Greedy-based approximation of frequency-weighted Gramian matrices for model reduction in multibody dynamics

DOI10.1002/zamm.201200014zbMath1331.70003OpenAlexW2059827386WikidataQ59899511 ScholiaQ59899511MaRDI QIDQ2856581

Bernard Haasdonk, Peter Eberhard, Jörg Fehr, Michael J. Fischer

Publication date: 29 October 2013

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.201200014

zbMATH Keywords

model reductionerror estimatorGramian matrixgreedy methodselastic multibody systems

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) System structure simplification (93B11) Control of mechanical systems (70Q05) Dynamics of multibody systems (70E55)

Related Items (12)

Interface reduction of linear mechanical systems with a modular setup ⋮ SVD-based improvements for component mode synthesis in elastic multibody systems ⋮ Component-level proper orthogonal decomposition for flexible multibody systems ⋮ The modal reduction method for multi-body dynamics with non-smooth contact ⋮ Monitoring the effects of vehicle components’ size on optimum structural crashworthiness ⋮ Well‐scaled, a‐posteriori error estimation for model order reduction of large second‐order mechanical systems ⋮ Damping optimization of parameter dependent mechanical systems by rational interpolation ⋮ Balanced truncation model order reduction in limited time intervals for large systems ⋮ Frequency-Limited Balanced Truncation with Low-Rank Approximations ⋮ Morembs—A Model Order Reduction Package for Elastic Multibody Systems and Beyond ⋮ Interface and model reduction for efficient explicit simulations - a case study with nonlinear vehicle crash models ⋮ Frequency limited Gramians-based structure preserving model order reduction for discrete time second-order systems

Uses Software

• rbMIT
• PMTBR
• MatMorembs

Cites Work

• Gramian-based model reduction for descriptor systems
• Numerical analysis of flexible multibody systems
• Algorithms for model reduction of large dynamical systems
• The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview
• Efficient balancing-based MOR for large-scale second-order systems
• Efficient reduced models anda posteriorierror estimation for parametrized dynamical systems by offline/online decomposition
• All optimal Hankel-norm approximations of linear multivariable systems and theirL,^∞-error bounds†
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Balanced truncation model reduction of second-order systems
• A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space

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