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Article(id=1227614517178331295, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.04.001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1656432000000, receivedDateStr=2022-06-29, revisedDate=1660147200000, revisedDateStr=2022-08-11, acceptedDate=null, acceptedDateStr=null, onlineDate=1770615708870, onlineDateStr=2026-02-09, pubDate=1714233600000, pubDateStr=2024-04-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770615708870, onlineIssueDateStr=2026-02-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770615708870, creator=13701087609, updateTime=1770615708870, updator=13701087609, issue=Issue{id=1227614514896634485, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='4', pageStart='539', pageEnd='728', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770615708325, creator=13701087609, updateTime=1770795248114, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228367559410512191, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228367559410512192, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=539, endPage=547, ext={EN=ArticleExt(id=1227614517438378146, articleId=1227614517178331295, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Representation of dynamic performance of stay cables driven by self-excited non-stationary vibration data, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Stay cables of cross-sea cable-stayed bridges will generate self-excited vibrations in non-extreme wind environments. Based on technologies of modern monitoring and data analysis，the digital features of the self-excited vibration of the stay cable can be captured immediately，and the real-time performance of dynamics about stay cables can be reflected accordingly. According to features of commonality in the long-term monitoring data of vibrating acceleration of stay cables from a main channel cable-stayed bridge of a cross-sea bridge，an automatic extraction method for the non-stationary sections of wind-induced self-excited vibration of the stay cable is proposed based on the vibrating acceleration time series signal’s Gaussian mixture model of the upper envelope and the power spectrum of the frequency domain. The strategies，that identify the dominant frequency based on the non-stationary time series of self-excited vibration，then identify the damping ratio using the data of the last descent section after band-pass filtering，are proposed. By the proposed strategies，the interference on the damping ratio identification from energy brought by the natural excitation of the ambient wind in the ascent sections of the vibration amplitude is excluded. Based on the identified results of dominant frequency-damping ratio in the non-stationary sections of the self-excited vibration，data clusters of the modal frequency-damping ratio corresponding to each order of the vibrating mode are obtained by clustering the frequency values. According to the discrete and skewed characteristics of the damping ratio data，the statistical law of using the eμ of log-normal distribution model and the quantile value of its cumulative distribution function to describe damping ratio of stay cables is proposed. The frequency centroid of each cluster，as well as the probability characteristic parameter of damping ratio are used as indicators to represent the current state of the dynamic performance of stay cables. The main conclusions for the background engineering include： the signal of vibrating acceleration of stay cables on the bridge has strong noise and large interference，they must be eliminated in the analysis of dynamic characteristic； the amplitude maximum of the acceleration of the self-excited vibration of the bridge’s stay cable has exceeded 3000 mm/s2，the vibration amplitude is large； the average level of the damping ratio of the bridge’s stay cable is about 0.03%，which is lower than the recommended value of the design code.

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跨海斜拉桥的拉索在非极端风环境下会产生自激振动，基于现代监测与数据分析技术可即时把握拉索自激振动的数字特征，并以此反映拉索的实时动力性能。根据某跨海大桥主航道斜拉桥拉索振动加速度长期监测数据中的共性特征，提出基于振动加速度时间序列信号上包络线高斯混合模型和频域功率谱的拉索风致自激振动非平稳段自动提取方法。提出基于各自激振动非平稳时间序列进行主导频率识别，并采用带通滤波后的最后1个下降段数据进行阻尼比识别的策略，排除了振动幅值上升段环境风自然激励带入能量对阻尼比识别的干扰。基于各自激振动非平稳段主导频率-阻尼比的识别结果，通过对频率值进行聚类，得到各阶模态对应的模态频率-阻尼比数据簇。根据阻尼比数据的离散、偏态特征提出采用对数正态分布模型的eμ和其累积分布函数的分位值来描述拉索阻尼比统计规律。采用各数据簇的频率质心以及阻尼比概率特征参数作为表征拉索动力性能当前状态的指标。针对背景工程的主要结论包括：桥梁拉索振动加速度信号噪声强、干扰大，在动力特征分析时须排除类似干扰；桥梁拉索的自激振动加速度幅值最高已超过3000 mm/s2，振动幅度较大；桥梁拉索的阻尼比平均水平约为0.03%，与设计规范推荐值相比偏低。

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丁幼亮（1979―），男，博士，研究员，博士生导师。 E-mail： 。
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赵瀚玮（1990—），男，博士，副研究员，硕士生导师。 E-mail： 。

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赵瀚玮（1990—），男，博士，副研究员，硕士生导师。 E-mail： 。

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赵瀚玮（1990—），男，博士，副研究员，硕士生导师。 E-mail： 。

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articleId=1227614517178331295, language=CN, label=图6, caption=1年内拉索模态参数的特征分析, figureFileSmall=DUV9MbQxgj0Mm7BqPncYoA==, figureFileBig=TnJkXKvRGmNotTPadOb5Tg==, tableContent=null), ArticleFig(id=1227639781434257812, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517178331295, language=EN, label=Tab.1, caption=

Centroid value of each cluster （order） about identified modal frequency data（Unit： Hz）

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第1阶(簇2)第2阶(簇9)第3阶(簇4)第4阶(簇6)第5阶(簇10)第6阶(簇7)第7阶(簇11)第8阶(簇5)第9阶(簇3)第10阶(簇8)第11阶(簇1)
5.55416.48377.41878.35049.284910.223811.164612.109213.053514.016914.9539
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识别各簇（阶）模态频率数据的质心（单位： Hz）

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第1阶(簇2)第2阶(簇9)第3阶(簇4)第4阶(簇6)第5阶(簇10)第6阶(簇7)第7阶(簇11)第8阶(簇5)第9阶(簇3)第10阶(簇8)第11阶(簇1)
5.55416.48377.41878.35049.284910.223811.164612.109213.053514.016914.9539
), ArticleFig(id=1227639781623001500, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517178331295, language=EN, label=Tab.2, caption=

Estimated value of probability characteristic parameters of the damping ratio of stay cables（Unit： %）

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eμCDF的0.05分位值CDF的0.1分位值CDF的0.9分位值CDF的0.95分位值
全部阻尼比数据0.03060.01140.01420.06590.0820
聚类簇7的阻尼比数据0.03200.01140.01430.07140.0897
), ArticleFig(id=1227639781719470494, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614517178331295, language=CN, label=表2, caption=

拉索阻尼比概率特征参数估计值（单位： %）

, figureFileSmall=null, figureFileBig=null, tableContent=
eμCDF的0.05分位值CDF的0.1分位值CDF的0.9分位值CDF的0.95分位值
全部阻尼比数据0.03060.01140.01420.06590.0820
聚类簇7的阻尼比数据0.03200.01140.01430.07140.0897
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自激非平稳振动数据驱动的拉索动力性能表征
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赵瀚玮 1, 2 , 丁幼亮 1, 2 , 李爱群 2, 3 , 张小楠 2 , 王智文 2, 4
振动工程学报 | 2024,37(4): 539-547
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振动工程学报 | 2024, 37(4): 539-547
自激非平稳振动数据驱动的拉索动力性能表征
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赵瀚玮1, 2 , 丁幼亮1, 2 , 李爱群2, 3, 张小楠2, 王智文2, 4
作者信息
  • 1东南大学混凝土及预应力混凝土结构教育部重点实验室, 江苏　南京　210096
  • 2东南大学土木工程学院,江苏　南京　210096
  • 3北京建筑大学北京未来城市设计高精尖创新中心, 北京　100044
  • 4深圳高速工程顾问有限公司, 广东　深圳　518049

    • 赵瀚玮（1990—），男，博士，副研究员，硕士生导师。 E-mail： 。

通讯作者:

丁幼亮（1979―），男，博士，研究员，博士生导师。 E-mail： 。
Representation of dynamic performance of stay cables driven by self-excited non-stationary vibration data
Han-wei ZHAO1, 2 , You-liang DING1, 2 , Ai-qun LI2, 3, Xiao-nan ZHANG2, Zhi-wen Wang2, 4
Affiliations
  • 1Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education，Southeast University，Nanjing 210096，China
  • 2School of Civil Engineering，Southeast University，Nanjing 210096，China
  • 3Beijing Advanced Innovation Center for Future Urban Design，Beijing University of Civil Engineering and Architecture，Beijing 100044，China
  • 4Shenzhen Expressway Engineering Consultants Co.，Ltd.，Shenzhen 518049，China
出版时间: 2024-04-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.04.001
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摘要
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跨海斜拉桥的拉索在非极端风环境下会产生自激振动，基于现代监测与数据分析技术可即时把握拉索自激振动的数字特征，并以此反映拉索的实时动力性能。根据某跨海大桥主航道斜拉桥拉索振动加速度长期监测数据中的共性特征，提出基于振动加速度时间序列信号上包络线高斯混合模型和频域功率谱的拉索风致自激振动非平稳段自动提取方法。提出基于各自激振动非平稳时间序列进行主导频率识别，并采用带通滤波后的最后1个下降段数据进行阻尼比识别的策略，排除了振动幅值上升段环境风自然激励带入能量对阻尼比识别的干扰。基于各自激振动非平稳段主导频率-阻尼比的识别结果，通过对频率值进行聚类，得到各阶模态对应的模态频率-阻尼比数据簇。根据阻尼比数据的离散、偏态特征提出采用对数正态分布模型的eμ和其累积分布函数的分位值来描述拉索阻尼比统计规律。采用各数据簇的频率质心以及阻尼比概率特征参数作为表征拉索动力性能当前状态的指标。针对背景工程的主要结论包括：桥梁拉索振动加速度信号噪声强、干扰大，在动力特征分析时须排除类似干扰；桥梁拉索的自激振动加速度幅值最高已超过3000 mm/s2，振动幅度较大；桥梁拉索的阻尼比平均水平约为0.03%，与设计规范推荐值相比偏低。

结构健康监测  /  桥梁拉索  /  自激振动  /  动力性能表征  /  非平稳行为

Stay cables of cross-sea cable-stayed bridges will generate self-excited vibrations in non-extreme wind environments. Based on technologies of modern monitoring and data analysis，the digital features of the self-excited vibration of the stay cable can be captured immediately，and the real-time performance of dynamics about stay cables can be reflected accordingly. According to features of commonality in the long-term monitoring data of vibrating acceleration of stay cables from a main channel cable-stayed bridge of a cross-sea bridge，an automatic extraction method for the non-stationary sections of wind-induced self-excited vibration of the stay cable is proposed based on the vibrating acceleration time series signal’s Gaussian mixture model of the upper envelope and the power spectrum of the frequency domain. The strategies，that identify the dominant frequency based on the non-stationary time series of self-excited vibration，then identify the damping ratio using the data of the last descent section after band-pass filtering，are proposed. By the proposed strategies，the interference on the damping ratio identification from energy brought by the natural excitation of the ambient wind in the ascent sections of the vibration amplitude is excluded. Based on the identified results of dominant frequency-damping ratio in the non-stationary sections of the self-excited vibration，data clusters of the modal frequency-damping ratio corresponding to each order of the vibrating mode are obtained by clustering the frequency values. According to the discrete and skewed characteristics of the damping ratio data，the statistical law of using the eμ of log-normal distribution model and the quantile value of its cumulative distribution function to describe damping ratio of stay cables is proposed. The frequency centroid of each cluster，as well as the probability characteristic parameter of damping ratio are used as indicators to represent the current state of the dynamic performance of stay cables. The main conclusions for the background engineering include： the signal of vibrating acceleration of stay cables on the bridge has strong noise and large interference，they must be eliminated in the analysis of dynamic characteristic； the amplitude maximum of the acceleration of the self-excited vibration of the bridge’s stay cable has exceeded 3000 mm/s2，the vibration amplitude is large； the average level of the damping ratio of the bridge’s stay cable is about 0.03%，which is lower than the recommended value of the design code.

structural health monitoring  /  stay cables of bridge  /  self-excited vibration  /  representation of dynamic performance  /  non-stationary behavior
赵瀚玮, 丁幼亮, 李爱群, 张小楠, 王智文. 自激非平稳振动数据驱动的拉索动力性能表征. 振动工程学报, 2024 , 37 (4) : 539 -547 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.04.001
Han-wei ZHAO, You-liang DING, Ai-qun LI, Xiao-nan ZHANG, Zhi-wen Wang. Representation of dynamic performance of stay cables driven by self-excited non-stationary vibration data[J]. Journal of Vibration Engineering, 2024 , 37 (4) : 539 -547 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.04.001
正文
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引言
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跨海斜拉桥的拉索在非极端风环境下会产生自激振动［1］，经常性的高幅自激振动虽然不会立即引起拉索或桥梁整体的脆性破坏，但可能会使拉索产生累积损伤，给桥梁的安全服役埋下隐患。为避免此类风险的发生，需要在线监控拉索风致自激振动行为，并进一步基于数据进行拉索动力性能实时表征。
计算理论是结构动力响应与特征研究的基础，早期学者们常对缆索承重桥梁及其索杆的动力学计算与模拟方法进行研究。胡俊等［2］建立了东海某大桥吊索在极值风荷载作用下的受力与可靠度特征。李寿英等［3］推导了西堠门大桥双吊索的运动微分方程并提出了有效的振动抑制方法。徐彦青等［4］采用数值模拟方法分析了设有阻尼装置的拉索的响应行为特征。YAN等［5］研究了不同边界条件的拉索模态计算与分析方法，并进一步提出了拉索的索力简化识别方案。朱金等［6］基于风-浪-车-桥数值模拟平台结果预测了随机车流-风联合作用下沿海大跨度斜拉桥拉索疲劳寿命。
理论计算虽然可以较为准确地模拟缆索承重桥梁及其索杆的风致动力学行为，但却无法考虑计算理论未知或难以模拟的因素。因此，学者们开始基于实验室试验结果探究结构风致响应机理与影响因素。华旭刚等［7-8］融合计算理论与风洞试验结果探讨了大跨度悬索桥的多阶模态竖向涡振特征及相关控制方法，进一步分析了并列耦合双吊索结构阻尼比与气动负阻尼的影响因素。GAO等［9］在风洞试验中复现了拉索多模态涡激振动和多模态风雨振的过程，并分析了水线对拉索风致振动的影响。刘庆宽等［10］和孙一飞等［11］对3种长短轴之比的微椭圆拉索模型进行测力和测振风洞试验，分析了其风致振动特性、驰振机理和响应时频特征。陈炜等［12］以矮寨大桥为背景工程，研究了设置减振架的双索股耦合振动模态特征。
实验室试验结果虽然可以帮助学者们确定缆索承重桥梁及其索杆风致振动的影响因素，但受限于试件的缩尺效应和测试后分析的非实时效应，难以反映结构风致振动的实时特征与演化过程。得益于测试、传输和数据分析理论的发展，一些学者开始借助结构健康监测（SHM）系统数据研究索杆在真实风环境下的振动行为与特征。WANG等［13］基于风速、加速度实测数据研究了苏通斜拉桥的风环境湍流特征与抖振响应特征。CANTERO等［14］基于多类时频信号处理方法探究并验证了吊索涡激振动与激励风环境脱落频率的相关性特征。HUA等［15］基于斜拉桥原型监测数据探讨了拉索风雨振的起振机理。GE等［16］基于长期健康监测数据总结了苏通大桥拉索风雨振的特征，并讨论了桥上车辆荷载对风雨振过程的影响程度。祝志文等［17］研究了洞庭湖大桥加劲索的涡激振动过程及其各模态分量信号的时、频域特征。刘宗杰等［18］基于长期监测数据分析了荆岳长江大桥风场特性与拉索振动时、频域特征参数之间的相关性和演化特征。HWANG等［19］识别和分析了大跨斜拉桥拉索的长期阻尼比特征和概率演化特征。
近年来，随着数据处理和机器学习理论的快速发展，一些学者开始尝试用相关方法研究大跨缆索承重桥梁的风致响应机理与特征［20-23］。但这些研究多是针对主梁构件的风致振动，针对缆、索、杆构件的研究较少。本文基于某跨海大桥主航道斜拉桥拉索的振动加速度长期监测数据，分析了拉索风致自激振动数据的时、频域共性特征，提出了一套风致自激振动非平稳数据驱动的拉索动力性能数字化表征方法，讨论了所得拉索多振动模态的频率-阻尼比参数的聚集与统计特征，并以此作为监控拉索实时动力性能的依据。
1　拉索自激振动数据共性特征
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本文以某跨海大桥主航道斜拉桥为背景工程，分析拉索在非极端风环境下的自激振动特征。背景工程桥梁为（110+236+458+236+110） m双塔空间双索面钢箱梁斜拉桥，桥塔采用钢筋混凝土框架结构。拉索的设计抗拉强度为1860 MPa，由多根7 mm高强度、低松弛平行镀锌钢丝组成［24］。背景工程桥梁上、下游索面的12×2根拉索分别安装了加速度计，拉索加速度计布置情况如图1所示，图中括号里的数字表示该处加速度计的数目。根据该桥拉索主要固有频率所处范围的设计资料，拉索加速度计采样频率设置为50 Hz，其安装位置距离桥面5 m，测点下方垂直距离约1.5 m处设置有外置阻尼器，主梁与拉索的锚固端安装有内置阻尼器。
由于各拉索在运营风环境下的振动特征相似，本文选取传感器测试结果较好的桥梁主跨香港侧1/4跨下游侧的拉索加速度计2020年全年的数据作为研究和分析的对象。图2中给出了2020年1—5月拉索振动加速度时间序列数据的信号特征。从图2（a）中可以发现：背景工程桥梁在运营风环境下的拉索振动加速度呈现非平稳段和平稳段交替出现的特征，其中，平稳段指代白噪声及类白噪声环境下的低幅振动数据段，非平稳段指代风荷载等环境作用下的高幅异常自激振动数据段。需要指出：平稳和非平稳是一个模糊的界定概念，不同信噪比的传感器和SHM系统的界定标准各不相同，后文会提到界定临界值的确定方法。可以注意到：由于实桥监测时干扰因素众多，振动加速度时间序列中会出现时间超过6 h的持续高幅非平稳振动信号。基于前人研究［25］，运营风环境作用下拉索自激振动难以保持长时间的持续高幅振动过程，故该类非平稳振动信号可认为是高水平噪声干扰混叠真实风致非平稳自激振动产生的信号特征。需要说明的是：本文所述的噪声是广义噪声，包括传感器及SHM系统设备自身、传感器与拉索固定不牢靠、极端复杂风环境或车载产生的多模态耦合受迫振动等一系列因素造成的扰动。图2（b）为图2（a）中点划线框数据的细节展示图，根据加速度数据采样频率可换算出该段数据历时约为7天，运营风环境难以使一根拉索产生持续7天的高幅振动；图2（c）为（a）中短虚线框数据的细节展示图，为一段典型的低噪声水平时间序列，其中的非平稳振动与平稳振动可以根据结构动力学专业知识被明确地辨识。进一步，采用快速傅里叶变换对图2中的典型时间序列数据进行频域功率谱分析，图3（a）为2（b）中长虚线圈中时间序列数据的频域功率谱；图3（b）为2（c）中典型单个非平稳段数据的频域功率谱；图3（c）为2（c）中典型平稳段数据的频域功率谱。
结合图2，3可以发现：高噪声水平下的拉索振动加速度时间序列数据和低噪声水平下的拉索振动加速度时间序列的平稳段数据，在频域中均呈现多个频率点同时处于高能量状态的特征；而低噪声水平下的拉索振动加速度时间序列的非平稳段数据，在频域中均呈现某一频率相比其余频率带处于更高能量状态的特征。图3中所示频域特征为所选取的较为明显的数据分析结果，通过大量分析，发现低噪声水平下的拉索振动加速度时间序列的非平稳段数据，在频域基本服从某一频率功谱率密度值大于其余频率带功率谱密度值2倍以上的特征。
综合本节分析可以发现该跨海大桥拉索自激振动的共性特征：
（1）在低噪声水平下，拉索的振动加速度时间序列信号存在多个独立非平稳振动段，各非平稳振动段的时域特征是其振动幅值远大于白噪声下的振动幅值，而各非平稳振动段的频域特征是其振动能量在某一频率明显大于其它频率带的振动能量。
（2）在高噪声水平下，由于广义噪声的干扰，拉索的振动加速度时间序列信号在时域上存在长时的高幅振动，且其频域特征是存在明显的多个高能量振动频率点；当然，此类振动加速度的高水平广义噪声的成因复杂，本文仅排除影响即可。
（3）拉索的振动加速度幅值最高已超过3000 mm/s2（见图2（a）中的最大振幅值），振动幅度较大，可能已处于阻尼不足的状态。
对于低噪声水平的情况，时间序列数据频域功率谱中各峰值对应的频率值理论上应为拉索的某阶固有频率。需要解释的是，运营状态下的桥梁或其构件（如拉索）的某阶固有频率并不固定为某一确定值，这是因为环境温度等外部因素会使其在长期运营过程中产生轻微变化。
2　拉索动力特征数字化识别
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2.1　自激振动非平稳段自动提取
基于上一节的分析可以发现：低噪声水平下的拉索自激非平稳振动段由于其高幅值、准单频的特征，非常适合用于识别拉索模态频率、阻尼比等动力特征参数。有桥梁、结构动力学专业知识背景的人员能基于前述信号特征识别拉索自激非平稳振动段，但为了实现桥梁运维的数字化、智能化，本节以2020年全年拉索振动加速度时间序列数据为分析对象，提出一种拉索自激非平稳振动段的自动提取方法，并以1—3月数据为例进行展示，如图4所示。
（1）提取拉索的振动加速度时间序列信号，计算振动加速度时间序列信号在每个既定长度段（本例中以每500数据为一段）的最大值，采用三次样条插值方法基于各既定长度段的最大值对最大值位置外的其余采样点坐标位置进行插值，并以所得插值曲线结果为振动时间序列信号的上包络线数据，如图4（a）所示。
（2）使用高斯混合模型（GMM）拟合上包络线数据的概率密度分布如图4（b）和下式所示：
式中　 μi，σi和ϕi分别为第i阶单高斯分布的均值、标准差和权重拟合参数；K为高斯混合模型的总阶数。拟合结果需采用通用的拟合优度检验方法进行检验。
（3）将高斯混合模型中均值最小的1至数阶单高斯分布拟合参数定义为振动加速度信号的平稳数据的统计特征参数，本例中定义第1~2阶单高斯分布拟合参数为振动加速度信号的平稳数据的统计特征参数；在（-∞，∞）上使得第2阶单高斯分布曲线的积分值归一化为1，得到其概率密度曲线。
（4）对第2阶高斯分布概率密度曲线进行积分，得到其累积分布函数（CDF）曲线，令振动加速度信号中振动幅值小于等于α的概率具有β的保证率，如下式所示：
式中　 为分位值小于等于α时的第2阶单高斯分布CDF值。计算给定β逼近于1时的α值，则可认为α为平稳数据和非平稳数据幅值的临界值。本例中取β=99.9%，计算所得α=173.46 mm/s2。
（5）从振动加速度的时间序列信号中截取上包络线数据连续大于α的对应数据段，选取截取的数据段中时间长度大于预设长度且振动加速度信号最大值大于预设值的数据段；进一步对各数据段进行频谱分析，取频域功率谱中最大峰值能量密度大于第二大峰值能量密度2倍以上、明显峰值数小于8个的数据段，以去掉上一节中所述高噪声水平数据（参数设置原则由大量如图3（a）和（b）中的数据的共性特征确定，具体参数值可能因桥梁的不同而不同，但原理类似）；最终所得数据段可作为自激振动非平稳段的有效结果，如图4（c）所示，图中短虚线为振动加速度时间序列，实线为拉索自激振动非平稳段有效结果。
从图4（c）中可以发现，采用本节所提方法能有效提取低噪声水平下的自激振动非平稳段，而对于高噪声水平数据，则仅提取其最后一段或数段非平稳段，达到了预期目的。需要说明的是：本文的背景工程桥梁所处环境复杂，其SHM系统的白噪声水平不稳定。因此，其低噪声水平下的平稳信号幅值特征包含GMM模型的第1~2阶共两阶单高斯分布的拟合结果。对于SHM系统调试得较好的桥梁，平稳信号幅值特征一般仅为GMM模型的最低1阶单高斯分布拟合结果。
2.2　基于非平稳段的模态参数识别
在提取了有效的拉索自激振动非平稳段后，就可以基于非平稳段数据进行拉索的模态参数识别。本节提出一种基于各自激振动非平稳时间序列的模态参数识别方法，如图5所示，并以某段提取的拉索自激振动非平稳段有效结果为例进行过程讨论。
（1）对提取的非平稳振动响应数据进行频域功率谱分析，识别非平稳振动功率谱中能量最大的频率结果Fr，并以Fr为该段自激振动非平稳时间序列的主导频率，采用能量最大频率正负一定范围（本文根据图3（c）中所识别的拉索各阶固有频率间最小间距的0.2倍，取其为±0.1 Hz）的带通滤波器对非平稳振动数据进行滤波，如图5（a）和（b）所示。
（2）采用既定长度数据段（本文中以每50数据为一段）区域最大值三次样条插值的方法计算滤波后非平稳振动响应数据的上包络线，搜索上包络线的固定份数等分段（本文中等分为50段）中最大值大于整个上包络线最大值固定比例（本文根据大量数据分析结果的查验，取其为9/10）的多个局部最大值，以最后1个局部最大值开始到一定长度后的极小值点的上包络线数据为上包络线最后1个下降段，如图5（c）所示。
（3）根据上包络线的最后1个下降段位置确定相应位置滤波后非平稳振动的最后1个下降段数据，该段数据可视为拉索振动的准自由衰减过程；计算滤波后非平稳振动最后1个下降段数据的快速傅里叶变换结果并求其共轭复数，进而求两者乘积（即共轭频谱互谱密度［26］，其等效于互相关函数的频域变换）的快速傅里叶逆变换结果，从快速傅里叶逆变换结果的前一半数据中截取固定长度（本文中取80~180倍50/Fr）的数据构造脉冲响应函数，并将其最大值归一化为1。
（4）采用欠阻尼单自由度系统的经典指数衰减函数拟合归一化后的脉冲响应函数的计算公式如下式所示：
式中　 ζ为结构阻尼比；t为振动的时间自变量；φ为振动的初相位；fn为振动的频率，一般可取fn=Fr；。A为脉冲响应函数的幅值，由于脉冲响应函数已进行归一化，可直接令A=1。
拟合参数中的阻尼比ζ拟合值即为基于该自激振动非平稳响应数据的拉索阻尼比识别结果，如图5（d）所示。
通过上述过程，可对每段非平稳数据进行独立的模态参数识别，并得到拉索自激振动的频率和阻尼比识别结果数据。如数据量足够多，就可把握拉索自激振动频率和阻尼比的大数据特征。
3　模态参数分析与动力性能表征
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基于每段拉索自激非平稳数据所识别出的主导频率和阻尼比结果数据，可以把握拉索当前动力性能所处状态。本节对2020年全年内对象拉索的自激振动非平稳段有效结果所识别的主导频率和阻尼比数据进行分析。
对主导频率数据进行聚类，并关联阻尼比识别结果，便可得到如图6（a）所示的频率-阻尼比二维数据聚类图。由于拉索结构型式简单，其识别的模态频率不存在混叠，基于K-means聚类、层次聚类等通用聚类方法皆可，本文采用凝聚式层次聚类法［27］，在此不做赘述。图6（a）中的编号为基于凝聚式层次聚类算法的聚类簇簇号，各簇（阶）模态频率数据的质心［27］如表1所示。值得注意的是：图6（a）与表1中的识别频率阶数小于图3（c）中基于平稳振动信号的识别频率阶数，这是因为风环境并不会激起所有阶次的固有频率；然而，桥梁设计与运维中要重点关注这类易于被风环境激起的固有频率阶次；因此，拉索自激非平稳振动的各簇频率数据质心更适用于表征拉索的频域动力特征，各阶（簇）频率的质心值会随着数据的累积而更精确。从图6（a）中可以发现，各阶模态的频率识别结果集中度较高，而各阶模态的阻尼比识别结果分布相对离散，这符合结构模态频率和阻尼比识别的一般特征。考虑到阻尼比数据频率直方图的偏态特征（如图6（b）和（c）所示），本节提出采用对数正态分布对全部阻尼比数据和各阶模态阻尼比数据进行概率密度分布拟合，如下式所示：
式中　 μ和σ分别为对数正态分布的均值和标准差。
图6（b）和（c）分别为全部阻尼比数据和第7个频率聚类簇（该簇中数据点的数量最大）的阻尼比数据的概率密度拟合结果，可以发现对数正态分布能够较好地描述阻尼比的概率密度分布特征。
在基于识别的阻尼比数据建立概率分布模型后，就可以采用其概率特征参数表征拉索当前的阻尼特性。本文推荐采用所建立的对数正态分布模型的eμ和其CDF的分位值作为表征拉索阻尼特性当前状态的动态指标，具体分位值可视实际工程需求而定，本文仅介绍方法。表2中给出了对象拉索全部阻尼比数据和聚类簇7的阻尼比数据的对数正态分布概率特征参数估计值，随着数据的累积，该值可更精确。从表2中可知，该拉索的阻尼比对于装有内外两套阻尼器的458 m主跨斜拉桥拉索而言处于偏低水平。现有规范推荐斜拉桥拉索阻尼比宜取为0.1%［28-29］。疑似该拉索发生阻尼器连接螺栓松动、锚固条件变化或结构损伤等异常事件，需要进行进一步巡检。其他各拉索分析过程类似，在此不做赘述。
根据第2和3节所提方法的整个过程，桥梁运维人员可基于由长期监测数据自动测算的各阶（簇）模态频率数据质心和阻尼比概率特征参数的动态结果，进行拉索动力性能表征和状态实时监控，并以此指导拉索及其阻尼器状态的巡检和维护。相关结果与方法也可为其他需要关注缆、索、杆风致振动效应的缆索承重桥的设计与运维提供参考。
4　结论
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以某跨海大桥主航道斜拉桥为背景工程，提出了一套自激非平稳振动数据驱动的斜拉桥拉索动力性能表征方法。该方法提出基于风致自激振动非平稳时间序列进行拉索模态参数自动识别与动力性能实时表征的策略，在自激振动非平稳段自动提取、非平稳序列准自由衰减特征确定、多模态振动频率集中趋势分析、离散阻尼比数据偏态特征描述共4方面进行创新。所提方法能有效确定拉索自激振动各非平稳段主导频率的实时估计值，并在阻尼比识别时排除结构振动幅值上升段环境风自然激励带入能量的干扰；最后采用数据聚类方法量化多阶模态频率的聚集特征，同时采用数据统计建模并计算其概率特征参数的方式克服识别阻尼比数据的离散性，动态表征拉索各阶模态的动力性能特征。全文根据风致自激振动信号时频特征给出了有效的实施过程范式。相关方法数字化程度高、智能化潜力大，可基于实时的SHM系统数据通过算法自动完成全过程，降低经验的依赖和人工的耗费。所提方法能实现从拉索振动加速度时间序列到自激振动非平稳段数据再到各阶模态频率-阻尼比指标的数据降维、解析与表征过程，为桥梁运维工作提供实时的数字化信息。
针对背景工程的主要结论包括：（1）桥梁拉索振动加速度信号噪声强、干扰大，监测结果经常出现连续数天处于高幅振动的状态，本文在动力特征分析时选择排除类似的高噪声水平段的干扰；（2）桥梁拉索的自激振动加速度幅值最高已超过3000 mm/s2，振动幅度较大，需要给予关注；（3）桥梁拉索的阻尼比平均水平约为0.03%，日常值的双边90%保证率的置信区间为0.0114%~0.0820%，与设计规范中拉索的阻尼比推荐值相比偏低，这可能是导致拉索振动加速度幅值较大的原因之一，其成因和机理须结合现场检查、风洞试验和数值模拟进一步探究。
基金
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  • 国家重点研发计划项目(2021YFF0500900)
  • 国家自然科学基金资助项目(52378288)
  • 国家自然科学基金资助项目(52008099)
  • 国家自然科学基金资助项目(51978154)
  • 江苏省自然科学基金资助项目(BK20200369)
  • 江苏省自然科学基金资助项目(BK20190013)
  • 中央高校基本科研业务费专项资金项目(2242022k30031)
  • 中央高校基本科研业务费专项资金项目(2242022k3003)
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2024年第37卷第4期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.04.001
  • 接收时间：2022-06-29
  • 首发时间：2026-02-09
  • 出版时间：2024-04-28
补充材料
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  • 收稿日期：2022-06-29
  • 修回日期：2022-08-11
基金
国家重点研发计划项目(2021YFF0500900)
国家自然科学基金资助项目(52378288)
国家自然科学基金资助项目(52008099)
国家自然科学基金资助项目(51978154)
江苏省自然科学基金资助项目(BK20200369)
江苏省自然科学基金资助项目(BK20190013)
中央高校基本科研业务费专项资金项目(2242022k30031)
中央高校基本科研业务费专项资金项目(2242022k3003)
作者信息
    1东南大学混凝土及预应力混凝土结构教育部重点实验室, 江苏　南京　210096
    2东南大学土木工程学院,江苏　南京　210096
    3北京建筑大学北京未来城市设计高精尖创新中心, 北京　100044
    4深圳高速工程顾问有限公司, 广东　深圳　518049

通讯作者:

丁幼亮（1979―），男，博士，研究员，博士生导师。 E-mail： 。
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https://castjournals.cast.org.cn/joweb/zdgcxb/CN/10.16385/j.cnki.issn.1004-4523.2024.04.001
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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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