Abstract
We present two model order reduction approaches based on different modelling strategies for a thermo-elastic assembly group model. Here, we consider the machine stand example given in Chap. 7. The focus is on capturing the structural variability. Therefore, we compare a switched linear systems (SLS) approach based on reduced order models determined by the Balanced Truncation (BT) method and a parametric model order reduction (PMOR) scheme based on an interpolatory projection method via the iterative rational Krylov algorithm (IRKA). In order to avoid the high dimensional coupled thermo-elastic system, additionally a Schur complement representation is applied to exploit the special structure of the one-sided coupling property of the system. The results show that both methods generate relative errors in the range of one per thousand.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Baur U, Beattie CA, Benner P, Gugercin S (2011) Interpolatory projection methods for parameterized model reduction. SIAM J Sci Comput 33(5):2489–2518
Bunse-Gerstner A, Kubalinska D, Vossen G, Wilczek D (2010) h 2-norm optimal model reduction for large scale discrete dynamical MIMO systems. J Comput Appl Math 233(5):1205–1216
Enns DF (1984) Model reduction with balanced realizations: an error bound and a frequency weighted generalization. In: The 23rd IEEE conference on decision and control, vol 23, pp 127–132
Freitas F, Rommes J, Martins N (2008) Gramian-based reduction method applied to large sparse power system descriptor models. IEEE Trans Power Syst 23(3):1258–1270
Gallivan K, Vandendorpe A, Van Dooren P (2008) \( {\mathcal{H}}_{2} \)-optimal model reduction of MIMO systems. Appl Math Lett 21:1267–1273
Geuss M, Diepold KJ (2013) An approach for stability-preserving model order reduction for switched linear systems based on individual subspaces. In: Roppenecker G, Lohmann B (eds) Methoden und Anwendungen der Regelungstechnik. Shaker Verlag, Aachen
Golub G, Van Loan C (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore
Gugercin S, Antoulas AC, Beattie C (2008) \( {\mathcal{H}}_{2} \) model reduction for large-scale dynamical systems. SIAM J Matrix Anal Appl 30(2):609–638
Haasdonk B, Ohlberger M (2009) Efficient reduced models for parametrized dynamical systems by offline/online decomposition. In: Proceedings of the MATHMOD 2009, 6th Vienna international conference on mathematical modelling
Laub AJ, Heath MT, Paige CC, Ward RC (1987) Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Trans Autom Control 32(2):115–122
Monshizadeh N, Trentelman HL, Çamlibel MK (2011) Simultaneous balancing and model reduction of switched linear systems. In: The 50th IEEE conference on decision and control and European control conference, pp 6552–6557
Moore BC (1981) Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans Autom Control AC-26(1):17–32
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lang, N., Saak, J., Benner, P. (2015). Model Order Reduction for Thermo-Elastic Assembly Group Models. In: Großmann, K. (eds) Thermo-energetic Design of Machine Tools. Lecture Notes in Production Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-12625-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-12625-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12624-1
Online ISBN: 978-3-319-12625-8
eBook Packages: EngineeringEngineering (R0)