Parametric model reduction of systems for active noise control

Up to now there seems to be no software package covering all aspects of designing mechatronic systems for active noise and vibration control: on the one hand coupled FE models of structure, aero acoustics, or piezo actuators, and on the other hand DAE's describing electronic components or methods for controller design and parametric optimization. Therefore, we have developed a toolbox which enables engineers to transfer and reduce automatically linear multi-field ANSYS® models into parametric Matlab® state space models. Note that the considered FE models are, in general, characterized by large non-symmetric and singular matrices due to fluid-structure coupling or neglecting piezo inductance. Hence, neither the built in model reduction of ANSYS® can be applied, which is restricted to symmetric systems with proportional damping, nor the one of Matlab®, which requires small full storage systems. Therefore, we implemented a hybrid reduction scheme combining modal reduction for singular non-symmetric systems and moment matching of the smooth remainder. The other focus of the article will be on parametric model reduction. Fitting models to measurements or optimizing designs requires parameterized models allowing fast evaluation. However, all time savings are lost, if another reduction has to be started for each set of new parameters. Common approaches rely on expansions of the full system matrices with respect to the parameters. However, this requires FE-meshes to be smoothly deformable into each other, which is a hard restriction for more realistic geometries. Therefore, we follow another approach: models are reduced independently to systems with standardized structure and size and interpolated only on this level. Relevance and challenges of finding system realizations suitable for interpolation are highlighted. Results are illustrated by applying the toolbox to some benchmark models including the LMS concrete car. Work is related to the Marie Curie RTN Smart Structures.