Using model order reduction for design optimization of structures and vibrations

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 line search optimization methods and Krylov-Pade type algebraic model order reduction techniques to speed up numerical optimization of dynamical systems. We prove that Krylov-Pade 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. More interestingly, we show that reduced models valid for the frequency range and a line in the parameter space are helpful for the reduction of the computation time for minimax optimization.