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

Abstract

The method of elastic multibody systems is frequently used to describe the dynamical behavior of the mechanical subsystems in multi-physics simulations. One important issue for the simulation of elastic multibody systems is the errorcontrolled reduction of the flexible body's degrees of freedom. By the use of second order frequency-weighted Gramian matrix based reduction techniques the distribution of the loads is taken into account a-priori and very accurate models can be obtained within a predefined frequency range and even a-priori error bounds are available. However, the calculation of the frequency-weighted Gramian matrices requires high computational effort. Hence, appropriate approximation schemes have to be used to find the dominant eigenspace of these matrices. In the current contribution, the matrix integral needed for calculating the Gramian matrices is approximated by quadratures using integral kernel snapshots. The number and location of these snapshots have a strong influence on the reduction results. Sophisticated snapshot selection methods based on Greedy algorithms from the reduced basis methods are used to construct the optimal location of snapshot frequencies. The method can be viewed as an automatic determination of optimal frequency weighting and as an adaptive learning of quadrature rules. One ingredient of Greedy algorithms is the need of error measures. To gain computational advantage two different error estimators are derived and used in the Greedy algorithm instead of the absolute or relative error.

Frequency Interval Gramians Based Structure Preserving Model Order Reduction for Second Order Systems

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“…Comparison of proposed and Krylov Technique . [Color figure can be viewed at wileyonlinelibrary.com]…”

The modal reduction method for multi‐body dynamics with non‐smooth contact

“…For the works on general multi‐body dynamics, mostly in smooth context, refer to and references therein. The theoretical and computational problems of model reduction in multi‐body systems in smooth context are studied, for example, in . Specifically, deals with a floating frame formulation, which is of main concern in the current paper.…”

Interface Reduction for CMS Methods and Alternative Model Order Reduction

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