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Article(id=1153982214330114106, tenantId=1146029695717560320, journalId=1146123222451335185, issueId=1153982211868053862, articleNumber=1671-1807(2025)02-0057-07, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1722441600000, receivedDateStr=2024-08-01, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1753060399849, onlineDateStr=2025-07-21, pubDate=1737734400000, pubDateStr=2025-01-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1753060399849, onlineIssueDateStr=2025-07-21, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1753060399849, creator=13701087609, updateTime=1753060399849, updator=13701087609, issue=Issue{id=1153982211868053862, tenantId=1146029695717560320, journalId=1146123222451335185, year='2025', volume='25', issue='2', pageStart='1', pageEnd='360', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1753060399262, creator=13701087609, updateTime=1753063120267, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1153993624627958610, tenantId=1146029695717560320, journalId=1146123222451335185, issueId=1153982211868053862, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1153993624627958611, tenantId=1146029695717560320, journalId=1146123222451335185, issueId=1153982211868053862, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=57, endPage=63, ext={EN=ArticleExt(id=1153982214825041996, articleId=1153982214330114106, tenantId=1146029695717560320, journalId=1146123222451335185, language=EN, title=Feature Analysis and Section Reduction Factor Calculation Method of Foot Joint for Large-size Angles, columnId=1151876674645226399, journalTitle=Science Technology and Industry, columnName=Technology Innovation, runingTitle=null, highlight=null, articleAbstract=

It is a trend to apply L320 and L360 high-strength angle members in ±800kV ultra high voltage(UHV) transmission lines. The current calculation method does not clarify the failure mode of tension member. Due to the quantities of bolts in the connection, each joint needs to be calculated multiple times, which is inconvenient in engineering. The training sets were established through the tests of multi alignment lines plate members and finite element analysis of large-size angles, and a random forest regression(RFR) model was constructed to perform feature analysis on the section reduction factor. The results show that the weight of adjacent alignment line(Δg1) is too high and for the thickness (t) is low in the current calculation method, which may easily cause significant fluctuations in the results while geometric dimensions of models are changed. The calculation method for section reduction factor is simplified through the optimization of RFR model feature analysis, and the results are stable and more consistent with the FEA models. The predictive model has good generalization ability and could be used in angles with 2 alignment lines in one leg.

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采用单肢布置2排以上高强螺栓的L320、L360高强角钢是特高压工程的发展趋势。现行计算方法没有明确其破裂面的形式,由于螺栓准线数多,计算时需对每个螺栓节点计算多次,不便于工程应用。通过多排孔板件试验、大角钢有限元计算建立训练集,构造随机森林回归模型对大角钢构件减孔数进行特征分析,结果表明,当单肢螺栓准线数增加后现行计算方法中相邻准距的权重过高、壁厚的偏低,在模型几何尺寸变化时计算结果容易产生较大波动;通过调参后的随机森林模型、特征选择后简化了螺栓减孔数计算方法,其计算结果稳定,与有限元模型更相符,泛化能力较好,也可用于两排螺栓减孔数计算。

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杨隆宇(1981—),男,博士,正高级工程师,研究方向为输电线路杆塔设计、钢结构稳定;

林恺(1984—),男,博士,教授,博士研究生导师,研究方向为引力波、量子引力理论、弯曲时空量子场论、计算物理等。

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杨隆宇(1981—),男,博士,正高级工程师,研究方向为输电线路杆塔设计、钢结构稳定;

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杨隆宇(1981—),男,博士,正高级工程师,研究方向为输电线路杆塔设计、钢结构稳定;

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林恺(1984—),男,博士,教授,博士研究生导师,研究方向为引力波、量子引力理论、弯曲时空量子场论、计算物理等。

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林恺(1984—),男,博士,教授,博士研究生导师,研究方向为引力波、量子引力理论、弯曲时空量子场论、计算物理等。

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编号 屈服强度/MPa 极限强度/MPa
18-1 272.0 395.2
6-1 284.7 395.5
18-2 290.9 392.2
6-2 277.7 403.8
18-3 296.2 390.9
6-3 281.1 387.2
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钢材材性试验

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编号 屈服强度/MPa 极限强度/MPa
18-1 272.0 395.2
6-1 284.7 395.5
18-2 290.9 392.2
6-2 277.7 403.8
18-3 296.2 390.9
6-3 281.1 387.2
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编号 F/kN 编号 F/kN 编号 F/kN
01-A20 489.3 06-B20 566.1 11-C20 590.5
02-A30 526.8 07-B30 565.0 12-C30 565.8
03-A40 539.7 08-B40 587.3 13-C40 594.2
04-A50 554.4 09-B50 592.4 14-C50 618.4
05=A60 567.5 11-B60 592.9 15-C60 622.1
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有限元构件极限承载力

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编号 F/kN 编号 F/kN 编号 F/kN
01-A20 489.3 06-B20 566.1 11-C20 590.5
02-A30 526.8 07-B30 565.0 12-C30 565.8
03-A40 539.7 08-B40 587.3 13-C40 594.2
04-A50 554.4 09-B50 592.4 14-C50 618.4
05=A60 567.5 11-B60 592.9 15-C60 622.1
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构件编号 构件编号
01-A-32-4M24-45-125 29-B-32-3M27-60-165
02-A-32-4M24-50-125 30-B-32-3M27-65-165
03-A-32-4M24-45-135 31-B-24-4M24-45-155
04-A-32-4M24-45-145 32-B-26-4M24-45-155
05-A-32-3M27-55-125 33-B-28-4M24-45-155
06-A-32-3M27-60-125 34-B-30-4M24-45-155
07-A-32-3M27-65-125 35-B-32-4M24-45-155
08-A-32-3M27-55-135 36-B-35-4M24-45-155
09-A-32-3M27-60-135 37-A-22-4M24-45-145
10-A-32-3M27-65-135 38-A-24-4M24-45-145
11-A-32-3M27-55-145 39-A-26-4M24-45-145
12-A-32-3M27-60-145 40-A-28-4M24-45-145
13-A-32-3M27-65-145 41-A-30-4M24-45-145
14-B-32-4M24-45-145 42-A-32-4M24-45-145
15-B-32-4M24-50-145 43-A-35-4M24-45-145
16-B-32-4M24-55-145 44-B-24-3M27-55-155
17-B-32-4M24-45-155 45-B-26-3M27-55-155
18-B-32-4M24-50-155 46-B-28-3M27-55-155
19-B-32-4M24-55-155 47-B-30-3M27-55-155
20-B-32-4M24-45-165 48-B-32-3M27-55-155
21-B-32-4M24-50-165 49-B-35-3M27-55-155
22-B-32-3M27-55-145 50-A-22-3M27-55-145
23-B-32-3M27-60-145 51-A-24-3M27-55-145
24-B-32-3M27-65-145 52-A-26-3M27-55-145
25-B-32-3M27-55-155 53-A-28-3M27-55-145
26-B-32-3M27-60-155 54-A-30-3M27-55-145
27-B-32-3M27-65-155 55-A-32-3M27-55-145
28-B-32-3M27-55-165 56-A-35-3M27-55-145
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大角钢模型

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构件编号 构件编号
01-A-32-4M24-45-125 29-B-32-3M27-60-165
02-A-32-4M24-50-125 30-B-32-3M27-65-165
03-A-32-4M24-45-135 31-B-24-4M24-45-155
04-A-32-4M24-45-145 32-B-26-4M24-45-155
05-A-32-3M27-55-125 33-B-28-4M24-45-155
06-A-32-3M27-60-125 34-B-30-4M24-45-155
07-A-32-3M27-65-125 35-B-32-4M24-45-155
08-A-32-3M27-55-135 36-B-35-4M24-45-155
09-A-32-3M27-60-135 37-A-22-4M24-45-145
10-A-32-3M27-65-135 38-A-24-4M24-45-145
11-A-32-3M27-55-145 39-A-26-4M24-45-145
12-A-32-3M27-60-145 40-A-28-4M24-45-145
13-A-32-3M27-65-145 41-A-30-4M24-45-145
14-B-32-4M24-45-145 42-A-32-4M24-45-145
15-B-32-4M24-50-145 43-A-35-4M24-45-145
16-B-32-4M24-55-145 44-B-24-3M27-55-155
17-B-32-4M24-45-155 45-B-26-3M27-55-155
18-B-32-4M24-50-155 46-B-28-3M27-55-155
19-B-32-4M24-55-155 47-B-30-3M27-55-155
20-B-32-4M24-45-165 48-B-32-3M27-55-155
21-B-32-4M24-50-165 49-B-35-3M27-55-155
22-B-32-3M27-55-145 50-A-22-3M27-55-145
23-B-32-3M27-60-145 51-A-24-3M27-55-145
24-B-32-3M27-65-145 52-A-26-3M27-55-145
25-B-32-3M27-55-155 53-A-28-3M27-55-145
26-B-32-3M27-60-155 54-A-30-3M27-55-145
27-B-32-3M27-65-155 55-A-32-3M27-55-145
28-B-32-3M27-55-165 56-A-35-3M27-55-145
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编号 减孔数 编号 减孔数 编号 减孔数
01 2.987 20 2.981 39 2.946
02 3.056 21 3.037 40 2.974
03 2.971 22 2.444 41 3.003
04 3.023 23 2.510 42 3.023
05 2.591 24 2.586 43 2.694
06 2.648 25 2.456 44 2.658
07 2.742 26 2.524 45 2.708
08 2.607 27 2.600 46 2.767
09 2.668 28 2.460 47 2.798
10 2.755 29 2.531 48 2.456
11 2.595 30 2.613 49 2.478
12 2.684 31 3.025 50 2.440
13 2.783 32 3.095 51 2.486
14 2.932 33 2.831 52 2.516
15 2.958 34 2.867 53 2.544
16 3.073 35 2.949 54 2.572
17 2.949 36 2.992 55 2.595
18 3.002 37 2.855 56 2.642
19 3.111 38 2.881
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大角钢模型减孔数

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编号 减孔数 编号 减孔数 编号 减孔数
01 2.987 20 2.981 39 2.946
02 3.056 21 3.037 40 2.974
03 2.971 22 2.444 41 3.003
04 3.023 23 2.510 42 3.023
05 2.591 24 2.586 43 2.694
06 2.648 25 2.456 44 2.658
07 2.742 26 2.524 45 2.708
08 2.607 27 2.600 46 2.767
09 2.668 28 2.460 47 2.798
10 2.755 29 2.531 48 2.456
11 2.595 30 2.613 49 2.478
12 2.684 31 3.025 50 2.440
13 2.783 32 3.095 51 2.486
14 2.932 33 2.831 52 2.516
15 2.958 34 2.867 53 2.544
16 3.073 35 2.949 54 2.572
17 2.949 36 2.992 55 2.595
18 3.002 37 2.855 56 2.642
19 3.111 38 2.881
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大规格角钢靴板节点特征分析与减孔数计算方法
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杨隆宇 1 , 林恺 2
科技和产业 | 科技创新 2025,25(2): 57-63
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科技和产业 | 科技创新 2025, 25(2): 57-63
大规格角钢靴板节点特征分析与减孔数计算方法
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杨隆宇1, 林恺2
作者信息
  • 1 中国电力工程顾问集团华北电力设计院有限公司, 北京 100120
  • 2 中国地质大学(武汉)地球物理与空间信息学院地球内部多尺度成像湖北省重点实验室, 武汉 430074

    • 杨隆宇(1981—),男,博士,正高级工程师,研究方向为输电线路杆塔设计、钢结构稳定;

    林恺(1984—),男,博士,教授,博士研究生导师,研究方向为引力波、量子引力理论、弯曲时空量子场论、计算物理等。

Feature Analysis and Section Reduction Factor Calculation Method of Foot Joint for Large-size Angles
Longyu YANG1, Kai LIN2
Affiliations
  • 1 North China Power Engineering Co. Ltd. of China Power Engineering Consulting Group, Beijing 100120, China
  • 2 Hubei Subsurface Multi-scale Imaging Key Laboratory, School of Geophysics and Geomatics,China University of Geosciences, Wuhan 430074, China
出版时间: 2025-01-25
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摘要
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采用单肢布置2排以上高强螺栓的L320、L360高强角钢是特高压工程的发展趋势。现行计算方法没有明确其破裂面的形式,由于螺栓准线数多,计算时需对每个螺栓节点计算多次,不便于工程应用。通过多排孔板件试验、大角钢有限元计算建立训练集,构造随机森林回归模型对大角钢构件减孔数进行特征分析,结果表明,当单肢螺栓准线数增加后现行计算方法中相邻准距的权重过高、壁厚的偏低,在模型几何尺寸变化时计算结果容易产生较大波动;通过调参后的随机森林模型、特征选择后简化了螺栓减孔数计算方法,其计算结果稳定,与有限元模型更相符,泛化能力较好,也可用于两排螺栓减孔数计算。

大规格钢  /  减孔数  /  随机森林  /  特征选择  /  板件试验  /  有限元分析

It is a trend to apply L320 and L360 high-strength angle members in ±800kV ultra high voltage(UHV) transmission lines. The current calculation method does not clarify the failure mode of tension member. Due to the quantities of bolts in the connection, each joint needs to be calculated multiple times, which is inconvenient in engineering. The training sets were established through the tests of multi alignment lines plate members and finite element analysis of large-size angles, and a random forest regression(RFR) model was constructed to perform feature analysis on the section reduction factor. The results show that the weight of adjacent alignment line(Δg1) is too high and for the thickness (t) is low in the current calculation method, which may easily cause significant fluctuations in the results while geometric dimensions of models are changed. The calculation method for section reduction factor is simplified through the optimization of RFR model feature analysis, and the results are stable and more consistent with the FEA models. The predictive model has good generalization ability and could be used in angles with 2 alignment lines in one leg.

large-size angle  /  the section reduction factor  /  random forest regression  /  features analysis  /  plate experiment  /  FEA.
杨隆宇, 林恺. 大规格角钢靴板节点特征分析与减孔数计算方法. 科技和产业, 2025 , 25 (2) : 57 -63 .
Longyu YANG, Kai LIN. Feature Analysis and Section Reduction Factor Calculation Method of Foot Joint for Large-size Angles[J]. Science Technology and Industry, 2025 , 25 (2) : 57 -63 .
正文
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将西部地区的清洁能源送到东南沿海的特高压线路是实现“双碳”目标的重要枢纽,经过多年实践目前特高压工程中广泛采用大肢宽的高强角钢来作为塔身主材,与组合截面构件相比其节点构造、构件自重都有优势,也便于现场安装[1-5]。对主材与塔脚板连接节点,当角钢肢宽、壁厚增大后需要单肢布置3、4排螺栓或使用更大直径螺栓以满足大角钢承载力要求。多年前已规划有L320、L360肢宽的高强大角钢[6],但最新的设计规范和技术文件中缺乏L320、L360肢宽角钢的螺栓布置、减孔数等内容[7-10],一定程度上限制大角钢的应用。
目前输电塔螺栓减孔数的研究主要较少,主要集中在中小规格角钢主材对接的内包角钢外贴板型节点[11-12],其角钢受力状态与螺栓数与单剪节点有较大差异。由于上述原因工程中假设双肢螺栓连接大角钢有多条可能的受拉破裂面,每种破裂面分别给出计算减孔数的公式。当主材单肢采用3、4排螺栓时,这种需多次试算取最不利的计算方式在应用时很烦琐;现有公式形式计算稳定性较差,当准线间距小幅变化时计算得到的减孔数大幅波动、与试验结果不符;特高压铁塔中大角钢接头节点数量较多,每处节点均采用此种计算流程明显降低设计效率。
本文在多排孔板件受拉试验的基础上,采用角钢靴板节点精细化有限元模型与机器学习[13-16]研究了大角钢截面破裂面的形式和螺栓减孔数、对大角钢模型进行特征分析。得到建议的多排螺栓减孔数计算公式可简化计算流程,不但适用单肢3、4排螺栓的情况,还具有较好的泛化能力适用于目前常见的单肢双排螺栓孔计算,提高了特高压工程主材节点计算准确性、大幅提高计算和校核效率。
1 板件试验
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试验构件使用Q235钢材制作,名义屈服强度235 MPa。材性试验试样从钢材中截取,共进行3组材性试验,试验结果如表1所示。
在INSTRON 1342动静态材料试验机上测得钢材的屈服强度平均值fy=281.2 MPa、抗拉强度平均值fu=395.5 MPa。板件两端设置18 mm厚Q420加载板,使用8.8级M24螺栓连接。
多排孔构件尺寸为332 mm×590 mm矩形板件(图1),分为A、B、C组,每组在准线方向相邻孔距(2S)分别为72 mm、96 mm、120 mm;相邻准距Δg1=Δg2=Δg,同组中每个构件分别为20~60 mm,级差为10 mm。
试件采用W5-687液压万能试验机单调加载,由于3个板件上螺栓孔数量多,按理论承载力的10%预加载以检查两端夹具固定情况、试验机工作状态,确保构件和试验机连接良好、拉力与变形关系稳定。在分级加载阶段,前25级荷载为理论承载力的2%,加载稳定1 min后进行下一级加载;达到理论承载力50%之后每级降为1%;当达到理论承载力的85%后按照每级10 kN加载直至螺孔变形显著增大节点无法稳定、自动卸荷时停止加载。试验装置如图2所示。
与双剪连接节点不同,单剪加载使板件处于偏心受拉状态,导致从板件正、反面的螺孔变形量不同;由于试验为单向加载,各派螺孔的型变量也不同。对各个构件都是靠近拉力方向的前2排螺孔变形更大。
减孔数试验构件螺孔数量多,由于构件S、Δg不相同,每个构件均需单独加工2个对应的加载板,因此进行有限元模型计算。单剪连接下螺杆传递到螺孔壁的压力是不均匀的,螺杆、螺帽、螺母、板件、加载板之间发生传力的部位用target170和conta174单元设置接触对,局部加密螺孔附近使用曲面网格。钢材的弹性模量、fy按材性试验结果取值,摩擦系数为0.3。
图3为模型网格划分,图4为#19-C40构件应力。计算结果表明孔壁受到不均匀压力后板件正、背面应力分布和高应力位置不同,达极限承载力后在螺孔周围有明显变形,单剪连接的板件受力和变形比双剪时更复杂。
表2为模型计算结果,图5为有限元模型(FEA)与构件试验结果(EXP)对比,平均相对误差(MRE)为3.35%,模型计算结果与试验相符。
2 大角钢模型
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对图6所示塔脚板靴板节点,最内侧第1排准线到角钢棱线的最小距离受多个因素控制[8],为了保证螺帽不压角钢内弧需满足
${g}_{1}-b-\delta -r-e/20$
式中:g1为最内侧准线;b为角钢肢宽;δ为加工误差;e为螺栓最大尺寸。
除了压弧以外还需考虑靴板处等厚双帽螺栓、螺杆出扣、套筒扳手和防盗螺栓拆卸工具的操作空间等几何尺寸的限制。
螺栓准距布置的紧凑度受相邻孔距限值影响[10],沿准线方向和相邻准线方向最小中心距为2.5 d,由此确定相邻准线最小距离Δg约为2.0 d。
根据上述S、Δg的限值和文献[8]要求列出有限元模型规格列于表3。表3中构件编号为“序号-肢宽-壁厚-螺栓-Δg-g1”,其中“A”表示L320肢宽,“B”表示L360肢宽,已覆盖两种规格角钢的所有壁厚范围,角钢每肢内相邻准线的Δg相同。
为提高计算效率需对模型做适当简化,单剪连接对角钢的影响随壁厚增加而增大,因此模型中保留了传力路径上的大角钢、螺栓、靴板,将靴板与塔腿斜材连接部分、靴板端部的肋板略去。Q420大角钢承载力高、与靴板连接的螺栓个数较多,模型中已经考虑螺栓连接长度大于15 d0的强度折减[7]。按大角钢工装要求[6]设置内弧,横截面肢端按目前工程中使用的设置(图7),使用采用solid187单元以适应这些曲面细节。
图8为Δg=55 mm的#22构件应力,第1排螺帽受不均匀压力、与螺杆连接处应力最大;前两排的应力都大于其他区域,破裂面上纵向纤维伸长最明显。表4中单肢螺栓排数、准距等有多种组合,但节点破坏时应力和变形最大的都是离拉力最近的前两排螺孔,不论3M27还是4M24角钢高应力区连线均为在这两排螺栓间交替前进形成锯齿形破裂面(图1中III-III破裂面)。
根据上述破裂面形式,L320、L360角钢减孔数应使用文献[7]中的III-III截面对应计算公式为
${A}_{n}=A-\left({n}_{0}{d}_{0}-\sum _{i=1}^{{n}_{0}-1}\frac{{S}_{i}^{2}}{4\Delta {g}_{i}}\right)t$
式中:A为角钢截面积;t为壁厚;Si和Δgi如图1所示,其中Δg2应减去t;n0为破裂面经过的螺孔数;d0为螺孔直径。
大角钢模型的计算结果列于表4,式(2)减孔数均高于模型计算结果,平均比模型大15.3%。
3 模型特征
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高强L320、L360角钢承载力高,单剪连接节点长度大,如进行构件试验材料量大、对试验机有较高要求;由于靴板节点螺栓数量多,采用有限元模型计算耗费算力大;所求的螺栓减孔数是模型拉力试验的间接量、需要对有限元结果分析后得到,进一步增加了分析的复杂性。大角钢节点包括角钢尺寸、螺孔布置、孔径等多个参数,对这种非线性比较强的问题采用袋装集成算法中的随机森林可取得较好的结果。随机森林由多个决策树集成,以每棵决策树的均值为结果,具有较好的鲁棒性和精确度[13-14]。
计算螺栓连接净截面的公式(2)包括A、n0、d0、Si、gi、t,对单肢3M27、4M24布置分别有8、9个特征;从Q420大角钢模型控制尺寸角度观察,由于在任一肢内螺栓纵向间距S、相邻准距(gi+1-gi)是固定值,需要b、t、n0、d0、S、Δg、g1共7个特征,为便于与有限元模型对比采用这种划分。在试验和有限元计算时减孔数是间接量,但采用机器学习做预测时可直接将减孔数作为标签。
表3中有限元模型计算结果作为原始数据,其中已经包括L320、L360肢宽角钢所有型号[6]。为优化决策树相似性和模型偏差采用Bootstrap法抽样,袋外数据(out of bag,OOB)用作验证训练后模型的精度。
基评估器的数量对模型精度的影响并不是单调增加的,但耗费的计算资源会越来越越大。表3中模型根据现行规范和工程数据[8-10]确定,是平衡的数据集,为避免过拟合在调参时使用k-fold交叉验证,评估指标为均方误差的负值(nMSE)。图9为验证结果,当基评估器数量为17时模型精度最佳,继续增大后nMSE开始上下波动。
图10为文献[7](code)、FEA(finite element analysis)模型、随机森林预测(predict)的螺栓间孔数,横坐标为表3中模型编号。随机森林能较好的预测FEA减孔数,计算结果没有出现过拟合,可以将其预测值用于扩充表3模型在后续分析中使用。文献[7]计算值虽然曲线上升、下降趋势与其他两种接近,但整体数值更高、变化幅度更大,而在角钢壁厚t变化的时候变化幅度又过小。
为研究图10中规范计算结果与fea、随机森林预测值的差异,将式(2)整理为
$n={n}_{0}-\sum _{i=1}^{{n}_{0}-1}\frac{{S}_{i}^{2}}{4{d}_{0}\Delta {g}_{i}}$
式中:n为减孔数,对大角钢有
$n={n}_{0}-\frac{{S}_{i}^{2}}{4{d}_{0}}\left(\frac{{n}_{0}-2}{\Delta {g}_{i}}+\frac{1}{\Delta {g}_{i}-t}\right)$
在几何尺寸、螺孔布置变化时式(4)中括号内第2项的变化幅度远小于第1项,二者差距随着单肢螺栓准线数的增多而加大,即该公式中权重Δg1的权重更大,当Δg1小幅增加时减孔数就显著上升。同时,式中t的权重相对而言过小,因此当仅在厚度方向变化时图10中减孔数几乎是水平线。
将所有模型的7个特征进行二次多项式回归,图11为得到的新特征的极差标准化后的系数。从图11中可知对减孔数影响最大的新特征组合是n0×g1、n0×Δg、t×n0、t×S。
式(2)和组合出的新特征中都没有b,均认为b对减孔数的影响较小;新特征中d0对减孔数影响较小的原因是M24和M27的d0相差较小、其值相对其他几何特征相比占比也小,而且在目前工程应用[8]中特征d0与S存在关联性。由此给出L320、L360大角钢减孔数的建议公式为
$n=\frac{{n}_{0}\Delta g+{g}_{1}+t/{n}_{0}}{4S}+1$
式中:Δg为角钢单肢内相邻准线距离;g1为图 6中第1排准线到角钢棱线距离;S为图1中斜方向相邻两孔的纵向距离;t为角钢壁厚;n0为图1中III-III破裂面经过的螺孔数。
图12为式(5)(suggested)与文献[7]、FEA模型对比,建议方法的结果位于二者之间、与FEA结果更相符。为验证其泛化能力增加右侧编号61~66构件,Q420 L220角钢,t=16~26 mm,单肢2M24, 螺栓准线等按文献[8]布置。结果表明,虽然建议方法根据L320、L360的单肢3排和4排螺栓模型得到,但通过机器学习方法调参、特征选择后它同样适用于肢宽更小、螺栓排数更少的减孔数计算。
4 结论
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通过板件试验、大角钢有限元模型、随机森林回归和特征分析,得到如下结论。
(1)当单肢布置3、4排螺栓时,由于文献[7]公式形式的原因单肢内相邻准距Δg1的权重快速上升、减孔数计算结果随之大幅变化,与有限元结果偏差较大;而壁厚t又在权重较低的项中,降低了其对减孔数的影响。
(2)根据L320、L360的FEA结果为建立的随机森林模型调参,对模型预测值进行特征选择,排除特征间的相关性后得到的建议的计算方法形式比文献[7]简洁,更便于工程应用。
(3)与文献[7]相比,当模型参数变化时建议的计算方法得到的减孔数的数值与变化规律与FEA模型更相符,计算结果稳定、没有出现随某个特征大幅波动的情况;且其泛化能力较好,经FEA验证可用于更小肢宽、单肢2排螺栓的角钢减孔数计算。
文献
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  • 接收时间：2024-08-01
  • 首发时间：2025-07-21
  • 出版时间：2025-01-25
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  • 收稿日期：2024-08-01
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    1 中国电力工程顾问集团华北电力设计院有限公司, 北京 100120
    2 中国地质大学(武汉)地球物理与空间信息学院地球内部多尺度成像湖北省重点实验室, 武汉 430074
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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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