Automatic and Sampling-Free Parametric Model Order Reduction of Vibro-Acoustic Systems

Abstract

Recently, a novel parametric model order reduction formulation has been derived for vibroacoustic systems that allows for the reduction of systems with low-rank parametric changes [1]. This scheme does not require sampling of the parameter space, in contrast to conventional parametric model reduction techniques. This means that a single reduction basis, obtained with conventional non-parametric model order reduction schemes, can be used for a wide range of parameter values. This is done by rewriting the system in a non-parametric form, in which the low-rank contributions act as inputs. A disadvantage of this scheme is that the size of the input matrix scales with the amount of chosen parameters, leading to a potentially large reduced basis when many parameters are considered. Therefore, in [2] an automatic Krylov reduction scheme has been proposed that utilizes the similarity in the reduced bases for inputs which are spaced closely together to still get a small reduced basis with a large number of inputs. This is done by using a combination of block second order Arnoldi with a singular value decomposition acting on the resulting basis. The algorithm includes an error estimator that uses a complementary approximation to calculate the error. The main advantages of this algorithm as compared to the commonly used iterative rational Krylov approach [3] are that only a small amount of system inversions are required and that the final reduced order model has the desired predefined relative error in the specified frequency band. In this paper the automatic Krylov reduction scheme and low-rank parametric model order reduction approach are combined and a suitable error estimator is derived, to arrive at compact but accurate parametric reduced order models. The effectiveness is shown with several examples.

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