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Article

Simultaneous Regression and Selection in Nonlinear Modal Model Identification

1
ATA Engineering Inc., San Diego, CA 92128, USA
2
Glowstik Inc., Denver, CO 80222, USA
3
Department of Engineering Physics, University of Wisconsin Madison, Madison, WI 53705, USA
4
Structural Sciences Center, Air Force Research Laboratory, Wright-Patterson AFB, Dayton, OH 45433, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Jean-Philippe Noël
Vibration 2021, 4(1), 232-247; https://doi.org/10.3390/vibration4010016
Received: 9 January 2021 / Revised: 22 February 2021 / Accepted: 24 February 2021 / Published: 13 March 2021
(This article belongs to the Special Issue Data-Driven Modelling of Nonlinear Dynamic Systems)
High fidelity finite element (FE) models are widely used to simulate the dynamic responses of geometrically nonlinear structures. The high computational cost of running long time duration analyses, however, has made nonlinear reduced order models (ROMs) attractive alternatives. While there are a variety of reduced order modeling techniques, in general, their shared goal is to project the nonlinear response of the system onto a smaller number of degrees of freedom. Implicit Condensation (IC), a popular and non-intrusive technique, identifies the ROM parameters by fitting a polynomial model to static force-displacement data from FE model simulations. A notable drawback of these models, however, is that the number of polynomial coefficients increases cubically with the number of modes included within the basis set of the ROM. As a result, model correlation, updating and validation become increasingly more expensive as the size of the ROM increases. This work presents simultaneous regression and selection as a method for filtering the polynomial coefficients of a ROM based on their contributions to the nonlinear response. In particular, this work utilizes the method of least absolute shrinkage and selection (LASSO) to identify a sparse set of ROM coefficients during the IC regression step. Cross-validation is used to demonstrate accuracy of the sparse models over a range of loading conditions. View Full-Text
Keywords: reduced order models; nonlinear dynamics; finite element analysis; nonlinear normal modes; parameter identification reduced order models; nonlinear dynamics; finite element analysis; nonlinear normal modes; parameter identification
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MDPI and ACS Style

Van Damme, C.; Madrid, A.; Allen, M.; Hollkamp, J. Simultaneous Regression and Selection in Nonlinear Modal Model Identification. Vibration 2021, 4, 232-247. https://doi.org/10.3390/vibration4010016

AMA Style

Van Damme C, Madrid A, Allen M, Hollkamp J. Simultaneous Regression and Selection in Nonlinear Modal Model Identification. Vibration. 2021; 4(1):232-247. https://doi.org/10.3390/vibration4010016

Chicago/Turabian Style

Van Damme, Christopher, Alecio Madrid, Matthew Allen, and Joseph Hollkamp. 2021. "Simultaneous Regression and Selection in Nonlinear Modal Model Identification" Vibration 4, no. 1: 232-247. https://doi.org/10.3390/vibration4010016

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