Common trends in model reduction of large nonlinear finite element (FE)-discretized systems involve Galerkin projection of the governing equations onto a low-dimensional linear subspace. Though this reduces the number of unknowns in the system, the computational cost for obtaining the reduced solution could still be high due to the prohibitive computational costs involved in the evaluation of nonlinear terms. Hyper-reduction methods are then used for fast approximation of these nonlinear terms. In the finite element context, the energy conserving sampling and weighing (ECSW) method has emerged as an effective tool for hyper-reduction of Galerkin-projection-based reduced-order models (ROMs). More recent trends in model reduction involve the use of nonlinear manifolds, which involves projection onto the tangent space of the manifold. While there are many methods to identify such nonlinear manifolds, hyper-reduction techniques to accelerate computation in such ROMs are rare. In this work, we propose an extension to ECSW to allow for hyper-reduction using nonlinear mappings, while retaining its desirable stability and structure-preserving properties. As a proof of concept, the proposed hyper-reduction technique is demonstrated over models of a flat plate and a realistic wing structure, whose dynamics have been shown to evolve over a nonlinear (quadratic) manifold. An online speed-up of over one thousand times relative to the full system has been obtained for the wing structure using the proposed method, which is higher than its linear counterpart using the ECSW.
Skip Nav Destination
Article navigation
August 2019
Research-Article
Hyper-Reduction Over Nonlinear Manifolds for Large Nonlinear Mechanical Systems
Shobhit Jain,
Shobhit Jain
Institute for Mechanical Systems,
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
e-mail: shjain@ethz.ch
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
e-mail: shjain@ethz.ch
1Corresponding author.
Search for other works by this author on:
Paolo Tiso
Paolo Tiso
Institute for Mechanical Systems,
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
Search for other works by this author on:
Shobhit Jain
Institute for Mechanical Systems,
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
e-mail: shjain@ethz.ch
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
e-mail: shjain@ethz.ch
Paolo Tiso
Institute for Mechanical Systems,
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
ETH Zürich Leonhardstrasse 21,
Zürich 8092, Switzerland
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 4, 2018; final manuscript received March 29, 2019; published online May 15, 2019. Assoc. Editor: Zdravko Terze.
J. Comput. Nonlinear Dynam. Aug 2019, 14(8): 081008 (11 pages)
Published Online: May 15, 2019
Article history
Received:
December 4, 2018
Revised:
March 29, 2019
Citation
Jain, S., and Tiso, P. (May 15, 2019). "Hyper-Reduction Over Nonlinear Manifolds for Large Nonlinear Mechanical Systems." ASME. J. Comput. Nonlinear Dynam. August 2019; 14(8): 081008. https://doi.org/10.1115/1.4043450
Download citation file:
Get Email Alerts
Investigation of Nonlinear Dynamic Behaviors of Vertical Rotor System Supported by Aerostatic Bearings
J. Comput. Nonlinear Dynam (January 2025)
Electric Circuit Analogs of First-Order Dual-Phase-Lag Diffusion
J. Comput. Nonlinear Dynam
Related Articles
Nonlinear Dynamics of a Rigid Block on a Rigid Base
J. Appl. Mech (March,1996)
Designing Against Capsize in Beam Seas: Recent Advances and New Insights
Appl. Mech. Rev (May,1997)
MOB Platform Nonlinear Dynamics in a Realistic (Random) Seaway
J. Offshore Mech. Arct. Eng (February,2002)
Uniform Flow Control for a Multipassage Microfluidic Sensor
J. Fluids Eng (February,2013)
Related Proceedings Papers
Related Chapters
Real-Time Prediction Using Kernel Methods and Data Assimilation
Intelligent Engineering Systems through Artificial Neural Networks
Real Time Human Detection using Covariance Matrices as Human Descriptor
International Conference on Computer and Automation Engineering, 4th (ICCAE 2012)
Holmorphic Automorphism Group of a Sort of Three Dimensional Hopf Manifold
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)