Abstract
Blind Source Separation (BSS) and Independent Component Analysis (ICA) techniques are emerging signal processing techniques that aim at identifying statistically independent sources from a linear mixture of such sources without requiring (or with little) a priori information about the input source signals. Recently, it has been shown that these techniques can also be utilized for Operational Modal Analysis (OMA), or Output-only Modal Analysis, where system characteristics are identified only on the basis of information available from the measured outputs. Second Order Blind Source Separation (SO-BSS) techniques are BSS algorithms that employ diagonalization of output correlation matrices in order to recover information about the original sources and the mixing matrix. Work presented in this paper aims at establishing a link between SO-BSS techniques (such as AMUSE and SOBI) and Stochastic Subspace Iteration (SSI) algorithm, which is a well known OMA algorithm. The paper presents the mathematical theory behind these algorithms and shows how these algorithms are related. In this manner, this work helps in enhancing the overall understanding of BSS techniques and their subsequent use for modal analysis purposes.
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References
Kerschen, G., Poncelet, F., Golinval, J.C. (2007), “Physical Interpretation of Independent Component Analysis in Structural Dynamics”, Mechanical Systems and Signal Processing (21), pp. 1561–1575.
Poncelet, F., Kerschen, G., Golinval, J.C. (2006), “Experimental Modal Analysis Using Blind Source Separation Techniques”; Proceedings of ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium.
Chauhan, S., Martell, R., Allemang, R. J. and Brown, D. L. (2007), “Application of Independent Component Analysis and Blind Source Separation Techniques to Operational Modal Analysis”, Proceedings of the 25th IMAC, Orlando (FL), USA.
McNiell, S.I., Zimmerman, D.C. (2008), “A Framework for Blind Modal Identification Using Joint Approximate Diagonalization”, Mechanical Systems and Signal Processing (22), pp. 1526–1548.
Van Overschee, P., De Moor, B. (1996), Subspace Identification for Linear Systems: Theory-Implementations-Applications, Kluwer Academic Publishers, Dordrecht, Netherlands.
Brincker, R., Andersen, P. (2006), “Understanding Stochastic Subspace Identification”, Proceedings of the 24th IMAC, St. Louis, Missouri.
Cichocki, A., Amari, S.; “Adaptive blind signal and image processing”, John Wiley and Sons, New York, 2002.
Hyvarinen, A., Karhunen, J., Oja, E.; “Independent Component Analysis”, John Wiley and Sons, New York, 2001.
Hyvarinen, A., Oja, E.; “Independent component analysis: Algorithms and applications”, Neural Networks, Vol. 13, p. 411–430, 2000.
Cardoso, J.F.; “Blind signal separation: statistical principles”, Proceedings of the IEEE, Vol. 86, Number 10, pp. 2009–2025, October, 1998.
Lathauwer, L.D., Bart De Moor, Vandewalle, J.; “An introduction to independent component analysis”, Journal of Chemometrics, Vol. 14, pp. 123–149, 2000.
ICA Central, http://www.tsi.enst.fr/icacentral/
Tony Bell’s ICA Webpage, http://www.cnl.salk.edu/~tony/ica.html
“Special Issue: Blind source separation”, Mechanical Systems and Signal Processing, Vol. 19 (6), pp. 1163–1380, November, 2005.
Tong, L., Soon, V.C., Huang, Y., Liu, R.; “AMUSE: a new blind identification algorithm”, Proceedings of IEEE ISCAS, pp. 1784–1787, Vol. 3, New Orleans, LA, 1990.
Belouchrani, A., Abed-Meraim, K.K., Cardoso, J.F., Moulines, E.; “Second order blind separation of correlated sources”, Proceedings of International Conference on Digital Signal Processing, pp. 346–351, 1993.
Cardoso, J.F., Souloumiac, A.; “Jacobi angles for simultaneous diagonalization”, SIAM Journal of Matrix Analysis and Applications, Vol. 17, Number 1, pp. 161–164, January, 1996.
Hori, G.; “A new approach to joint diagonalization”, Proceedings of 2nd International Workshop on ICA and BSS, ICA’ 2000, pp. 151–155, Helsinki, Finland, June 2000.
Shelly, S.J.; “Investigation of discrete modal filters for structural dynamic applications”, PhD Dissertation, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, 1991.
Allemang, R.J.; “Vibrations: Experimental modal analysis”, Structural Dynamics Research Laboratory, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, 1999, http://www.sdrl.uc.edu/sdrl_jscript_homepage.html
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Antoni, J., Chauhan, S. (2011). Second Order Blind Source Separation techniques (SO-BSS) and their relation to Stochastic Subspace Identification (SSI) algorithm. In: Proulx, T. (eds) Structural Dynamics, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9834-7_16
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DOI: https://doi.org/10.1007/978-1-4419-9834-7_16
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