Abstract
We consider linear dynamical systems including random variables to model uncertainties of physical parameters. The output of the system is expanded into a series with orthogonal basis functions. Our aim is to identify a sparse approximation, where just a low number of basis functions is required for a sufficiently accurate representation. The coefficient functions of the expansion are approximated by a quadrature method or a sampling technique. The performance of a quadrature scheme can be described by a larger linear dynamical system, which is weakly coupled. We apply methods of model order reduction to the coupled system, which results in a sparse approximation of the original expansion. The approximation error is estimated by Hardy norms of transfer functions. Furthermore, we present numerical results for a test example modelling the electric circuit of a band pass filter.
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Pulch, R. (2018). Quadrature Methods and Model Order Reduction for Sparse Approximations in Random Linear Dynamical Systems. In: Langer, U., Amrhein, W., Zulehner, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-75538-0_19
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DOI: https://doi.org/10.1007/978-3-319-75538-0_19
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