
Citation: | LI Yongle, PAN Junzhi, TI Zilong, RAO Gang. Inversion Method of Vortex-Induced Vibration Amplitude for Long-Span Bridges with Partially Installed Noise Barrier[J]. Journal of Southwest Jiaotong University, 2023, 58(1): 183-190. doi: 10.3969/j.issn.0258-2724.20210172 |
The sectional model test in wind tunnels is often used to measure the vortex-induced vibration (VIV) of long-span bridges. Since the sectional model test is based on two-dimensional theory, when the bridge has different aerodynamic configurations along the span due to the partial installation of noise barriers, it is difficult to measure the VIV response directly through the sectional model test. Based on the empirical linear VIV model, an assessment method of VIV between the sectional model and prototype bridge that considers the effects of multiple aerodynamic configurations is proposed. Firstly, the sectional model test is performed on the models with and without barriers respectively. Then, the prototype response of the noise barriers installed and not installed along the span is investigated by ANSYS harmonic analysis, and the corresponding amplitude of the vortex-induced force is obtained. Finally, according to the actual installation position of the noise barrier along the span, the vortex-induced force is imposed on the bridge and the prototype response with the partially installed noise barrier is obtained. In addition, based on the method in this paper, various noise barrier installation schemes are numerically simulated. The results indicate that fully enclosed noise barrier will significantly reduce the aerodynamic performance of the main girder and the overall VIV will be affected by partial installation of barrier to a large degree. The method in this paper can estimate the prototype response of multi-aerodynamic configurations bridges through the results of sectional model tests. The installation of the noise barrier should be arranged on the side span as far as possible under the conditions of noise reduction. If the arrangement length exceeds the position of the bridge tower, it should be shortened as much as possible to reduce the vortex-induced response.
随着我国轨道交通的快速发展,轨道交通接触网的规模不断扩大,对接触网运行安全性的要求不断提高,接触网检修作业的任务日渐加重. 科学合理地安排接触网的检修计划,可以有效利用现有检修资源、提高检修作业的效率、节省检修费用,有效保障接触网系统的安全可靠.
现阶段接触网检修计划基本依靠人工编制,由于接触网设备类型多、数量大,设备间关联关系复杂,人工编制检修计划不仅效率低下,而且较难对检修任务做全面考虑,编制的检修计划经济性与可行性较差,容易出现漏修、过修与失修等问题,严重影响了接触网的安全运行. 近年随着信息技术的发展,自动编制技术在铁路行业各领域得到广泛研究与应用,如列车运行图计划编制、线路维修计划编制、编组站计划编制、列车解体计划编制、乘务计划编制、调车作业计划编制等[1-6],极大提高了作业任务的合理性与经济性,也为接触网检修任务的自动编制提供了有益的参考.
目前,接触网检修理念研究主要有两类,一是以状态为中心,以设备监测数据为基础,建立劣化模型预测设备状态变化,并据此安排检修任务,文献[7-8]提出将故障预测与健康管理(prognostics health management, PHM)以及主动维护应用于高速铁路牵引供电系统中,实现策略的决策与优化,可根据设备状态按需检修,有效解决了过修或者欠修的不足. 但依据该理念编制检修计划需要大量状态检测与监测数据,同时需要较强的数据实时分析与处理能力,较难直接应用到实际中. 二是以可靠性为中心,通过建立设备寿命分布模型,以此为基础优化检修计划编制,如文献[9-10]针对现有的接触网预防性维修模式,推导了系统可靠性与维修费用的数学关系;文献[11]运用ID3 (iterative dichotmizer 3)决策树算法构建出接触网维修决策树模型,通过决策树发掘影响接触网主要设备异常或故障的主要因素,从而获得相对科学合理的检修方案;文献[12]开发了接触网设备管理子系统以及检修沙盘模型、手持终端子系统,实现了图表可视化、生产作战指挥图和报表定制等功能,但该系统的检修计划依赖人工编制;文献[13-14]获得了各设备的最优维修间隔,并以设备类别为最小单位编制检修计划,但编制结果没考虑接触网设备的位置分布,无法在实际中得到应用.
本文在满足检修作业特性的基础上,针对接触网设备沿线分布、点状与条状设备并存等特性,考虑检修作业的连续性,利用整数规划方法,提出基于弹性周期区间的接触网检修计划自动编制模型,设计相应的启发式求解算法,通过实际算例验证模型和算法的有效性,为铁路接触网检修计划的自动编制提供一种有效方法.
定义1 接触网检修涉及的所有设备集合称为检修任务集,根据设备在接触网中的位置可划分为线条状全面检修类子集合与点状单项设备类子集合.
定义2 检修任务指接触网设备周期性人工检修,对于设备发生故障或病害后所采取的事后修理(又称为纠错性维修)不属于本文定义的检修任务.
定义3 接触网检修工作量以设备检修次数定义,不考虑不同设备检修时间的差异性问题.
模型假设如下:
1) 区域路网中接触网检修设备已确定,模型只需考虑如何安排任务使目标费用最小.
2) 所有检修任务集合中的元素在计划时间范围内按照检修周期执行.
3) 运营过程中的纠错性维修,不影响计划中检修任务的安排.
目前的计划检修体制要求设备到期必修,一般不允许超周期运行. 这样特定的检修方式极大限制了各设备检修过程中实现时空配合的可能性,考虑设备本身具有一定的过载能力,提出一种弹性周期区间的方法,如图1所示.
图1中:T为《普速铁路接触网运行维修规则》[15]规定的标准检修周期;
接触网检修计划的编制是在给定的任务检修时间内,将需要进行检修的设备进行排列组合,确保检修任务顺利开展,主要目的是通过数学方法解决预防性检修计划编制问题. 检修计划可分解为年度、月度、天窗日计划等,其本质差异仅在于考虑的编制时间段不同,其中年度检修计划是分解编制的基础.
以接触网年度检修计划自动编制为例,模型输入包括设备所处的位置、检修周期等基本信息,模型约束主要包括设备检修优先级约束、线条状设备检修连续性约束等. 基于弹性周期区间的接触网年度检修计划自动编制模型(automatically compilingmodel for overhaul plan of catenary based on elastic period interval,ACM-OPC-EPI)框架如图2所示.
接触网检修计划编制的目的是在满足设备运行可靠性约束的基础上,希望以最小的检修成本,按要求完成所有接触网设备的检修作业任务.
1) ACM-OPC-EPI目标函数
设备超周期惩罚费用目标F1和额外检修路径代价目标F2如式(1)和式(2)所示.
minF1=∑l∈LC∑e∈D(l)C∑t∈TSP(el)FX(el)t, |
(1) |
minF2=∑l∈LC∑e∈D(l)C∑t∈TSP(el)CtX(el)t, |
(2) |
式中:LC为工区股道集合,;
X(el)t={1,股道l设备e被安排在第t个时间编制区段,0,股道l设备e未被安排在第t个时间编制区段. |
上述目标中,式(1)表示设备检修间隔偏离标准检修周期最小,以保证标准周期内检修率最大化. 当设备修安排未超周期时,将
P(el)F={0,DLE(el)C⩽t(el)−t(el)p<E(el)C,t(el)−t(el)p−E(el)CE(el)C,E(el)C⩽t(el)−t(el)p<ULE(el)C, |
式中:
式(2)描述了各时间编制区段检修任务编制的集中性.
2) ACM-OPC-EPI约束条件
设备弹性周期编制区间约束如式(3)所示.
t(el)p+ULE(el)C∑t(el)=t(el)p+DLE(el)CX(el)t=1, |
(3) |
式中:
检修工作量约束如式(4)和式(5)所示.
∑l∈LC∑e∈D(l)C∑t∈TSX(el)t⩽1.05Nt, |
(4) |
∑l∈LC∑e∈D(l)C∑t∈TSX(el)t⩾0.95Nt, |
(5) |
式中:
设备编制优先级约束如式(6)所示.
{F(el)R>F((e+1)l)R,P(el)F>P((e+1)l)F,F(el)R<F((e+1)l)R,P(el)F<P((e+1)l)F, |
(6) |
式中:
F(el)R={2,tLs−t(el)p>ULE(el)C, e∈P(l)D,1,tLs−t(el)p>ULE(el)C, e∈L(l)D,0,tLs−t(el)p⩽ULE(el)C, e∈D(l)C, |
式中:
线条状设备杆号区域连续性约束和连续区间设备数量的最小值约束分别如式(7)和式(8)所示.
P((e+1)l)tX((e+1)l)t−P(el)tX(el)t⩽2, |
(7) |
max {P(el)tX(el)t}−min {P(el)tX(el)t}>RC, |
(8) |
式中:
计划编制时间范围内设备是按频次的周期检修如式(9)所示.
X(el)t=X(el)t+zE(el)C, |
(9) |
式中:
F(el)={⌈TLE(el)C⌉,DLE(el)C⩽t(el)−t(el)p<E(el)C,0,E(el)C⩽t(el)−t(el)p<ULE(el)C, |
式中:
接触网检修计划需同时满足超周期惩罚费用最小与检修路径代价最小两个目标,结合多目标规划中的分层序列法思想,提出了求解ACM-OPC-EPI模型的启发式算法,算法流程如图3所示.
求解ACM-OPC-EPI模型的启发式算法原则如下:
1) 接触网检修计划的编制应优先考虑检修周期问题,设备检修必须处于弹性检修周期之内,以确保接触网运行的安全性.
2) 其次考虑接触网线条状设备与点状设备并存的情况,在编制过程中考虑点状设备与线条状设备之间的空间距离问题,使计划编制结果在空间上尽量集中,以节省检修时间与出行费用,确保检修计划编制的经济性.
某供电工区所辖设备情况如表1所示,其中线条状连续设备包括接触悬挂、附加悬挂、所亭供电线,点状单项设备包括分段绝缘器、关节式分相/分相绝缘器、远动隔离开关及操作机构、避雷器及接地装置,合计作业任务检修6333台次. 各设备标准检修周期参考《普速铁路接触网运行维修规则》[15].
设备类型 | 设备名称 | 标号 | 单位 | 周期 | |
线条状设备全面 检修 | 接触悬挂 | A | 条•km | 36 月 | |
附加悬挂 | 回流线 | 条•km | 36 月 | ||
架空地线 | 条•km | 36 月 | |||
加强线 | 条•km | 36 月 | |||
所亭供电线 | 供电线 | 条•km | 36 月 | ||
架空地线 | 条•km | 36 月 | |||
点状单项设备 检修 | 分段绝缘器 | B1 | 组 | 6 月 | |
关节式分相、分相绝缘器 | B2 | 组 | 6 月 | ||
远动隔离开关及操作机构 | B3 | 台 | 6 月 | ||
避雷器及接地装置 | B4 | 台 | 12 月 |
设置区域最小连续杆号检修工作量
TS | 1 月 | 2 月 | 3 月 | 4 月 | 5 月 | 6 月 | 7 月 | 8 月 | 9 月 | 10 月 | 11 月 | 12 月 |
比率/% | 5 | 5 | 15 | 8 | 8 | 15 | 6 | 6 | 10 | 10 | 6 | 6 |
求解结果以平铺计划表形式展示如表3,表中垂直方向表示编制区间的计划时段(1月—12月),水平方向上分为线条状设备以及单项设备(其中,A、B1 ~ B4表示设备编号),线条状以连续杆号区间形式进行平铺展示(例:892 ~ 946),单项设备以设备类别进行杆号单独显示(例:266,268,…),其中线条状设备的检修台次以设备履历表中杆号区间包含的设备进行统计(即“/”后的数字,例:/91). 由结果可以看出:各编制区间检修工作计划符合各约束条件,线条状设备与单项设备在空间位置上普遍集中,符合实际需求.
编制 时间段 | 股道 L1 | 股道 L2 | 月检/ 台次 | |||||||||
A | B1 | B2 | B3 | B4 | A | B1 | B2 | B3 | B4 | |||
1 月 | 892 ~ 946 /91 1052 ~ 1082 /96 | 898,1004 | 553 ~ 635 /134 | 561 | 324 | |||||||
2 月 | 260 ~ 360 /165 | 266,268, 270,272, 274,276, 278,280 | 264,268, 278,284 | 262,284, 350 | 259 ~ 353 /150 | 265,267, 269,271, 273,275, 277,279 | 263,267,277,281, 285 | 261,283, 349 | 346 | |||
3 月 | 362 ~ 474 /285 520 ~ 672 /273 | 562 | 355 ~ 457 /260 877 ~ 945 /126 | 897 | 946 | |||||||
4 月 | 674 ~ 816 /262 | 770 | 459 ~ 501 /86 771 ~ 829 /150 | 487,769 | 501 | |||||||
5 月 | 948 ~ 982 /82 818 ~ 890 /185 | 947 ~ 1001 /122 831 ~ 875 /115 | 1305 | 505 | ||||||||
6 月 | 984 ~ 1050 /184 1084 ~ 1178 /288 | 1494 | 1590 | 637 ~ 769 /201 1003 ~ 1089 /264 | 1487 | 1003 | 941 | |||||
7 月 | 1180 ~ 1212 /102 | 503 ~ 551 /125 1155 ~ 1203 /150 | 265,267, 269,271, 273,275, 277,279 | 263,267,267,281, 285 | 390 | |||||||
8 月 | 1214 ~ 1258 /138 | 1205 ~ 1283 /240 | 378 | |||||||||
9 月 | 476 ~ 518 /86 1260 ~ 1320 /186 | 266,268, 270,272, 274,276, 278,280 | 264,268, 278,284 | 488 | 1091 ~ 1153 /192 1285 ~ 1333 /150 | 627 | ||||||
10 月 | 1372 ~ 1496 /378 | 1335 ~ 1415 /246 | 1305 | 625 | ||||||||
11 月 | 1322 ~ 1370 /150 | 1417 ~ 1491 /222 | 1487 | 373 | ||||||||
12 月 | 1498 ~ 1590 /178 | 1494 | 1590 | 1488 | 1493 ~ 1589 /196 | 377 | ||||||
年检/ 台次 | 3129 | 2 | 16 | 10 | 9 | 3129 | 2 | 16 | 12 | 8 | 6333 |
该部分计划采用人工编制时需要7 d左右,而采用本文方法后求解时间仅135 s,比原来方法节省99.98%,速度远高于人工编制;原来人工编制的检修计划检修路径总里程为858.0 km, 本文方法生成的检修计划检修路径总里程为573.5 km,检修路径比原来减少33.16%,在同样完成设备检修任务的情况下,降低了检修成本.
1) 针对接触网检修作业设备多、地理位置分散、单项的点状设备与线索的条状设备并存的特点,提出一种接触网检修计划智能编制方法,可在给定接触网检修范围的基础上,实现接触网检修计划的自动编制,与现行的人工编制方法相比,速度快、效率高.
2) 接触网检修计划的智能编制方法,以弹性检修周期区间为基础,以检修作业出行路径和超周期检修时间总数最小为目标,可实现所辖接触网设备检修计划的自动编制,避免超修和漏修的情况.
3) 以某供电分区接触网设备检修计划为例,实现了该工区接触网设备检修计划的自动编制,得到了该工区接触网年度检修的平铺计划表. 计划编制用时短、覆盖设备全面,编制结果满足现场实际检修作业的需要.
致谢:广东省城市轨道交通工程建造新技术企业重点实验室资助(2017B030302009).
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设备类型 | 设备名称 | 标号 | 单位 | 周期 | |
线条状设备全面 检修 | 接触悬挂 | A | 条•km | 36 月 | |
附加悬挂 | 回流线 | 条•km | 36 月 | ||
架空地线 | 条•km | 36 月 | |||
加强线 | 条•km | 36 月 | |||
所亭供电线 | 供电线 | 条•km | 36 月 | ||
架空地线 | 条•km | 36 月 | |||
点状单项设备 检修 | 分段绝缘器 | B1 | 组 | 6 月 | |
关节式分相、分相绝缘器 | B2 | 组 | 6 月 | ||
远动隔离开关及操作机构 | B3 | 台 | 6 月 | ||
避雷器及接地装置 | B4 | 台 | 12 月 |
TS | 1 月 | 2 月 | 3 月 | 4 月 | 5 月 | 6 月 | 7 月 | 8 月 | 9 月 | 10 月 | 11 月 | 12 月 |
比率/% | 5 | 5 | 15 | 8 | 8 | 15 | 6 | 6 | 10 | 10 | 6 | 6 |
编制 时间段 | 股道 L1 | 股道 L2 | 月检/ 台次 | |||||||||
A | B1 | B2 | B3 | B4 | A | B1 | B2 | B3 | B4 | |||
1 月 | 892 ~ 946 /91 1052 ~ 1082 /96 | 898,1004 | 553 ~ 635 /134 | 561 | 324 | |||||||
2 月 | 260 ~ 360 /165 | 266,268, 270,272, 274,276, 278,280 | 264,268, 278,284 | 262,284, 350 | 259 ~ 353 /150 | 265,267, 269,271, 273,275, 277,279 | 263,267,277,281, 285 | 261,283, 349 | 346 | |||
3 月 | 362 ~ 474 /285 520 ~ 672 /273 | 562 | 355 ~ 457 /260 877 ~ 945 /126 | 897 | 946 | |||||||
4 月 | 674 ~ 816 /262 | 770 | 459 ~ 501 /86 771 ~ 829 /150 | 487,769 | 501 | |||||||
5 月 | 948 ~ 982 /82 818 ~ 890 /185 | 947 ~ 1001 /122 831 ~ 875 /115 | 1305 | 505 | ||||||||
6 月 | 984 ~ 1050 /184 1084 ~ 1178 /288 | 1494 | 1590 | 637 ~ 769 /201 1003 ~ 1089 /264 | 1487 | 1003 | 941 | |||||
7 月 | 1180 ~ 1212 /102 | 503 ~ 551 /125 1155 ~ 1203 /150 | 265,267, 269,271, 273,275, 277,279 | 263,267,267,281, 285 | 390 | |||||||
8 月 | 1214 ~ 1258 /138 | 1205 ~ 1283 /240 | 378 | |||||||||
9 月 | 476 ~ 518 /86 1260 ~ 1320 /186 | 266,268, 270,272, 274,276, 278,280 | 264,268, 278,284 | 488 | 1091 ~ 1153 /192 1285 ~ 1333 /150 | 627 | ||||||
10 月 | 1372 ~ 1496 /378 | 1335 ~ 1415 /246 | 1305 | 625 | ||||||||
11 月 | 1322 ~ 1370 /150 | 1417 ~ 1491 /222 | 1487 | 373 | ||||||||
12 月 | 1498 ~ 1590 /178 | 1494 | 1590 | 1488 | 1493 ~ 1589 /196 | 377 | ||||||
年检/ 台次 | 3129 | 2 | 16 | 10 | 9 | 3129 | 2 | 16 | 12 | 8 | 6333 |
设备类型 | 设备名称 | 标号 | 单位 | 周期 | |
线条状设备全面 检修 | 接触悬挂 | A | 条•km | 36 月 | |
附加悬挂 | 回流线 | 条•km | 36 月 | ||
架空地线 | 条•km | 36 月 | |||
加强线 | 条•km | 36 月 | |||
所亭供电线 | 供电线 | 条•km | 36 月 | ||
架空地线 | 条•km | 36 月 | |||
点状单项设备 检修 | 分段绝缘器 | B1 | 组 | 6 月 | |
关节式分相、分相绝缘器 | B2 | 组 | 6 月 | ||
远动隔离开关及操作机构 | B3 | 台 | 6 月 | ||
避雷器及接地装置 | B4 | 台 | 12 月 |
TS | 1 月 | 2 月 | 3 月 | 4 月 | 5 月 | 6 月 | 7 月 | 8 月 | 9 月 | 10 月 | 11 月 | 12 月 |
比率/% | 5 | 5 | 15 | 8 | 8 | 15 | 6 | 6 | 10 | 10 | 6 | 6 |
编制 时间段 | 股道 L1 | 股道 L2 | 月检/ 台次 | |||||||||
A | B1 | B2 | B3 | B4 | A | B1 | B2 | B3 | B4 | |||
1 月 | 892 ~ 946 /91 1052 ~ 1082 /96 | 898,1004 | 553 ~ 635 /134 | 561 | 324 | |||||||
2 月 | 260 ~ 360 /165 | 266,268, 270,272, 274,276, 278,280 | 264,268, 278,284 | 262,284, 350 | 259 ~ 353 /150 | 265,267, 269,271, 273,275, 277,279 | 263,267,277,281, 285 | 261,283, 349 | 346 | |||
3 月 | 362 ~ 474 /285 520 ~ 672 /273 | 562 | 355 ~ 457 /260 877 ~ 945 /126 | 897 | 946 | |||||||
4 月 | 674 ~ 816 /262 | 770 | 459 ~ 501 /86 771 ~ 829 /150 | 487,769 | 501 | |||||||
5 月 | 948 ~ 982 /82 818 ~ 890 /185 | 947 ~ 1001 /122 831 ~ 875 /115 | 1305 | 505 | ||||||||
6 月 | 984 ~ 1050 /184 1084 ~ 1178 /288 | 1494 | 1590 | 637 ~ 769 /201 1003 ~ 1089 /264 | 1487 | 1003 | 941 | |||||
7 月 | 1180 ~ 1212 /102 | 503 ~ 551 /125 1155 ~ 1203 /150 | 265,267, 269,271, 273,275, 277,279 | 263,267,267,281, 285 | 390 | |||||||
8 月 | 1214 ~ 1258 /138 | 1205 ~ 1283 /240 | 378 | |||||||||
9 月 | 476 ~ 518 /86 1260 ~ 1320 /186 | 266,268, 270,272, 274,276, 278,280 | 264,268, 278,284 | 488 | 1091 ~ 1153 /192 1285 ~ 1333 /150 | 627 | ||||||
10 月 | 1372 ~ 1496 /378 | 1335 ~ 1415 /246 | 1305 | 625 | ||||||||
11 月 | 1322 ~ 1370 /150 | 1417 ~ 1491 /222 | 1487 | 373 | ||||||||
12 月 | 1498 ~ 1590 /178 | 1494 | 1590 | 1488 | 1493 ~ 1589 /196 | 377 | ||||||
年检/ 台次 | 3129 | 2 | 16 | 10 | 9 | 3129 | 2 | 16 | 12 | 8 | 6333 |