Abstract
We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters.
Highlights
The numerical simulation of dynamical systems in frequency domain is of utmost importance in several engineering fields, among which electronic circuit design, acoustics, resonance modeling and control for large structures, and many others
As long as the system state is not necessary for the application at hand, it is common to work directly with the system output. In this case as well, the methods can be further split into two subgroups, the boundary between the two is more vague: some approaches set up the surrogate by solving a unique global interpolation problem [20, 24, 26], whereas others build it by first constructing several models in frequency only, and combining them over parameter space [17, 43, 44]
The field of parametric MOR (pMOR) is closely entwined with the study of parametric dynamical systems in the frequency domain
Summary
The numerical simulation of dynamical systems in frequency domain is of utmost importance in several engineering fields, among which electronic circuit design, acoustics, resonance modeling and control for large structures, and many others. As long as the system state is not necessary for the application at hand, it is common to work directly with the system output In this case as well, the methods can be further split into two subgroups, the boundary between the two is more vague: some approaches set up the surrogate by solving a unique global interpolation problem [20, 24, 26], whereas others build it by first constructing several (rational) models in frequency only, and combining them over parameter space [17, 43, 44].
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