# Error Estimation for the Simulation of Elastic Multibody Systems

@article{Fehr2018ErrorEF,
title={Error Estimation for the Simulation of Elastic Multibody Systems},
author={J{\"o}rg Fehr and Dennis Grunert and Ashish Bhatt and Bernard Haasdonk},
journal={PAMM},
year={2018},
volume={18}
}
• Published 1 December 2018
• Computer Science
• PAMM
One important issue in the development of complex technical system is the use of rapid simulations to evaluate substructures / surrogate models for system level simulations. For safety‐critical simulations, it is essential to know the error introduced by model order reduction (MOR) used to create the surrogate models to decide whether the simulation can be trusted or not. Typically, a‐priori error estimates, e.g., the sum of neglected singular values in balanced truncation are used. They…
2 Citations
A Posteriori Error Estimation in Model Order Reduction of Elastic Multibody Systems with Large Rigid Motion
• Mathematics
IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018
• 2019
We consider the equation of motion of an elastic multibody system in absolute coordinate formulation (ACF). The resulting nonlinear second order DAE of index two has a unique solution and is reduced
Well‐scaled, a‐posteriori error estimation for model order reduction of large second‐order mechanical systems
• Computer Science
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
• 2020
The spectral theorem, power series expansions, monotonicity properties, and self‐tailored algorithms are used to largely speed up the offline phase by one polynomial order both in terms of computation time as well as storage complexity.

## References

SHOWING 1-10 OF 24 REFERENCES
A-posteriori error estimation for second order mechanical systems
• Engineering
• 2012
An a-posteriori error estimator for linear first order systems is extended for error estimation of mechanical second order systems, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.
Interpolation and Truncation Model Reduction Techniques in Coupled Elastic Multibody Systems
• Computer Science
• 2014
It will be shown that for connected systems, the moment matching conditions which are introduced with interpolation methods for single components also hold for the assembly, and error bounds that arise in balanced truncation methods do not hold after the introduction of connections to the environment.
Greedy‐based approximation of frequency‐weighted Gramian matrices for model reduction in multibody dynamics
• Computer Science
• 2013
The method can be viewed as an automatic determination of optimal frequency weighting and as an adaptive learning of quadrature rules that is derived and used in the Greedy algorithm instead of the absolute or relative error.
Morembs—A Model Order Reduction Package for Elastic Multibody Systems and Beyond
• Computer Science
• 2018
An MOR toolbox bridging the gap between theoretical, algorithmic, and numerical developments to an end-user-oriented program, usable by non-experts, was developed called ‘Model Order Reduction of Elastic Multibody Systems' (Morembs).
Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline/online decomposition
• Computer Science, Mathematics
• 2011
The a posteriori error estimation technique can straightforwardly be applied to all traditional projection-based reduction techniques of non-parametric and parametric linear systems, such as model reduction, balanced truncation, moment matching, proper orthogonal decomposition (POD) and so on.
Error indicators for fully automatic extraction of heat-transfer macromodels for MEMS
• Engineering
• 2005
In this paper, we present three heuristic error indicators for the iterative model order reduction of electro-thermal MEMS models via the Arnoldi algorithm. Such error indicators help a designer to
Krylov Projection Methods for Model Reduction
The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation, based on which three algorithms for model reduction are proposed, which are suited for parallel or approximate computations.
H2 Model Reduction for Large-Scale Linear Dynamical Systems
• Computer Science, Mathematics
SIAM J. Matrix Anal. Appl.
• 2008
A new unifying framework for the optimal $\mathcal{H}_2$ approximation problem is developed using best approximation properties in the underlying Hilbert space and leads to a new set of local optimality conditions taking the form of a structured orthogonality condition.
A Survey on Model Reduction of Coupled Systems
• Mathematics
• 2008
In this paper we give an overview of model order reduction techniques for coupled systems. We consider linear time-invariant control systems that are coupled through input-output relations and