A Machine Learning Approach to Nonlinear Modal Analysis

  • K. WordenEmail author
  • P. L. Green
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw–Pierre approach is rather demanding technically, depending as it does on the construction of a polynomial mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach to the Shaw–Pierre method which exploits the idea of independence to optimise the parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD).


Nonlinear systems Nonlinear modal analysis Nonlinear normal modes Invariant manifolds Principal orthogonal decomposition 


  1. 1.
    Ewins DJ (2000) Modal testing: theory, practice and application. Wiley-Blackwell, ChichesterGoogle Scholar
  2. 2.
    Vakakis AF (1997) Non-linear normal modes (NNMs) and their applications in vibration theory. Mech Syst Signal Process 11:3–22CrossRefGoogle Scholar
  3. 3.
    Mikhlin YV (2010) Nonlinear normal modes for vibrating mechanical systems. Review of theoretical developments. Appl Mech Rev 63:606802Google Scholar
  4. 4.
    Worden K, Tomlinson GR (2001) Nonlinearity in structural dynamics: detection, modelling and identification. Institute of Physics PressGoogle Scholar
  5. 5.
    Worden K, Tomlinson GR (2007) Nonlinearity in experimental modal analysis. Philos Trans R Soc Ser A 359:113–130CrossRefGoogle Scholar
  6. 6.
    Murdock J (2002) Normal form theory and unfoldings for local dynamical systems. Springer, BerlinGoogle Scholar
  7. 7.
    Rosenberg RM (1962) The normal modes of nonlinear n-degree-of-freedom systems. J Appl Mech 29:7–14CrossRefzbMATHGoogle Scholar
  8. 8.
    Shaw SW, Pierre C (1993) Normal modes for non-linear vibratory systems. J Sound Vib 164:85–124CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Kerschen G, Peeters M, Golinval J-C, Vakakis AF (2009) Nonlinear normal modes. Part I: a useful framework for the structural dynamicist. Mech Syst Signal Process 23:170–194CrossRefGoogle Scholar
  10. 10.
    Peeters M, Viguié R, Sérandour G, Kerschen G, Golinval J-C (2009) Nonlinear normal modes. Part II: toward a practical computation using numerical continuation techniques. Mech Syst Signal Process 23:195–216CrossRefGoogle Scholar
  11. 11.
    Feeny BF, Kappgantu R (1998) On the physical interpretation of proper orthogonal modes in vibrations. J Sound Vib 211:607–616CrossRefGoogle Scholar
  12. 12.
    Worden K, Manson G (2012) On the identification of hysteretic systems. Part I: fitness landscapes and evolutionary identification. Mech Syst Signal Process 29:201–212CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2014

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Dynamics Research GroupUniversity of SheffieldSheffieldUK

Personalised recommendations