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Improving empirical characteristic multiplier estimation through a change of basis

Publication ,  Journal Article
Little, JA; Turner, JD; Mann, BP
Published in: Journal of Sound and Vibration
December 8, 2020

This paper applies empirical Floquet theory to extract characteristic multipliers from time series data and builds upon prior works by significantly reducing the influence of experimental noise. Characteristic multipliers (CMs), which are the eigenvalues of the transition matrix governing the evolution of transient solutions over one period of motion, quantify the local stability of periodic orbits and can be estimated experimentally without knowledge of the system model. Traditionally, empirical CM estimates were obtained from the transient dynamics observed by subtracting measured steady-state behavior from a recorded perturbed response. The subtraction of two experimentally measured quantities amplifies noise, producing inaccurate CM estimates. By applying a moving integral to isolate the transient dynamics, this work provides an approach to reduce, rather than amplify, the influence of noise on empirical CM results. This approach is applied to the reconstructed phase space of a numerical example and an experimental system to demonstrate the improvements.

Duke Scholars

Published In

Journal of Sound and Vibration

DOI

EISSN

1095-8568

ISSN

0022-460X

Publication Date

December 8, 2020

Volume

488

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
 

Citation

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Little, J. A., Turner, J. D., & Mann, B. P. (2020). Improving empirical characteristic multiplier estimation through a change of basis. Journal of Sound and Vibration, 488. https://doi.org/10.1016/j.jsv.2020.115613
Little, J. A., J. D. Turner, and B. P. Mann. “Improving empirical characteristic multiplier estimation through a change of basis.” Journal of Sound and Vibration 488 (December 8, 2020). https://doi.org/10.1016/j.jsv.2020.115613.
Little JA, Turner JD, Mann BP. Improving empirical characteristic multiplier estimation through a change of basis. Journal of Sound and Vibration. 2020 Dec 8;488.
Little, J. A., et al. “Improving empirical characteristic multiplier estimation through a change of basis.” Journal of Sound and Vibration, vol. 488, Dec. 2020. Scopus, doi:10.1016/j.jsv.2020.115613.
Little JA, Turner JD, Mann BP. Improving empirical characteristic multiplier estimation through a change of basis. Journal of Sound and Vibration. 2020 Dec 8;488.
Journal cover image

Published In

Journal of Sound and Vibration

DOI

EISSN

1095-8568

ISSN

0022-460X

Publication Date

December 8, 2020

Volume

488

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences