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Article(id=1149738725858526020, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738718707237637, articleNumber=1003-3033(2024)08-0222-09, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2024.08.1882, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1708444800000, receivedDateStr=2024-02-21, revisedDate=1716739200000, revisedDateStr=2024-05-27, acceptedDate=null, acceptedDateStr=null, onlineDate=1752048673357, onlineDateStr=2025-07-09, pubDate=1724774400000, pubDateStr=2024-08-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752048673357, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752048673357, creator=13701087609, updateTime=1752048673357, updator=13701087609, issue=Issue{id=1149738718707237637, tenantId=1146029695717560320, journalId=1146031787341344770, year='2024', volume='34', issue='8', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752048671651, creator=13701087609, updateTime=1756376992009, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1167893010143519453, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738718707237637, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1167893010143519454, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738718707237637, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=222, endPage=230, ext={EN=ArticleExt(id=1149738726026298186, articleId=1149738725858526020, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Susceptibility evaluation based on connection cloud model and improved conflict evidence fusion method for debris flow disaster, columnId=1149735802789348081, journalTitle=China Safety Science Journal, columnName=Technology and engineering of disaster prevention and mitigation, runingTitle=null, highlight=null, articleAbstract=

Debris flow，as a common geological disaster，has a complex formation mechanism with numerous influencing factors and multiple uncertainties. To comprehensively consider the synergistic effects of various influencing factors，based on information fusion and uncertainty analysis theory，this paper proposed a debris flow susceptibility evaluation method based on evidence theory and cloud model. Firstly，the BPA function of key evaluation indicators for debris flow susceptibility was calculated using a connection cloud model. Subsequently，the reliability and uncertainty of the indicators' BPA were modified using Lance distance and DENG entropy，respectively，resulting in a corrected BPA. Finally，evidence fusion was performed on the corrected BPA based on Dempster-Shafer (D-S) evidence theory to achieve debris flow susceptibility assessment，followed by a case validation. The results show that the connection cloud model used in this paper overcomes the limitation that the normal cloud model requires indicators to follow the normal distribution when calculating BPA，and it considers the randomness and uncertainty of indicator distribution. The proposed method's evaluation results are generally consistent with those of four other commonly used evidence fusion methods，proving it to be effective and feasible for debris flow susceptibility evaluation. The conflict evidence fusion method improved based on Lance distance and DENG entropy can enhance the convergence speed and precision of evidence fusion，making the results more accurate and reliable.

, correspAuthors=Zhao XU, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Guangyao CHEN, Sihao LI, Yangze LIANG, Zhenzhao XIA, Zhao XU), CN=ArticleExt(id=1149738735484453031, articleId=1149738725858526020, tenantId=1146029695717560320, journalId=1146031787341344770, language=CN, title=基于联系云和改进冲突证据融合算法的泥石流易发性评价, columnId=1149735802885817075, journalTitle=中国安全科学学报, columnName=防灾减灾技术与工程, runingTitle=null, highlight=null, articleAbstract=

泥石流作为一种常见的地质灾害，其形成机制复杂，影响指标众多且呈现多重不确定性，为综合考虑多种影响因素协同作用，基于信息融合和不确定性分析理论，提出一种基于证据理论和云模型的泥石流易发评价方法。首先，应用联系云模型(CCM)计算泥石流易发性关键评价指标的基本概率分配函数(BPA);然后，引入兰氏距离和邓氏熵，分别修正指标BPA的可信度和不确定度，得到修正后的BPA;最后，基于D-S证据理论对修正BPA进行证据融合，实现泥石流易发性评价，并进行实例验证。结果表明：所采用的CCM能够克服正态云模型计算BPA时要求指标为正态分布的缺陷，并考虑的指标分布的随机性和不确定性；提出的方法与其他4种常用的证据融合方法评价结果基本吻合，用于泥石流易发性评价有效可行；基于兰氏距离和邓氏熵改进的冲突证据融合算法可提高证据融合的收敛速度和精度，并且结果更准确可靠。

, correspAuthors=徐照, authorNote=null, correspAuthorsNote=
** 徐照(1982—)，男，江苏徐州人，博士，教授，主要从事智慧建造与管理等方面的研究。E-mail：。
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陈光耀 (1996—)，男，安徽定远人，博士研究生，主要研究方向为不确定性分析、城市韧性、最优化和分数阶微积分建模。E-mail：。

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陈光耀 (1996—)，男，安徽定远人，博士研究生，主要研究方向为不确定性分析、城市韧性、最优化和分数阶微积分建模。E-mail：。

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陈光耀 (1996—)，男，安徽定远人，博士研究生，主要研究方向为不确定性分析、城市韧性、最优化和分数阶微积分建模。E-mail：。

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A connection cloud-evidence theory coupling model for prediction of rockburst intensity[J]. 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language=EN, label=Table 1, caption=

Susceptibility evaluation results and comparison of debris flow

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样本 BPA最终融合结果Fus5(Ai) 文中方法 博弈论-联系云[24] 模糊综合评价[24]
A1(I级) A2(II级) A3(III级) A4(IV级) A5(Θ)
1 0.000 0 0.000 7 0.998 9 0.000 0 0.000 4 III III IV
2 0.000 5 0.000 0 0.999 9 0.000 0.000 1 III III III
3 0.000 0 0.000 0 1.000 0 0.000 0 0.000 0 III III IV
4 0.000 0 0.000 0 1.000 0 0.000 0 0.000 0 III III III
5 0.000 0 0.000 0 1.000 0 0.000 0 0.000 0 III III III
6 0.000 1 0.000 0 0.992 9 0.006 8 0.000 1 III III III
7 0.000 0 0.000 1 0.999 3 0.000 6 0.000 0 III III II
8 0.002 0 0.000 1 0.003 6 0.985 3 0.011 1 IV IV IV
9 0.000 0 0.000 1 0.999 5 0.000 0 0.000 4 III III IV
10 0.000 1 0.000 0 1.000 0 0.000 0 0.000 0 III III I
11 0.000 0 0.00 00 0.599 3 0.198 0 0.202 7 III IV IV
), ArticleFig(id=1167877651554382223, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738725858526020, language=CN, label=表1, caption=

泥石流易发性评价结果及对比

, figureFileSmall=null, figureFileBig=null, tableContent=
样本 BPA最终融合结果Fus5(Ai) 文中方法 博弈论-联系云[24] 模糊综合评价[24]
A1(I级) A2(II级) A3(III级) A4(IV级) A5(Θ)
1 0.000 0 0.000 7 0.998 9 0.000 0 0.000 4 III III IV
2 0.000 5 0.000 0 0.999 9 0.000 0.000 1 III III III
3 0.000 0 0.000 0 1.000 0 0.000 0 0.000 0 III III IV
4 0.000 0 0.000 0 1.000 0 0.000 0 0.000 0 III III III
5 0.000 0 0.000 0 1.000 0 0.000 0 0.000 0 III III III
6 0.000 1 0.000 0 0.992 9 0.006 8 0.000 1 III III III
7 0.000 0 0.000 1 0.999 3 0.000 6 0.000 0 III III II
8 0.002 0 0.000 1 0.003 6 0.985 3 0.011 1 IV IV IV
9 0.000 0 0.000 1 0.999 5 0.000 0 0.000 4 III III IV
10 0.000 1 0.000 0 1.000 0 0.000 0 0.000 0 III III I
11 0.000 0 0.00 00 0.599 3 0.198 0 0.202 7 III IV IV
), ArticleFig(id=1167877651696988560, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738725858526020, language=EN, label=Table 2, caption=

Evaluation results and comparison of different evidence fusion rules

, figureFileSmall=null, figureFileBig=null, tableContent=
样本 (Ai) 1 2 3 4 5 6 7 8 9 10 11
Demptser A1(I级) 0.000 0 0.998 8 0.000 0 0.001 2 0.000 0 0.000 0 0.000 0 0.508 3 0.000 0 0.000 0 0.003 5
A2(II级) 0.003 4 0.001 2 0.000 0 0.002 7 1.000 0 0.001 0 0.000 0 0.209 6 0.000 3 1.000 0 0.002 3
A3(III级) 0.994 0 0.000 0 0.999 3 0.995 5 0.000 0 0.965 8 0.990 6 0.122 1 0.998 0 0.000 0 0.865 3
A4(IV级) 0.002 7 0.000 0 0.000 6 0.000 3 0.000 0 0.033 2 0.009 3 0.159 2 0.001 7 0.000 0 0.126 2
A5(Θ) 0.000 0 0.000 0 0.000 0 0.000 2 0.000 0 0.000 0 0.000 0 0.000 7 0.000 0 0.000 0 0.002 7
评价结果 III I III III II III III I III II III
MURPHY[23] A1(I级) 0.000 0 0.000 9 0.000 0 0.000 5 0.000 4 0.004 9 0.001 0 0.002 8 0.000 0 0.000 3 0.000 0
A2(II级) 0.012 5 0.000 0 0.000 0 0.000 9 0.000 0 0.000 5 0.003 2 0.000 1 0.006 4 0.000 0 0.000 0
A3(III级) 0.972 6 0.998 2 0.986 9 0.995 1 0.999 5 0.955 6 0.986 6 0.047 8 0.960 3 0.999 7 0.466 0
A4(IV级) 0.000 1 0.000 0 0.000 2 0.000 0 0.000 0 0.029 1 0.009 1 0.824 7 0.000 4 0.000 0 0.129 6
A5(Θ) 0.014 9 0.000 9 0.012 9 0.003 6 0.000 1 0.009 9 0.000 1 0.124 6 0.032 9 0.000 0 0.404 3
评价结果 III III III III III III III IV III III III
DENG[16] A1(I级) 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 2 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0
A2(II级) 0.002 1 0.000 0 0.000 0 0.000 1 0.000 0 0.000 1 0.000 0 0.000 0 0.000 4 0.000 0 0.000 0
A3(III级) 0.981 6 0.999 0 0.994 3 0.998 2 0.999 9 0.989 2 0.999 3 0.001 5 0.944 1 1.000 0 0.344 7
A4(IV级) 0.000 0 0.000 0 0.000 1 0.000 0 0.000 0 0.006 4 0.000 7 0.883 8 0.000 8 0.000 0 0.101 6
A5(Θ) 0.016 2 0.001 0 0.005 5 0.001 7 0.000 1 0.004 1 0.000 0 0.114 6 0.054 7 0.000 0 0.553 7
评价结果 III III III III III III III IV III III Θ
WANG[24] A1(I级) 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 3 0.000 0 0.000 1 0.000 0 0.000 0 0.000 0
A2(II级) 0.004 2 0.000 0 0.000 0 0.000 2 0.000 0 0.000 1 0.000 1 0.000 0 0.001 4 0.000 0 0.000 0
A3(III级) 0.981 9 0.999 1 0.992 0 0.997 8 0.999 9 0.985 5 0.997 9 0.008 0 0.957 2 1.000 0 0.414 6
A4(IV级) 0.000 0 0.000 0 0.000 2 0.000 0 0.000 0 0.010 3 0.002 0 0.869 8 0.000 5 0.000 0 0.118 4
A5(Θ) 0.013 9 0.000 9 0.007 9 0.001 9 0.000 1 0.003 8 0.000 0 0.122 1 0.040 9 0.000 0 0.467 0
评价结果 III III III III III III III IV III III Θ
), ArticleFig(id=1167877651864760721, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738725858526020, language=CN, label=表2, caption=

不同证据融合规则的评价结果及对比

, figureFileSmall=null, figureFileBig=null, tableContent=
样本 (Ai) 1 2 3 4 5 6 7 8 9 10 11
Demptser A1(I级) 0.000 0 0.998 8 0.000 0 0.001 2 0.000 0 0.000 0 0.000 0 0.508 3 0.000 0 0.000 0 0.003 5
A2(II级) 0.003 4 0.001 2 0.000 0 0.002 7 1.000 0 0.001 0 0.000 0 0.209 6 0.000 3 1.000 0 0.002 3
A3(III级) 0.994 0 0.000 0 0.999 3 0.995 5 0.000 0 0.965 8 0.990 6 0.122 1 0.998 0 0.000 0 0.865 3
A4(IV级) 0.002 7 0.000 0 0.000 6 0.000 3 0.000 0 0.033 2 0.009 3 0.159 2 0.001 7 0.000 0 0.126 2
A5(Θ) 0.000 0 0.000 0 0.000 0 0.000 2 0.000 0 0.000 0 0.000 0 0.000 7 0.000 0 0.000 0 0.002 7
评价结果 III I III III II III III I III II III
MURPHY[23] A1(I级) 0.000 0 0.000 9 0.000 0 0.000 5 0.000 4 0.004 9 0.001 0 0.002 8 0.000 0 0.000 3 0.000 0
A2(II级) 0.012 5 0.000 0 0.000 0 0.000 9 0.000 0 0.000 5 0.003 2 0.000 1 0.006 4 0.000 0 0.000 0
A3(III级) 0.972 6 0.998 2 0.986 9 0.995 1 0.999 5 0.955 6 0.986 6 0.047 8 0.960 3 0.999 7 0.466 0
A4(IV级) 0.000 1 0.000 0 0.000 2 0.000 0 0.000 0 0.029 1 0.009 1 0.824 7 0.000 4 0.000 0 0.129 6
A5(Θ) 0.014 9 0.000 9 0.012 9 0.003 6 0.000 1 0.009 9 0.000 1 0.124 6 0.032 9 0.000 0 0.404 3
评价结果 III III III III III III III IV III III III
DENG[16] A1(I级) 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 2 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0
A2(II级) 0.002 1 0.000 0 0.000 0 0.000 1 0.000 0 0.000 1 0.000 0 0.000 0 0.000 4 0.000 0 0.000 0
A3(III级) 0.981 6 0.999 0 0.994 3 0.998 2 0.999 9 0.989 2 0.999 3 0.001 5 0.944 1 1.000 0 0.344 7
A4(IV级) 0.000 0 0.000 0 0.000 1 0.000 0 0.000 0 0.006 4 0.000 7 0.883 8 0.000 8 0.000 0 0.101 6
A5(Θ) 0.016 2 0.001 0 0.005 5 0.001 7 0.000 1 0.004 1 0.000 0 0.114 6 0.054 7 0.000 0 0.553 7
评价结果 III III III III III III III IV III III Θ
WANG[24] A1(I级) 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 3 0.000 0 0.000 1 0.000 0 0.000 0 0.000 0
A2(II级) 0.004 2 0.000 0 0.000 0 0.000 2 0.000 0 0.000 1 0.000 1 0.000 0 0.001 4 0.000 0 0.000 0
A3(III级) 0.981 9 0.999 1 0.992 0 0.997 8 0.999 9 0.985 5 0.997 9 0.008 0 0.957 2 1.000 0 0.414 6
A4(IV级) 0.000 0 0.000 0 0.000 2 0.000 0 0.000 0 0.010 3 0.002 0 0.869 8 0.000 5 0.000 0 0.118 4
A5(Θ) 0.013 9 0.000 9 0.007 9 0.001 9 0.000 1 0.003 8 0.000 0 0.122 1 0.040 9 0.000 0 0.467 0
评价结果 III III III III III III III IV III III Θ
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基于联系云和改进冲突证据融合算法的泥石流易发性评价
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陈光耀 1 , 李司豪 1 , 梁阳泽 1 , 夏震昭 2 , 徐照 1, **
中国安全科学学报 | 防灾减灾技术与工程 2024,34(8): 222-230
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中国安全科学学报 | 防灾减灾技术与工程 2024, 34(8): 222-230
基于联系云和改进冲突证据融合算法的泥石流易发性评价
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陈光耀1 , 李司豪1, 梁阳泽1, 夏震昭2, 徐照1, **
作者信息
  • 1 东南大学 土木工程学院，江苏 南京 211189
  • 2 华中科技大学 土木与水利工程学院，湖北 武汉 430074

    • 陈光耀 (1996—)，男，安徽定远人，博士研究生，主要研究方向为不确定性分析、城市韧性、最优化和分数阶微积分建模。E-mail：。

通讯作者:

** 徐照(1982—)，男，江苏徐州人，博士，教授，主要从事智慧建造与管理等方面的研究。E-mail：。
Susceptibility evaluation based on connection cloud model and improved conflict evidence fusion method for debris flow disaster
Guangyao CHEN1 , Sihao LI1, Yangze LIANG1, Zhenzhao XIA2, Zhao XU1, **
Affiliations
  • 1 School of Civil Engineering，Southeast University，Nanjing Jiangsu 211189，China
  • 2 School of Civil and Hydraulic Engineering，Huazhong University of Science and Technology，Wuhan Hubei 430074，China
出版时间: 2024-08-28 doi: 10.16265/j.cnki.issn1003-3033.2024.08.1882
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摘要
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泥石流作为一种常见的地质灾害，其形成机制复杂，影响指标众多且呈现多重不确定性，为综合考虑多种影响因素协同作用，基于信息融合和不确定性分析理论，提出一种基于证据理论和云模型的泥石流易发评价方法。首先，应用联系云模型(CCM)计算泥石流易发性关键评价指标的基本概率分配函数(BPA);然后，引入兰氏距离和邓氏熵，分别修正指标BPA的可信度和不确定度，得到修正后的BPA;最后，基于D-S证据理论对修正BPA进行证据融合，实现泥石流易发性评价，并进行实例验证。结果表明：所采用的CCM能够克服正态云模型计算BPA时要求指标为正态分布的缺陷，并考虑的指标分布的随机性和不确定性；提出的方法与其他4种常用的证据融合方法评价结果基本吻合，用于泥石流易发性评价有效可行；基于兰氏距离和邓氏熵改进的冲突证据融合算法可提高证据融合的收敛速度和精度，并且结果更准确可靠。

联系云模型(CCM)  /  泥石流  /  易发性评价  /  基本概率分配函数(BPA)  /  冲突证据融合  /  兰氏距离  /  邓氏熵  /  证据理论

Debris flow，as a common geological disaster，has a complex formation mechanism with numerous influencing factors and multiple uncertainties. To comprehensively consider the synergistic effects of various influencing factors，based on information fusion and uncertainty analysis theory，this paper proposed a debris flow susceptibility evaluation method based on evidence theory and cloud model. Firstly，the BPA function of key evaluation indicators for debris flow susceptibility was calculated using a connection cloud model. Subsequently，the reliability and uncertainty of the indicators' BPA were modified using Lance distance and DENG entropy，respectively，resulting in a corrected BPA. Finally，evidence fusion was performed on the corrected BPA based on Dempster-Shafer (D-S) evidence theory to achieve debris flow susceptibility assessment，followed by a case validation. The results show that the connection cloud model used in this paper overcomes the limitation that the normal cloud model requires indicators to follow the normal distribution when calculating BPA，and it considers the randomness and uncertainty of indicator distribution. The proposed method's evaluation results are generally consistent with those of four other commonly used evidence fusion methods，proving it to be effective and feasible for debris flow susceptibility evaluation. The conflict evidence fusion method improved based on Lance distance and DENG entropy can enhance the convergence speed and precision of evidence fusion，making the results more accurate and reliable.

connection cloud model(CCM)  /  debris flow  /  susceptibility evaluation  /  basic probability assignment (BPA)  /  conflict evidence fusion  /  Lance distance  /  DENG entropy  /  evidence fusion
陈光耀, 李司豪, 梁阳泽, 夏震昭, 徐照. 基于联系云和改进冲突证据融合算法的泥石流易发性评价. 中国安全科学学报, 2024 , 34 (8) : 222 -230 . DOI: 10.16265/j.cnki.issn1003-3033.2024.08.1882
Guangyao CHEN, Sihao LI, Yangze LIANG, Zhenzhao XIA, Zhao XU. Susceptibility evaluation based on connection cloud model and improved conflict evidence fusion method for debris flow disaster[J]. China Safety Science Journal, 2024 , 34 (8) : 222 -230 . DOI: 10.16265/j.cnki.issn1003-3033.2024.08.1882
正文
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0 引言
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泥石流是一种常见的地质灾害，具有突发性和极强破坏性等特点，并直接威胁到人民的生命财产安全，故准确有效地评价泥石流的易发性对防灾减灾具有重要意义。
目前，国内外学者基于泥石流现场实测数据和相关试验结果，已基于不同理论提出多种评价方法，如可拓方法[1]、博弈论法[2]、模糊综合评价[3]、灰色关联分析[4]、基于地理信息系统技术[5]和以人工神经网络和大数据技术为基础为代表的机器学习[6⇓-8]等方法，并取得了有益的进展。由于泥石流成因复杂[9]，影响因素多且具有多重不确定性，以上方法在实际应用中均有一定局限性。证据理论作为一种成熟的信息融合技术，具有处理不确定信息的能力，已在各个领域得到广泛应用[10]，而应用证据理论的关键步骤在于构建合理有效的基本概率分配函数(Basic Probability Assignment，BPA)。如何合理确定BPA是一个开放性问题，目前，在工程实际应用中，BPA的确定主要依靠专家经验打分，但这种方法显然具有较大的主观性[11]。为减少人为主观因素影响，相继有学者提出以岭函数[12]和三角模糊数为代表的隶属函数法[13]以及正态云模型法[14]，而上述方法中，隶属函数法对指标及其相互作用的随机模糊性描述欠佳；正态云模型(Normal Cloud Model，NCM )可综合考虑专家知识经验和指标实际分布特点，为NCM和证据理论的耦合应用提供新思路。尽管NCM可考虑评价指标BPA的随机模糊性，但它在应用时是默认评价指标在无限区间内服从正态分布的，然而，大量实际问题的指标一般是在有限区间内，且不符合正态分布，故采用NCM计算BPA依然有待改进。同时，当处理高冲突证据时，传统Dempster证据融合规则往往会出现与实际情况相悖的结论，而如何解决这一问题依然尚无统一方案。
鉴于此，笔者拟构建一种基于联系云和改进冲突证据融合算法的泥石流易发性评价方法。首先，采用有限区间非对称联系云模型(Connection Cloud Model，CCM)来确定BPA，以克服NCM的缺陷。然后，引入兰氏距离[15]和邓氏熵[16]分别度量证据的可信度和不确定度，并综合二者计算证据的融合权重进而合理修正BPA，以期实现对泥石流易发性更准确和客观的评价，为泥石流灾害风险快速预警提供一种新途径。
1 CCM与改进冲突证据融合算法
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1.1 CCM
云模型可实现定量和定性之间的相互转化[17]，但传统NCM生成的云是理想的无限区间正态云，且一般要求指标分布服从正态分布，而实际不确定性问题中评价指标分布形式具有多样性，可能无法满足这一要求。因此，传统NCM虽能描述研究问题的随机模糊性，但忽略了实测指标值分布特征，以及结果在相邻等级间的转化态势[18]，不利于实际工程应用，而近期发展的CCM集成了联系数理论中的“同异反”(Identical-Discrepancy-Contrary，IDC)思想，可统一定量描述和处理主客体之间确定和不确定性信息及转换态势特点[18]。其相应定义如下：若研究对象评价分为p级，对应评价指标共有n个，则第j个指标在第i等级的上界和下界分别为U B j i和L B j i，其对应的一维联系云实际是由以期望 E x j i为分界点的左右2朵非对称云组合构成，且拥有各自的联系云数字特征，将待测样本第j个评价指标的实测值x代入到构建的CCM中，则可计算出隶属于第i等级的联系度 μ j i(x)，关于联系云的数字特征计算方法和详细构建流程可查看文献[18]。基于IDC关系的等级区间划分如图1所示。
1.2 基于CCM的BPA确定方法
基于CCM的BPA确定方法如下：
1) 计算样本联系度。若待测样本为x=[x1，x2，…，xn]，且泥石流易发性共有p个分级，其中，xj表示该样本中第j个指标的实测值，则通过下式求出xj隶属于第i分级的联系度μi j，用矩阵形式可表示为U(x)=[ μ j i ] p × n。
m j ( A p + 1 ) = 1 - m a x ( μ j 1 ， μ j 2 ， … ， μ j p )
式中mj( A p + 1)为第j个指标隶属等级不确知的BPA值，也可表示为mj(Θ)。
2) 计算样本BPA矩阵M(x)。为满足BPA定义[14]要求，需对联系度作如下转换补充定义：
m j ( A i ) = μ i j · m a x ( μ j 1 ， μ j 2 ， … ， μ j p ) ∑ i = 1 p μ j i
M (x) = m 1 ( A 1 ) m 2 ( A 1 ) … m n ( A 1 ) m 1 ( A 2 ) m 2 ( A 2 ) … m n ( A 2 ) ︙ ︙ ︙ m 1 ( A p ) m 2 ( A p ) … m n ( A p ) m 1 ( A p + 1 ) m 2 ( A p + 1 ) … m n ( A p + 1 )
式中mj(Ai)为第j个指标隶属于第i个等级的BPA值。
1.3 基于可信度和不确定度的冲突证据融合方法
针对经典Dempster证据融合规则在处理高冲突证据时常出现不合常理的结果，为此提出综合考虑证据可信度和不确定度的改进冲突证据融合方法，其具体实现步骤如下：
步骤1:计算样本x的可信度向量R(x)。随着证据理论的完善，相继有学者提出不同的证据间距离的度量方法，如周氏距离、马氏距离和闵氏距离等，周氏距离受证据BPA分散程度影响，在衡量证据冲突程度方面欠佳[19];马氏距离计算需引进矩阵协方差计算，对大规模数据而言计算量过大；而闵氏距离要求各证据有相同的维数属性，这会降低证据的一致性。故文中采用兰氏距离[15]用于证据可信度计算，计算过程如下：
1) 若第i个和第j个证据分别记为Ei和Ej，则证据Ei、Ej之间兰氏距离dij为：
d ( E i ， E j ) = d i j = 1 p + 1 ∑ k = 1 p + 1 | m i ( A k ) - m j ( A k ) | [ m i ( A k ) + m j ( A k ) ]
2) 计算证据Ei和Ej之间的相似度sij:
s i j = 1 - d i j ( i ， j = 1，2 ， … ， n )
证据Ej对应的可信度Rj:
R j = ∑ j = 1 ， j ≠ i n s i j 2 / ∑ i = 1 n ∑ j = 1 ， j ≠ i n s i j 2
R ( x ) = [ R 1 ， R 2 ， … ， R n ]
步骤2:计算样本x的不确定度向量V(x)。邓氏熵是邓勇对香农熵的广义化改进[20]。邓氏熵越大，表明证据不确定度越大，故可采用邓氏熵度量证据的不确定度，计算过程如下：
1) 计算任意证据Ej的邓氏熵Cj:
C j = - ∑ A k ⊆ Θ m j ( A k ) · l o g 2 m j ( A k ) 2 [ A k ] - 1
2) 基于邓氏熵计算样本x的不确定度向量：
V j = e x p ( - C j ) ∑ j = 1 n e x p ( - C j )
V ( x ) = [ V 1 ， V 2 ， … ， V n ]
步骤3:计算融合权重W(x)并修正初始BPA。当某证据和其他证据一致性程度越高时，说明该证据与其他证据的差异度越小，即可信度R越高，在证据融合时应赋予更大权重；而证据的邓氏熵C越大时，表明该证据的不确定程度越高，即证据越模糊，理应被赋予更小的权重。因此，将证据的可信度和不确定度综合考虑来计算证据的融合权重是一种更合理的方法，计算模型如下：
w j = R j × V j ∑ j = 1 n ( R j × V j ) W ( x ) = [ w 1 ， w 2 ， … ， w n ]
m ' j ( A i ) = ∑ j = 1 n [ w j · m j ( A i ) ]
M ' (x) = m ' 1 ( A 1 ) m ' 2 ( A 1 ) … m ' n ( A 1 ) m ' 1 ( A 2 ) m ' 2 ( A 2 ) … m ' n ( A 2 ) ︙ ︙ ︙ m ' 1 ( A p ) m ' 2 ( A p ) … m ' n ( A p ) m ' 1 ( A p + 1 ) m ' 2 ( A p + 1 ) … m ' n ( A p + 1 )
式中：m'j(Ai)为修正后的BPA值；M'(x)为修正后样本x的BPA矩阵。
步骤4:进行证据融合并判定样本隶属等级。应用Dempster证据融合规则对M'(x)进行证据融合，并根据最终“最大支持信度原则”判定样本x的泥石流易发性隶属等级。
1.4 评价流程
根据上述理论介绍，基于CCM的改进证据融合泥石流易发性评价流程如图2所示。
2 泥石流易发性评价实例分析
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由于泥石流发生机制复杂且影响因素指标众多，故泥石流易发性评价指标及其分级标准目前尚无统一定论。结合薛喜成对西秦岭调查结果的研究分析[21]，选取沟谷岸坡坡度X1、沟床纵坡比降X2、植被覆盖率X3、单位面积固体物源储量X4、汇水面积X5、雨季降水量X6共6项常见的泥石流易发性评价指标，其中，X1、X2、X3属于形貌条件，X4属于地质条件，X5和X6属于水文条件，并将泥石流易发性等级分为不易发(I)、低易发(II)、中易发(III)和高易发(IV)构建分级标准，详细标准可查阅文献[22]。根据该分级标准可得评价指标的，以指标X6为例，其CCM如图3所示。
2.1 实例数据与计算结果
选取西秦岭泥石流现场调查结果实测数据[21]共计11个样本进行验证，样本的各项指标实测值见文献[22]。基于图2流程，最终可得各样本的BPA最终融合结果见表1。由表1可知：文中方法对11个样本的评价结果和博弈论-云模型法[22]评价结果基本一致，表明文中方法用于泥石流易发性评价有效可行。对于样本11，文中方法将其判定为III级，而博弈论-云模型法将其判定为IV级。事实上，根据文献[22]的结果，博弈论-云模型法得到的III级和IV级联系度分别为0.43和0.445，差距极小，因此，样本11应判定为介于III级和IV级更合理，故将其判定为III级也是准确合理的；对于样本1，模糊综合评价法判定为IV级，而通过对样本1的分析可发现，样本1中指标X1、X2、X3和X6均为III级，指标X4为IV级，指标X5为II级，通过文献[22]计算得到的指标组合权重可知：各指标权重占比差异极小，且隶属于等级III的指标最多，因此，样本1判定为III级更合理，其余样本3、7、9、10同理。
2.2 关于改进证据融合方法的对比讨论
为体现改进证据融合方法优越性，分别采用目前常见的Dempster融合规则、MURPHY融合规则[23]、DENG融合规则[16]和WANG融合规则[24]对实例中11个样本进行评价对比。由于不同的初始BPA矩阵在进行证据融合时必定会产生不同的融合结果，因此，为控制自变量的统一，确保对比的严谨性，这4种融合规则所融合的初始BPA矩阵均与文中方法相同，4种证据融合规则的最终融合结果见表2，不同样本的最终融合结果分布如图4所示。
2.2.1 证据融合精度对比
综合表2和图4m可见：传统Dempster规则在除编号8和11以外的9个样本融合收敛精度表现上均超过0.95，且融合精度和融合稳定性均要优于Murphy规则、DENG规则和WANG规则。但在样本2、5、8和10的预测上，应用Dempster规则却出现了误判，且在样本8上出现了收敛精度低于0.55的较差表现。为探究出现该结果的原因，求得样本8中指标X5和X6的证据冲突系数K56=0.012 2，接近于0，说明指标X5和X6间存在高证据冲突；同理求得样本2中X3和X6之间冲突系数K36=0.054 5、样本5中X1和X3之间冲突系数K13=0.000 0和样本10中X5和X6之间冲突系数K56=0.000 1，均同样较小且接近于0。因此，传统的Dempster规则在处理高证据冲突问题时易出现失效误判的结果；而Murphy规则、DENG规则和WANG规则经过相关改进后可有效处理高冲突证据问题，取得了可靠准确的评价结果，但依然存在着个别样本融合精度不足和融合结果不稳定等缺陷，且DENG规则和WANG规则在样本11上出现了Θ误判，无法获得评价结果；而基于证据可信度和不确定度的改进证据融合方法仅在样本11的融合精度小于0.9，在其余10个样本上均稳定大于0.95，故文中融合方法在融合精度和融合稳定性上均优于其他4种融合规则。
在证据融合中，不确知情况(Θ)的融合结果过大不仅对评价无实际意义，还会对确知情况的正常评价造成干扰，因此，将不确知情况的BPA尽可能分配给其他确知情况(如I—IV级)，进而收敛到0也是衡量融合规则性能的一个方面。图5m显示了5种证据融合规则对11个样本的不确知情况(Θ)的最终BPA融合结果。结果显示：5种融合规则中仅有文中方法和Dempster法可使不确知情况的最终融合结果收敛到低于0.25的较低水平，其中，Dempster方法表现最好，收敛精度及稳定性优于其余4种证据融合规则。
2.2.2 证据融合收敛速度对比
证据融合收敛速度是衡量融合规则性能的另一个指标，5种规则在不同融合次数下的融合结果和不确知情况的融合结果如图4a—图4k和图5a—图5k所示。从图4f—图4g可以看出，Dempster规则在处理样本6和7时，融合收敛曲线在第一次融合后出现了异常的大幅度递减情况，而在其余个别样本上收敛速度表现虽良好，但收敛趋势极不稳定，无法始终保持单调递增的状态；MURPHY规则、DENG规则和WANG规则在经过改进后，收敛稳定性明显要优于Dempster规则，但在收敛速度和收敛精度方面仍有提升潜力；而改进融合规则在11个样本上的收敛速度、收敛精度和收敛稳定性上表现均要明显优于上述4种融合规则，对大规模数据的证据融合具有明显优势。同理，图5a—图5k为不确知情况BPA再分配的收敛曲线，其中，文中方法的收敛速度和收敛精度也优于其他4种规则，可在2次融合次数内将不确知情况的BPA尽可能的分配给其他确知情况，进而使不确知情况BPA融合结果很快收敛到接近于0的较低水平，减小对决策的干扰。尤其在样本11上，MURPH、DENG和WANG这3种规则均出现了融合结果的异常递增现象，这也导致DENG和WANG这2种规则最终得了不确知情况的误判。
综上所述，基于兰氏距离和邓氏熵的改进冲突证据融合方法充分考虑了证据的可信度和不确定度等因素，能较大程度降低冲突证据造成的不利影响，能更有效地处理证据冲突问题，并且融合阶段收敛速度更快、融合精度更高，得到预测结果也更加稳定可靠。
3 结论
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1) 将不确定人工智能领域的云模型和证据理论耦合后应用于泥石流易发性的分级评价中，采用改进冲突证据融合方法进行证据融合，不仅能反映多种泥石流易发性影响因素的协同作用，还可以提高评价预测的准确性和客观性。
2) 针对泥石流评价指标具有随机模糊性的特点，采用基于联系数理论改进的CCM求解指标BPA。该方法不仅能够模拟泥石流易发性评价指标随机模糊性的特点，还可以克服传统云模型要求评价指标须满足无限区间内为正态分布的缺陷，为证据理论中BPA确定提供新参考。
3) 针对传统冲突证据融合规则融合精度低，收敛速度慢的缺陷，引入兰氏距离和邓氏熵来分别度量证据体的可信度和不确定度，并综合二者更合理地确定证据融合权重。实例应用和与传统证据融合方法的对比结果表明：改进冲突证据融合方法较传统方法能更好地处理证据冲突，且收敛速度更快，融合精度更高更稳定，更有利于决策。
4) 将云模型和证据理论耦合用于泥石流灾害的预测评价目前研究较少，相关诸多问题仍有待进一步深入研究讨论，如是否有更加合理的将联系度转化为BPA的转化方法、更加合理的泥石流易发性分级标准等。
基金
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  • 国家自然科学基金(72071043)
  • 教育部人文社科基金(20YJAZH114)
  • 江苏省自然科学基金(BK20201280)
  • 江苏省研究生科研创新计划项目(KYCX23_0286)
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2024年第34卷第8期
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文章信息
doi: 10.16265/j.cnki.issn1003-3033.2024.08.1882
  • 接收时间：2024-02-21
  • 首发时间：2025-07-09
  • 出版时间：2024-08-28
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  • 收稿日期：2024-02-21
  • 修回日期：2024-05-27
基金
国家自然科学基金(72071043)
教育部人文社科基金(20YJAZH114)
江苏省自然科学基金(BK20201280)
江苏省研究生科研创新计划项目(KYCX23_0286)
作者信息
    1 东南大学 土木工程学院，江苏 南京 211189
    2 华中科技大学 土木与水利工程学院，湖北 武汉 430074

通讯作者:

** 徐照(1982—)，男，江苏徐州人，博士，教授，主要从事智慧建造与管理等方面的研究。E-mail：。
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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