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

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Model Reduction of Complex Dynamical Systems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 171))

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Abstract

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.

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Authors and Affiliations

  1. BMW Research, New Technologies, Innovations, Parkring 19, 85748, Garching, Germany

    Rupert Ullmann

  2. Chair of Structural Mechanics, TU Munich, Arcisstraße 21, 80333, München, Germany

    Rupert Ullmann & Gerhard Müller

  3. TU Munich, Arcisstraße 21, 80333, München, Germany

    Stefan Sicklinger

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  1. Rupert Ullmann
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  2. Stefan Sicklinger
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  3. Gerhard Müller
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Correspondence to Rupert Ullmann .

Editor information

Editors and Affiliations

  1. Dynamics of Complex Technical Systems, Max Planck Institute, Magdeburg, Sachsen-Anhalt, Germany

    Peter Benner

  2. Institute of Mathematics, Technical University of Berlin, Berlin, Germany

    Tobias Breiten

  3. Institute for Numerical Analysis, TU Braunschweig, Braunschweig, Germany

    Heike Faßbender

  4. Mathematisches Institut, Universität Koblenz-Landau, Campus Koblenz, Koblenz, Germany

    Michael Hinze

  5. Institut für Mathematik, Universität Augsburg, Augsburg, Germany

    Tatjana Stykel

  6. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Ralf Zimmermann

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Ullmann, R., Sicklinger, S., Müller, G. (2021). Optimization-Based Parametric Model Order Reduction for the Application to the Frequency-Domain Analysis of Complex Systems. In: Benner, P., Breiten, T., Faßbender, H., Hinze, M., Stykel, T., Zimmermann, R. (eds) Model Reduction of Complex Dynamical Systems. International Series of Numerical Mathematics, vol 171. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-72983-7_8

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