Enhanced Power Spectral Density Transmissibility Matrix for Operational Modal Analysis of Structures
Publication: Journal of Structural Engineering
Volume 145, Issue 6
Abstract
The approach for identifying modal parameters of a structure from power spectral density transmissibility matrices, called the PSDTM-SVD method, is improved to identify modal parameters (including damping ratios) in a condition when the structure is not completely loaded. Therefore, an enhanced PSDTM-SVD method is proposed based on the use of a modified Moore-Penrose inverse to evaluate the singularity of the transmissibility matrices at the system poles and thus determine natural frequencies, mode shapes, and damping ratios. In the inverse modified operation, it is necessary to use a maximum number of singular values, which depends on the rank of the transmissibility matrix. One cause of the reduction of the matrix rank is the number of uncorrelated loads present in the structure. In this way, we propose a procedure for the automatic identification of the number of singular values that must be used in the Moore-Penrose inverse. Different numerical examples of a beam model subjected to colored noise excitations and data from an operational vibration bridge test showed that the proposed method is capable of identifying modal parameters.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to thank CAPES (Brazilian Coordination of Improvement of Higher Education Personnel), CNPq (Brazilian National Council for Technological and Scientific Development), and FAPESP (São Paulo Research Foundation) for their financial support of this research.
References
Araujo, I. G., and J. E. Laier. 2015. “Operational modal analysis approach based on multivariable transmissibility with different transferring outputs.” J. Sound Vib. 351 (1): 90–105. https://doi.org/10.1016/j.jsv.2015.04.024.
Araújo, I. G., and J. E. Laier. 2014. “Operational modal analysis using SVD of power spectral density transmissibility matrices.” Mech. Syst. Sig. Process. 46 (1): 129–145. https://doi.org/10.1016/j.ymssp.2014.01.001.
Araújo, I. G., J. A. G. Sánchez, and P. Andersen. 2018. “Modal parameter identification based on combining transmissibility functions and blind source separation techniques.” Mech. Syst. Sig. Process. 105 (15): 276–293. https://doi.org/10.1016/j.ymssp.2017.12.016.
Brincker, R., and C. Ventura. 2015. Introduction to operational modal analysis. Hoboken, NJ: Wiley.
Brincker, R., and L. Zhang. 2009. “Frequency domain decomposition revisited.” In Proc., 3rd Int. Operational Modal Analysis Conf., 615–626. Odense, Denmark: Syddansk Universitet Campusvej.
Brincker, R., L. Zhang, and P. Andersen. 2000. “Modal identification from ambient responses using frequency domain decomposition.” In Proc., 18th Int. Modal Analysis Conf., 625–630. Thousand Oaks, CA: Sage Publications.
Chopra, A. K. 2001. Dynamics of structures: Theory and applications to earthquake engineering. Hoboken, NJ: Prentice-Hall.
Devriendt, C., and P. Guillaume. 2007. “The use of transmissibility measurements in output-only modal analysis.” Mech. Syst. Sig. Process. 21 (7): 2689–2696. https://doi.org/10.1016/j.ymssp.2007.02.008.
Devriendt, C., and P. Guillaume. 2008. “Identification of modal parameters from transmissibility measurements.” J. Sound Vib. 314 (1–2): 343–356. https://doi.org/10.1016/j.jsv.2007.12.022.
Devriendt, C., G. Steenackers, G. De Sitter, and P. Guillaume. 2010. “From operating deflection shapes towards mode shapes using transmissibility measurements.” Mech. Syst. Sig. Process. 24 (3): 665–677. https://doi.org/10.1016/j.ymssp.2009.10.018.
Devriendt, C., W. Weijtjens, G. De Sitter, and P. Guillaume. 2013. “Combining multiple single-reference transmissibility functions in a unique matrix formulation for operational modal analysis.” Mech. Syst. Sig. Process. 40 (1): 278–287. https://doi.org/10.1016/j.ymssp.2013.04.008.
Do, V.-D., T.-P. Le, and A. Beakou. 2017. “Transmissibility based operational modal analysis in presence of harmonics.” In Proc., Congrès International de Géotechnique–Ouvrages–Structures, 972–980. New York: Springer.
Ku, C. J., J. E. Cermak, and L.-S. Chou. 2007. “Random decrement based method for modal parameter identification of a dynamic system using acceleration responses.” J. Wind Eng. Ind. Aerodyn. 95 (6): 389–410. https://doi.org/10.1016/j.jweia.2006.08.004.
Leclere, Q., N. B. Roozen, and C. Sandier. 2014. “On the use of the H-s estimator for the experimental assessment of transmissibility matrices.” Mech. Syst. Sig. Process. 43 (1–2): 237–245. https://doi.org/10.1016/j.ymssp.2013.09.008.
Magalhaes, F., A. Cunha, E. Caetano, and R. Brincker. 2010. “Damping estimation using free decays and ambient vibration tests.” Mech. Syst. Sig. Process. 24 (5): 1274–1290. https://doi.org/10.1016/j.ymssp.2009.02.011.
Overschee, P. V., B. L. D. Moor, D. A. Hensher, J. M. Rose, W. H. Greene, K. Train, W. Greene, E. Krause, J. Gere, and R. Hibbeler. 1996. Subspace identification for the linear systems: Theory–Implementation. Boston: Kluwer Academic Publishers.
Peeters, B., H. Van der Auweraer, P. Guillaume, and J. Leuridan. 2004. “The PolyMAX frequency-domain method: A new standard for modal parameter estimation?” Shock Vibr. 11 (3–4): 395–409. https://doi.org/10.1155/2004/523692.
Weijtjens, W., G. De Sitter, C. Devriendt, and P. Guillaume. 2014a. “Operational modal parameter estimation of MIMO systems using transmissibility functions.” Automatica 50 (2): 559–564. https://doi.org/10.1016/j.automatica.2013.11.021.
Weijtjens, W., J. Lataire, C. Devriendt, and P. Guillaume. 2014b. “Dealing with periodical loads and harmonics in operational modal analysis using time-varying transmissibility functions.” Mech. Syst. Sig. Process. 49 (1–2): 154–164. https://doi.org/10.1016/j.ymssp.2014.04.008.
Yan, W., and W. Ren. 2013. “On the use of continuous wavelet transmissibility for structural operational modal analysis.” J. Struct. Eng. 139 (9): 1444–1456. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000711.
Yan, W.-J., and W.-X. Ren. 2012. “Operational modal parameter identification from power spectrum density transmissibility.” Comput. Aided Civ. Infrastruct. Eng. 27 (3): 202–217. https://doi.org/10.1111/j.1467-8667.2011.00735.x.
Yan, W.-J., and W.-X. Ren. 2015. “An enhanced power spectral density transmissibility (EPSDT) approach for operational modal analysis: Theoretical and experimental investigation.” Eng. Struct. 102 (1): 108–119. https://doi.org/10.1016/j.engstruct.2015.08.009.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 145 • Issue 6 • June 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 26, 2018
Accepted: Nov 6, 2018
Published online: Mar 27, 2019
Published in print: Jun 1, 2019
Discussion open until: Aug 27, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.