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Article(id=1207658085674488800, tenantId=1146029695717560320, journalId=1205116883411038211, issueId=1207658076900008717, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=null, receivedDateStr=null, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1765857724826, onlineDateStr=2025-12-16, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1765857724826, onlineIssueDateStr=2025-12-16, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1765857724826, creator=13701087609, updateTime=1765857724826, updator=13701087609, issue=Issue{id=1207658076900008717, tenantId=1146029695717560320, journalId=1205116883411038211, year='2025', volume='23', issue='2', pageStart='189', pageEnd='376', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1765857722735, creator=13701087609, updateTime=1765862348176, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1207677477451833566, tenantId=1146029695717560320, journalId=1205116883411038211, issueId=1207658076900008717, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1207677477451833567, tenantId=1146029695717560320, journalId=1205116883411038211, issueId=1207658076900008717, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=346, endPage=350, ext={EN=ArticleExt(id=1207658086135862269, articleId=1207658085674488800, tenantId=1146029695717560320, journalId=1205116883411038211, language=EN, title=Preventive maintenance strategy for single component of electric multiple units with bi-objective optimization, columnId=1207658078934246168, journalTitle=Chinese Journal of Construction Machinery, columnName=Performance Mensuration, Experimentation and Fault Diagnosis, runingTitle=null, highlight=null, articleAbstract=

In order to explore the effects of maintenance difficulty degree of component on the maintenance cost and availability of the model. Taking a mechanical component of electric multiple unit (EMU) as the research object, and a component reliability threshold as the decision variable, the two-parameter Weibull distribution is adopted to describe the evolution law of component failure rate, combined with the existing fixed period multi-level imperfect maintenance rule of EMU in China, a preventive maintenance strategy for single component of EMU with bi-objective optimization is established. Bi-level imperfect maintenance is implemented in the maintenance mode and the concept of efficiency-cost ratio is introduced to discriminate the selection of each maintenance method of the component. Considering four factors, the difficulty of detecting parts, the location of parts, the difficulty of disassembling parts and the complexity of parts. Analytic hierarchy process (AHP) is adopted to quantify the maintenance difficulty degree and to study impact on the cost and availability of maintenance. The analysis shows that the maintenance model considering the maintenance difficulty can effectively reduce the maintenance cost and improve the availability, which provides a theoretical reference for the development of the maintenance strategy of EMU.

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为研究部件维护难易程度差异对模型维护成本和可用度的影响，以动车组某机械部件为研究对象，部件可靠度阈值为决策变量，采取两参数威布尔分布描述部件故障率演化规律。结合我国现行动车组多级修程修制，建立了双目标优化的动车组单部件预防性维护策略。在维护方式上实施两级非完美维护，引入效费比的概念判别部件每次维护方式的选取。综合考虑部件故障部位检测难易程度、部件安装位置、部件拆卸难易程度、部件复杂度这4方面因素，采取层次分析法量化部件维护难易程度，研究其对维护成本和可用度的影响。算例分析表明：考虑维护难易程度的维护模型能够有效降低维护成本和提升可用度，为动车组维护策略的制定提供了理论参考。

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佟景泉（1984—），男，讲师，硕士。E-mail：

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佟景泉（1984—），男，讲师，硕士。E-mail：

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佟景泉（1984—），男，讲师，硕士。E-mail：

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refAbstract=null), Reference(id=1207748680111727494, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, doi=null, pmid=null, pmcid=null, year=2016, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[9], rfOrder=8, authorNames=王少敏, journalName=null, refType=null, unstructuredReference=王少敏. 动车组转向架关键零部件的故障规律及维护策略研究[D]. 北京：北京交通大学，2016., articleTitle=动车组转向架关键零部件的故障规律及维护策略研究, refAbstract=null), Reference(id=1207748680187224968, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, doi=null, pmid=null, pmcid=null, year=2022, volume=null, issue=2, pageStart=116, pageEnd=119，125, url=null, language=null, rfNumber=[10], rfOrder=9, authorNames=薛朝改, 谷雨, 曹武军, journalName=机械设计与制造, refType=null, unstructuredReference=薛朝改，谷雨，曹武军，等. 多部件重要度系统机会维修策略的优化[J]. 机械设计与制造，2022（2）：116-119，125., articleTitle=多部件重要度系统机会维修策略的优化, refAbstract=null), Reference(id=1207748680271111051, 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Component maintenance parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值参数数值
初级维护成本cpr/元550初级维护时间tpr/d1
高级维护成本csu/元950高级维护时间tsu/d3
单位故障成本cr/元2150单位故障时间tr/d2
), ArticleFig(id=1207748678278816582, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, language=CN, label=表1, caption=

部件维护参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数数值参数数值
初级维护成本cpr/元550初级维护时间tpr/d1
高级维护成本csu/元950高级维护时间tsu/d3
单位故障成本cr/元2150单位故障时间tr/d2
), ArticleFig(id=1207748678371091272, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, language=EN, label=Tab.2, caption=

Optimization results

, figureFileSmall=null, figureFileBig=null, tableContent=
最优目标Rmin维护间隔时间序列/d维护级别序列C/元Cp/元Cr/元A Tp/d Tr/d 故障小修次数
C0.9074-136-184-219-243-258-294-323-3420-0-0-0-0-1-0-0-113 6156 3007 3150.943 014.06.80.98
A0.66113-208-282-3360-0-0-016 7142 75013 9640.950 75.013.01.87
), ArticleFig(id=1207748678480143181, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, language=CN, label=表2, caption=

优化结果

, figureFileSmall=null, figureFileBig=null, tableContent=
最优目标Rmin维护间隔时间序列/d维护级别序列C/元Cp/元Cr/元A Tp/d Tr/d 故障小修次数
C0.9074-136-184-219-243-258-294-323-3420-0-0-0-0-1-0-0-113 6156 3007 3150.943 014.06.80.98
A0.66113-208-282-3360-0-0-016 7142 75013 9640.950 75.013.01.87
), ArticleFig(id=1207748678601778001, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, language=EN, label=Tab.3, caption=

Changes in maintenance cost composition under different values

, figureFileSmall=null, figureFileBig=null, tableContent=
方案γCr/元C/元Cr在C中占比/%
14.461 89 42915 72959.95
23.461 87 31513 61553.73
32.461 85 20211 50245.23
), ArticleFig(id=1207748678702441301, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, language=CN, label=表3, caption=

不同γ值下维护成本组成变化

, figureFileSmall=null, figureFileBig=null, tableContent=
方案γCr/元C/元Cr在C中占比/%
14.461 89 42915 72959.95
23.461 87 31513 61553.73
32.461 85 20211 50245.23
), ArticleFig(id=1207748678798910296, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, language=EN, label=Tab.4, caption=

Changes in maintenance time composition under different values

, figureFileSmall=null, figureFileBig=null, tableContent=
方案γTr/dT/dTr在Tp+Tr中占比/%
14.461 816.7421.7477.00
23.461 812.9917.9972.21
32.461 89.2414.2464.88
), ArticleFig(id=1207748678903767902, tenantId=1146029695717560320, journalId=1205116883411038211, articleId=1207658085674488800, language=CN, label=表4, caption=

不同γ值下维护时间组成变化

, figureFileSmall=null, figureFileBig=null, tableContent=
方案γTr/dT/dTr在Tp+Tr中占比/%
14.461 816.7421.7477.00
23.461 812.9917.9972.21
32.461 89.2414.2464.88
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双目标优化的动车组单部件预防性维护策略
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佟景泉 1 , 强生杰 2 , 何雨畅 3 , 卢艳丽 1
中国工程机械学报 | 性能检测、试验及故障诊断 2025,23(2): 346-350
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中国工程机械学报 | 性能检测、试验及故障诊断 2025, 23(2): 346-350
双目标优化的动车组单部件预防性维护策略
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佟景泉1 , 强生杰2, 何雨畅3, 卢艳丽1
作者信息
  • 1.广东交通职业技术学院 轨道交通学院，广东 广州 510650
  • 2.华东交通大学 交通运输工程学院，江西 南昌 330013
  • 3.中国铁路武汉局集团有限公司，湖北 武汉 430061

    • 佟景泉（1984—），男，讲师，硕士。E-mail：

Preventive maintenance strategy for single component of electric multiple units with bi-objective optimization
Jingquan TONG1 , Shengjie QIANG2, Yuchang HE3, Yanli LU1
Affiliations
  • 1. School of Rail Transit, Guangdong Communication Polytechnic, Guangzhou 510650, Guangdong, China
  • 2. School of Transportation Engineering, East China Jiaotong University, Nanchang 330013, Jiangxi, China
  • 3. China Railway Wuhan Group Co., Ltd., Wuhan 430061, Hubei, China
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摘要
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为研究部件维护难易程度差异对模型维护成本和可用度的影响，以动车组某机械部件为研究对象，部件可靠度阈值为决策变量，采取两参数威布尔分布描述部件故障率演化规律。结合我国现行动车组多级修程修制，建立了双目标优化的动车组单部件预防性维护策略。在维护方式上实施两级非完美维护，引入效费比的概念判别部件每次维护方式的选取。综合考虑部件故障部位检测难易程度、部件安装位置、部件拆卸难易程度、部件复杂度这4方面因素，采取层次分析法量化部件维护难易程度，研究其对维护成本和可用度的影响。算例分析表明：考虑维护难易程度的维护模型能够有效降低维护成本和提升可用度，为动车组维护策略的制定提供了理论参考。

动车组  /  维护难易程度  /  决策变量  /  两级非完美  /  效费比

In order to explore the effects of maintenance difficulty degree of component on the maintenance cost and availability of the model. Taking a mechanical component of electric multiple unit (EMU) as the research object, and a component reliability threshold as the decision variable, the two-parameter Weibull distribution is adopted to describe the evolution law of component failure rate, combined with the existing fixed period multi-level imperfect maintenance rule of EMU in China, a preventive maintenance strategy for single component of EMU with bi-objective optimization is established. Bi-level imperfect maintenance is implemented in the maintenance mode and the concept of efficiency-cost ratio is introduced to discriminate the selection of each maintenance method of the component. Considering four factors, the difficulty of detecting parts, the location of parts, the difficulty of disassembling parts and the complexity of parts. Analytic hierarchy process (AHP) is adopted to quantify the maintenance difficulty degree and to study impact on the cost and availability of maintenance. The analysis shows that the maintenance model considering the maintenance difficulty can effectively reduce the maintenance cost and improve the availability, which provides a theoretical reference for the development of the maintenance strategy of EMU.

electric multiple unit  /  maintenance difficulty degree  /  decision variable  /  bi-level imperfect  /  efficiency-cost ratio
佟景泉, 强生杰, 何雨畅, 卢艳丽. 双目标优化的动车组单部件预防性维护策略. 中国工程机械学报, 2025 , 23 (2) : 346 -350 .
Jingquan TONG, Shengjie QIANG, Yuchang HE, Yanli LU. Preventive maintenance strategy for single component of electric multiple units with bi-objective optimization[J]. Chinese Journal of Construction Machinery, 2025 , 23 (2) : 346 -350 .
正文
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近年来，我国动车组保有量与高铁运营里程迅速提升，截至2022年底，全国高铁营业里程达到4.2万 km。随着动车组运用规模的不断扩大，动车组维护市场也具有较大空间，制定合理的维护策略对降低维护成本和提高运用效率具有显著作用。
曹蕾等[1]采取威布尔分布描述k-out-of-n系统的部件层故障率演化规律，以维护成本率最小化为目标，求解各部件预防性维护周期。李聪波等[2]为实现机床设备维护和车间调度方案的相互协调，基于威布尔分布确定设备故障率演化规律。周炳海等[3]采取部件可靠性判别部件维护时机，以总成本最优为目标建立多部件生产系统预防性维护模型。赵斐等[4]对退化至预定可靠度阈值的系统采取不完美维护，以确定系统维护周期。柳剑等[5]以目前农机装备故障或退化数据为依据，分析系统退化状态与装备任务可靠性之间的关联影响。上述文献基于部件故障率演化规律和可靠度阈值优化维护决策模型，取得了较好的效果。
现有维护策略优化大多将维护活动视为降低部件故障率水平的手段，忽略了维护活动自身对维护策略制定的影响。动车组列车作为多学科交融的集成系统，各部件的材料、结构、功能差异显著，维护时难易程度相差较大。张成光[6]考虑维护难易程度和资源配置情况对维护模型选择的影响。孙妍婷[7]将维护难易程度视为评判设备重要度的影响因素。齐彦昆等[8]考虑不同部件维护难易程度差异对维护成本的影响，建立了两级非完美维护方式的多部件系统预防性维护模型。上述文献的研究大多关注于优化维护成本，其对追求经济效益与运用效率的铁路运维而言不够全面。随着维护难度的上升，部件维护所需的时间也在增加，进而影响到部件的可用度。
轮对直接承载车辆对钢轨传递的重量，通过轮轨作用力，保障列车的直行和回转运行。随着动车组运行速度的提升，轮对与轨道相互作用力逐渐增大，进而易产生车轮多边形化、轮对剥离、擦伤、扁疤等故障。王少敏[9]通过分析动车组轮对维修故障数据，确定轮对故障分布规律，进一步构建基于威布尔分布的故障率演化模型。合理地制定轮对维护策略对降低维护成本和提升可用度具有重要作用。本文以部件维护成本和可用度为优化目标，以可靠度为约束条件，结合我国动车组现行的多级别修程修制，建立两级非完美维护模型。在此基础上，综合考虑部件故障部位检测难易程度、部件安装位置、部件拆卸难易程度、部件复杂度这4方面因素，运用层次分析法量化维护难易程度，进而研究其对维护成本和可用度的影响。
1　维护模型的建立
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1.1　故障率演化规律建模
为保障部件在运行过程中具有良好的服役状态，预设置可靠度阈值Rmin，要求部件全生命周期内的可靠度均高于Rmin，使部件发生故障的风险可控，
式中：Ti为部件第i-1至i次预防性维护的时间间隔；λi(t)为部件第i-1至i次预防性维护间隔的故障率函数；i的取值范围为1≤i≤n，n为部件在维护策略规划期内的维护次数；t为本次运行区间的任意时刻。
为描述部件的故障率随服役时间延长逐渐增加的实际情况与修复效果随维护次数增多而逐渐减弱的特征，采取混合故障率演化模型表示部件故障率的演化规律，
式中：ai为役龄递减因子；bi为故障率递增因子；i为维护次数。
1.2　维护方式判别方法
基于我国动车组多级别维护体系，将采取初级维护和高级维护这2种维护方式。受维护成本、维护时间等因素的影响，高级维护对部件故障率的修复效果要明显优于初级维护，但维护过程中消耗的各类资源，如维护成本和维护时间等，也显著多于初级维护。为便于部件维护方式的选取，引入维护方式选择因子Ai：
当Ai=0时，部件采取初级维护；Ai=1时，部件采取高级维护。维护方式选择因子Ai决定了维护时部件故障率函数的役龄递减因子和故障率递增因子，分别为
式中：、分别为初级维护与高级维护的役龄递减因子；、分别为初级维护与高级维护的故障率递增因子。
为判别部件维护方式，采取效费比的概念进行维护方式决策，效费比主要受维护成本和故障率改善量的影响，
式中：、分别为维护前部件故障率水平与维护后部件故障率水平。
初级维护和高级维护的效费比分别为
式中：cpr、csu分别为初级维护成本与高级维护成本。
维护方式选择因子Ai可进一步表示为
1.3　维护难易程度评价函数
受部件材料、结构、功能等方面的影响，维护时的难易程度具有明显差异。为量化评价动车组部件的维护难易程度，采取层次分析法进行建模。关于动车组部件维护难易度的影响因素，主要考虑以下4个因素[9-11]：
（1）部件的故障部位检测难易程度；
（2）部件的安装位置；
（3）部件的拆卸难易程度；
（4）部件的复杂度。
为便于部件维护难易程度的量化，引入维护难易程度因子γ。上述4种因素分别按检测难度、安装位置、拆卸难易程度、复杂度在1~10区间进行评分。部件维护难易度的影响因素采取层次分析法进行求解。
首先，构造各影响因素之间的判别矩阵：
式中：um1m2为第m1行影响因素相比较于第m2列影响因素的比值。
其次，计算判别矩阵E的最大特征根，代入齐次线性方程组，求解最大特征根对应的特征向量，归一化处理后即为对应矩阵权重值αj。
维护难易程度因子可表示为
式中：γ为维护难易程度因子；pj为第j个影响因素的评分；αj为第j个影响因素的权重值。
2　目标函数
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2.1　维护成本建模
（1）预防性维护成本：预防性维护成本是指动车组根据修程修制在预定维护时机进行维护活动所需的成本，可表示为
式中：cpr为初级维护成本；csu为高级维护成本。
（2）故障维护成本：故障维护成本是指动车组在运行过程中发生随机性故障进行临时维护所需的成本。考虑到部件的维护难易程度，可表示为
式中：cr为单位故障维护成本；为部件小修次数。
综上所述，在维护策略规划期内，部件的维护总成本为
2.2　可用度建模
（1）预防性维护时间：预防性维护时间是指动车组根据修程修制在预定维护时机进行维护活动所需的时间，可表示为
式中：tpr、tsu分别为初级维护与高级维护所需的时间。
（2）故障维护时间：故障维护时间是指动车组在运行过程中发生随机性故障进行临时维护所需的时间。考虑到部件的维护难易程度，可表示为
式中：tr为单位故障维护时间。
维护总时间由预防性维护时间和故障维护时间组成，可表示为
综上所述，在维护策略规划期内，部件的可用度为
式中：Tplan为部件维护策略规划期。
3　算例分析
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以动车组轮对为研究对象，引用文献[9]对轮对历史故障数据进行拟合研究，进一步优化部件维护策略。威布尔分布广泛应用于机械电子设备的故障率描述，动车组轮对作为机械部件，其故障率亦服从威布尔分布，其表达式为
式中：β、η分别为威布尔分布的特征参数与尺寸参数，取β=3.2，η=149。
部件的其他维护参数值选取见表1。在描述高级维护优于初级维护部件修复效果的同时，考虑到随着维护次数的增加，修复效果逐渐减弱的实际情况，设定初级维护和高级维护的故障率递增因子分别为，；初级维护和高级维护的役龄递减因子分别为，。
专家对部件维护难易程度各影响因素之间的判别基于式（10）可获得矩阵：
求解上述矩阵的最大特征根，代入齐次线性方程组，求解最大特征根对应的特征向量，即为各影响因素的权重值。对各影响因素进行评分，进一步代入式（11），可获得维护难易程度因子γ=3.461 8。以可靠度阈值Rmin为决策变量，部件维护成本和可用度为优化目标，在0≤Rmin≤0.97决策范围内，以0.01为搜索步长，分别获取部件的维护成本（图1）与可用度随可靠度阈值Rmin变化曲线（图2），优化结果见表2。
结合图1、图2和表2分析可知：当Rmin=0.90时，部件的维护总成本最优；当Rmin=0.66时，部件的可用度最优。进一步分析可知，当可靠度阈值选取较低时，允许部件上线服役时间较长，预防性维护次数较少，部件故障小修次数较多，进而导致故障维护成本较高和故障维护时间较长，使维护策略的维护总成本偏高，且可用度偏低。当可靠度阈值选取过高时，允许部件上线服役时间较短，预防性维护次数较多，部件故障小修次数较少，进而导致预防性维护成本较高和预防性维护时间较长，使维护策略的维护总成本偏高，且可用度偏低。
通过分析维护级别序列可知，维护前期大多采取初级维护，而在维护后期部件故障率水平较高，适当采取高级维护具有更好的修复效果。为进一步分析维护难易程度γ对维护成本和维护时间的影响，在基于表2优化可靠度阈值的前提下，选取不同γ值进行分析，优化结果见表3、表4。
分析表3和表4可知，相比于方案2和方案3，方案1的Cr和Tr明显更高，且Cr和Tr分别在C和A中占比更突出。这是由于维护难易程度因子对部件的故障维护成本和故障维护时间具有直接显著影响，且故障维护成本和故障维护时间分别在维护总成本和维护总时间中占据较大比例，因此对维护难易程度因子的研究对部件的维护总成本和可用度优化具有显著作用。
不同γ值部件的Rmin-C和Rmin-A曲线分别如图3、图4所示。随着Rmin取值的逐渐增大，不同γ值的维护总成本和可用度差距逐渐减小。这是由于Rmin取值较小时，部件故障次数较多，导致γ取值较大方案的Cr和Tr较高；而随着Rmin取值逐渐增大，部件故障次数逐渐减少，预防性维护成本和预防性维护时间分别在维护总成本和维护总时间中逐渐突出，使得不同γ值的维护总成本和可用度差距逐渐减小。
4　结论
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（1）本文采取两级非完美的维护方式，部件服役前期采取初级维护即可满足可靠度要求，而服役后期故障率水平较高，需采取高级维护保障轮对的可靠度水平，贴合维护现场情况。
（2）维护难易程度较高部件的可靠度阈值变动对维护成本和可靠度的影响更为突出，制定动车组维护策略时应更关注此类部件，适当调整可靠度阈值，更好地满足运营方和维护方对维护成本和可用度的差异化需求。
基金
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  • 国家自然科学基金青年科学基金资助项目(72001081)
  • 广东省科技创新战略专项资金资助项目(pdjh2024b571)
  • 广东交通职业技术学院校级科研资助项目(GDCP-ZX-2021-002-N1)
文献
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2025年第23卷第2期
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  • 首发时间：2025-12-16
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基金
国家自然科学基金青年科学基金资助项目(72001081)
广东省科技创新战略专项资金资助项目(pdjh2024b571)
广东交通职业技术学院校级科研资助项目(GDCP-ZX-2021-002-N1)
作者信息
    1.广东交通职业技术学院 轨道交通学院，广东 广州 510650
    2.华东交通大学 交通运输工程学院，江西 南昌 330013
    3.中国铁路武汉局集团有限公司，湖北 武汉 430061
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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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