Optimization-Based Parametric Model Order Reduction for the Application to the Frequency-Domain Analysis of Complex Systems

A parametric model order reduction approach for the frequency-domain analysis of complex industry models is presented. Linear time-invariant subsystem models are reduced for the use in domain integration approaches in the context of structural dynamics. These subsystems have a moderate number of resonances in the considered frequency band but a high-dimensional input parameter space and a large number of states. A global basis approach is chosen for model order reduction, in combination with an optimization-based greedy search strategy for the model training. Krylov subspace methods are employed for local basis generation, and a goal-oriented error estimate based on residual expressions is developed as the optimization objective. As the optimization provides solely local maxima of the non-convex error in parameter space, an in-situ and a-posteriori error evaluation strategy is combined. On the latter, a statistical error evaluation is performed based on Bayesian inference. The method finally enables parametric model order reduction for industry finite element models with complex modeling techniques and many degrees of freedom. After discussing the method on a beam example, this is demonstrated on an automotive example.