Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T06:56:21.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Least action criteria for blind separation of structural modes

Published online by Cambridge University Press:  14 February 2014

J. Antoni ,
S. Chauhan ,
T. Monnier  and
K. Gryllias
J. Antoni*
Affiliation:
Laboratoire Vibrations Acoustique, University of Lyon, 69621 Villeurbanne, France
S. Chauhan
Affiliation:
Bruel & Kjaer Sound and Vibration Measurement A/S, Skodsborgvej 307, 2850 Naerum, Denmark
T. Monnier
Affiliation:
Laboratoire Vibrations Acoustique, University of Lyon, 69621 Villeurbanne, France
K. Gryllias
Affiliation:
Laboratoire Vibrations Acoustique, University of Lyon, 69621 Villeurbanne, France
*
a Corresponding author: jerome.antoni@insa-lyon.fr

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It was recently shown that blind source separation (BSS), as originally developed in the signal processing community, can be used in operational modal analysis to separate the responses of a structure into its individual modal contributions. This, in turn, allows the application of simple single-of-degree-freedom techniques to identify the modal parameters of interest. Several publications have recently attempted to give a posteriori physical interpretations to BSS – as initially developed in telecommunication signal processing – when applied to the field of structural dynamics. This paper proposes to follow the route the other way round. It shows that several separation criteria purposely dedicated to operational modal analysis can be deduced from general physical considerations. Three such examples are introduced, based on very different properties that uniquely characterise a structural mode. The first criterion, coined the “principle of shortest envelope”, conjectures that the envelope of a modal response has, among all possible envelopes, the shortest length. That such a principle leads to the governing differential equation of a single-degree-of-freedom oscillator is proved from calculus of variation. The second criterion, coined the “principle of minimum spectral variance”, conjectures that the frequency spectrum of a structural mode is maximally concentrated around its central frequency. Finally, the third criterion, coined the “principle of least spectral complexity”, states that a structural mode has the lowest possible entropy in the frequency domain. All three criteria can be expressed in terms of a mixing matrix whose columns contain the unknown mode shapes. The recovery of the latter is then trivially achieved by minimising the criteria. Extensive simulations show that the proposed criteria lead to figures of merit very similar to those of the state-of-the-art, while at the same time providing physical insight that other algorithms issued form the signal processing community may dramatically lack.

Keywords

Operational modal analysisblind source separationleast action principlecalculus of variationstructural dynamicsAnalyse modale opérationnelleséparation aveugle de sourcesprincipe de moindre actioncalcul des variationsdynamique des structures
Type
Research Article
Information
Mechanics & Industry , Volume 14 , Issue 6 , 2013 , pp. 397 - 411
Copyright
© AFM, EDP Sciences 2014

References

P. Van Overschee, B. De Moor, Subspace Identification for Linear Systems: Theory-Implementations-Applications, Kluwer Academic Publishers, Dordrecht, Netherlands, 1996
R. Brincker, P. Andersen, Understanding stochastic subspace identification, Proceedings of the 24th IMAC, St. Louis, Missouri, 2006
Kerschen, G., Poncelet, F., Golinval, J.-C., Physical interpretation of independent component analysis in structural dynamics, Mech. Syst. Signal Process. 21 (2007) 1561−1575 CrossRefGoogle Scholar
Poncelet, F., Kerschen, G., Golinval, J.-C., Verhelst, D., Output-only modal analysis using blind source separation techniques”, Mech. Syst. Signal Process. 21 (2007) 2335−2358 CrossRefGoogle Scholar
Zhou, W., Chelidze, D., Blind source separation based vibration mode identification, Mech. Syst. Signal Process. 21 (2007) 3072−3087 CrossRefGoogle Scholar
S. Chauhan, R. Martell, R.J. Allemang, D.L. Brown, Application of independent component analysis and blind source separation techniques to operational modal analysis, Proceedings of the 25th IMAC, Orlando (FL), USA, 2007
McNiell, S.I., Zimmerman, D.C., A Framework for blind modal identification using joint approximate diagonalization, Mech. Syst. Signal Process. 22 (2008) 1526−1548 CrossRefGoogle Scholar
Hazra, Roffel, A.J., Narasimhan, S., Pandey, M.D., Modified cross-correlation method for the blind identification of structures, J. Eng. Mech. 136 (2010) 889−897 Google Scholar
McNeill, S.I., Zimmerman, D.C., Relating independent components to free-vibration modal responses, Shock and Vibration 17 (2010) 161−170 CrossRefGoogle Scholar
Swaminathan, B. Sharma, S. Chauhan, Utilization of blind source separation techniques for modal analysis, Proceedings of the 28th IMAC, Jacksonville (FL), USA, 2010
Jing, H., Yuan, H.-Q., Wu, F.-G., Research on dynamic response of MDOF systems using independent component analysis, Wuhan Ligong Daxue Xuebao/Journal of Wuhan University of Technology 32 (2010) 68−72 Google Scholar
Zhang, X.-D., Yao, Q.-F., Method of modal parameters identification based on blind sources separation, Zhendong yu Chongji/Journal of Vibration and Shock 29 (2010) 150−153 Google Scholar
Jing, H., Yuan, H.-Q., Zhao, Y., Structural modal parameter identification based on independent component analysis, Zhendong yu Chongji/Journal of Vibration and Shock 29 (2010) 137−141 Google Scholar
Fu, Z.-C., Cheng, W., Xu, C., Modal parameter identification via robust second-order blind identification method, Zhendong yu Chongji/Journal of Vibration and Shock 29 (2010) 108−111 Google Scholar
V.H. Nguyen, J.C. Golinval, Damage detection using blind source separation techniques, Proceedings of the 29th IMAC, Jacksonville (FL), USA, 2011
Antoni, J., Braun, S., Special Issue: Blind Source Separation, Mech. Syst. Signal Process. 19 (2005) 1163−1380 CrossRefGoogle Scholar
Antoni, J., Blind separation of vibration components: principles and demonstrations, Mech. Syst. Signal Process. 19 (2005) 1166−1180 CrossRefGoogle Scholar
J. Antoni, S. Chauhan, Second Order Blind Source Separation techniques (SO-BSS) and their relation to Stochastic Subspace Identification (SSI) algorithm, IMAC XXVIII (International Modal Analysis Conference), Jacksonville, Florida, 2010
J. Antoni, S. Chauhan, An Alternating Least Squares (ALS) based Blind Source Separation Algorithm for Operational Modal Analysis, IMAC XXIX (International Modal Analysis Conference), Jacksonville, Florida, 2011
Antoni, J., Chauhan, S., A study and extension of second-order blind source separation to operational modal analysis, J. Sound Vib. 332 (2013) 1079−1106 CrossRefGoogle Scholar
A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, E. Moulines, A blind source separation technique using second order statistics, IEEE Trans. Signal Process. 45 (1997) pp. 434−444
Cardoso, J.-F., Blind signal separation: statistical principles, Proc. IEEE 86 (1998) 2009−2025 CrossRefGoogle Scholar
Hyvarinen, , Oja, E., Independent component analysis: algorithms and applications, Neural Netw. 13 (2000) 411−430 CrossRefGoogle Scholar
Hyvarinen, J. Karhunen, E. Oja, Independent Component Analysis, John Wiley and Sons, New York, 2001
A. Cichocki, S. Amari, Adaptive blind signal and image processing, John Wiley and Sons, New York, 2002
S.J. Shelly, Investigation of discrete modal filters for structural dynamic applications, PhD Dissertation, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, 1991
M. Feldman, Hilbert Transform Applications in Mechanical Vibration, Wiley, 2011
V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1989
A. Bellino, A. Fasana, E. Gandino, L. Garibaldi, S. Marchesiello, A time-varying inertia pendulum: modelling and experiments, Mech. Syst. Signal Process., Available online 22 May 2013
http://www.me.mtu.edu/imac_oma/ (last visit 08/08/2013)