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证据推理理论及其应用

周志杰 唐帅文 胡昌华 曹友 王杰

周志杰, 唐帅文, 胡昌华, 曹友, 王杰. 证据推理理论及其应用. 自动化学报, 2021, 47(5): 970−984 doi: 10.16383/j.aas.c190676
引用本文: 周志杰, 唐帅文, 胡昌华, 曹友, 王杰. 证据推理理论及其应用. 自动化学报, 2021, 47(5): 970−984 doi: 10.16383/j.aas.c190676
Zhou Zhi-Jie, Tang Shuai-Wen, Hu Chang-Hua, Cao You, Wang Jie. Evidential reasoning theory and its applications. Acta Automatica Sinica, 2021, 47(5): 970−984 doi: 10.16383/j.aas.c190676
Citation: Zhou Zhi-Jie, Tang Shuai-Wen, Hu Chang-Hua, Cao You, Wang Jie. Evidential reasoning theory and its applications. Acta Automatica Sinica, 2021, 47(5): 970−984 doi: 10.16383/j.aas.c190676

证据推理理论及其应用

doi: 10.16383/j.aas.c190676
基金项目: 国家自然科学基金(61773388, 61751304, 61833016, 61702142), 海南省重点研发计划(ZDYF2019007)资助
详细信息
    作者简介:

    周志杰:火箭军工程大学教授. 2010年获得清华大学博士学位. 主要研究方向为证据推理, 置信规则库, 故障诊断, 安全性评估.E-mail: zhouzj04@tsinghua.org.cn

    唐帅文:火箭军工程大学博士研究生. 2017年获得火箭军工程大学学士学位. 主要研究方向为证据推理, 故障诊断, 安全性评估.E-mail: tsw631845201@163.com

    胡昌华:火箭军工程大学教授, 长江学者. 1996年获得西北工业大学博士学位. 主要研究方向为故障诊断, 寿命预测. 本文通信作者.E-mail: hch66603@163.com

    曹友:火箭军工程大学博士研究生. 2017年获得哈尔滨理工大学学士学位. 主要研究方向为证据推理, 置信规则库, 安全性评估.E-mail: cy936756268@163.com

    王杰:火箭军工程大学博士研究生. 2018年获得合肥工业大学学士学位. 主要研究方向为证据推理, 故障诊断, 安全性评估.E-mail: wj2802877478@163.com

Evidential Reasoning Theory and Its Applications

Funds: Supported by National Natural Science Foundation of China (61773388, 61751304, 61833016, 61702142) and Key Research and Development Plan of Hainan Province (ZDYF2019007)
More Information
    Author Bio:

    ZHOU Zhi-Jie Professor at Rocket Force University of Engineering. He received his Ph.D. degree from Tsinghua University in 2010. His research interest covers evidential reasoning, belief rule base, fault diagnosis, and safety assessment

    TANG Shuai-Wen Ph.D. candidate at Rocket Force University of Engineering. He received his bachelor degree from Rocket Force University of Engineering in 2017. His research interest covers evidential reasoning, fault diagnosis, and safety assessment

    HU Chang-Hua Professor at Rocket Force University of Engineering, Cheung Kong Scholar. He received his Ph.D. degree from Northwestern Polytechnical University in 1996. His research interest covers fault diagnosis and life prediction. Corresponding author of this paper

    CAO You Ph.D. candidate at Rocket Force University of Engineering. He received his bachelor degree from Harbin University of Science and Technology in 2017. His research interest covers evidential reasoning, belief rule base, and safety assessment

    WANG Jie Ph.D. candidate at Rocket Force University of Engineering. He received his bachelor degree from Hefei University of Technology in 2018. His research interest covers evidential reasoning, fault diagnosis, and safety assessment

  • 摘要:

    证据理论既能够灵活处理不确定信息, 包括随机性、模糊性、不准确性和不一致性, 又能够有效融合定量信息和定性知识. 目前, 证据理论已广泛应用于评估与决策等多个领域中, 包括多属性决策分析、信息融合、模式识别和专家系统等. 本文从D-S证据理论出发, 针对Dempster组合规则存在的“反直觉”问题和组合爆炸, 主要围绕置信分布理论系统地梳理了证据理论的发展过程, 总结分析了国内外典型文献, 最后从实际应用对证据理论进行了简要的评述和展望.

  • 图  1  论文的整体框架

    Fig.  1  The overall framework of this paper

    表  1  证据的基本概率分配

    Table  1  Basic probability assignment of evidence

    基本概率质量 犯罪嫌疑人
    Peter Paul Mary
    ${m_1}$ 0.99 0.01 0
    ${m_2}$ 0 0.01 0.99
    下载: 导出CSV

    表  2  证据的置信分布

    Table  2  Belief distribution of evidence

    证据 命题
    $A$ $B$
    ${e_1}$ 0.8 0.2
    ${e_2}$ 0.4 0.6
    下载: 导出CSV

    表  3  证据组合结果的比较

    Table  3  Comparison of evidence combination results

    组合规则 概率质量 $\emptyset $ $A$ $B$ $\Theta$ $P(\Theta )$
    Dempster 组合规则 ${m_1}$ 0 0.1600 0.0400 0.8000 0
    ${m_2}$ 0 0.3200 0.4800 0.2000 0
    $\displaystyle\sum\nolimits_{C \cap D = \theta } \displaystyle{ {m_1}(C){m_2}(D)}$ 0.0896 0.3392 0.4112 0.1600 0
    $m$ 0 0.3726 0.4517 0.1757 0
    原始 ER 算法 ${m_1}$ 0 0.1600 0.0400 0 0.8000
    ${m_2}$ 0 0.3200 0.4800 0 0.2000
    ${m_{\theta ,e(2)}}$ 0 0.3726 0.4517 0 0.1757
    ${p_{\theta ,e(2)}}$ 0 0.4520 0.5480 0 0
    ER 规则 ${\widetilde m_1}$ 0 0.4000 0.1000 0 0.5000
    ${\widetilde m_2}$ 0 0.2909 0.4364 0 0.2727
    ${\widehat m_{\theta ,e(2)}}$ 0 0.1632 0.1272 0 0.0600
    ${m_{\theta ,e(2)}}$ 0 0.4658 0.3630 0 0.1712
    ${p_{\theta ,e(2)}}$ 0 0.5620 0.4380 0 0
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-09-24
  • 录用日期:  2019-12-15
  • 网络出版日期:  2021-05-21
  • 刊出日期:  2021-05-20

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