A multi-point parameterized model reduction for large parametric systems by using Krylov-subspace techniques

This paper presents a multi-point parameterized model reduction method based on Krylov-subspace techniques for large parametric systems where the parametric dependence in system matrices can be nonaffine and the parameters are in a wide range. First, a large parametric system is approximated as a weighted combination of different linear parametric systems, which are obtained by Taylor expansion on the different selected parameter expansion points. Then, a numerically stable algorithm based on self-moments and cross-moments is proposed to obtain a reduced parametric system with high fidelity in the full ranges of the parameters. The accuracy of the obtained reduced parametric systems can be improved by applying the multi-point expansions and weighted functions proposed in this paper. Two benchmarks in practical applications are assessed by employing different parameterized model reduction methods. The numerical simulation results verify the effectiveness of the proposed method.

[1]  Benoit Boulet,et al.  Robust controller order reduction , 2009, 2009 American Control Conference.

[2]  Fabian Duddeck,et al.  Model Order Reduction Methods for Explicit FEM. , 2016 .

[3]  Jacob K. White,et al.  A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[4]  Michael Green,et al.  Parametric interpolation, H∞ -control and model reduction , 1990 .

[5]  Prashant G. Mehta,et al.  Structure-preserving model reduction of nonlinear building thermal models , 2014, Autom..

[6]  Luca Daniel,et al.  A Piecewise-Linear Moment-Matching Approach to Parameterized Model-Order Reduction for Highly Nonlinear Systems , 2007, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[7]  Victor Sreeram,et al.  A frequency weighted model order reduction technique and error bounds , 2014, Autom..

[8]  M. Ahmadloo,et al.  Parameterized Model Order Reduction of Electromagnetic Systems Using Multiorder Arnoldi , 2010, IEEE Transactions on Advanced Packaging.

[9]  Peter Benner,et al.  A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching , 2014 .

[10]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[11]  A. Armaou,et al.  Design of APOD-based switching dynamic observers and output feedback control for a class of nonlinear distributed parameter systems , 2015 .

[12]  Caroline Kulcsar,et al.  Model order reduction of random parameter-dependent linear systems , 2015, Autom..

[13]  Mohammad Abid Bazaz,et al.  A review of parametric model order reduction techniques , 2012, 2012 IEEE International Conference on Signal Processing, Computing and Control.

[14]  Maria Prandini,et al.  Model reduction of switched affine systems , 2016, Autom..

[15]  Davood Babaei Pourkargar,et al.  Modification to adaptive model reduction for regulation of distributed parameter systems with fast transients , 2013 .

[16]  R. Freund.  Krylov-subspace methods for reduced-order modeling in circuit simulation , 2000 .

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

[18]  Gene H. Golub,et al.  The Lanczos-Arnoldi algorithm and controllability , 1984 .

[19]  Yao-Lin Jiang,et al.  Time domain model order reduction using general orthogonal polynomials for K-power bilinear systems , 2016, Int. J. Control.

[20]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[21]  C.J.M. Lasance.  Two benchmarks to facilitate the study of compact thermal modeling phenomena , 2001 .

[22]  D. Chandra,et al.  Model order reduction using Fuzzy C-Means clustering , 2014 .

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

[24]  Tobias Breiten,et al.  Near-optimal frequency-weighted interpolatory model reduction , 2013, Syst. Control. Lett..

[25]  D.J. Murray-Smith,et al.  Model reduction by an extended complex curve-fitting approach , 1993 .

[26]  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.

[27]  Boris Lohmann,et al.  Parametric Model Order Reduction by Matrix Interpolation , 2010, Autom..

[28]  Peter Benner,et al.  A Robust Algorithm for Parametric Model Order Reduction , 2007 .

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

[30]  Yao-Lin Jiang,et al.  Model order reduction of MIMO bilinear systems by multi-order Arnoldi method , 2016, Syst. Control. Lett..

[31]  Ricardo C. L. F. Oliveira,et al.  LMI Relaxations for Reduced-Order Robust ${\cal H}_{\infty}$ Control of Continuous-Time Uncertain Linear Systems , 2012, IEEE Transactions on Automatic Control.

[32]  Tobias Breiten,et al.  Krylov subspace methods for model order reduction of bilinear control systems , 2010, Syst. Control. Lett..

[33]  Yoram Halevi,et al.  Parameter-dependent model order reduction , 1997 .

[34]  Thanh-Son Nguyen.  Interpolation Based Parametric Model Order Reduction (Interpolation Basiert Parametrischen Modellreduktion) , 2012 .