Non-linear System Identification Using the Hilbert-Huang Transform and Complex Non-linear Modal Analysis

  • Vaclav Ondra
  • Ibrahim A. Sever
  • Christoph W. Schwingshackl
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Modal analysis is a well-established method for analysis of linear dynamic structures, but its extension to non-linear structures has proven to be much more problematic. A number of viewpoints on non-linear modal analysis as well as a range of different non-linear system identification techniques have emerged in the past, each of which tries to preserve a subset of properties of the original linear theory. The objective of this paper is to discuss how the Hilbert-Huang transform can be used for detection and characterization of non-linearity, and to present an optimization framework which combines the Hilbert-Huang transform and complex non-linear modal analysis for quantification of the selected model. It is argued that the complex non-linear modes relate to the intrinsic mode functions through the reduced order model of slow-flow dynamics. The method is demonstrated on simulated data from a system with cubic non-linearity.


Non-linear system identification Hilbert-Huang transform Complex non-linear modal analysis Detection and characterization of non-linearity Complex non-linear modes 



The authors are grateful to Rolls-Royce plc for providing the financial support for this project and for giving permission to publish this work. This work is part of a Collaborative R and T Project “SAGE 3 WP4 Nonlinear Systems” supported by the CleanSky Joint Undertaking and carried out by Rolls-Royce plc and Imperial College.


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Copyright information

© The Society for Experimental Mechanics, Inc. 2017

Authors and Affiliations

  • Vaclav Ondra
    • 1
  • Ibrahim A. Sever
    • 2
  • Christoph W. Schwingshackl
    • 1
  1. 1.Imperial College LondonLondonUK
  2. 2.Rolls-Royce plcDerbyUK

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