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Using Krylov‐Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain
Author(s) -
Yue Yao,
Meerbergen Karl
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3357
Subject(s) - reduction (mathematics) , model order reduction , frequency domain , mathematical optimization , function (biology) , line search , range (aeronautics) , control theory (sociology) , vibration , optimization problem , mathematics , computer science , algorithm , mathematical analysis , engineering , physics , projection (relational algebra) , geometry , computer security , quantum mechanics , evolutionary biology , artificial intelligence , radius , biology , aerospace engineering , control (management)
SUMMARY In many engineering problems, the behavior of dynamical systems depends on physical parameters. In design optimization, these parameters are determined so that an objective function is minimized. For applications in vibrations and structures, the objective function depends on the frequency response function over a given frequency range, and we optimize it in the parameter space. Because of the large size of the system, numerical optimization is expensive. In this paper, we propose the combination of Quasi‐Newton type line search optimization methods and Krylov‐Padé type algebraic model order reduction techniques to speed up numerical optimization of dynamical systems. We prove that Krylov‐Padé type model order reduction allows for fast evaluation of the objective function and its gradient, thanks to the moment matching property for both the objective function and the derivatives towards the parameters. We show that reduced models for the frequency alone lead to significant speed ups. In addition, we show that reduced models valid for both the frequency range and a line in the parameter space can further reduce the optimization time. Copyright © 2012 John Wiley & Sons, Ltd.