Research article Special Issues

Modal identification of civil structures via covariance-driven stochastic subspace method

  • Received: 26 April 2019 Accepted: 13 June 2019 Published: 19 June 2019
  • It is usually of great importance to identify modal parameters for dynamic analysis and vibration control of civil structures. Unlike the cases in many other fields such as mechanical engineering where the input excitation of a dynamic system may be well quantified, those in civil engineering are commonly characterized by unknown external forces. During the last two decades, stochastic subspace identification (SSI) method has been developed as an advanced modal identification technique which is driven by output-only records. This method combines the theory of system identification, linear algebra (e.g., singular value decomposition) and statistics. Through matrix calculation, the so-called system matrix can be identified, from which the modal parameters can be determined. The SSI method can identify not only the natural frequencies but also the modal shapes and damping ratios associated with multiple modes of the system simultaneously, making it of particular efficiency. In this study, main steps involved in the modal identification process via the covariance-driven SSI method are introduced first. A case study is then presented to demonstrate the accuracy and efficiency of this method, through comparing the corresponding results with those via an alternative method. The effects of noise contaminated in output signals on identification results are stressed. Special attention is also paid to how to determine the mode order accurately.

    Citation: Zhi Li, Jiyang Fu, Qisheng Liang, Huajian Mao, Yuncheng He. Modal identification of civil structures via covariance-driven stochastic subspace method[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5709-5728. doi: 10.3934/mbe.2019285

    Related Papers:

  • It is usually of great importance to identify modal parameters for dynamic analysis and vibration control of civil structures. Unlike the cases in many other fields such as mechanical engineering where the input excitation of a dynamic system may be well quantified, those in civil engineering are commonly characterized by unknown external forces. During the last two decades, stochastic subspace identification (SSI) method has been developed as an advanced modal identification technique which is driven by output-only records. This method combines the theory of system identification, linear algebra (e.g., singular value decomposition) and statistics. Through matrix calculation, the so-called system matrix can be identified, from which the modal parameters can be determined. The SSI method can identify not only the natural frequencies but also the modal shapes and damping ratios associated with multiple modes of the system simultaneously, making it of particular efficiency. In this study, main steps involved in the modal identification process via the covariance-driven SSI method are introduced first. A case study is then presented to demonstrate the accuracy and efficiency of this method, through comparing the corresponding results with those via an alternative method. The effects of noise contaminated in output signals on identification results are stressed. Special attention is also paid to how to determine the mode order accurately.


    加载中


    [1] B. L. Clarkson and C. A. Mercer, Use of cross correlation in studying the response of lightly damped structures to random forces, Am. I. Aeronaut. Astronaut. J., 3 (1965), 2287–2291.
    [2] H. Akaike, Fitting autoregressive models for prediction, Ann. I. Stat. Math., 21 (1969), 243–247.
    [3] S. R. Ibrahim and E. C. Mikulcik, A time domain modal vibration test technique, Shock and Vibration Bulletin, 43 (1973), 21–37.
    [4] H. A. Cole Jr, On-line failure detection and damping measurement of aerospace structures by random decrement signatures, NASA Cr-2205: Washington, DC, USA, (1973).
    [5] J. S. Bendat, Spectral techniques for nonlinear system analysis and identification, Shock Vib., 1 (1993), 21–31.
    [6] J. S. Bendat and A. G. Piersol, Engineering applications of correlation and spectral analysis, J. Wiley, & Sons NY., (1993).
    [7] R. Brincker, L. Zhang and P. Andersen, Modal identification from ambient responses using frequency domain decomposition. Process of the 18th International Modal Analysis Conference San Antonio, Texas, (2000), 625–630.
    [8] G. H. J. Ill, T. G. Carrie and J. P. Lauffer, The natural excitation technique (NExT) for modal parameter extraction from operating wind turbines, NASA STI/Rec on Technical Report N., 93 (1993), 260–277.
    [9] G. H. James, T. G. Carne and J. P. Lauffer, The natural excitation technique (NExT) for modal parameter extraction from operating structures, Int. J. Anal. Exp. Mod. Anal., 10 (1995), 260.
    [10] N. E. Huang, Z. Shen, S. R. Long, et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A-Math. Phys. Eng. Sci., 454 (1998), 903–995.
    [11] J. N. Yang, Y. Lei, S. W. Pan, et al., System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: Normal modes. Earthq. Eng. Struct. Dyn., 32 (2003), 1443–1467.
    [12] J. N. Yang, Y. Lei, S. W. Pan, et al., System identification of linear structures based on Hilbert–Huang spectral analysis. Part 2: Complex modes. Earthq. Eng. Struct. Dyn., 32 (2003), 1533–1554.
    [13] J. L. Beck and L. S. Katafygiotis, Updating models and their uncertainties, I: Bayesian statistical framework. J. Eng. Mech., 124 (1998), 455–461.
    [14] S. K. Au, Fast Bayesian ambient modal identification in the frequency domain, Part Ⅰ: posterior most probable value. Mech. Syst. Signal Proc., 26 (2012), 60–75.
    [15] C. T. Ng and S. K. Au, Modal shape scaling and implications in modal identification with known input, Eng. Struct., 156 (2018), 411–416.
    [16] K. Liu, Modal parameter estimation using the state space method. J. Sound Vibr., 197 (1996), 387–402.
    [17] P. Van Overschee and B. De Moor, Subspace identification for linear systems: Theory, Implementation, Applications, Kluwer Academic Publishers, Dordrecht, Netherlands, (1996).
    [18] R. S. Pappa and J. N. Juang, Some experiences with the eigensystem realization algorithm, J. Sound Vibr., 22 (1988), 30–34.
    [19] B. Jaishi, W. X. Ren, Z. H. Zong, et al., Dynamic and seismic performance of old multi-tiered temples in Nepal, Eng. Struct., 25 (2003), 1827–1839.
    [20] C. Gontier, Energetic classifying of vibration modes in subspace stochastic modal analysis, Mech. Syst. Signal Proc., 19 (2005), 1–19.
    [21] L. Hermans and H. Van der Auweraer, Modal testing and analysis of structures under operational conditions: industrial applications, Mech. Syst. Signal Proc., 13 (1999), 193–216.
    [22] W. X. Ren, W. Zatar and I. E. Harik, Ambient vibration-based seismic evaluation of a continuous girder bridge, Eng. Struct., 26 (2004), 631–640.
    [23] W. X. Ren, T. Zhao and I. E. Harik, Experimental and analytical modal analysis of steel arch bridge. J. Struct. Eng., 130 (2004), 1022–1031.
    [24] W. X. Ren and Z. H. Zong, Output-only modal parameter identification of civil engineering structures, Struct. Eng. Mech, 17 (2004), 429–444.
    [25] D. J. Ewins, Modal testing: theory and practice, Research Studies Press, 15 (1984).
    [26] J. N. Juang, Applied System Identification, PTR Prentice Hall, Englewood Cliffs, NJ., 3 (1994).
    [27] Benveniste and L. Mevel, Nonstationary consistency of subspace methods. IEEE T. Automat. Contr., 52 (2007), 974–984.
    [28] G. Golub and C. F. VanLoan, Matrix Computations, Johns Hopkins University Press, Baltimore, MD: The Johns Hopkins University Press, (1996).
    [29] E. Reynders, R. Pintelon and G. De Roeck, Uncertainty bounds on modal parameters obtained from stochastic subspace identification, Mech. Syst. Signal Proc., 22 (2008), 948–969.
    [30] W. Heylen, S. Lammens and P. Sas, Modal analysis theory and testing, Katholieke, Universteit Leuven, Departement Werktuigkunde, (2005).
    [31] P. Welch, The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms, IEEE T. Audio Electroacoust., 15 (1967), 70–73.
    [32] Q. S. Li, X. Li and Y. C. He, Monitoring wind characteristics and structural performance of a supertall building during a landfall typhoon. J. Struct. Eng., 142 (2016), 04016097.
    [33] Y. C. He and Q. S. Li, Time–frequency analysis of structural dynamic characteristics of tall buildings, Struct. Infrastruct. Eng., 8 (2015), 971–989.
    [34] Q. S. Li, Y. C. He, Y. H. He, et al., Monitoring of wind effects of a landfall typhoon on a 600 m high skyscraper, Struct. Infrastruct. Eng., 15 (2019), 54–71.
    [35] H. Akaike, Power spectrum estimation through autoregressive model fitting, Ann. Inst. Stat. Math., 21 (1969), 407–419.
    [36] H. A. Cole Jr, Method and apparatus for measuring the damping characteristics of a structure, United State Patent, 3 (1971).
    [37] H. A. Cole Jr, On-the-line analysis of random vibrations. AIAA /ASME 9th Structural Dynamics Materials Conference, (1968), 68–288.
    [38] Y. C. He and Q. S. Li, Dynamic responses of a 492m high tall building with active tuned mass damping system during a typhoon, Struct. Control Health Monit., 21 (2014), 705–720.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4145) PDF downloads(796) Cited by(11)

Article outline

Figures and Tables

Figures(9)  /  Tables(1)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog