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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。
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关键词:
- DS(Dempster-Shafer)证据理论 /
- 证据冲突 /
- 组合规则 /
- 信息融合 /
- 皮尔逊相关系数
Abstract:The advantages of DS (Dempster-Shafer) evidence theory in dealing with uncertain information have been widely used in various fields. This paper proposes an improved DS evidence theory algorithm for the existence of evidence conflicts in traditional DS. Firstly, combined with the correlation limitation of Pearson correlation coefficient and the correction of zero factor of fusion process, the weight of distribution and the overall unrelated evidence body is greatly reduced, and the overall importance of the evidence body is corrected. Secondly, the DS combination rule calculation is performed to corrected basic probability assignment (BPA) to obtain the fusion result. Compared with the performance of other improved DS theory algorithms in solving common conflict evidence and the number of evidence body fusion, the proposed algorithm has faster convergence rate and higher fusion BPA on credible proposition, which proves the effectiveness of the proposed algorithm.
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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 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 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。 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 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 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 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 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 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 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 -
[1] DEMPSTER A P.Upper and lower probabilities induced by a multivalued mapping[J]. Annals of Mathematical Statistics, 1967, 38(2):325-339. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=eaf8916114a82f94688c64bb594f2f09 [2] SIKAI L, JUN Y.A satellite-borne SAR target recognition method based on supplementary feature fusion[C]//2018 IEEE 3rd International Conference on Cloud Computing and Big Data Analysis(ICCCBDA).Piscataway, NJ: IEEE Press, 2018: 326-330. [3] JIA R S, LIU C, SUN H M, et al.A situation assessment method for rock burst based on multi-agent information fusion[J]. Computers & Electrical Engineering, 2015, 45:22-32. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=1e7de284225ab7b7587dec2e1ddc65d7 [4] XU X B, ZHENG J, XU D L, et al.Information fusion method for fault diagnosis based on evidential reasoning rule[J]. Control Theory and Applications, 2015, 32(9):1170-1182. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy201509005 [5] 丁怡洁, 王社良, 赵歆冬.基于改进证据理论的结构损伤识别研究[J].振动与冲击, 2018, 37(2):108-113. http://d.old.wanfangdata.com.cn/Periodical/zdycj201802016DING Y J, WANG S L, ZHAO X D.Structural damage detection based on improved evidence theory[J]. Journal of Vibration and Shock, 2018, 37(2):108-113(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/zdycj201802016 [6] 席在芳, 令狐强, 易畅, 等.基于改进冲突系数的证据理论组合新方法[J].中南大学学报(自然科学版), 2018, 49(7):134-143. http://d.old.wanfangdata.com.cn/Periodical/zngydxxb201807017XI Z F, LINGHU Q, YI C, et al.A novel combination of evidence theory based on improved conflict coefficient[J]. Journal of Central South University (Science and Technology), 2018, 49(7):134-143(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/zngydxxb201807017 [7] ZADEH L A.Review of a mathematical theory of evidence[J]. AI Magazine, 1984, 5(3):81-83. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_cond-mat%2f9906076 [8] SUN R, HUANG H Z, MIAO Q.Improved information fusion approach based on DS evidence theory[J]. Journal of Mechanical Science and Technology, 2008, 22(12):2417-2425. [9] 胡昌华, 司小胜, 周志杰, 等.新的证据冲突衡量标准下的D-S改进算法[J].电子学报, 2009, 37(7):1578-1583. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dianzixb200907032HU C H, SI X S, ZHOU Z J, et al.An improved D-S algorithm under the new measure criteria of evidence conflict[J]. Acta Electronica Sinica, 2009, 37(7):1578-1583(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dianzixb200907032 [10] LI S B, LIU G K, TANG X H, et al.An ensemble deep convolutional neural network model with improved D-S evidence fusion for bearing fault diagnosis[J]. Sensors, 2017, 17(8):1729. [11] LI Y B, CHEN J, YE F, et al.The improvement of D-S evidence theory and its application in IR/MMW target recognition[J]. Journal of Sensors, 2016(2016):1903792. [12] YAGER R R.On the Dempster-Shafer framework and new combination rules[J]. Information Sciences, 1987, 41(2):93-137. doi: 10.1016-0020-0255(87)90007-7/ [13] 孙全, 叶秀清, 顾伟康.一种新的基于证据理论的合成公式[J].电子学报, 2000, 28(8):117-119. http://d.old.wanfangdata.com.cn/Periodical/dianzixb200008036SUN Q, YE X Q, GU W K.A new combination rules of evidence theory[J]. Acta Electronica Sinica, 2000, 28(8):117-119(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/dianzixb200008036 [14] MURPHY C K.Combining belief functions when evidence conflicts[J]. Decision Support Systems, 2000, 29(1):1-9. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ023782605/ [15] 邓勇, 施文康, 朱振福.一种有效处理冲突证据的组合方法[J].红外与毫米波学报, 2004, 23(1):27-32. http://d.old.wanfangdata.com.cn/Periodical/hwyhmb200401006DENG Y, SHI W K, ZHU Z F.Efficient combination approach of conflict evidence[J]. Journal Infrared Millimeter and Waves, 2004, 23(1):27-32(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hwyhmb200401006 [16] 魏永超.基于皮尔逊系数的冲突证据合成新方法[J].电讯技术, 2012, 52(4):466-471. http://d.old.wanfangdata.com.cn/Periodical/dianxjs201204009WEI Y C.A novel D-S combination method of conflicting evidences based on Pearson correlation coefficient[J]. Telecommunication Engineering, 2012, 52(4):466-471(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/dianxjs201204009 [17] 李弼程, 王波, 魏俊, 等.一种有效的证据理论合成公式[J].数据采集与处理, 2002, 17(1):33-36. http://d.old.wanfangdata.com.cn/Periodical/sjcjycl200201008LI B C, WANG B, WEI J, et al.An efficient combination rule of evidence theory[J]. Journal of Data Acquisition & Processing, 2002, 17(1):33-36(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/sjcjycl200201008