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基于Welch法的协方差随机子空间方法的模态参数识别

李雪艳 官宇航 罗铭涛 吴博宇

李雪艳, 官宇航, 罗铭涛, 吴博宇. 基于Welch法的协方差随机子空间方法的模态参数识别. 力学学报, 2022, 54(10): 2850-2860 doi: 10.6052/0459-1879-22-256
引用本文: 李雪艳, 官宇航, 罗铭涛, 吴博宇. 基于Welch法的协方差随机子空间方法的模态参数识别. 力学学报, 2022, 54(10): 2850-2860 doi: 10.6052/0459-1879-22-256
Li Xueyan, Guan Yuhang, Luo Mingtao, Wu Boyu. Modal parameter identification of covariance-based stochastic subspace identification based on Welch method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2850-2860 doi: 10.6052/0459-1879-22-256
Citation: Li Xueyan, Guan Yuhang, Luo Mingtao, Wu Boyu. Modal parameter identification of covariance-based stochastic subspace identification based on Welch method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2850-2860 doi: 10.6052/0459-1879-22-256

基于Welch法的协方差随机子空间方法的模态参数识别

doi: 10.6052/0459-1879-22-256
基金项目: 国家重点研发计划(2019YFC1511004-05), 广东省重点领域研发计划(2019B111106001)和广东省自然科学基金(2017A030313272)资助项目
详细信息
    作者简介:

    李雪艳, 副教授, 主要研究方向: 结构健康监测、损伤识别、振动控制. E-mail: celixy@jnu.edu.cn

  • 中图分类号: TU375.4

MODAL PARAMETER IDENTIFICATION OF COVARIANCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION BASED ON WELCH METHOD

  • 摘要: 对工程结构进行环境激励下的模态参数识别具有重要意义, 而随机子空间法作为适合环境激励下模态参数识别的时域方法, 由于噪声和复杂激励的原因, 会产生虚假模态、真实模态遗漏、系统自动定阶难和计算效率等问题, 这些问题阻碍了该方法在实际工程中的广泛应用. 本文提出了基于Welch法的随机子空间方法, 通过Welch法对振动响应在频域进行去噪、降低环境激励和其他不确定性因素影响的处理, 把结构固有模态从噪声和激励频率中突显出来, 形成富含更多结构模态的Toeplitz矩阵, 然后进行奇异值分解和状态矩阵计算, 最后进行特征值分析. 为了实现自动定阶, 对不同奇异值分量构建的状态矩阵得到的特征参数, 进行模糊C均值聚类分析和模态的平均相位偏移分析, 剔除虚假模态, 实现结构模态参数的自动识别. 并把本文所提出方法应用于一座大跨悬索桥的实测加速度响应分析, 和一座七十层的高层建筑的加速度响应分析, 跟频域分解法、传统随机子空间法和基于相关分析的随机子空间法的计算结果进行了比较, 发现基于Welch方法的随机子空间法相比于传统随机子空间法和基于相关分析的随机子空间法, 在避免模态遗漏和计算效率方面有显著提高, 而相对于频域分解法则在自动识别和剔除虚假模态方面有明显优势.

     

  • 图  1  基于Welch法的随机子空间法的流程图

    Figure  1.  Flow of stochastic subspace identification based on Welch method

    图  2  悬索桥上加速度计的布置

    Figure  2.  Arrangement of accelerometers on suspension bridge

    图  3  悬索桥的加速度响应

    Figure  3.  Acceleration response of suspension bridge

    图  4  频域分解法FDD、传统SSI、基于相关分析的SSI和基于Welch法的SSI的某大跨悬索桥的频率识别

    Figure  4.  Frequency identification of a long-span suspension bridge by FDD, traditional SSI, SSI based on correlation analysis and SSI based on Welch method

    图  5  对各聚类所对应的振型进行MPD分析得到的MPD分布图

    Figure  5.  the distribution of MPD obtained by MPD analysis of vibration modes corresponding to each cluster

    图  6  使用基于Welch法的SSI和FDD法得到的悬索桥的三阶振型分量对比

    Figure  6.  Comparison of three orders mode shape components of suspension bridges obtained by using SSI based on Welch method and FDD

    图  7  某高层建筑的传感器布置图

    Figure  7.  Sensor layout of a high-rise building

    图  8  某大厦的第68层处测点的加速度响应

    Figure  8.  Acceleration response of a certain measuring point in a high-rise building

    图  9  某大厦的频率识别

    Figure  9.  Frequency identification of a building

    表  1  大跨悬索桥的频率识别结果(Hz)

    Table  1.   The identified frequency results of long-span suspension bridge (Hz)

    Mode No.FDDTraditional
    SSI
    SSI based on
    correlation
    SSI based on
    Welch method
    10.13430.1348
    20.16780.1708
    30.22890.23620.2344
    40.2747
    50.36620.36660.3688
    60.46080.4579
    70.56460.56240.56450.5618
    80.6775
    90.79350.78950.7948
    100.91550.910.9137
    111.0411.0381.038
    121.121.1251.118
    131.2881.2811.2861.354
    141.4191.4181.414
    151.5411.5491.541
    161.6721.6971.668
    171.7851.7781.7921.79
    181.9041.9061.906
    192.0281.9881.985
    下载: 导出CSV

    表  2  某大厦的频率识别结果(Hz)

    Table  2.   The identified frequency results of a building (Hz)

    Mode No.FDDTraditional SSISSI based on
    correlation
    SSI based on
    Welch method
    10.1740.17210.1727
    20.3830.37950.38130.385
    30.67440.67230.6727
    40.73090.73090.73040.7302
    50.99330.99480.9946
    61.2911.2861.289
    71.4081.411.408
    81.4651.4661.467
    91.6051.5841.6051.605
    101.7851.788
    111.9621.9591.968
    122.1182.139
    132.2842.3082.2812.279
    142.4932.52.4962.495
    152.82.799
    163.1573.152
    173.3653.3723.374
    183.6213.632
    194.8814.893
    下载: 导出CSV
  • [1] Jiang H, Guo XD, Yang HL. Research on modal parameters identification of bridge structure under ambient excitation. Journal of Vibration and Shock, 2008, 27(11): 126-129
    [2] Liu ZZ, Chen K, Guo LD, et al. Modal parameter identification of a bridge under ambient excitation. Journal of Vibration, Measurement & Diagnosis, 2010, 30(3): 300-303
    [3] 李雪艳, 张惠民. 基于应变脉冲响应协方差的损伤识别方法研究. 力学学报, 2017, 49(5): 1081-1090 (Li Xueyan, Zhang Huimin. Study of damage idenfication method based on the covariance of strain impulse response function. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1081-1090 (in Chinese)
    [4] 刘宇飞,辛克贵,樊健生等. 环境激励下结构模态参数识别方法综述. 工程力学, 2014, 31(4): 46-53 (Liu Yufei, Xin Kegui, Fan Jiansheng, et al. A review of structure modal identification methods through ambient excitation. Engineering Mechanics, 2014, 31(4): 46-53 (in Chinese)
    [5] Kraemer P, Friedmann H. Vibration-based structural health monitoring for offshore wind turbines - Experimental validation of stochastic subspace algorithms. Wind & Structures, 2015, 21: 693-707
    [6] Xu X, Zhang X, Zhu W, et al. Modal parameter identification of a quayside container crane based on data-driven stochastic subspace identification. Journal of Vibration Engineering & Technologies, 2021, 9(5): 919-938
    [7] 胡异丁, 李丹, 任伟新等. 基于延时随机子空间方法的非白噪声环境激励结构模态参数识别. 振动与冲击, 2015, 34(8): 71-76 (Hu Yiding, Li Dan, Ren Weixin, et al. Modal parameter identification of structures under non-white noise ambient excitations using delay-index-based stochastic subspace method. Journal of Vibration and Shock, 2015, 34(8): 71-76 (in Chinese)
    [8] Reynders E, Maes K, Lombaert G, et al. Uncertainty quantification in operational modal analysis with stochastic subspace identification: Validation and applications. Mechanical Systems and Signal Processing, 2015, 66: 13-30
    [9] Overschee PV, Moor BD. Subspace Identification for Linear Systems: Theory—Implementation—Applications. Berlin, Germany: Business Media, 2012
    [10] Peeters B, Roeck GD. Reference based stochastic subspace identification for output-only modal analysis. Mechanical Systems and Signal Processing, 1999, 13(6): 855-878 doi: 10.1006/mssp.1999.1249
    [11] Guo J, Hu CJ, Zhu MJ, et al. Monitoring-based evaluation of dynamic characteristics of a long span suspension bridge under typhoons. Journal of Civil Structural Health Monitoring, 2021, 11: 397-410
    [12] Li JT, Zhu XQ, Law SS, et al. Indirect bridge modal parameters identification with one stationary and one moving sensors and Stochastic Subspace Identification. Journal of Sound and Vibration, 2019, 446: 1-21 doi: 10.1016/j.jsv.2019.01.024
    [13] Liu XL, Zhao SX, Wang PP, et al. Improved data-driven stochastic subspace identification with autocorrelation matrix modal order estimation for bridge modal parameter extraction using GB-SAR Data. Buildings, 2022, 12: 253
    [14] 肖祥, 任伟新. 实时工作模态参数数据驱动随机子空间识别. 振动与冲击, 2009, 28(8): 148-206 (Xiao Xiang, Ren Weixin. Improved data-driven stochastic subspace identification of online operational modal parameters. Journal of Vibration and Shock, 2009, 28(8): 148-206 (in Chinese) doi: 10.3969/j.issn.1000-3835.2009.08.034
    [15] 常军, 张启伟, 孙利民. 随机子空间产生虚假模态及模态遗漏的原因分析. 工程力学, 2007, 24(11): 57-62 (Chang Jun, Zhang Qiwei, Sun Limin. Analysis how stochastic subspace identification bring false modes and mode absence. Engineering Mechanics, 2007, 24(11): 57-62 (in Chinese)
    [16] 秦世强, 蒲黔辉, 施洲. 环境激励下大型桥梁模态参数识别的一种方法. 振动与冲击, 2012, 31(2): 95-100 (Qin Shiqiang, Pu Qianhui, Shi Zhou. A method of modal parameters identification using ambient vibration measurements for a large-scale bridge. Journal of Vibration and Shock, 2012, 31(2): 95-100 (in Chinese) doi: 10.3969/j.issn.1000-3835.2012.02.020
    [17] Lu LJ, Zhou HF, Ni YQ, et al. Output-only modal analysis for non-synchronous data using stochastic sub-space identification. Engineering Structures, 2021, 230(12): 111702
    [18] Lin CS, Wu YX. Response-only parametric estimation of structural systems using a modified stochastic subspace identification technique. Applied Science, 2021, 11: 11751
    [19] 陈永高, 钟振宇. 环境激励下桥梁结构模态参数识别的改进随机子空间算法. 振动与冲击, 2020, 39(16): 9 (Chen Yonggao, Zhong Zhenyu. An improved stochastic subspace method for modal parameter identification for bridge structures under ambient excitation. Journal of Vibration and Shock, 2020, 39(16): 9 (in Chinese)
    [20] 周筱航, 单德山, Khan I等. 多输入多输出桥梁结构时变模态参数的滑窗时域识别. 应用基础与工程科学学报, 2020, 28(5): 1145-1157 (Zhou Xiaohang, Shan Deshan, Inamullah Khan, et al. Sliding window time-domain method for identifying time-varying modal parameter of multi-input and multi-output bridge structure. Journal of Basic Science and Engineering, 2020, 28(5): 1145-1157 (in Chinese)
    [21] Jin N, Yang YB, Dimitrakopoulos EG, et al. Application of short-time stochastic subspace identification to estimate bridge frequencies from a traversing vehicle. Engineering Structures, 2021, 230(4): 111688
    [22] 张永祥, 刘心, 褚志刚等. 基于随机子空间法的模态参数自动提取. 机械工程学报, 2018, 54(9): 187-194 (Zhang Yongxiang, Liu Xin, Chu Zhigang, et al. Autonomous modal parameter extraction based on stochastic subspace identification. Journal of Mechanical Engineering, 2018, 54(9): 187-194 (in Chinese)
    [23] Wen P, Khan I, He J, et al. Application of improved combined deterministic-stochastic subspace algorithm in bridge modal parameter identification. Shock and Vibration, 2021(13): 1-11
    [24] Brandt A. A signal processing framework for operational modal analysis in time and frequency domain. Mechanical Systems and Signal Processing, 2019, 115: 380-393
    [25] 贺敏, 梁鹏, 李琳国等. 基于两阶段改进的FCM法的模态参数自动识别. 东南大学学报(自然科学版), 2019, 49(5): 940-948 (He Min, Liang Peng, Li Linguo, et al. Automatic modal parameter identification based on improved two-stage FCM algorithm. Journal of Southeast University (Natural Science Edition) , 2019, 49(5): 940-948 (in Chinese) doi: 10.3969/j.issn.1001-0505.2019.05.018
    [26] 刘长良, 武英杰, 甄成刚. 基于变分模态分解和模糊C均值聚类的滚动轴承故障诊. 中国电机工程学报, 2015, 35(13): 3358-3365 (Liu Changliang, Wu Yingjie, Zhen Chenggang. Rolling bearing fault diagnosis based on variational mode decomposition and fuzzy C means clustering. Proceedings of the CSEE, 2015, 35(13): 3358-3365 (in Chinese)
    [27] 王舒玉. 塑料燃油箱模态分析与验证. [硕士论文]. 北京: 清华大学, 2018

    Wang Shuyu. Modal analysis and verificaiton of plastic fuel tank. [Master Thesis]. Beijing: Tsinghua University, 2018 (in Chinese))
    [28] 孟礼. 某汽车座椅的结构分析与模态优化. [硕士论文]. 重庆: 重庆大学, 2019

    Meng Li. Structure analysis and modal optimization of an automobile seat. [Master Thesis]. Chongqing: Chongqing University, 2018 (in Chinese))
    [29] Pal NR, Bezdek JC. On cluster validity for the fuzzy C-means model. IEEE Transactions on Fuzzy Systems, 1995, 3(3): 370-379 doi: 10.1109/91.413225
    [30] Reynders E, Houbrechts J, Roeck GD. Fully automated (operational) modal analysis. Mechanical Systems and Signal Processing, 2012, 29(5): 228-250
    [31] 夏祥麟. 环境激励模态分析方法的比较. [硕士论文]. 长沙: 中南大学, 2013

    Xia Xianglin. The comparison of modal analysis methods under ambient vibration. [Master Thesis]. Changsha: Central South University, 2013 (in Chinese))
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出版历程
  • 收稿日期:  2022-06-08
  • 录用日期:  2022-07-30
  • 网络出版日期:  2022-07-31
  • 刊出日期:  2022-10-18

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