Improvement of Krylov-Subspace-Reduced Models by Iterative Mode-Truncation

摘要

Model order reduction techniques are well established in control theory and likewise in structural mechanics, e.g. when dealing with Elastic Multi-Body-Systems. Apart from the reduction method used, the objective lies in finding a minimal reliable model dimension with desired quality. Extensive research has been conducted concerning Krylov-subspace methods. Rational Krylov-subspace methods based on the second-order Arnoldi-algorithm (SOAR) turned out to give promising results. Current investigations are about generating an optimal reduced model by iteratively choosing the expansion points based on a predefined model dimension. Still, the sufficient choice of this initial dimension is uncertain. The novel approach consists of a two-stage strategy and starts with a fairly large reduced model based on a fixed number and distribution of expansion points. By an iterative post-treatment, the dispensable Krylov-modes are truncated. For an efficient and fast calculation, a special reordering scheme for the Krylov-modes is introduced. Numerical experiments at different mechanical models show, that the novel technique is comparatively fast and confidently generates reliable models with a minimal dimension.