A Modal Identification Algorithm Combining Blind Source Separation and State Space Realization

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DOI: 10.4236/jsip.2013.42025    4,043 Downloads   7,068 Views   Citations
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ABSTRACT

A modal identification algorithm is developed, combining techniques from Second Order Blind Source Separation (SOBSS) and State Space Realization (SSR) theory. In this hybrid algorithm, a set of correlation matrices is generated using time-shifted, analytic data and assembled into several Hankel matrices. Dissimilar left and right matrices are found, which diagonalize the set of nonhermetian Hankel matrices. The complex-valued modal matrix is obtained from this decomposition. The modal responses, modal auto-correlation functions and discrete-time plant matrix (in state space modal form) are subsequently identified. System eigenvalues are computed from the plant matrix to obtain the natural frequencies and modal fractions of critical damping. Joint Approximate Diagonalization (JAD) of the Hankel matrices enables the under determined (more modes than sensors) problem to be effectively treated without restrictions on the number of sensors required. Because the analytic signal is used, the redundant complex conjugate pairs are eliminated, reducing the system order (number of modes) to be identified half. This enables smaller Hankel matrix sizes and reduced computational effort. The modal auto-correlation functions provide an expedient means of screening out spurious computational modes or modes corresponding to noise sources, eliminating the need for a consistency diagram. In addition, the reduction in the number of modes enables the modal responses to be identified when there are at least as many sensors as independent (not including conjugate pairs) modes. A further benefit of the algorithm is that identification of dissimilar left and right diagonalizers preclude the need for windowing of the analytic data. The effectiveness of the new modal identification method is demonstrated using vibration data from a 6 DOF simulation, 4-story building simulation and the Heritage court tower building.

Cite this paper

S. McNeill, "A Modal Identification Algorithm Combining Blind Source Separation and State Space Realization," Journal of Signal and Information Processing, Vol. 4 No. 2, 2013, pp. 173-185. doi: 10.4236/jsip.2013.42025.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] L. Tong, V. C. Soon, Y. Huang and R. Liu, “AMUSE: A New Blind Identification Algorithm,” Proceedings of IEEE International Symposium on Circuits and Systems, New Orleans, 1-3 May 1990, pp. 1784-1787. doi:10.1109/ISCAS.1990.111981
[2] A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso and E. Moulines, “A Blind Source Separation Technique Using Second-Order Statistics,” IEEE Transactions on Signal Processing, Vol. 45, No. 2, 1997, pp. 434-444. doi:10.1109/78.554307
[3] S. Chauhan, R. J. Allemang, R. Martell and D. L. Brown, “Application of Independent Component Analysis and Blind Source Separation Techniques to Operational Modal Analysis,” Proceedings of the 25th International Modal Analysis Conference, Orlando, 19-22 February 2007.
[4] F. Poncelet, G. Kerschen, J.-C. Golinval and D. Verhelst, “Output-Only Modal Analysis Using Blind Source Separation Techniques,” Mechanical Systems and Signal Processing, Vol. 21, No. 6, 2007, pp. 2335-2358. doi:10.1016/j.ymssp.2006.12.005
[5] W. Zhou and D. Chelidze, “Blind Source Separation Based Vibration Mode Identification,” Proceedings of the 25th International Modal Analysis Conference, Orlando, 19-22 February 2007, pp. 3072-3087.
[6] S. I. McNeill and D. C. Zimmerman, “A Framework for Blind Modal Identification Using Joint Approximate Diagonalization,” Mechanical Systems and Signal Processing, Vol. 22, No. 7, 2007, pp. 1526-1548. doi:10.1016/j.ymssp.2008.01.010
[7] S. I. McNeill, “Modal Identification Using Blind Source Separation Techniques,” Ph.D. Dissertation, University of Houston, Houston, 2007.
[8] S. I. McNeill and D. C. Zimmerman, “Blind Modal Identification Applied to Output-Only Building Vibration,” Proceedings of the 28th International Modal Analysis Conference, Jacksonville, 2010.
[9] S. I. McNeill, “An Analytic Formulation for Blind Modal Identification,” Journal of Vibration and Control, Vol. 18, No. 14, 2012, pp. 2111-2121. doi:10.1177/1077546311429146
[10] A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso and E. Moulines, “A Blind Source Separation Technique Using Second-Order Statistics,” IEEE Transactions on Signal Processing, Vol. 45, No. 2, pp. 434-444. doi:10.1109/78.554307
[11] P. Tichavsky and A. Yeredor, “Fast Approximate Joint Diagonalization Incorporating Weight Matrices,” IEEE Transactions of Signal Processing, Vol. 57. No. 3, 2009, pp. 878-891. doi:10.1109/TSP. 2008.2009271
[12] P. Tichavsky, A. Yeredor and J. Nielsen, “A Fast Approximate Joint Diagonalization Algorithm Using a Criterion with a Block Diagonal Weight Matrix,” Proceedings of the 2008 International Conference on Acoustics, Speech and Signal Processing, Las Vegas, 31 March-4 April 2008, pp. 3321-3324.
[13] P. Tichavsky, “UWEDGE_C—Complex Version (Version for Complex-Valued Matrices and Complex-Valued Mixing) of the Algorithm UWEDGE,” 2010. http://si.utia.cas.cz/downloadPT.htm
[14] F. Abazarsa, S. Ghahari, F. Nateghi and E. Taciroglu, “Response-Only Modal Identification of Structures Using Limited Sensors,” Structural Control and Health Monitoring, Vol. 20, No. 6, 2013, pp. 987-1006. doi:10.1002/stc.1513
[15] F. Abazarsa, S. Ghahari, F. Nateghi and E. Taciroglu, “Blind Modal Identification of Non-Classically Damped Systems from Free or ambient Vibration Records,” Earthquake Spectra, in Press.
[16] S. I. McNeill, “Extending Blind Modal Identification to the Underdetermined Case for Ambient Vibration,” Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, Houston, 9-15 November 2012.
[17] L. De Lathauwer and J. Castaing, “Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization,” IEEE Transactions on Signal Processing, Vol. 56, No. 3, 2008, pp. 1096-1105. doi:10.1109/TSP.2007.908929
[18] J. Antoni and S. Chauhan, “Second Order Blind Source Separation Techniques (SO-BSS) and Their Relation to Stochastic Subspace Identification (SSI) Algorithm,” Proceedings of the 28th International Modal Analysis Conference (IMAC), 2010.
[19] J. Antoni and S. Chauhan, “A Study and Extension of Second-Order Blind Source Separation to Operational Modal Analysis,” Journal of Sound and Vibration, Vol. 332, No. 4, 2013, pp. 1079-1106. doi:10.1016/j.jsv.2012.09.016
[20] A.-J. van der Veen, “Joint Diagonalization via Subspace Fitting Techniques,” International Conference on Acoustics, Speech, and Signal Processing—ICASSP, Salt Lake City, 7-11 May 2001, pp. 2773-2776.
[21] R. J. Allemang and D. L. Brown, “A Correlation Coefficient for Modal Vector Analysis,” Proceedings of the 1st International Modal Analysis Conference, Orlando, 8-10 November 1982, pp. 110-116.
[22] C. Ventura, R. Brinker, E. Dascotte and P. Anderson “FEM Updating of the Heritage Court Building Structure,” Proceedings of the 19th International Modal Analysis Conference, Kissimmee, 5-8 February, 2001, pp. 324-330.
[23] B. Peeters, “System Identification and Damage Detection in Civil Engineering,” Ph.D. Dissertation, Katholike Universite Leuven, Belgium, 2000.

  
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