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Article(id=1295068093143864190, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295068001842262748, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202509058, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1758211200000, receivedDateStr=2025-09-19, revisedDate=1760457600000, revisedDateStr=2025-10-15, acceptedDate=1762704000000, acceptedDateStr=2025-11-10, onlineDate=1786697894606, onlineDateStr=2026-08-14, pubDate=1777046400000, pubDateStr=2026-04-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1786697894606, onlineIssueDateStr=2026-08-14, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1786697894606, creator=13701087609, updateTime=1786697894606, updator=13701087609, issue=Issue{id=1295068001842262748, tenantId=1146029695717560320, journalId=1210938733613449225, year='2026', volume='55', issue='4', pageStart='1', pageEnd='190', issueExtLink='null', onlineDate='null', pubDate='1777046400000', pubDateStr='2026-04-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1786697872839, creator='13701087609', updateTime=1786698854295, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1295072118417416228, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295068001842262748, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1295072118417416229, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295068001842262748, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=175, endPage=182, ext={EN=ArticleExt(id=1295068093336802175, articleId=1295068093143864190, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Risk assessment of reactor faults based on fault tree and Bayesian network, columnId=1295068056598900878, journalTitle=Thermal Power Generation, columnName=Power generation techonology forum, runingTitle=null, highlight=null, articleAbstract=

In view of the limitations of excessive reliance on subjective experience in reactor fault risk assessment, a comprehensive evaluation method based on fault tree and fuzzy Bayesian network is proposed. A fault tree model covering three fault manifestations, abnormal vibration, abnormal temperature rise, and abnormal oil chromatography, is built to clarify the causal logic of 22 risk factors and then mapped into a Bayesian network. Trapezoidal fuzzy numbers are used to handle linguistic uncertainty in expert judgment, and expert weights are combined to obtain basic event probabilities. Forward reasoning yields the overall reactor fault probability, while backward reasoning and fault importance indices are simultaneously involved to identify key fault causes. Case analysis shows that the method accurately assesses fault risk, identifies fault causes, and provides a basis for operation and maintenance decisions. The proposed comprehensive evaluation method based on fault tree and fuzzy Bayesian network effectively reduces subjective dependence in reactor fault risk assessment, offering high practical value and broad application prospects.

, authors=Yale LIU, Hongzhong MA, Yutong CHEN, Huadong LIU, authorsList=Yale LIU, Hongzhong MA, Yutong CHEN, Huadong LIU, authorCompany=null, correspAuthors=null, 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, fund=null), CN=ArticleExt(id=1295068095593337736, articleId=1295068093143864190, tenantId=1146029695717560320, journalId=1210938733613449225, language=CN, title=基于故障树与模糊贝叶斯网络的电抗器故障风险评估, columnId=1211002409581679375, journalTitle=热力发电, columnName=发电技术论坛, runingTitle=null, highlight=null, articleAbstract=

针对电抗器故障风险评估中过度依赖主观经验的问题，提出一种基于故障树与模糊贝叶斯网络的综合评估方法。通过建立涵盖振动异常、温升异常和油色谱异常3类故障表现的故障树模型，梳理22项风险因子的因果逻辑，并将其转换为贝叶斯网络。采用梯形模糊数处理专家评价的语言不确定性，结合专家权重计算底事件概率，通过正向推理得到电抗器整体故障概率，利用逆向推理和故障重要度指标识别关键故障原因。实例分析表明，该方法能够精准评估故障风险，识别故障原因，并为运维决策提供依据。所提出的基于故障树与模糊贝叶斯网络的综合评估方法有效解决了电抗器故障风险评估中依赖主观经验的问题，具有较高的应用价值和广阔的应用前景。

, authors=刘亚乐, 马宏忠, 陈昱同, 刘华冬, authorsList=刘亚乐, 马宏忠, 陈昱同, 刘华冬, authorCompany=null, correspAuthors=null, authorNote=

刘亚乐（1999），硕士研究生，主要研究方向为电抗器故障诊断，。

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刘亚乐（1999），硕士研究生，主要研究方向为电抗器故障诊断，。

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刘亚乐（1999），硕士研究生，主要研究方向为电抗器故障诊断，。

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Hoboken: John Wiley & Sons, 2007: 120-135., articleTitle=null, refAbstract=null)], funds=[Fund(id=1295068104778863557, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, awardId=51577050, language=EN, fundingSource=National Natural Science Foundation of China(51577050), fundOrder=null, country=null), Fund(id=1295068104854361030, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, awardId=51577050, language=CN, fundingSource=国家自然科学基金项目(51577050), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1295068095849190281, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, xref=null, ext=[AuthorCompanyExt(id=1295068095857578890, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, companyId=1295068095849190281, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=College of Electrical and Power Engineering, Hohai University, Nanjing 211100, China), AuthorCompanyExt(id=1295068095861773195, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, companyId=1295068095849190281, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=河海大学电气与动力工程学院，江苏 南京 211100)])], figs=[ArticleFig(id=1295068097749210026, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Fig.1, caption=Bayesian network model for reactor fault risk, figureFileSmall=AnYcm7Hm1B9maRfxq0LN/w==, figureFileBig=6dCVQ4U8M3rvmCLLmUrQjw==, tableContent=null), ArticleFig(id=1295068097828901803, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=图1, caption=电抗器故障风险贝叶斯网络模型, figureFileSmall=AnYcm7Hm1B9maRfxq0LN/w==, figureFileBig=6dCVQ4U8M3rvmCLLmUrQjw==, tableContent=null), ArticleFig(id=1295068097979896748, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Fig.2, caption=Bayesian network in forward reasoning, figureFileSmall=XGLYov1NfTs1xq3j65WmLQ==, figureFileBig=aqG5e5kWOwirFdqs8vs5EQ==, tableContent=null), ArticleFig(id=1295068098034422701, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=图2, caption=正向推理时的贝叶斯网络, figureFileSmall=XGLYov1NfTs1xq3j65WmLQ==, figureFileBig=aqG5e5kWOwirFdqs8vs5EQ==, tableContent=null), ArticleFig(id=1295068099716338606, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Fig.3, caption=Bayesian network in backward reasoning, figureFileSmall=4RJS08IufjG6breV+sDxZA==, figureFileBig=a8aFRtZISdwexQ3nOgAjRA==, tableContent=null), ArticleFig(id=1295068099817001903, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=图3, caption=逆向推理时的贝叶斯网络, figureFileSmall=4RJS08IufjG6breV+sDxZA==, figureFileBig=a8aFRtZISdwexQ3nOgAjRA==, tableContent=null), ArticleFig(id=1295068099930248112, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Fig.4, caption=FII bar chart of each node, figureFileSmall=cKAEz6Lv5R11ikIeVj66BA==, figureFileBig=1XZRRaqckrECQOvnoF+a0A==, tableContent=null), ArticleFig(id=1295068099993162673, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=图4, caption=各节点的FII柱状图, figureFileSmall=cKAEz6Lv5R11ikIeVj66BA==, figureFileBig=1XZRRaqckrECQOvnoF+a0A==, tableContent=null), ArticleFig(id=1295068100072854450, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Tab.1, caption=

Risk factors of reactor failure

, figureFileSmall=null, figureFileBig=null, tableContent=
故障状态层逻辑推理层基础风险层
绕组松动B1
单点夹件松动B2
对角夹件松动B3
单边夹件松动B4
振动异常E1双边夹件松动B5
预紧力松动B6
铁芯变形B7
叠片松动B8
线圈绕制不良B9
匝间短路B10
电抗器故障T层间短路B11
接地短路B12
多点接地B13
温升异常E2绝缘老化B14
绝缘材料不达标B15
漏油B16
接触不良B17
清洁不足B18
受潮B19
油色谱异常E3污闪B20
过电压击穿B21
油质劣化B22
), ArticleFig(id=1295068102006428600, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=表1, caption=

电抗器故障风险因子

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故障状态层逻辑推理层基础风险层
绕组松动B1
单点夹件松动B2
对角夹件松动B3
单边夹件松动B4
振动异常E1双边夹件松动B5
预紧力松动B6
铁芯变形B7
叠片松动B8
线圈绕制不良B9
匝间短路B10
电抗器故障T层间短路B11
接地短路B12
多点接地B13
温升异常E2绝缘老化B14
绝缘材料不达标B15
漏油B16
接触不良B17
清洁不足B18
受潮B19
油色谱异常E3污闪B20
过电压击穿B21
油质劣化B22
), ArticleFig(id=1295068102115480505, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Tab.2, caption=

Trapezoidal fuzzy numbers represented by grade 7 natural language variables

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语言变量对应的梯形模糊数
VL（0，0，0.005，0.010）
L（0.005，0.010，0.013，0.018）
ML（0.013，0.018，0.020，0.025）
M（0.020，0.025，0.028，0.033）
MH（0.028，0.033，0.035，0.040）
H（0.035，0.040，0.043，0.048）
VH（0.043，0.048，0.050，0.050）
), ArticleFig(id=1295068102174200762, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=表2, caption=

7级自然语言变量表示的梯形模糊数

, figureFileSmall=null, figureFileBig=null, tableContent=
语言变量对应的梯形模糊数
VL（0，0，0.005，0.010）
L（0.005，0.010，0.013，0.018）
ML（0.013，0.018，0.020，0.025）
M（0.020，0.025，0.028，0.033）
MH（0.028，0.033，0.035，0.040）
H（0.035，0.040，0.043，0.048）
VH（0.043，0.048，0.050，0.050）
), ArticleFig(id=1295068102249698235, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Tab.3, caption=

Expert weight standard

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项目1项目2项目3项目4
教育背景权重从业年限/年权重历史评估准确性/%权重参与项目/个权重
专科0.5<50.5<600.5<30.5
本科0.75~100.760~700.73~60.7
硕士0.810~200.870~850.86~100.8
博士1.0>201.0>851.0>101.0
), ArticleFig(id=1295068102329390012, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=表3, caption=

专家权重标准

, figureFileSmall=null, figureFileBig=null, tableContent=
项目1项目2项目3项目4
教育背景权重从业年限/年权重历史评估准确性/%权重参与项目/个权重
专科0.5<50.5<600.5<30.5
本科0.75~100.760~700.73~60.7
硕士0.810~200.870~850.86~100.8
博士1.0>201.0>851.0>101.0
), ArticleFig(id=1295068102409081789, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Tab.4, caption=

Expert comprehensive weight standard

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专家教育背景权重从业年限权重历史评估准确性权重参与项目权重综合权重
1博士（1.0）>20年（1.0）>85%（1.0）>10个（1.0）1.00
2硕士（0.8）10~20年（0.8）70%~85%（0.8）6~10个（0.8）0.80
3本科（0.7）5~10年（0.7）60%~70%（0.7）3~6个（0.7）0.70
4硕士（0.8）10~20年（0.8）70%~85%（0.8）6~10个（0.8）0.80
5博士（1.0）5~10年（0.7）70%~85%（0.8）6~10个（0.8）0.82
6本科（0.7）>20年（1.0）>85%（1.0）>10个（1.0）0.94
7硕士（0.8）>20年（1.0）70%~85%（0.8）>10个（1.0）0.90
), ArticleFig(id=1295068102484579262, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=表4, caption=

专家综合权重标准

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专家教育背景权重从业年限权重历史评估准确性权重参与项目权重综合权重
1博士（1.0）>20年（1.0）>85%（1.0）>10个（1.0）1.00
2硕士（0.8）10~20年（0.8）70%~85%（0.8）6~10个（0.8）0.80
3本科（0.7）5~10年（0.7）60%~70%（0.7）3~6个（0.7）0.70
4硕士（0.8）10~20年（0.8）70%~85%（0.8）6~10个（0.8）0.80
5博士（1.0）5~10年（0.7）70%~85%（0.8）6~10个（0.8）0.82
6本科（0.7）>20年（1.0）>85%（1.0）>10个（1.0）0.94
7硕士（0.8）>20年（1.0）70%~85%（0.8）>10个（1.0）0.90
), ArticleFig(id=1295068102555882431, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Tab.5, caption=

Risk rating of reactor failure

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节点专家1专家2专家3专家4专家5专家6专家7
B1VLLLVLVLLL
B2VLVLLLLLVL
B3LLVLLVLVLL
B4MLLLMLLLL
B5VLLVLVLLLVL
B6LVLLVLVLVLVL
B7VLVLLLLVLL
B8LLMLMLLLML
B9VLVLVLLLVLL
B10VLLLVLVLVLVL
B11VLVLLLVLVLVL
B12VLLVLVLLVLVL
B13VLVLLVLVLVLVL
B14LMLLLLLML
B15VLVLVLLLVLVL
B16MLLMLMLLLML
B17VLVLVLLLVLVL
B18VLLLLLLVL
B19MLMLLLLLL
B20LLMLLLLL
B21VLVLLLLLVL
B22MLMLMLLLLML
), ArticleFig(id=1295068104241992640, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=表5, caption=

电抗器故障风险评级

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节点专家1专家2专家3专家4专家5专家6专家7
B1VLLLVLVLLL
B2VLVLLLLLVL
B3LLVLLVLVLL
B4MLLLMLLLL
B5VLLVLVLLLVL
B6LVLLVLVLVLVL
B7VLVLLLLVLL
B8LLMLMLLLML
B9VLVLVLLLVLL
B10VLLLVLVLVLVL
B11VLVLLLVLVLVL
B12VLLVLVLLVLVL
B13VLVLLVLVLVLVL
B14LMLLLLLML
B15VLVLVLLLVLVL
B16MLLMLMLLLML
B17VLVLVLLLVLVL
B18VLLLLLLVL
B19MLMLLLLLL
B20LLMLLLLL
B21VLVLLLLLVL
B22MLMLMLLLLML
), ArticleFig(id=1295068104359433153, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Tab.6, caption=

Probability of each node in forward reasoning

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事件概率事件概率
B10.008B140.013
B20.008B150.006
B30.008B160.015
B40.013B170
B50.007B180.009
B60.006B190.013
B70.008B200.012
B80.014B210.008
B90.007B220.015
B100.006E10.075
B110.006E20.068
B120.006E30.047
B130.005
), ArticleFig(id=1295068104464290754, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=表6, caption=

正向推理时各节点概率

, figureFileSmall=null, figureFileBig=null, tableContent=
事件概率事件概率
B10.008B140.013
B20.008B150.006
B30.008B160.015
B40.013B170
B50.007B180.009
B60.006B190.013
B70.008B200.012
B80.014B210.008
B90.007B220.015
B100.006E10.075
B110.006E20.068
B120.006E30.047
B130.005
), ArticleFig(id=1295068104564954051, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=EN, label=Tab.7, caption=

Probability of each node in backward reasoning

, figureFileSmall=null, figureFileBig=null, tableContent=
事件概率
B10.044
B20.043
B30.045
B40.074
B50.038
B60.032
B70.043
B80.078
B90.038
B100.031
B110.031
B120.032
B130.025
B140.074
B150.032
B160.085
B170.032
B180.049
B190.074
B200.067
B210.043
B220.085
E10.421
E20.379
E30.265
), ArticleFig(id=1295068104653034436, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068093143864190, language=CN, label=表7, caption=

逆向推理时各节点概率

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事件概率
B10.044
B20.043
B30.045
B40.074
B50.038
B60.032
B70.043
B80.078
B90.038
B100.031
B110.031
B120.032
B130.025
B140.074
B150.032
B160.085
B170.032
B180.049
B190.074
B200.067
B210.043
B220.085
E10.421
E20.379
E30.265
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基于故障树与模糊贝叶斯网络的电抗器故障风险评估
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刘亚乐 , 马宏忠 , 陈昱同 , 刘华冬
热力发电 | 发电技术论坛 2026,55(4): 175-182
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热力发电 |发电技术论坛 2026 , 55 (4) : 175 -182
基于故障树与模糊贝叶斯网络的电抗器故障风险评估
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刘亚乐（1999），硕士研究生，主要研究方向为电抗器故障诊断，。

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刘亚乐（1999），硕士研究生，主要研究方向为电抗器故障诊断，。

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刘亚乐 , 马宏忠, 陈昱同, 刘华冬
作者信息
  • 河海大学电气与动力工程学院，江苏 南京 211100
作者简介:

刘亚乐（1999），硕士研究生，主要研究方向为电抗器故障诊断，。

Risk assessment of reactor faults based on fault tree and Bayesian network
Yale LIU , Hongzhong MA, Yutong CHEN, Huadong LIU
Affiliations
  • College of Electrical and Power Engineering, Hohai University, Nanjing 211100, China
出版时间: 2026-04-25 doi: 10.19666/j.rlfd.202509058
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摘要
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针对电抗器故障风险评估中过度依赖主观经验的问题，提出一种基于故障树与模糊贝叶斯网络的综合评估方法。通过建立涵盖振动异常、温升异常和油色谱异常3类故障表现的故障树模型，梳理22项风险因子的因果逻辑，并将其转换为贝叶斯网络。采用梯形模糊数处理专家评价的语言不确定性，结合专家权重计算底事件概率，通过正向推理得到电抗器整体故障概率，利用逆向推理和故障重要度指标识别关键故障原因。实例分析表明，该方法能够精准评估故障风险，识别故障原因，并为运维决策提供依据。所提出的基于故障树与模糊贝叶斯网络的综合评估方法有效解决了电抗器故障风险评估中依赖主观经验的问题，具有较高的应用价值和广阔的应用前景。

电抗器故障  /  故障树分析  /  贝叶斯网络  /  模糊集  /  故障原因识别

In view of the limitations of excessive reliance on subjective experience in reactor fault risk assessment, a comprehensive evaluation method based on fault tree and fuzzy Bayesian network is proposed. A fault tree model covering three fault manifestations, abnormal vibration, abnormal temperature rise, and abnormal oil chromatography, is built to clarify the causal logic of 22 risk factors and then mapped into a Bayesian network. Trapezoidal fuzzy numbers are used to handle linguistic uncertainty in expert judgment, and expert weights are combined to obtain basic event probabilities. Forward reasoning yields the overall reactor fault probability, while backward reasoning and fault importance indices are simultaneously involved to identify key fault causes. Case analysis shows that the method accurately assesses fault risk, identifies fault causes, and provides a basis for operation and maintenance decisions. The proposed comprehensive evaluation method based on fault tree and fuzzy Bayesian network effectively reduces subjective dependence in reactor fault risk assessment, offering high practical value and broad application prospects.

reactor malfunction  /  fault tree analysis  /  Bayesian network  /  fuzzy set  /  fault cause identification
刘亚乐, 马宏忠, 陈昱同, 刘华冬. 基于故障树与模糊贝叶斯网络的电抗器故障风险评估. 热力发电, 2026 , 55 (4) : 175 -182 . DOI: 10.19666/j.rlfd.202509058
Yale LIU, Hongzhong MA, Yutong CHEN, Huadong LIU. Risk assessment of reactor faults based on fault tree and Bayesian network[J]. Thermal Power Generation, 2026 , 55 (4) : 175 -182 . DOI: 10.19666/j.rlfd.202509058
正文
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随着电网装机容量的飞速发展，电抗器作为电网中重要的电气设备，在维持电压稳定、拟制谐波、防止系统过电压等方面起着举足轻重的作用[1]。但是，电抗器长期工作于高电压、大电流、强磁场环境中，其铁芯、绕组、绝缘系统、冷却系统故障时有发生[2-5]，同时，电抗器的设计制造缺陷与不当维护也会导致其发生故障[6-7]。这些故障不仅会造成电抗器性能下降，若不及时维修，还会造成电抗器损坏，甚至引发更严重事故，威胁其他电气设备安全稳定运行。电抗器异常状态可总结为振动异常、温升异常和油色谱异常3种异常指标。目前，电抗器故障诊断过度依赖主观经验且效率低下，如何准确评估电抗器的故障风险，识别故障具体原因，成为目前亟待解决的问题。
近年来，国内外学者围绕电抗器风险评估开展了大量研究。赵文清等[8]使用贝叶斯网络针对特高压绝缘、局部过热和振动噪声等3项指标检测电抗器是否工作于正常状况。于鑫等[9]采用模糊层次分析法，通过分析运行参数、环境监测、维护信息构建了电抗器状态评价体系，使用不同的电抗器运行指标对其运行状态进行综合评定。卫星等[10]对变电站中的电抗器所发生的局部放电异常和绝缘异常进行健康状况评分，以确定电抗器是否工作在正常工况下。邵宇鹰等[11]提出了一种基于小波变换图像增强与残差神经网络的电抗器状态辨识方法，可以准确识别电抗器表面放电故障、绕组松动故障和铁芯松动故障。高树国等[12]根据R-square确定电抗器振动的最佳监测点，在最佳监测点对振动信号依据经验模态分解与随机森林提出一种多参量融合的故障检测方法，可以准确区分电抗器的不同松动情况。李子彬等[13]提出粒子群优化长短时记忆神经网络以及dropout值改进长短时记忆神经网络的方法，可以准确区分电抗器发生不同种类的松动故障。赵若妤等[14]提出一种基于经验小波变换及多尺度形态谱的高压并联电抗器故障诊断方法，可以准确区分电抗器的不同运行工况。
综上所述，现有研究只聚焦于如何识别电抗器的具体故障，而对电抗器风险因子及故障原因识别鲜有研究，为此，本文提出一种基于故障树与模糊贝叶斯网络的电抗器故障风险评估方法。通过故障树分析法分析电抗器潜在的故障原因，建立涵盖振动异常、温升异常、油色谱异常3种异常表现形式，将故障树转换为贝叶斯网络，邀请专家对电抗器发生的各种故障进行概率估计，利用梯形模糊推理专家评价中的语言不确定性，预测电抗器风险状态，进行故障原因识别。最后，通过该方法对某水电站的电抗器故障概率进行计算与分析。
1　电抗器故障风险评估
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为全面了解电抗器故障风险因子，实地调研了多处电抗器所发生的故障，分类汇总为振动异常、温升异常、油色谱异常3种主要的电抗器故障表现形式。在充分考虑电抗器可能发生的各类故障的基础上，总结出22种风险因子。为进一步分析各种风险因子发生后造成后果的严重性，对这22种风险因子按照故障类别进行分类。为便于后续建模与分析，本文将风险因子与故障类别进行编号，其中Bi（i=1，2，…，22）表示基础风险层中第i个基础风险事件；Ei（i=1，2，3）表示逻辑推理层中振动异常、温升异常和油色谱异常3个故障表现类型；T表示故障状态层中的电抗器故障，表1为电抗器故障风险因子。
2　基于故障树和模糊贝叶斯网络的风险评估流程
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2.1　建立风险故障树模型
故障树模型（fault tree model，FTM）[15]是一个用于分析系统故障原因的逻辑图形工具，它通过树状结构逆向追溯导致系统失效的各种可能因素，帮助识别潜在风险、评估系统可靠性。
基于表1中电抗器故障风险因子，以Bi为底事件，表示基础风险层中的22个具体故障类别；Ei为中间事件，表示逻辑推理层中的3个故障种类；T为顶事件，表示故障状态层中的电抗器故障。对顶事件和中间事件进行逻辑推理和关联性分析，构建电抗器故障风险故障树。
2.2　建立模糊贝叶斯网络模型
电抗器故障的风险故障树模型虽然可以直观呈现风险要素之间的逻辑层级关系，但其基于单向演绎推理的固有机制存在分析效率局限，且由于故障树采用布尔逻辑，无法具体表述各个故障发生的概率。为解决故障树的上述缺点，本文提出将故障树与贝叶斯网络深度结合，既可继承故障树对关键要素的层次化表达能力，又能基于条件概率将逻辑门概率化，方便进一步分析。
贝叶斯网络（Bayesian networks，BN），亦称置信网络，是一种通过有向无环图[16]表征变量间因果关系的概率模型。在故障树模型的基础上，通过融合电抗器的历史运行数据，实现故障树结构向贝叶斯网络的概率化转换。该转换过程严格保持事件的对应关系，贝叶斯网络中的风险变量节点与故障树各层级事件形成精准映射，以底事件构成基础风险层，中间事件构成逻辑推理层，顶事件构成故障状态层，如图1所示。
2.3　底事件节点概率确定
在模糊集理论[17]的框架下，对于特定论域U中的任意元素x∈U，均存在一个定义在区间[0，1]上的实数值F（x）与之关联。该函数值F（x）表征元素x对模糊集A的隶属程度，而函数F（x）则被定义为模糊集A的隶属函数。本文采用梯形模糊数表示底事件发生概率的模糊估计，梯形模糊数的隶属函数由4个参数（a, b, c, d）确定且满足a≤b≤c≤d，在区间[b, c]内隶属度为1，两侧线性变化，具体隶属函数为：
F(x)={0, x<ax−ab−a, a⩽x<b1, b⩽x<cd−xd−c, c⩽x<d0, x⩾d
采用7级自然语言变量进行分析，7级自然语言变量表示为非常低（very low，VL）、低（low，L）、比较低（medium low，ML）、中等（medium，M）、比较高（medium high，MH）、高（high，H）、非常高（very high，VH）[18]。用7级自然语言变量表示的梯形模糊数的隶属函数参数如表2所示。
对电抗器的风险评估不仅需要扎实的理论知识，还需要大量的实践经验，故在邀请专家进行评估时，引入专家权重标准，标准如表3所示。专家权重的4个维度设定参考了德尔菲法和层次分析法的权重确定原则：教育背景反映专家的理论基础，从业年限体现实践经验积累，历史评估准确性通过专家过往项目的预测偏差率进行客观量化，参与项目数量代表专家经验的广度。
具体求解步骤如下。
1）在7级自然语言变量的框架下，邀请专家评估电抗器的各个故障风险因子所发生的概率，设定第n个专家对m种故障中的第i种故障认定的概率对应的梯形模糊数的隶属函数参数Pi，n为：
Pi,n=(ai,n,bi,n,ci,n,di,n)
式中：Pi，n为第n个专家对第i种故障的模糊概率评估；ai，n、bi，n、ci，n、di，n均为Pi，n的4个特征参数。
2）对梯形模糊数的隶属函数参数进行加权计算，权重因素为wj（j=1，2，3，4），其中j表示专家权重标准的维度序号。令评估专家的教育背景权重w1=0.2、从业年限权重w2=0.2、历史评估准确性权重w3=0.3、参与项目权重w4=0.3，γn，j为第n个专家在第j个维度上的权重标准取值（n=1，2，...，N，N为专家总数），则有：
Wj=∑j=14Wjγn,j
Pi=(a˜i,b˜i,c˜i,d˜i)=(∑n=1NWnan∑n=1NWn,∑n=1NWnbn∑k=1NWn,∑n=1NWncn∑n=1NWn,∑n=1NWndn∑n=1NWn)
式中：Wn为第n个专家的综合权重；Pi为第i种故障经所有专家加权后的综合梯形模糊数的隶属函数参数；a˜i、b˜i、C˜i、d˜i均为Pi的4个特征参数。
3）对梯形模糊数的隶属函数参数使用加权平均法进行去模糊化处理，可得第i种故障发生的确定概率值P˜i：
P˜i=a˜i+2b˜i+2c˜i+d˜i6
式中：P˜i为第i种底事件的最终发生概率。
2.4　风险分析
2.4.1　正向推理
正向推理是从已知原因节点的状态或概率出发，通过条件概率表（CPT）和网络结构，逐步推导结果节点的概率分布的过程。
中间事件节点概率计算公式如式（6）所示：
P(Ei=1)=1−∏k=1m(1−P(Bi=1))
式中：Ei表示第i个中间事件；Bk表示第k个底事件；m表示中间事件Ei下属底事件数量；P（Bk=1）表示底事件Bk发生的概率；P（Ei=1）表示中间事件Ei发生的概率。
顶事件节点概率计算公式为：
P(T=1)=1−∏i=1n(1−P(Ei=1))
式中：P（T=1）表示顶事件发生的概率；n表示中间事件的总数。
2.4.2　逆向推理
逆向推理指从结果节点的状态或概率出发，反向推导其原因节点的后验概率分布的过程。其计算公式基于贝叶斯定理：
P(Bk|T=1)=P(T=1|Bk)×P(Bk)P(T=1)
式中：P（Bk|T=1）表示顶事件发生时底事件Bk的后验概率；P（T=1|Bk）表示底事件Bk发生时顶事件的条件概率；P（Bk）表示底事件Bk的先验概率；P（T=1）表示顶事件的先验概率。
2.4.3　具体故障原因识别
具体故障原因识别是指通过系统化的技术手段与分析流程，在设备发生异常或故障时，准确判定故障的类型和根本原因的过程。其核心在于结合设备运行数据、监测信号及故障特征，利用专业的检测方法，将宏观的异常现象与微观的故障机理相关联，从而实现对故障原因的精确识别。本文提出使用故障重要度指标（fault importance index，FII）进行衡量。
故障重要度指标（FII）通过量化各底事件对顶事件的贡献程度实现，计算公式为：
FII=P(Bk|T=1)−P(Bk)1−P(Bk)
3　实际案例分析
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3.1　电抗器故障特点
电抗器的故障具有隐蔽性强、故障类型多样、环境依赖性显著、故障发展具有累积性、突发性故障后果严重等特点，因此需要对电抗器各个故障发生概率进行具体分析。
本文以某水电站的电抗器故障为例，具体说明采用本文方法对电抗器可能发生的各种故障进行风险评估的方法和步骤。
3.2　节点概率计算
由于电抗器故障数据的稀缺性，本次评估通过邀请专家根据其自身所了解的信息对电抗器故障风险进行评价。各专家综合权重标准如表4所示，专家所给出的风险评级结果如表5所示。
以B1为例，计算基础风险层各事件概率，步骤如下：
1）计算梯形模糊数，计算结果如式（10）、式（11）所示：
{a˜1=0.003b˜1=0.007c˜1=0.009d˜1=0.014
P1=(0.003,0.007,0.009,0.014)
2）对梯形模糊数进行去模糊化，具体如式（12）：
P˜1=a˜1+2b˜1+2c˜1+d˜16=0.008
故B1的发生概率为0.008。
3.3　推理分析
3.3.1　正向推理
表6为正向推理时各节点概率。当电抗器正常运行时，经过正向推理，可知电抗器故障发生的概率，帮助运维人员了解电抗器发生故障的概率。
运维人员在根据以往经验知晓电抗器各种故障发生概率的基础上，可确定电抗器各风险因子概率。对表6通过GeNIe 4.1软件进行仿真，可得正向推理时的贝叶斯网络，如图2所示。
在电抗器故障概率服从专家给出的概率的前提下，计算得出电抗器在年检过程中发现发生故障的概率为17.8%，不发生故障的概率为82.2%。在导致电抗器发生故障的原因中，可能性比较大的有单边夹件松动、叠片松动、绝缘老化、漏油、受潮、油质劣化，需要运维人员着重注意以上几种故障。
3.3.2　逆向推理与具体故障原因识别
假定电抗器故障发生，可以推算出各风险因子的发生概率，图3为逆向推理时的贝叶斯网络。在此基础上，可以得出各节点的发生概率（表7），并可计算出各节点的FII（图4），进而可以分析出导致电抗器故障的关键因素。
FII值越大，表明Bk对顶事件的贡献越大，即为重点故障，定义FII>0.06的事件为重点故障。由图4可见，B4（单边夹件松动）、B8（叠片松动）、B14（绝缘老化）、B16（漏油）、B19（受潮）、B22（油质劣化）这6个节点的FII均大于0.06，这与正向推理时得到的风险概率大体一致，即可得出这6个风险因子是导致电抗器故障的关键风险因子，应当重点关注。
进一步，单边夹件松动与叠片松动属于振动异常故障，故当传感器检测到电抗器振动异常时，这2个故障应当优先检测；同样的，当检测到温升异常时，应当优先检查漏油、绝缘老化故障；当检测到油色谱异常时，应当优先检查受潮、油质劣化故障。优先检查重点故障，可最大程度避免电抗器发生严重故障。
4　结论
收起
本文提出了一种结合故障树分析与模糊贝叶斯网络的综合评估方法。通过构建涵盖振动异常、温升异常、油色谱异常共3种异常类型以及22项风险因子的故障树模型，并转换为贝叶斯网络，结合梯形模糊数量化专家评价的语言不确定性，有效降低了传统方法对精确概率数据的依赖，提升了风险评估的客观性和全面性。
以某水电站电抗器为案例的实证分析表明，电抗器在年检中发现出现故障的概率为17.8%，虽然电抗器发生故障的概率不是很高，但一旦发生故障，尤其是严重故障，将会造成巨大损失，故对电抗器故障要进行及时处理。通过FII值识别出单边夹件松动、叠片松动、绝缘老化、漏油、受潮、油质劣化为关键风险因子，其FII值均超过0.06。研究进一步结合故障类型与检测信号，提出了优先检测策略：振动异常时优先排查单边夹件松动和叠片松动，温升异常时重点关注漏油和绝缘老化，油色谱异常时聚焦于受潮和油质劣化。
基金
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  • 国家自然科学基金项目(51577050)
文献
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2026年第55卷第4期
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doi: 10.19666/j.rlfd.202509058
  • 接收时间：2025-09-19
  • 首发时间：2026-08-14
  • 出版时间：2026-04-25
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  • 收稿日期：2025-09-19
  • 修回日期：2025-10-15
  • 录用日期：2025-11-10
基金
National Natural Science Foundation of China(51577050)
国家自然科学基金项目(51577050)
作者信息
    河海大学电气与动力工程学院，江苏 南京 211100
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