Optimization on vibration reduction of longitudinal constraint system in suspension bridges based on KPSO algorithm
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摘要: 为实现运营期风和车流作用下悬索桥纵向约束体系减振优化，融合Kriging代理模型和具备全局寻优能力的粒子群优化(PSO)算法，构建了KPSO算法；基于已有风-车-桥耦合振动系统，分析了运营期正常风、随机车流、车流制动和台风作用下某大跨悬索桥的纵向振动特性，分析了刚性中央扣和变参数黏滞阻尼器等参数对悬索桥减振的敏感性；以梁端和塔顶纵向位移、吊索缆端-梁端相对纵向位移为指标，以指标累积值控制效率为目标，开展了不同权重系数的荷载水平下悬索桥纵向约束体系的减振优化设计。分析结果表明：算例中样本试验值和代理模型计算值间的估计误差均小于5%，构建的KPSO算法可为悬索桥纵向约束体系的最优化设计提供算法基础；刚性中央扣对吊索缆端-梁端相对纵向位移的减振控制显著，梁端阻尼器仅对梁端纵向位移和靠近梁端吊索的缆端-梁端相对纵向位移的减振控制显著，但不利于跨中短吊索的纵向减振，且短吊索缆端-梁端相对纵向位移均随阻尼系数增大而增大，随速度指数增大而减小；悬索桥纵向减振效率按刚性中央扣+阻尼器体系、仅有跨中刚性中央扣体系、仅有梁端阻尼器体系的顺序依次减小。由此可见，综合考虑阻尼力最小原则，建议悬索桥采用刚性中央扣+阻尼器[1.0 MN·(m·s-1)-0.2]的纵向约束体系。Abstract: To achieve optimization on vibration reduction of the longitudinal constraint system in the suspension bridge under the wind and traffic flow loads during operation, the Kriging-particle swarm optimization (KPSO) algorithm was constructed by integrating the Kriging surrogate model and the particle swarm optimization (PSO) algorithm with global optimization capability. Based on the existing wind-vehicle-bridge coupling vibration system, the longitudinal vibration characteristics of a large-span suspension bridge under normal wind, random traffic flow, traffic flow braking, and typhoon loads during operation were analyzed. The parameter sensitivity of the rigid central buckle and the variable parameter viscous damper to vibration reduction of the suspension bridge was analyzed. By taking the longitudinal displacement at girder end and tower top, as well as the relative longitudinal displacement at suspender cable end and girder end, as the indicators and taking the control efficiency of the cumulative value of the indicators as the goal, the vibration reduction optimization design of the longitudinal constraint system in the suspension bridge under different weight coefficients of load levels was carried out. The analysis results show that the estimation error between the sample test value and the calculated value obtained from the surrogate model is less than 5% in the case, indicating that the constructed KPSO algorithm can provide an algorithmic basis for the optimal design of the longitudinal constraint system in suspension bridges. The rigid central buckle has a significant vibration reduction control effect on the relative longitudinal displacement at suspender cable end and girder end, while the damper at girder end only has a significant vibration reduction control effect on the longitudinal displacement at girder end and the relative longitudinal displacement at cable end and girder end of suspenders near the girder end. However, it is not conducive to the longitudinal vibration reduction of short suspenders in mid span, and the relative longitudinal displacement at the short suspender cable end and girder end increases with a rising damping coefficient and decreases with a higher velocity index. The longitudinal vibration reduction efficiency of suspension bridges in descending order is as follows: rigid central buckle+damper system, only rigid central buckle system in mid span, and only damper system at girder end. Therefore, according to the principle of minimum damping force, the longitudinal constraint system of rigid central buckle+damper [1.0 MN·(m·s-1)-0.2] for the suspension bridge is recommended.
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图 5 变参数黏滞阻尼器本构关系模型
Figure 5. Constitutive relationship model of variable parameter viscoelastic damper
图 7 悬索桥风场模拟点分布
Figure 7. Distribution of wind field simulation points for suspension bridge
图 9 42节点脉动风速时程模拟结果
Figure 9. Simulation results of fluctuating wind speed time- history at node 42
图 12 TS39缆梁纵向相对位移时程
Figure 12. Cable-girder longitudinal relative displacement time-history of TS39
图 16 不同阻尼系数下缆梁纵向相对位移最值
Figure 16. Cable-girder longitudinal relative displacement maximum under different damping coefficients
图 17 不同速度指数下缆梁纵向相对位移最值
Figure 17. Cable-girder longitudinal relative displacement maximum under different speed indices
图 19 不同工况下迭代次数与适应度值的关系
Figure 19. Relationship of iteration and fitness value under different working conditions
表 1 悬索桥频率计算值与实测值
Table 1. Values of calculated frequency and measured of a suspension bridge
模态 理论计算频率f1/Hz 实测频率f2/Hz 相对误差(f2-f1)f2-1/% 一阶横弯 正对称 0.096 72 0.100 3.28 一阶竖弯 正对称 0.166 03 0.164 1.24 一阶扭转 反对称 0.343 40 0.375 8.43 一阶竖弯伴随纵飘 0.138 36 0.129 7.26 
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表 2 设计变量x1代表值
Table 2. Represent values of design variable x1
MN 参数x1 水平1 水平2 水平3 水平4 水平5 代表值 1.0 1.5 2.0 2.5 3.0 备注 梁端阻尼器阻尼系数参数取值
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表 3 设计变量x2代表值
Table 3. Represent values of design variable x2
参数x2 水平1 水平2 水平3 水平4 水平5 水平6 水平7 水平8 代表值 0.1 0.2 0.3 0.4 0.5 刚性中央扣 刚性中央扣+阻尼器(x1, 0.1) 刚性中央扣+阻尼器(x2, 0.2)
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表 4 不同工况的加权系数组合
Table 4. Weighted coefficient combinations under different working conditions
工况 加权系数 备注 w1 w2 w3 工况Ⅰ 1.0 0.0 0.0 仅考虑风-随机车流联合 工况Ⅱ 0.9 0 0.1 考虑风-随机车流联合及车流制动工况 工况Ⅲ 0.9 0.1 0.0 考虑风-随机车流联合及台风工况 工况Ⅳ 0.8 0.1 0.1 同时考虑风-随机车流联合、车流制动工况、台风工况 工况Ⅴ 0.7 0.0 0.3 考虑风-随机车流联合及车流制动工况 工况Ⅵ 0.7 0.3 0.0 考虑风-随机车流联合及台风工况
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表 5 不同工况下纵向约束体系减振优化参数
Table 5. Optimization parameters for vibration reduction of longitudinal constraint system under different working conditions
工况 x1 x2水平值 控制效率/% 工况Ⅰ 1.074 7.51 93.19 工况Ⅱ 1.088 7.51 94.71 工况Ⅲ 1.055 7.52 86.99 工况Ⅳ 1.067 7.52 88.51 工况Ⅴ 1.140 7.50 96.96 工况Ⅵ 1.021 7.53 74.61
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[1] 王浩, 李爱群, 杨玉冬, 等. 中央扣对大跨悬索桥动力特性的影响[J]. 中国公路学报, 2006, 19(6): 49-53.WANG Hao, LI Ai-qun, YANG Yu-dong, et al. Influence of central buckle on dynamic behavior of long-span suspension bridge[J]. China Journal of Highway and Transport, 2006, 19(6): 49-53. [2] 王浩, 李爱群. 中央扣对大跨度悬索桥风致抖振响应的影响[J]. 土木工程学报, 2009, 42(7): 78-84.WANG Hao, LI Ai-qun. Influence of central buckle on wind- induced buffeting response of long-span suspension bridges[J]. China Civil Engineering Journal, 2009, 42(7): 78-84. [3] 焦常科, 李爱群, 王浩, 等. 中央扣对三塔悬索桥地震反应的影响[J]. 东南大学学报(自然科学版), 2010, 40(1): 160-164.JIAO Chang-ke, LI Ai-qun, WANG Hao, et al. Influence of central buckle on seismic response of triple-tower suspension bridges[J]. Journal of Southeast University (Natural Science Edition), 2010, 40(1): 160-164. [4] 徐勋, 强士中, 贺拴海. 中央扣对大跨悬索桥动力特性和汽车车列激励响应的影响[J]. 中国公路学报, 2008, 21(6): 57-63.XU Xun, QIANG Shi-zhong, HE Shuan-hai. Influence of central buckle on dynamic behavior and response of long-span suspension bridge under vehicle group excitation[J]. China Journal of Highway and Transport, 2008, 21(6): 57-63. [5] 徐勋, 强士中. 中央扣对大跨悬索桥动力特性和地震响应的影响研究[J]. 铁道学报, 2010, 32(4): 84-91.XU Xun, QIANG Shi-zhong. Influence of central buckle on dynamic behavior and seismic response of long-span suspension bridge[J]. Journal of the China Railway Society, 2010, 32(4): 84-91. [6] 彭旺虎, 邵旭东. 设置中央扣悬索桥的扭转自振分析[J]. 中国公路学报, 2013, 26(5): 76-87.PENG Wang-hu, SHAO Xu-dong. Analysis of free torsional vibration of suspension bridges with center ties[J]. China Journal of Highway and Transport, 2013, 26(5): 76-87. [7] 王连华, 孙璋鸿, 崔剑锋, 等. 车辆激励下中央扣对悬索桥梁端位移的影响[J]. 湖南大学学报(自然科学版), 2019, 46(3): 18-24.WANG Lian-hua, SUN Zhang-hong, CUI Jian-feng, et al. Effects of central buckle on end displacement of suspension bridges under vehicle excitation[J]. Journal of Hunan University (Natural Sciences), 2019, 46(3): 18-24. [8] LIU Z, GUO T, HUANG L, et al. Fatigue life evaluation on short suspenders of long-span suspension bridge with central clamps[J]. Journal of Bridge Engineering, 2017, 22(10): 04017074. [9] 赵国辉, 高建华, 刘健新, 等. 悬索桥线性液体黏滞阻尼器阻尼系数优化[J]. 交通运输工程学报, 2013, 13(3): 33-39. doi: 10.19818/j.cnki.1671-1637.2013.03.005 ZHAO Guo-hui, GAO Jian-hua, LIU Jian-xin, et al. Damping coefficient optimization of linear fluid viscous damper for suspension bridge[J]. Journal of Traffic and Transportation Engineering, 2013, 13(3): 33-39. doi: 10.19818/j.cnki.1671-1637.2013.03.005 [10] 胡国辉. 大跨度混合梁斜拉桥地震响应分析及阻尼器参数优化[D]. 成都: 西南交通大学, 2017.HU Guo-hui. Seismic response analysis of long-span hybrid girder cable-stayed bridge and its optimization of damper parameters[D]. Chengdu: Southwest Jiaotong University, 2017. [11] 王波, 马长飞, 刘鹏飞, 等. 基于随机地震响应的斜拉桥粘滞阻尼器参数优化[J]. 桥梁建设, 2016, 46(3): 17-22.WNAG Bo, MA Chang-fei, LIU Peng-fei, et al. Parameter Optimization of viscous damper for cable-stayed bridge based on stochastic seismic responses[J]. Bridge Construction, 2016, 46(3): 17-22. [12] XU X, LI Z, LIU W, et al. Investigation of the wind-resistant performance of seismic viscous dampers on a cable-stayed bridge[J]. Engineering Structures, 2017, 145: 283-292. [13] 梁剑青, 欧进萍. 大跨斜拉桥桥面风致抖振的粘滞阻尼控制分析[J]. 地震工程与工程振动, 2006, 26(1): 139-144.LIANG Jian-qing, OU Jin-ping. Lateral buffeting control of long-span cable-stayed bridge deck by viscous dampers[J]. Earthquake Engineering and Engineering Vibration, 2006, 26(1): 139-144. [14] NIE L, SONG H, FAN L. Discussion on effects of fluid viscous damper on protecting function for expansion joints in long span bridges[J]. Journal of Earthquake Engineering and Engineering Vibration, 2007, 27(2): 131-136. [15] YANG M G, YANG Z Q. Investigation concerning vibration reduction of self-anchored suspension bridge under vehicle braking forces[J]. Advanced Materials Research, 2011, 163: 2689-2692. [16] YANG M G, YANG Z Q. Longitudinal vibration control of floating system bridge subject to vehicle braking force with viscous dampers[J]. Advanced Materials Research, 2012, 446: 1256-1260. [17] GUO T, LIU J, ZHANG Y, et al. Displacement monitoring and analysis of expansion joints of long-span steel bridges with viscous dampers[J]. Journal of Bridge Engineering, 2015, 20(9): 04014099. [18] GUO T, LIU J, HUANG L. Investigation and control of excessive cumulative girder movements of long-span steel suspension bridges[J]. Engineering Structures. 2016, 125: 217-226. [19] GUO T, UUANG L, LIU J, et al. Damage mechanism of control springs in modular expansion joints of long-span bridges[J]. Journal of Bridge Engineering, 2018, 23(7): 04018038. [20] 吕龙, 李建中. 粘滞阻尼器对地震、列车制动和运行作用下公铁两用斜拉桥振动控制效果分析[J]. 工程力学, 2015, 32(12): 139-146.LYU Long, LI Jian-zhong. Study on vibration control effect of viscous dampers for rail-cum-road cable-stayed bridge during earthquake, train braking and running[J]. Engineering Mechanics, 2015, 32(12): 139-146. [21] 吕龙, 李建中. 列车制动和运行下大跨度公铁两用斜拉桥纵向振动分析[J]. 铁道学报, 2017, 39(3): 90-95.LYU Long, LI Jian-zhong. Study on longitudinal vibration of longs-pan rail-cum-road cable-stayed bridge induced by train braking and running[J]. Journal of the China Railway Society, 2017, 39(3): 90-95. [22] 吕龙, 薛小强. 列车制动力对大跨度铁路斜拉桥地震响应影响[J]. 地震工程与工程振动, 2018, 38(4): 180-185.LYU Long, XUE Xiao-qiang. Influence of train braking force on seismic response of long-span railway cable-stayed bridges[J]. Earthquake Engineering and Engineering Vibration, 2018, 38(4): 180-185. [23] 吕江, 张仲勇, 宋腾腾, 等. 新型多功能粘滞阻尼器研究及应用[J]. 世界桥梁, 2020, 48(6): 60-63.LYU Jiang, ZHANG Zhong-yong, SONG Teng-teng, et al. Study and application of a new-type multifunctional viscous damper[J]. World Bridges, 2020, 48(6): 60-63. [24] 马长飞, 汪正兴, 王波, 等. 武汉杨泗港长江大桥变参数粘滞阻尼约束体系研究[J]. 桥梁建设, 2019, 49(增1): 45-50.MA Chang-fei, WANG Zheng-xing, WANG Bo, et al. Study of viscous damping system with variable parameters for Yangsigang changjiang river bridge in Wuhan[J]. Bridge Construction, 2019, 49(S1): 45-50. [25] LIANG L, FENG Z, XU Y, et al. A parallel scheme of friction dampers and viscous dampers for girder-end longitudinal displacement control of a long-span suspension bridge under operational and seismic conditions[J]. Buildings, 2023, 13(2): 412. [26] HU S, HU R, YANG M, et al. Seismic behavior of the combined viscous-steel damping system for a long-span suspension bridge considering wave-passage effect[J]. Journal of Bridge Engineering, 2023, 28(7): 04023034. [27] ZHAO Y, HUANG P, LONG G, et al. Influence of fluid viscous damper on the dynamic response of suspension bridge under random traffic load[J]. Advances in Civil Engineering, 2020(1): 1857378. [28] 韩万水. 风-汽车-桥梁系统空间耦合振动研究[D]. 上海: 同济大学, 2006.HAN Wan-shui. Three-dimensional coupling vibration of wind-vehicle-bridge system[D]. Shanghai: Tongji University, 2006. [29] 武隽, 刘焕举, 黄平明, 等. 大跨桥梁台风风场全过程动态数值模拟[J]. 振动与冲击, 2019, 38(14): 260-266.WU Jun, LIU Huan-ju, HUANG Ping-ming, et al. Numerical simulation on the whole dynamic process of a typhoon field passing through a long span bridge[J]. Journal of Vibration and Shock, 2019, 38(14): 260-266. [30] 李光玲, 韩万水, 张路, 等. 极端制动车载下悬索桥伸缩缝服役状态评估[J]. 振动与冲击, 2022, 41(15): 186-195, 251.LI Guang-ling, HAN Wan-shui, ZHANG Lu, et al. Service state evaluation for expansion joints of suspension bridge under extreme vehicle braking load[J]. Journal of Vibration and Shock, 2022, 41(15): 186-195, 251. [31] 陈静, 唐傲天, 刘震, 等. 一种基于Kriging模型加点策略的多目标粒子群优化算法[J]. 吉林大学学报(理学版), 2020, 58(5): 1159-1166.CHEN Jing, TANG Ao-tian, LIU Zhen, et al. A multi-objective particle swarm optimization algorithm based on Kriging model infilling strategy[J]. Journal of Jilin University (Science Edition), 2020, 58(5): 1159-1166. [32] WANG Y, MA C, WANG C, et al. Characteristics analysis and optimization design of bridge crane based on improved particle swarm optimization algorithm[J]. Journal of Low Frequency Noise, Vibration and Active Control, 2023, 42(1): 253-271. [33] 王英杰, 楚杭, 陈云峰, 等. 基于GM(1, 1)模型与相关向量机的轨道不平顺区间预测[J]. 交通运输工程学报, 2023, 23(6): 135-145. doi: 10.19818/j.cnki.1671-1637.2023.06.007WANG Ying-jie, CHU Hang, CHEN Yun-feng, et al. Interval prediction of track irregularity based on GM(1, 1) model and relevance vector machine[J]. Journal of Traffic and Transportation Engineering, 2023, 23 (6): 135-145. doi: 10.19818/j.cnki.1671-1637.2023.06.007 [34] LIU Z, GUO T, HEBDON M H, et al. Corrosion fatigue analysis and reliability assessment of short suspenders in suspension and arch bridges[J]. Journal of Performance of Constructed Facilities, 2018, 32(5): 04018060. [35] SUN Z, NING S, SHEN Y. Failure investigation and replacement implementation of short suspenders in a suspension bridge[J]. Journal of Bridge Engineering, 2017, 22(8): 05017007. -
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