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基于EM算法和模态形式的状态空间模型自降阶工作模态分析

施袁锋 朱正言 陈鹏 戴靠山

施袁锋, 朱正言, 陈鹏, 戴靠山. 基于EM算法和模态形式的状态空间模型自降阶工作模态分析[J]. 工程力学, 2021, 38(9): 15-25. doi: 10.6052/j.issn.1000-4750.2020.08.0618
引用本文: 施袁锋, 朱正言, 陈鹏, 戴靠山. 基于EM算法和模态形式的状态空间模型自降阶工作模态分析[J]. 工程力学, 2021, 38(9): 15-25. doi: 10.6052/j.issn.1000-4750.2020.08.0618
SHI Yuan-feng, ZHU Zheng-yan, CHEN Peng, DAI Kao-shan. OPERATIONAL MODAL ANALYSIS USING EM ALGORITHM AND MODAL-FORM STATE-SPACE MODEL WITH AUTO MODEL ORDER REDUCTION[J]. Engineering Mechanics, 2021, 38(9): 15-25. doi: 10.6052/j.issn.1000-4750.2020.08.0618
Citation: SHI Yuan-feng, ZHU Zheng-yan, CHEN Peng, DAI Kao-shan. OPERATIONAL MODAL ANALYSIS USING EM ALGORITHM AND MODAL-FORM STATE-SPACE MODEL WITH AUTO MODEL ORDER REDUCTION[J]. Engineering Mechanics, 2021, 38(9): 15-25. doi: 10.6052/j.issn.1000-4750.2020.08.0618

基于EM算法和模态形式的状态空间模型自降阶工作模态分析

doi: 10.6052/j.issn.1000-4750.2020.08.0618
基金项目: 国家自然科学基金项目(51878426);四川大学-自贡市校地科技合作专项资金项目(2019CDZG-13);成都市科技项目(2019-GH02-00081-HZ)
详细信息
    作者简介:

    施袁锋(1980−),男,上海人,副教授,博士,主要从事结构健康监测研究(E-mail: shiyuanfeng@scu.edu.cn)

    朱正言(1997−),男,湖北人,硕士生,主要从事结构健康监测研究(E-mail: zhengyan.zhu@foxmail.com)

    陈 鹏(1994−),男,重庆人,硕士生,主要从事空间结构研究(E-mail: 21912212@zju.edu.cn)

    通讯作者:

    戴靠山(1977−),男,江苏人,教授,博士,主要从事工程结构防灾减灾研究(E-mail: kdai@scu.edu.cn)

  • 中图分类号: TU311;O32

OPERATIONAL MODAL ANALYSIS USING EM ALGORITHM AND MODAL-FORM STATE-SPACE MODEL WITH AUTO MODEL ORDER REDUCTION

  • 摘要: 工作模态分析具有试验简单、经济可行等优点,在工程实际中有广泛的应用。在基于状态空间模型的模态分析中,模型阶次的确定是获得准确和稳定的模态参数的关键问题之一。该文结合期望最大(EM)算法和模态形式状态空间模型来实现模型自降阶和模态参数估计。将状态空间模型变换到模态形式,使待估计参数量得到精简的同时,可直接估计各阶模态响应。引入表征各阶模态响应在实际响应中占比的模态贡献作为模型降阶的指标,在EM求解模型极大似然估计时实现模型降阶。同时结合频谱图分析和阻尼比阈值剔除虚假模态,以获得实际的结构模态信息。通过数值结构模拟和现场结构实测的数据分析,结果表明该文方法具有较好的适用性和有效性。
  • 图  1  自降阶工作模态分析流程图

    Figure  1.  Flowchart of operational modal analysis with auto model order reduction

    图  2  6自由度结构模型简图

    Figure  2.  Schematic diagram of 6-DOF structural model

    图  3  6自由度加速度响应奇异值频谱图

    Figure  3.  Singular value spectrum of measured accelerations of 6-DOF structure

    图  4  6自由度结构EM自降阶迭代过程

    Figure  4.  EM iteration process with auto order reduction of 6-DOF structure

    图  5  6自由度振型识别结果

    Figure  5.  Identified mode shapes of 6-DOF structure

    图  6  6自由度结构质点2处(10 s~20 s)加速度响应分析

    Figure  6.  Analysis of acceleration response at mass No.2 of 6-DOF structure (10 s-20 s)

    图  7  6自由度结构质点2处(10 s~20 s)各阶模态响应及贡献

    Figure  7.  Modal response and contribution ratio at mass No.2 of 6-DOF structure (10 s-20 s)

    图  8  广州塔水平加速度传感器布置简图

    Figure  8.  Layout diagram of horizontal acceleration sensor placement for Canton Tower

    图  9  广州塔传感器(6、12和16)加速度响应曲线

    Figure  9.  Acceleration responses from sensors (6, 12 and 16) on Canton Tower

    图  10  广州塔加速度响应奇异值频谱图

    Figure  10.  Singular value spectrum of acceleration responses of Canton Tower

    图  11  广州塔EM自降阶迭代过程

    Figure  11.  EM iteration process with auto order reduction of Canton Tower

    图  12  广州塔识别模型的响应估计残差奇异值频谱图

    Figure  12.  Singular value spectrum of residuals of the identified model for Canton Tower

    图  13  广州塔前12阶振型在x方向的分量(横截面长轴)

    Figure  13.  The x-component of the first 12 identified modes of Canton Tower (the longitudinal axis of the cross section)

    图  14  广州塔前12阶振型在y方向的分量(横截面短轴)

    Figure  14.  The y-component of the first 12 identified modes of Canton Tower (the transverse axis of the cross section)

    表  1  6自由度模态分析结果

    Table  1.   Modal analysis results of 6-DOF structure

    模态阶次i频率 fi /Hz阻尼比 ζi /(%)模态贡献$c^i $
    理论值识别值理论值识别值
    11.2941.2975.004.320.063
    23.5933.5783.172.390.424
    35.7205.7683.503.290.418
    47.5137.5404.054.280.507
    58.9098.9564.544.130.398
    610.15510.0355.004.920.399
    下载: 导出CSV

    表  2  广州塔本文方法与NExT-ERA[23]识别结果比较

    Table  2.   Comparison of the identified results of the proposed method and NExT-ERA[23] for Canton Tower

    模态
    阶次 i
    本文方法NExT-ERA[23]
    频率 fi/Hz阻尼比 ζi/(%)模态贡献$c^i $频率fi/Hz阻尼比 ζi/(%)
    1 0.094 0.94 0.054 0.094 1.176
    2 0.139 0.38 0.134 0.138 0.899
    3 0.366 0.37 0.075 0.366 0.418
    4 0.424 0.21 0.072 0.424 0.327
    5 0.475 0.08 0.087 0.475 0.217
    6 0.506 0.14 0.082 0.506 0.302
    7 0.523 0.20 0.174 0.523 0.325
    8 0.796 0.28 0.196 0.795 0.238
    9 0.965 0.37 0.153 0.965 0.286
    10 1.150 0.16 0.027 1.150 0.138
    11 1.191 0.10 0.050 1.191 0.136
    12 1.252 0.17 0.016 1.251 0.175
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-08-31
  • 修回日期:  2020-11-30
  • 网络出版日期:  2021-03-02
  • 刊出日期:  2021-09-13

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