Modeling structural variability in reduced order models of machine tool assembly groups via parametric MOR. Issue 1 (December 2013)

• Record Type: Journal Article
• Authors: Benner, Peter; Lang, Norman; Saak, Jens
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 13:Issue 1(2013)
• Page Start: 481
• Page End: 482
• Publication Date: 2013-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201310233
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We present a parametric model order reduction (PMOR) method applied to a parameter depending generalized state‐space system, which describes the evolution of the temperature field on a vertical stand of a machine tool assembly group induced by a moving tool slide. The position of this slide parametrizes the input matrix of the associated system. The main idea is to compute projection matrices <italic>V_j</italic>, <italic>W_j</italic> in certain parameter sample points μ<italic>_j</italic> and concatenate them to the projection bases <italic>V</italic>, <italic>W</italic>, respectively, as described in [1]. Instead of using the iterative rational Krylov algorithm (IRKA) to produce the projection matrices in each parameter sample point as suggested there, here we use the well known method of balanced truncation (BT). The numerical results show that for the same reduced order r obtained from <italic>V</italic>, <italic>W</italic> ∈ ℝ^{<italic>n</italic>×<italic>r</italic>}, BT produces a parametric reduced order model (ROM) of similar accuracy as IRKA in less time. (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>