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Identifying Robust Subspaces for Dynamically Consistent Reduced-Order Models

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Nonlinear Dynamics, Volume 2

Abstract

Nonlinear models for large/complex structures are hard to simulate for parametric studies of long-time dynamical behaviors. Reduced order models (ROMs) provide tools that both allow long-time dynamical simulations and reduce data storage requirements. In data-based model reduction, there is usually no consistent way to determine if the obtained ROM is robust to the variations in system parameters. Here, we use two concepts of “dynamical consistency” and “subspace robustness” to evaluate ROMs validity for parametric studies. The application of these concepts is demonstrated by reducing a nonlinear finite element model of a cantilever beam in a two well potential field. The resulting procedure can be used for developing and evaluating ROMs that are robust to the variations in the parameters or operating conditions.

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Notes

  1. 1.

    As an example, POMs capturing maximal energy for a deterministic steady state motion will be generally different from POMs for a stochastically excited system.

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Acknowledgements

This paper is based upon work supported by the National Science Foundation under Grant No. 1100031.

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Authors and Affiliations

  1. Department of Mechanical, Industrial and Systems Engineering, Rhode Island University, Kingston, RI, 02881, USA

    David Chelidze

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  1. David Chelidze
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Correspondence to David Chelidze .

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Editors and Affiliations

  1. University of Liege, Liege, Belgium

    Gaetan Kerschen

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© 2014 The Society for Experimental Mechanics, Inc.

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Chelidze, D. (2014). Identifying Robust Subspaces for Dynamically Consistent Reduced-Order Models. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04522-1_11

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  • DOI: https://doi.org/10.1007/978-3-319-04522-1_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04521-4

  • Online ISBN: 978-3-319-04522-1

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