International Journal for Numerical Methods in Engineering vol:90 issue:10 pages:1207-1232
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. Due to 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 signicant 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.