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TRAX: An approach for the time rational analysis of complex dynamic systems

TRAX: An approach for the time rational analysis of complex dynamic systems
TRAX: An approach for the time rational analysis of complex dynamic systems
This paper introduces a theoretical and algorithmic reduced model approach to efficiently evaluate time responses of complex dynamic systems. The proposed approach combines four main components: analytical expressions of the average of the system’s transfer functions in the frequency domain, precise and convergent rational approximations of these exact expressions, exact evaluation of these approximations through model reduction in rational Krylov subspaces, and semi-analytical interpolation at just a few frequency points. The resulting algorithmic principles to evaluate the time response of a particular system are relatively straightforward: one first evaluates the response of the system with slight additional damping at a few frequencies and one then projects or reduces the system in the subspace spanned by these responses. The time response of the reduced model implicitly provides a precise evaluation of that of the original system. The properties of the reduced models and the precision of the proposed approach are studied and applications on complex matrix systems are presented and discussed. While the theory and numerical algorithms are presented in a matrix context, they are also transposable in a continuous functional context.
time response, dynamic system, vibro-acoustics, shock response, frequency averaging, model reduction, rational krylov-pade projection
0029-5981
1371-1399
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c

Lecomte, Christophe (2015) TRAX: An approach for the time rational analysis of complex dynamic systems. International Journal for Numerical Methods in Engineering, 102 (7), 1371-1399. (doi:10.1002/nme.4841).

Record type: Article

Abstract

This paper introduces a theoretical and algorithmic reduced model approach to efficiently evaluate time responses of complex dynamic systems. The proposed approach combines four main components: analytical expressions of the average of the system’s transfer functions in the frequency domain, precise and convergent rational approximations of these exact expressions, exact evaluation of these approximations through model reduction in rational Krylov subspaces, and semi-analytical interpolation at just a few frequency points. The resulting algorithmic principles to evaluate the time response of a particular system are relatively straightforward: one first evaluates the response of the system with slight additional damping at a few frequencies and one then projects or reduces the system in the subspace spanned by these responses. The time response of the reduced model implicitly provides a precise evaluation of that of the original system. The properties of the reduced models and the precision of the proposed approach are studied and applications on complex matrix systems are presented and discussed. While the theory and numerical algorithms are presented in a matrix context, they are also transposable in a continuous functional context.

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Lecomte 2015 Preprint - TRAX.. an approach for the time rational analysis of complex dynamic systems.pdf - Accepted Manuscript
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More information

Published date: 28 January 2015
Keywords: time response, dynamic system, vibro-acoustics, shock response, frequency averaging, model reduction, rational krylov-pade projection
Organisations: Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 370197
URI: http://eprints.soton.ac.uk/id/eprint/370197
ISSN: 0029-5981
PURE UUID: 11ba820e-439c-4d49-a25f-0e78f25a0e0c

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Date deposited: 28 Oct 2014 11:17
Last modified: 14 Mar 2024 18:13

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Author: Christophe Lecomte

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