1, m2, m3, m4, m5
    传统DS m(A)=0 m(A)=0 m(A)=0 m(A)=0
    m(B)=0.8571 m(B)=0.6316 m(B)=0.3288 m(B)=0.1228
    m(C)=0.1429 m(C)=0.3684 m(C)=0.6712 m(C)=0.8772
    文献[12] m(A)=0 m(A)=0 m(A)=0 m(A)=0
    m(B)=0.18 m(B)=0.018 m(B)=0.0018 m(B)=0.00018
    m(C)=0.03 m(C)=0.0105 m(C)=1.00368 m(C)=0.00129
    m(Θ)=0.79 m(Θ)=0.9715 m(Θ)=0.99452 m(Θ)=0.99853
    文献[13] m(A)=0.090 m(A)=0.160 m(A)=0.194 m(A)=0.211
    m(B)=0.377 m(B)=0.201 m(B)=0.160 m(B)=0.138
    m(C)=0.102 m(C)=0.125 m(C)=0.137 m(C)=0.144
    m(Θ)=0.431 m(Θ)=0.486 m(Θ)=0.509 m(Θ)=0.507
    文献[14] m(A)=0.1543 m(A)=0.3500 m(A)=0.6027 m(A)=0.7958
    m(B)=0.7469 m(B)=0.5224 m(B)=0.2627 m(B)=0.0932
    m(C)=0.0988 m(C)=0.1276 m(C)=0.1346 m(C)=0.1110
    文献[15] m(A)=0.1543 m(A)=0.5816 m(A)=0.8060 m(A)=0.8909
    m(B)=0.7469 m(B)=0.2439 m(B)=0.0482 m(B)=0.0086
    m(C)=0.0988 m(C)=0.1745 m(C)=0.1458 m(C)=0.1005
    本文算法 m(A)=0.0047 m(A)=0.6368 m(A)=0.9887 m(A)=0.9978
    m(B)=0.8531 m(B)=0.2294 m(B)=0.0037 m(B)=0.0003
    m(C)=0.1422 m(C)=0.1338 m(C)=0.0076 m(C)=0.0019
    下载: 导出CSV

    表  5  数据正常情况下证据模型的焦元分布

    Table  5.   Focal element distribution of evidence model under normal data

    证据体 A B C
    m1 0.90 0 0.10
    m2 0.88 0.01 0.11
    m3 0.50 0.20 0.30
    m4 0.98 0.01 0.01
    m5 0.90 0.05 0.05
    下载: 导出CSV

    表  6  冲突证据数据1

    Table  6.   Conflict evidence data 1

    证据体 A B C
    m1 0.98 0.01 0.01
    m2 0 0.01 0.99
    m3 0.50 0.20 0.30
    m4 0.98 0.01 0.01
    m5 0.90 0.05 0.05
    下载: 导出CSV

    表  7  冲突证据数据2

    Table  7.   Conflict evidence data 2

    证据体 A B C
    m1 0.98 0.01 0.01
    m2 0 0.01 0.99
    m3 0.90 0 0.10
    m4 0.90 0.01 0.01
    下载: 导出CSV

    表  8  数据正常情况下证据合成结果

    Table  8.   Evidence fusion results under normal data

    算法 m1, m2 m1, m2, m3 m1, m2, m3, m4 m1, m2, m3, m4, m5
    文献[16] m(A)=0.96733 m(A)=0.8523845 m(A)=0.8853891 m(A)=0.889182
    m(B)=0.000985 m(B)=0.04143542 m(B)=0.03264323 m(B)=0.03395038
    m(C)=0.031685 m(C)=0.1043324 m(C)=0.0777387 m(C)=0.07212327
    m(Θ)=0 m(Θ)=0.00184768 m(Θ)=0.0042289 m(Θ)=0.0017443
    本文算法 m(A)=0.98628 m(A)=0.99172 m(A)=0.99991 m(A)=0.999995
    m(B)=0.00002 m(B)=0.00002 m(B)=0 m(B)=0
    m(C)=0.01370 m(C)=0.00826 m(C)=0.00008 m(C)=0.000005
    下载: 导出CSV

    表  9  冲突证据数据1合成结果

    Table  9.   Fusion results of conflict evidence data 1

    算法 m1, m2 m1, m2, m3 m1, m2, m3, m4 m1, m2, m3, m4, m5
    文献[16] m(A)=0.40545 m(A)=0.5978023 m(A)=0.758134 m(A)=0.8019236
    m(B)=0.004505 m(B)=0.0571966 m(B)=0.02902133 m(B)=0.02697639
    m(C)=0.590045 m(C)=0.1756906 m(C)=0.05264324 m(C)=0.03020729
    m(Θ)=0 m(Θ)=0.16931 m(Θ)=0.16020142 m(Θ)=0.1408926
    本文算法 m(A)=0.01785 m(A)=0.95279 m(A)=0.99986 m(A)=0.999996
    m(B)=0.00019 m(B)=0.00001 m(B)=0 m(B)=0
    m(C)=0.98195 m(C)=0.04720 m(C)=0.00014 m(C)=0.000004
    下载: 导出CSV

    表  10  冲突证据数据2合成结果

    Table  10.   Fusion results of conflict evidence data 2

    算法 m1, m2 m1, m2, m3 m1, m2, m3, m4
    文献[16] m(A)=0.4851 m(A)=0.9337065 m(A)=0.9683049
    m(B)=0.01 m(B)=0.0005023976 m(B)=0.000206358
    m(C)=0.5049 m(C)=0.0145743 m(C)=0.002402914
    m(Θ)=0 m(Θ)=0.0512168 m(Θ)=0.02908585
    本文算法 m(A)=0.16388 m(A)=0.99895 m(A)=0.99997
    m(B)=0.00836 m(B)=0 m(B)=0
    m(C)=0.82776 m(C)=0.00105 m(C)=0.00003
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-05-28
  • 录用日期:  2019-09-12
  • 刊出日期:  2020-03-20

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