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Article(id=1228011508462973359, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228011505698931621, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.01.002, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1652112000000, receivedDateStr=2022-05-10, revisedDate=1660492800000, revisedDateStr=2022-08-15, acceptedDate=null, acceptedDateStr=null, onlineDate=1770710358967, onlineDateStr=2026-02-10, pubDate=1706371200000, pubDateStr=2024-01-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770710358967, onlineIssueDateStr=2026-02-10, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770710358967, creator=13701087609, updateTime=1770710358967, updator=13701087609, issue=Issue{id=1228011505698931621, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='1', pageStart='1', pageEnd='190', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770710358308, creator=13701087609, updateTime=1770795378159, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228368104862974870, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228011505698931621, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228368104862974871, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228011505698931621, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=11, endPage=19, ext={EN=ArticleExt(id=1228011509930979771, articleId=1228011508462973359, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Time-varying synchronization factor of crowd jumping load, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The synchronization factor is a measurement for the consistency of actions between individuals in a jumping crowd，as well as a key metric in the modeling of crowd jumping loads. Most of the existing synchronization factors are defined as mean parameters during a long period of time，and thus cannot accurately reflect the time-varying characteristics of individual differences between jumpers. Their calculation is based on ground reaction force or feature point trajectory records that can only be obtained under laboratory conditions，making it difficult to apply them to the safety operation and maintenance of the engineering structures in actual scenarios directly. In this regard，this paper proposes a new time-varying synchronization factor for crowd-jumping loads. By introducing multiple objects tracking technology to monitor the real-time synchronization variation of the subject jumping processes as the basis for the factor calculation，this study carries out a multi-person jumping experiment with a wireless force measurement shoe pad. By comparing with the test results，the validity of the proposed time-varying synchronization factor and the effectiveness of the multi object tracking technology are verified. The results can be used for the intelligent operation and maintenance of the engineering structure，as well as the simulation of the time-varying crowd jumping loads.

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协同性因子是跳跃人群中各单人间动作一致程度的度量指标，是人致结构振动分析中人群跳跃荷载建模的关键参数。现有协同性因子大都是定义在较长时段内的均值参数，其计算依据也是实验室条件下才能获取的地反力或特征点轨迹等，不能准确反映跳跃者个体差异的时变特性，也难以直接应用于实际场景下结构的振动监测。对此，提出了人群跳跃荷载的时变协同性因子，采用计算机视觉中的多目标跟踪技术对跳跃人群进行实时监测，并计算协同性因子。开展了佩戴无线测力鞋垫的多人跳跃实验，通过与实验结果的对比，验证了时变协同性因子的合理性以及多目标跟踪技术的有效性，可用于工程结构的安全运维、人致结构振动分析和人群跳跃时变荷载的模拟。

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陈隽 （1972―），男，博士，教授。 E-mail： 。
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于秉仟 （1998—），男，硕士研究生。 E-mail： 。

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于秉仟 （1998—），男，硕士研究生。 E-mail： 。

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于秉仟 （1998—），男，硕士研究生。 E-mail： 。

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Comparison of current load measurement methods

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测量方法实现方式优点缺点
直接法由测力板或测力台直接测量精度高设备间同步差，价格昂贵，难以用于人群
间接法由3D动作捕捉等间接测量快速、经济、无同步性问题精度较低，设备难以部署到工程实际中
反算法由结构动力响应反演跳跃荷载适用于实际结构，体现人-结耦合动力学反问题存在不适定性
), ArticleFig(id=1228042464896938104, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228011508462973359, language=CN, label=表1, caption=

现有荷载测量方法对比

, figureFileSmall=null, figureFileBig=null, tableContent=
测量方法实现方式优点缺点
直接法由测力板或测力台直接测量精度高设备间同步差，价格昂贵，难以用于人群
间接法由3D动作捕捉等间接测量快速、经济、无同步性问题精度较低，设备难以部署到工程实际中
反算法由结构动力响应反演跳跃荷载适用于实际结构，体现人-结耦合动力学反问题存在不适定性
), ArticleFig(id=1228042465056321664, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228011508462973359, language=EN, label=Tab.2, caption=

Information of the test subjects

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编号鞋垫尺寸性别年龄/岁身高/cm体重/kg
A小女2716363
B大男2318393
C中男2117157
), ArticleFig(id=1228042465177956491, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228011508462973359, language=CN, label=表2, caption=

测试者信息

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编号鞋垫尺寸性别年龄/岁身高/cm体重/kg
A小女2716363
B大男2318393
C中男2117157
), ArticleFig(id=1228042465320562831, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228011508462973359, language=EN, label=Tab.3, caption=

Statistical results of ρ1s of each test （10~30 s）

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实验编号变化范围均值±方差
1.5 Hz-10.446~0.8590.663±0.084
1.5 Hz-20.296~0.8040.583±0.110
2.0 Hz-10.827~0.9990.965±0.034
2.0 Hz-20.837~0.9990.967±0.036
2.5 Hz-10.763~0.9990.932±0.052
2.5 Hz-20.739~0.9990.920±0.049
3.0 Hz-10.826~0.9990.965±0.035
3.0 Hz-20.869~0.9990.965±0.029
3.5 Hz-10.514~0.9690.842±0.095
3.5 Hz-20.191~0.9390.582±0.189
), ArticleFig(id=1228042465408643219, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228011508462973359, language=CN, label=表3, caption=

各工况实验的ρ1s统计结果（10~30 s）

, figureFileSmall=null, figureFileBig=null, tableContent=
实验编号变化范围均值±方差
1.5 Hz-10.446~0.8590.663±0.084
1.5 Hz-20.296~0.8040.583±0.110
2.0 Hz-10.827~0.9990.965±0.034
2.0 Hz-20.837~0.9990.967±0.036
2.5 Hz-10.763~0.9990.932±0.052
2.5 Hz-20.739~0.9990.920±0.049
3.0 Hz-10.826~0.9990.965±0.035
3.0 Hz-20.869~0.9990.965±0.029
3.5 Hz-10.514~0.9690.842±0.095
3.5 Hz-20.191~0.9390.582±0.189
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人群跳跃荷载时变协同性因子研究
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于秉仟 1 , 陈隽 1, 2 , 李洋 1
振动工程学报 | 2024,37(1): 11-19
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振动工程学报 | 2024, 37(1): 11-19
人群跳跃荷载时变协同性因子研究
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于秉仟1 , 陈隽1, 2 , 李洋1
作者信息
  • 1同济大学土木工程学院，上海　200092
  • 2同济大学土木工程防灾国家重点实验室，上海　200092

    • 于秉仟 （1998—），男，硕士研究生。 E-mail： 。

通讯作者:

陈隽 （1972―），男，博士，教授。 E-mail： 。
Time-varying synchronization factor of crowd jumping load
Bing-qian YU1 , Jun CHEN1, 2 , Yang LI1
Affiliations
  • 1College of Civil Engineering, Tongji University, Shanghai 200092, China
  • 2State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
出版时间: 2024-01-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.01.002
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摘要
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协同性因子是跳跃人群中各单人间动作一致程度的度量指标，是人致结构振动分析中人群跳跃荷载建模的关键参数。现有协同性因子大都是定义在较长时段内的均值参数，其计算依据也是实验室条件下才能获取的地反力或特征点轨迹等，不能准确反映跳跃者个体差异的时变特性，也难以直接应用于实际场景下结构的振动监测。对此，提出了人群跳跃荷载的时变协同性因子，采用计算机视觉中的多目标跟踪技术对跳跃人群进行实时监测，并计算协同性因子。开展了佩戴无线测力鞋垫的多人跳跃实验，通过与实验结果的对比，验证了时变协同性因子的合理性以及多目标跟踪技术的有效性，可用于工程结构的安全运维、人致结构振动分析和人群跳跃时变荷载的模拟。

人群跳跃荷载  /  时变协同性因子  /  多目标跟踪  /  智能运维

The synchronization factor is a measurement for the consistency of actions between individuals in a jumping crowd，as well as a key metric in the modeling of crowd jumping loads. Most of the existing synchronization factors are defined as mean parameters during a long period of time，and thus cannot accurately reflect the time-varying characteristics of individual differences between jumpers. Their calculation is based on ground reaction force or feature point trajectory records that can only be obtained under laboratory conditions，making it difficult to apply them to the safety operation and maintenance of the engineering structures in actual scenarios directly. In this regard，this paper proposes a new time-varying synchronization factor for crowd-jumping loads. By introducing multiple objects tracking technology to monitor the real-time synchronization variation of the subject jumping processes as the basis for the factor calculation，this study carries out a multi-person jumping experiment with a wireless force measurement shoe pad. By comparing with the test results，the validity of the proposed time-varying synchronization factor and the effectiveness of the multi object tracking technology are verified. The results can be used for the intelligent operation and maintenance of the engineering structure，as well as the simulation of the time-varying crowd jumping loads.

crowd jumping load  /  time-varying synchronization factor  /  multiple object tracking  /  intelligent operation and maintenance
于秉仟, 陈隽, 李洋. 人群跳跃荷载时变协同性因子研究. 振动工程学报, 2024 , 37 (1) : 11 -19 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.01.002
Bing-qian YU, Jun CHEN, Yang LI. Time-varying synchronization factor of crowd jumping load[J]. Journal of Vibration Engineering, 2024 , 37 (1) : 11 -19 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.01.002
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1　概述
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随着材料科学的不断创新和工程结构设计、施工技术的持续进步，工程结构向轻质化、大跨化发展，大跨楼盖、悬臂看台、连廊等结构呈现出频率低、质量轻和阻尼小等特征，容易因人致动力荷载（步行、跳跃等）而产生振动，引发结构振动的适用性甚至安全性问题［1］。例如，2015年4月，中国台北“小巨蛋”体育馆的一场演唱会，歌迷随着音乐跳动导致附近民宅振动，引起居民投诉［2］；2018年11月，南京奥体中心的一场演唱会在4首歌曲后，因结构振动显著而被紧急叫停［3］。2021年10月，荷兰奈梅亨体育场的一处看台在球迷集体跳跃庆祝下发生大幅振动并最终坍塌，所幸并未造成人员伤亡［4］。此类问题屡见报端引起了广泛的社会关注，也对人致结构振动，特别是人群荷载的研究提出了新的挑战。
合理、准确的荷载模型是人致结构振动分析的前提。在步行、跳跃、屈伸律动等常见的人致荷载类型中，跳跃荷载的动力效应最为显著［5］。尤其在体育比赛、音乐会等场景中，人群的跳跃运动易受到集体口号、音乐节拍等外部指令的引导，形成节奏性协同运动而导致更大的结构振动幅度。目前，国内外学者对单人跳跃荷载已开展了深入、系统的研究，先后提出了确定性［6-8］和随机性［6，9-10］两大类荷载模型。相比之下，人群跳跃荷载的研究仍然较少。由于不同跳跃者的动作不可能完全一致，因此人群荷载并非单人荷载的简单叠加，需要解决不同跳跃者之间协同性量化表达这一建模难点。已有研究提出了一些协同性指标［7，11］，但大都是定义在较长时段内的、平均意义上的指标。实际情况下，每个跳跃者往往会随着节拍、周围人的动作和自身疲劳等情况随时调整自己的动作，即人群跳跃协同性具有典型的时变特征，相关指标研究中应充分考虑其时变特性。
缺少合适的实验手段是人群跳跃荷载时变协同性研究的技术难题。目前人群跳跃荷载的实验测试主要有直接法、间接法和反算法三种，各自的原理和优缺点如表1所示。显然，现有测试方法或需要依托特殊实验设备且在实验室环境中实现；或需要实时测量结构的动力响应，因而难以部署到体育场馆看台等实际场景中，监测其服役期承受人群荷载的协同性。近年来，Krizhevsky等［12］基于深度学习的计算机视觉技术取得了飞速发展，在不同领域已有成熟的应用。考虑到体育场馆看台等公共空间往往布设有大量监控摄像头，可作为监测其服役期人群跳跃协同性的硬件基础。
综上，本研究提出了人群跳跃时变协同性因子，并给出其计算公式，发展出一套基于计算机视觉中多目标跟踪技术的监测方案，可作为一种工程结构智能运维手段，部署到体育场馆等场所中提供预警。最后，通过大量不同频率的人群跳跃实验，检验了时变协同性的合理性和监测方案的可行性。
2　跳跃人群的时变协同性
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2.1　既有跳跃协同性因子
人群荷载具有一定的随机性，并非单人荷载的线性叠加，体现为个体内变异性（intra-variability）和个体间变异性（inter-variability）［13］。前者表示跳跃过程中单个测试者个体运动状态的不一致性，即个体会不断调整自己的跳跃动作；后者则表示跳跃过程中多个测试者个体运动状态之间的不一致性，即个体单独跳跃时的运动状态与个体在人群中随周围人一起跳跃时的运动状态不同。
在体育赛事、音乐演唱会等场景中，观众跟随音乐节拍、口号等一起跳跃，形成人群跳跃荷载。Kasperski等［6］的研究表明，人群的协同性来源于对外部引导节奏把控的个人能力和受周围人群影响表现出的从众特性。因而，对协同性的量化是人群跳跃荷载建模的基础，国内外学者主要有两种研究思路。一是，从协同性的本质出发，将不同跳跃者荷载时程的时间差或相位差定义为协同性因子，并统计分析其概率分布。如Sim等［7］将协同性因子定义为单次跳跃脉冲与外部节拍器节拍的时间差；Parkhouse等［14］则将跳跃荷载的一阶谐波初相位作为协同性因子；二是，从荷载的角度出发，用人群荷载折减系数来定义协同性因子，如谭寰［13］的研究。
两种协同性因子定义虽然出发点不同，但都是基于测试者在较长时段内的连续跳跃时程来计算，忽略了个体内变异性，仅考虑了较长时段内平均意义上的个体间变异性。然而，在实际跳跃过程中，每个跳跃者会不断根据自身能力和周围人的影响调整姿态，因此最后呈现的人群协同性因子应该是一个时变指标。
2.2　时变跳跃协同性因子
针对上一节所述问题，本文在前期工作［13］基础上，提出了一种新的、随时间变化的跳跃协同性因子，由下式在长度的移动时间窗口内计算（如图1所示）：
式中　 为时刻人群跳跃协同性因子；为时段内第i个人单人跳跃加速度的均方根值；为相同时段内所有人平均跳跃加速度时程的均方根值；Np为人群总人数。
上式定义的时变跳跃协同性因子的取值范围为［0，1］。越接近1，则人群在时刻的跳跃动作越一致，即人群协同性越好，人群荷载效应越显著；接近0（如跳跃者恰好两两反向），则人群跳跃协同性最弱。
3　YOLOv5+DeepSORT多目标跟踪方案
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多目标跟踪（Multiple Object Tracking，MOT）是在单个图像序列（如视频）中跟踪多个目标（如车辆、人物）的位置，进而获取它们运动轨迹的技术。本研究利用MOT从人群跳跃的视频中获取每个人的轨迹，进而计算人群的时变协同性。根据目标初始化方法的不同，当前的MOT算法主要有无检测跟踪（Detection Free Tracking，DFT）和检测跟踪（Detection Based Tracking，DBT）两种［15］。
DFT不依靠目标检测，直接在视频的初始帧中手动框选目标，然后在后续帧中持续定位这些目标。大部分早期MOT算法如光流法［16-17］即属于此类，由于需要较多的手动干预，方法通常鲁棒性较差，且无法跟踪序列中出现的新目标。近年来，随着大量数据的累积及计算硬件性能的提升，深度学习方法已经在计算机视觉［12，18-19］、自然语言处理［20-21］等领域取得重大发展。YOLO［19］，Faster R-CNN［22］等深度学习类的DBT算法逐步成为主流MOT解决方案。DBT方法先由检测器逐帧检测出目标，再由目标跟踪算法对多个目标实现帧间数据关联，从而获得它们的轨迹。图2对比了DFT和DBT两种解决方案。本研究采用DBT方案由YOLOv5目标检测和DeepSORT跟踪算法两个模块构成。
3.1　YOLOv5目标检测算法
现有目标检测算法包括以YOLO［19，23-25］系列为代表的一阶段算法，以R-CNN［18，22，26-27］系列为代表的两阶段算法。一阶段方法没有单独的初步定位阶段，直接得到分类和目标定位结果，具有较快的计算速度，适合作为DBT方案中的目标检测任务部分以实现实时在线跟踪。其中，YOLOv5是继承了YOLOv4优点、更轻量级的最新网络结构［23］。图3展示了本文采用的YOLOv5-m网络的整体架构，图例中提供了每个模块的细观结构描述。
3.2　DeepSORT目标跟踪算法
DeepSORT［28］ （Simple Online and Realtime Tracking with a Deep Association Metric）是在SORT［29］基础上发展来的，可以实现对多目标轨迹的动态更新、创建和终结，图4是算法流程图。
考虑到实际场景中可能存在的身体遮挡问题等，本研究将人头作为跟踪目标。对每个目标，DeepSORT使用8维向量表征其在当前帧的状态。其中，表示目标检测框中心位置坐标，γ表示检测框长宽比，h表示检测框高度，则表示前面四个参数的速度信息。DeepSORT基于匈牙利算法，将卡尔曼滤波预测的目标状态与检测器在当前帧的检测结果进行级联匹配和IOU匹配，并用匹配结果完成轨迹的卡尔曼滤波更新。相比SORT，DeepSORT的最大改进是引入了一个预训练的卷积神经网络（其主要目的是解决目标的重识别问题），提取检测结果的表观特征向量。对第i条轨迹的卡尔曼滤波预测结果和第j个检测结果，DeepSORT分别计算运动特征指标d（1）（i，j）和表观特征指标d（2）（i，j），以线性加权的方式得出关联指标ci，j，以布尔型变量相乘的方式构造表示是否允许匹配发生的指标bi，j，如下式所示：
式中　 为控制运动特征指标和表现特征指标影响的超参数，取为0.5。
进而构造匈牙利算法的成本矩阵C和阈值矩阵B，从而实现对目标的表观特征和运动特征的综合考量。
4　跳跃实验
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4.1　实验设备与步骤
为验证本研究提出的时变协同性计算与监测方案的有效性，安排三位测试者穿着LoadSol测力鞋垫进行了验证实验，如图5所示。测力鞋垫装有内嵌的压力传感器，可通过蓝牙信号将测试者的足底竖向跳跃荷载时程数据传输至智能手机。三位测试者的信息如表2所示。
实验中，三位测试者在节拍器的指引下完成5个工况共10组的固定频率跳跃。参考人体生理条件及国内外已有实验，5个工况的跳跃频率分别为1.5，2.0，2.5，3.0和3.5 Hz，每个工况进行2组实验。测试者在每组实验中需完成持续30 s以上的连续跳跃，并休息至无疲惫感后再进行下一组跳跃。每组实验过程中用固定机位的iPhone12 Pro后置摄像头进行视频拍摄，摄制帧率30 FPS，分辨率为1920×1080。
4.2　实验记录
图6展示了1.5 Hz固定频率跳跃工况下一位测试者的原始实验数据，包括鞋垫获得的竖向跳跃荷载时程，以及YOLOv5+DeepSORT跟踪测试者头部得到的像素加速度时程。需要说明，由于记录设备不同，上述两条曲线不是严格时间同步的。
5　实验验证与应用
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5.1　目标跟踪算法验证
将YOLOv5+DeepSORT方法用于实验视频，可获得三位测试者在10组实验中共30条头部像素运动加速度时程数据。对应地，测力鞋垫记录了30条跳跃荷载时程曲线。通过对30组数据时域和频域特征的对比，可以检验本文建议算法的性能。
图7比较了测试者A在2.5 Hz的固定频率下跳跃时，经过峰值归一化的视频目标跟踪结果和测力鞋垫记录。从时域特征（图7（a））看，测试者在10 s中总共有25次跳跃，目标跟踪算法成功捕捉了每次跳跃荷载脉冲对应的加速度脉冲；从频域特征（图7（b））看，目标跟踪结果和测力鞋垫记录的频谱特征较为一致，频谱峰值均集中在主频2.5 Hz附近。可见，本文建议的目标跟踪算法可以很好地捕捉跳跃者的运动信息。
5.2　时变协同性因子性能：阶段差异
图8对比了5个工况共10组三人跳跃实验的1 s时变协同性因子曲线（即Δt=1 s）与谭寰［13］提出的、针对跳跃全过程的时不变协同性因子，每组实验按“跳跃频率-实验次数”来编号。表3则展示了各实验中跳跃过程的10~30 s时段（称为稳定时段）内协同性因子的统计结果。
结果显示，当跳跃引导频率为1.5 Hz（过慢）或3.5 Hz（过快）时，由于测试者难以长时间维持该频率的稳定跳跃，因此图8（a），（b），（i）和（j）展现出波动剧烈且较低水平的协同性，其稳定时段的协同性因子均值也较小，方差较大。当跳跃引导频率适中（2.0~3.0 Hz），时变协同性曲线表现相似的变化模式（图8（c）~（h））。以最常见，也是一般人最适应的跳跃频率2.0 Hz为例（图8（c），（d）），曲线可分为三个阶段：
（1）跳跃初始阶段（0~5 s）。所有测试者从静止状态开始跳跃，并逐渐自我调整以适应节拍频率，此阶段内时变协同性因子曲线前期波动显著，后期逐步变大；
（2）稳定跳跃阶段（5~35 s）。所有测试者逐渐适应节拍频率，时变协同性稳定且维持在很高水平（0.85~1.0）；
（3）跳跃结束阶段（>35 s）。由于测试者出现疲惫、预期跳跃即将结束等影响，出现跟不上节拍的情况，协同性因子曲线出现明显波动乃至下降。
显然，对于多人协同跳跃的全过程，本研究提出的时变协同性因子能较好地解释测试者在不同频率的节拍引导下的表现差异。与本文提出的时变协同性因子相比，现有的时不变协同性因子是定义在整个跳跃过程上、平均意义上的参数。在如图8（a），（b），（i）和（j）所示人群协同性波动较为剧烈（表现为时变协同性因子ρ1s方差较大）的情况下，现有的协同性因子忽略了跳跃过程中人群协同性实际较大的危险时段（例如图8（a）中的5~30 s）。而在概述中提到的荷兰奈梅亨体育场看台坍塌的工程事故案例中，人群从开始起跳到协同跳跃引发事故所经历的时间仅10 s左右。可见，相较现有时不变的协同性因子，本文提出的时变协同性因子可更为全面地考虑人群跳跃协同性的变化及由此而来的结构危险状态。
5.3　时变协同性因子性能：特定事件
图9展示了2.5 Hz时的一次协同跳跃实验时变协同性的计算结果。在视频第4.34 s，图9左图表明三位测试者还在适应节拍，从测试者们的膝盖状态可见他们的动作不同步，测试者A和C正屈膝起跳，而测试者B膝盖伸直已接近离地，此时的1 s协同性因子仅为0.3226；在视频第29.42 s，三位测试者已适应了2.5 Hz的节拍引导，跳跃动作协同一致，对应的1 s协同性因子为0.8726。这一结果表明，本研究提出的时变协同性因子可以准确、定量地描述跳跃过程中各跳跃者间的协同性情况。
5.4　应用场景
时变协同性因子反映人群跳跃过程中动作一致性的实时变化，可应用于服役期结构的智能运维和人群荷载模拟两大场景。
以体育场馆的看台结构运维为例，在比赛或其他群体活动时，利用多目标跟踪技术由实时监控视频可获取人群跳跃的运动轨迹，并计算人群跳跃的时变协同性，即可构建基于协同性监测的预警系统。具体应用时，先设定协同性因子阈值（如0.8，0.9等），若监测到当前的协同性超限，则结构可能处于“危险时段”，需向管理者发出预警，提醒其引入人工干预，从而防止不利振动地持续扩大。上述协同性监测系统的工作机制如图10所示，由于无需额外安装和维护新的设备，只需利用场地既有的视频监控系统即可搭建，是一种低成本、轻量级的监测方案，也可作为传统的基于结构响应的安全性监测系统的补充。当然，应用时对于密集人群的目标跟踪，还需要进一步解决相互遮挡对轨迹获取带来的问题。
人群荷载模拟方面，协同性因子是单人荷载到人群荷载的桥梁，本文提出的协同性因子将协同性的时变特性纳入考量，可为人群荷载建模提供工具和思路。
6　结论
收起
既有的跳跃协同性因子既无法体现人群跳跃过程中个体差异的时变特性，也不具备工程结构实时安全运维价值。针对此问题，本文提出了人群跳跃的时变协同性因子，并引入计算机视觉中的多目标跟踪技术作为监测手段，通过5个频率工况共10组的3人跳跃实验，验证了时变协同性因子的合理性以及多目标跟踪技术的有效性，主要结论如下：
（1）提出的时变协同性因子可以准确、定量地反映人群跳跃的协同性水平及其变化规律。
（2）YOLOv5+DeepSORT的多目标跟踪算法可以很好地捕捉测试者跳跃运动的时频特征，进而指示人群协同性的变化。
基金
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  • 国家自然科学基金资助项目(52178151)
文献
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2024年第37卷第1期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.01.002
  • 接收时间：2022-05-10
  • 首发时间：2026-02-10
  • 出版时间：2024-01-28
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  • 收稿日期：2022-05-10
  • 修回日期：2022-08-15
基金
国家自然科学基金资助项目(52178151)
作者信息
    1同济大学土木工程学院，上海　200092
    2同济大学土木工程防灾国家重点实验室，上海　200092

通讯作者:

陈隽 （1972―），男，博士，教授。 E-mail： 。
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