Stochastic Modal Appropriation (SMA)

  • M. Abdelghani
  • M. I. Friswell
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


All available modal identification algorithms (for example SSI, FDD, ARMA) are based on the principle of subspaces in the sense that the pole is identified which characterizes the signal subspace and the noise subspace is taken automatically as its orthogonal complement. This is a response type characterization. For structural dynamics applications however, one is interested in different subspaces, namely the non-conservative subspace and the conservative subspace. The only currently available method that does this is the force appropriation method for in-laboratory testing. In this work, we propose an In-Operation structural identification algorithm based on a different principle, namely the anti-symmetry principle. The idea is as follows: Consider the response of a structure. Construct the anti-symmetric response depending on a certain unknown parameter and consider the resultant of both. This introduces a rotation to the original signal. By varying the parameter, one spans a lot of different subspaces and by proper (mathematically derived) operations on these subspaces and the original one it is possible to cancel out one subspace leaving the data in a single subspace from which the proper parameters can be estimated. This idea is formulated mathematically for a SDOF system subject to unmeasured white noise excitation and it is shown that it provides highly accurate modal parameter estimates.


In-operation modal analysis Modal appropriation Output-only modal analysis Identification 


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    Abdelghani, M., Inman, D.J.: Modal appropriation for use with in-operation modal analysis. J Shock Vib. 2015, 537030 (2015)Google Scholar
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    Balmès, E., Chapelier, C., Lubrina, P., Fargette, P.: An evaluation of modal testing results based on the force appropriation method. International Modal Analysis Conference, Orlando (1996).Google Scholar
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    Meirovitch, L.: Elements of Vibration Analysis. McGraw-Hill, New York (1986)zbMATHGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2019

Authors and Affiliations

  • M. Abdelghani
    • 1
  • M. I. Friswell
    • 2
  1. 1.University of SousseSousseTunisia
  2. 2.College of Engineering, University of Swansea, Bay CampusSwanseaUK

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