Parametric Model Order Reduction by Matrix Interpolation

Abstract In this paper, a new framework for model order reduction of LTI parametric systems is introduced. After generating and reducing several local original models in the parameter space, a parametric reduced-order model is calculated by interpolating the system matrices of the local reduced models. The main task is to find compatible system representations with optimal interpolation properties. Two approaches for this purpose are presented together with several numerical simulations. Zusammenfassung In diesem Beitrag wird ein neuer Rahmen zur Modellordnungsreduktion parametrischer LZI-Systeme vorgestellt. Er sieht zunächst die Reduktion des Originalmodells in einigen Stützstellen des Parameterraums vor. Anschließend wird ein reduziertes parametrisches System generiert, indem die Systemmatrizen der lokalen Reduktionen durch geeignete Transformationen kompatibel gemacht und interpoliert werden. Hierfür werden zwei alternative Verfahren beschrieben, deren Eigenschaften an drei numerischen Testfällen dargestellt werden.

[1]  Roni Khazaka,et al.  Parametric model order reduction technique for design optimization , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[2]  Jacob K. White,et al.  A multiparameter moment-matching model-reduction approach for generating geometrically parameterized interconnect performance models , 2004, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[3]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[4]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[5]  Kyle A. Gallivan,et al.  A method for generating rational interpolant reduced order models of two-parameter linear systems , 1999 .

[6]  Oliver Sawodny.  Modellbildung, Identifikation und Simulation in der Automatisierungstechnik , 2012, Autom..

[7]  Peter Benner,et al.  Interpolatory Projection Methods for Parameterized Model Reduction , 2011, SIAM J. Sci. Comput..

[8]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[9]  Boris Lohmann,et al.  Generating a Parametric Finite Element Model of a 3D Cantilever Timoshenko Beam Using Matlab , 2009 .

[10]  Sani R. Nassif,et al.  Modeling interconnect variability using efficient parametric model order reduction , 2005, Design, Automation and Test in Europe.

[11]  R. Freund.  Model reduction methods based on Krylov subspaces , 2003, Acta Numerica.

[12]  Wim Desmet,et al.  Concurrent mechatronic design approach for active control of cavity noise , 2008 .

[13]  Andras Varga,et al.  Enhanced Modal Approach for Model Reduction , 1995 .

[14]  Peter Benner,et al.  Modellreduktion für parametrisierte Systeme durch balanciertes Abschneiden und InterpolationModel Reduction for Parametric Systems Using Balanced Truncation and Interpolation , 2009, Autom..