An Alternating Least Squares (ALS) based Blind Source Separation Algorithm for Operational Modal Analysis

  • J. Antoni
  • S. Chauhan
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


In a former paper (“Second Order Blind Identification (SOBI) and its relation to Stochastic Subspace Identification (SSI) algorithm”, 28th IMAC, 2010), the authors established the link between the popular SSI algorithm used in output-only modal analysis and the Second Order Blind Identification (SOBI) algorithm developed for blind source separation in the field of signal processing. It was concluded that the two algorithms, although seemingly very different, are actually jointly diagonalizing the same covariance matrix over a range of time-lags. This is explicit in SOBI and implicit in SSI. One main difference, however, is that SOBI focuses on estimating the (real) modal matrix as a joint diagonalizer, but without taking advantage of the specific structure of the covariance matrix formed by the Markov coefficients and by incorrectly assuming no-damping or very low damping. On the other hand, SSI specifically exploits the covariance matrix structure so as to estimate complex modes, but puts less emphasis on the “joint diagonalizing” property of the modal matrix. The aim of this communication is to introduce a new algorithm based on Alternating Least Squares (ALS) approach that combines advantages of both SOBI and SSI in order to return improved estimates of modal parameters. It is shown in this work that this algorithm is capable of identifying complex modes, closely spaced modes and heavily damped and can also be expanded to deal with the cases where there are less number of sensors available than the number modes to be estimated. The suggested approach therefore is a step towards expanding the applicability of BSS based approaches to Operational Modal Analysis applications.


Modal Parameter Independent Component Analysis Blind Source Separation Alternative Little Square Experimental Modal Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Cichocki, A., Amari, S., Adaptive blind signal and image processing, John Wiley and Sons, New York, 2002.Google Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    Special Issue: Blind source separation, Mechanical Systems and Signal Processing, Vol. 19 (6), pp. 1163-1380, November, 2005.Google Scholar
  4. 4.
    Kerschen, G., Poncelet, F., Golinval, J.C., Physical Interpretation of Independent Component Analysis in Structural Dynamics, Mechanical Systems and Signal Processing (21), pp. 1561-1575, 2007.Google Scholar
  5. 5.
    Poncelet, F., Kerschen, G., Golinval, J.C., Experimental Modal Analysis Using Blind Source Separation Techniques, Proceedings of ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium, 2006.Google Scholar
  6. 6.
    Chauhan, S., Martell, R., Allemang, R. J. and Brown, D. L., Application of Independent Component Analysis and Blind Source Separation Techniques to Operational Modal Analysis, Proceedings of the 25th IMAC, Orlando (FL), USA, 2007.Google Scholar
  7. 7.
    McNiell, S.I., Zimmerman, D.C., A Framework for Blind Modal Identification Using Joint Approximate Diagonalization, Mechanical Systems and Signal Processing (22), pp. 1526-1548, 2008.Google Scholar
  8. 8.
    McNiell, S.I., Zimmerman, D.C., Blind Modal Identification Applied to Output-only Building Vibration, Proceedings of the 28th IMAC, Jacksonville (FL), USA, 2010.Google Scholar
  9. 9.
    Antoni, J., Chauhan, S., Second Order Blind Source Separation Techniques (SO-BSS) and Their Relation to Stochastic Subspace Identification (SSI) Algorithm, Proceedings of the 28th IMAC, Jacksonville (FL), USA, 2010.Google Scholar
  10. 10.
    Van Overschee, P., De Moor, B., Subspace Identification for Linear Systems: Theory-Implementations-Applications, Kluwer Academic Publishers, Dordrecht, Netherlands, 1996.Google Scholar
  11. 11.
    Brincker, R., Andersen, P., Understanding Stochastic Subspace Identification, Proceedings of the 24th IMAC, St. Louis, Missouri, 2006.Google Scholar
  12. 12.
    Allemang, R.J.; Vibrations: Experimental modal analysis, Structural Dynamics Research Laboratory, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, 1999,
  13. 13.
    Ten Berge, J.M.F, Least Squares Optimization in Multivariate Analysis, DSWO Press, Leiden, The Netherlands, 1993.Google Scholar
  14. 14.
    Tucker, L.R., Some mathematical notes on three-mode factor analysis, Psychometrika, 31, 279-311, 1966.MathSciNetCrossRefGoogle Scholar
  15. 15.
    Vega-Montoto, L. & Wentzell, P.D., Maximum likelihood parallel factor analysis (MLPARAFAC), Journal of Chemometrics, 17, 237-253, 2003.CrossRefGoogle Scholar
  16. 16.
    Tomasi, G. & Bro, R., A comparison of algorithms for fitting the Parafac model, Computational Statistics & Data Analysis, 50, 1700-1734, 2006.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MechanicsUniversity of Technology of Compiegne, Centre de Recherche de RoyallieuCompiegneFrance
  2. 2.Bruel & Kjaer Sound and Vibration Measurement A/SNaerumDenmark

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