Model reduction for dynamical systems with quadratic output

被引:11
作者
Van Beeumen, R. [1 ]
Van Nimmen, K. [2 ,3 ]
Lombaert, G. [2 ]
Meerbergen, K. [1 ]
机构
[1] Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Belgium
[2] Katholieke Univ Leuven, Dept Civil Engn, B-3001 Heverlee, Belgium
[3] Katholieke Hogesch Sint Lieven, Dept Ind Engn, Ghent, Belgium
关键词
model reduction; quadratic output; Arnoldi method; modal superposition; recycling; LANCZOS-ALGORITHM; COMPUTATION;
D O I
10.1002/nme.4255
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Finite element models for structures and vibrations often lead to second order dynamical systems with large sparse matrices. For large-scale finite element models, the computation of the frequency response function and the structural response to dynamic loads may present a considerable computational cost. Pade via Krylov methods are widely used and are appreciated projection-based model reduction techniques for linear dynamical systems with linear output. This paper extends the framework of the Krylov methods to systems with a quadratic output arising in linear quadratic optimal control or random vibration problems. Three different two-sided model reduction approaches are formulated based on the Krylov methods. For all methods, the control (or right) Krylov space is the same. The difference between the approaches lies, thus, in the choice of the observation (or left) Krylov space. The algorithms and theory are developed for the particularly important case of structural damping. We also give numerical examples for large-scale systems corresponding to the forced vibration of a simply supported plate and of an existing footbridge. In this case, a block form of the Pade via Krylov method is used. Copyright (c) 2012 John Wiley & Sons, Ltd.
引用
收藏
页码:229 / 248
页数:20
相关论文
共 28 条
[1]   A method for interpolating on manifolds structural dynamics reduced-order models [J].
Amsallem, David ;
Cortial, Julien ;
Carlberg, Kevin ;
Farhat, Charbel .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2009, 80 (09) :1241-1258
[2]  
ANTOULAS A. C., 2005, ADV DES CONTROL, DOI 10.1137/1.9780898718713
[3]  
Bai Z., 1998, Electronic Transaction on Numerical Analysis, V7, P1
[4]   Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method [J].
Bai, ZJ ;
Su, YF .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 26 (05) :1692-1709
[5]   A partial Pade-via-Lanczos method for reduced-order modeling [J].
Bai, ZJ ;
Freund, RW .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 332 :139-164
[6]  
Benner P., 2005, DIMENSION REDUCTION
[7]  
Bennighof J. K., 1998, P 39 AIAA ASME ASCE
[8]   KRYLOV SPACE METHODS ON STATE-SPACE CONTROL-MODELS [J].
BOLEY, DL .
CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 1994, 13 (06) :733-758
[9]  
Calladine C., 1989, Theory of Shell Structures
[10]   EFFICIENT LINEAR CIRCUIT ANALYSIS BY PADE-APPROXIMATION VIA THE LANCZOS PROCESS [J].
FELDMANN, P ;
FREUND, RW .
IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, 1995, 14 (05) :639-649