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DFG Transregio SFB 96
Thermo-energetic design of machine tools
A systemic approach to solve the conflict between power efficiency, accuracy and productivity demonstrated at the example of machining production

Projekt A06

Model Order Reduction for Thermo-Elastic Assembly Group Models




Project director:
  • Prof. Dr. Peter Benner
    Technische Universität Chemnitz,
    Department of Mathematics,
    Reichenhainerstr. 41, 09107 Chemnitz, Germany
    Tel: +49 (0)371-531-38367
    E-mail: benner@mathematik.tu-chemnitz.de
    and
    Max Planck Institut for Dynamics of Complex Technical Systems Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg, Germany
    Tel: +49 (0)391-6110-450
    E-mail: benner@mpi-magdeburg.mpg.de
Researcher:
  • Dr. Jens Saak
    Technische Universität Chemnitz,
    Department of Mathematics,
    Reichenhainerstr. 41, 09107 Chemnitz, Germany
    Tel: +49 (0)371-531-32142
    E-mail: saak@mathematik.tu-chemnitz.de
    and
    Max Planck Institut for Dynamics of Complex Technical Systems Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg, Germany
    Tel: +49 (0)391-6110-216
    E-mail: saak@mpi-magdeburg.mpg.de
  • Norman Lang
    Technische Universität Chemnitz,
    Department of Mathematics,
    Reichenhainerstr. 41, 09107 Chemnitz, Germany
    Tel: +49 (0)371-531-39794
    E-mail: norman.lang@mathematik.tu-chemnitz.de
    and
    Max Planck Institut for Dynamics of Complex Technical Systems Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg, Germany
    Tel: +49 (0)391-6110-413
    E-mail: norman.lang@mpi-magdeburg.mpg.de
Graduate research assistant: Duration: 07/2011-06/2015

Project description:
Coupled FEM models resulting from thermoelastic modeling of machine tools are much to complex to allow short simulation runtimes, especially in cases where many simulations regarding different parameterizations are required. Here model order reduction can help reduce the simulation times. To this end highly accurate FEM models are to be rewritten in the form of I/O systems. Afterwards modern automatic parametric model reduction techniques shall be applied to reduce the model dimension to a size that allows for fast simulation and meets prescribed accuracy bounds.


Project News:

Preprint: Balanced truncation model reduction for linear time-varying systems


October 12th, 2015
Norman Lang, Jens Saak and Tatjana Stykel present a practically realizable implementation of the balanced truncation method for linear time-varying systems in terms of a differential Lyapunov equation solver based on a symmetric indefinite factorization of the solution.
Related publications:

@Article{BenHLetal18a,
author = {Benner, P. and Herzog, R. and Lang, N. and Riedel, I. and Saak, J.},
title = {Optimal sensor placement based on model order reduction},
journal = {Proceedings of the Conference on Thermal Issues in Machine Tools},
year = 2018,
note={to appear} }
Optimal sensor placement based on model order reduction
Peter Benner, Roland Herzog, Norman Lang, Ilka Riedel, Jens Saak;
Proceedings of the CIRP sponsored Conference on Thermal Issues in Machine Tools  :  
2018.
to appear.
@Article{BenHLetal18b,
author = {Benner, P. and Herzog, R. and Lang, N. and Riedel, I. and Saak, J.},
title = {Comparison of Model Order Reduction Methods for Optimal Sensor Placement for Thermo-Elastic Models},
journal = {Engineering Optimization},
year = 2018,
note = {accepted} }
Comparison of Model Order Reduction Methods for Optimal Sensor Placement for Thermo-Elastic Models
Peter Benner; Roland Herzog; Norman Lang; Ilka Riedel; Jens Saak;
Engineering Optimization  :  
2018.
accepted.
@PhdThesis{Lan17,
author = {Lang, N.},
fauthor = {Lang, Norman},
title = {Numerical Methods for Large-Scale Linear Time-Varying Control Systems and related Differential Matrix Equations},
school = TUChemnitz,
address = {Chemnitz, Germany},
year = 2017,
month = jun,
type = {Dissertation} }
Numerical Methods for Large-Scale Linear Time-Varying Control Systems and Related Differential Matrix Equations
Norman Lang;
2017.
submitted June 27th 2017, defended November 13th 2017, to appear.
@InProceedings{LanBNetal17,
author = {{Lang}, N. and {Benner}, P. and {Naumann}, A. and {Wensch}, J.},
title = {Simulation gekoppelter Baugruppen: Effiziente Zeitintegrationsverfahren und Modellordnungsreduktion},
booktitle = {Tagungsband des 5. Kolloquiums zum SFB/TR 96: Thermo-Energetische Gestaltung von Werkzeugmaschinen - Modellierung und Simulation},
pages = {18-32},
year = 2017,
editor = {C. Brecher} }
Simulation gekoppelter Baugruppen: Effiziente Zeitintegrationsverfahren und Modellordnungsreduktion;
Norman Lang, Peter Benner, Andreas Naumann, Jörg Wensch;
in C. Brecher: Tagungsband des 5. Kolloquiums zum SFB/TR 96: Thermo-Energetische Gestaltung von Werkzeugmaschinen - Modellierung und Simulation  :  Pages 18-32;
2017. ISBN/ISSN: 978-3-86780-516-2
@Article{NauLPetal16,
author = {Naumann, A. and Lang, N. and Partzsch, M. and Beitelschmidt, M. and Benner, P. and Voigt, A. and Wensch, J.},
title = {Computation of thermo-elastic deformations on machine tools - a study of numerical methods},
journal = {Production Engineering},
year = 2016,
doi = {10.1007/s11740-016-0674-7},
url = {http://dx.doi.org/10.1007/s11740-016-0674-7},
pages = {1--11} }
Computation of thermo-elastic deformations on machine tools - A study of numerical methods;
Andreas Naumann, Norman Lang, Marian Partzsch, Michael Beitelschmidt, Peter Benner, Axel Voigt, Jörg Wensch;
Production Engineering Research & Development  :  
Springer Berlin Heidelberg; 2016.
DOI: 10.1007/s11740-016-0674-7.
@InProceedings{NauWVetal16,
author = {{Beitelschmidt}, M. and {Partzsch}, M. and {Benner}, P. and {Lang}, N. and {Wensch}, J. and {Voigt}, A. and {Naumann}, A.},
title = {Berechnung von thermo-elastischen Deformation in WZM - Vergleich numerischer Verfahren},
booktitle = {Tagungsband des 4. Kolloquiums zum SFB/TR 96: Thermo-Energetische Gestaltung von Werkzeugmaschinen - Modellierung und Simulation},
pages = {83-97},
year = 2016,
editor = {C. Brecher}
Berechnung von thermo-elastischen Deformation in WZM - Vergleich numerischer Verfahren;
Michael Beitelschmidt, Marian Partzsch, Peter Benner, Norman Lang, Jörg Wensch, Axel Voigt, Andreas Naumann;
in C. Brecher: Tagungsband des 4. Kolloquiums zum SFB/TR 96: Thermo-Energetische Gestaltung von Werkzeugmaschinen  :  Pages 83-97;
2016. ISBN/ISSN: 978-3-95735-038-1
@article{morLanSS16,
author = {N. Lang and J. Saak and T. Stykel},
title = {Balanced truncation model reduction for linear time-varying systems},
journal = MCMDS,
volume = 22,
number = 4,
pages = {267--281},
year = 2016,
doi = {10.1080/13873954.2016.1198386},
URL = {http://dx.doi.org/10.1080/13873954.2016.1198386} }
Balanced truncation model reduction for linear time-varying systems;
Norman Lang, Jens Saak, Tatjana Stykel;
Mathematical and Computer Modelling of Dynamical Systems  :  Volume 22, Issue 4, Pages 267-281;
Taylor & Francis; 2016. ISBN/ISSN: 1387-3954, 1744-505
DOI: 10.1080/13873954.2016.1198386, also available as preprint from https://www.tu-chemnitz.de/mathematik/csc/2015/.
@ARTICLE{LanMS15,
author = {Lang, N. and Mena, H. and Saak, J.},
title = {On the benefits of the $LDL^T$ factorization for large-scale differential matrix equation solvers },
journal = {Linear Algebra and its Applications},
publisher = {Elsevier},
volume = {480},
month = sep,
year = 2015,
pages = {44--71},
doi = {10.1016/j.laa.2015.04.006},
}
On the benefits of the LDLT factorization for large-scale differential matrix equation solvers;
Norman Lang, Hermann Mena, Jens Saak;
Linear Algebra and its Applications  :  Volume 480, Pages. 44-71;
Elsevier; 2015.
DOI: 10.1016/j.laa.2015.04.006.
@InCollection{morLanSB15,
author = {Norman Lang, Jens Saak, Peter Benner},
title = {{M}odel {O}rder {R}eduction for {T}hermo-{E}lastic {A}ssembly {G}roup {M}odels},
booktitle = {{T}HERMO-{E}NERGETIC {D}ESIGN OF {M}ACHINE {T}OOLS},
publisher = {Springer International Publishing},
address = {Switzerland},
isbn = {978-3-319-12624-1},
doi = {10.1007/978-3-319-12625-8_8},
year = {2015},
chapter = {8},
pages = {85--93},
}
Model Order Reduction for Thermo-Elastic Assembly Group Models;
Norman Lang, Jens Saak, Peter Benner;
in Knut Großmann: Thermo-energetic Design of Machine Tools  :  Lecture Notes in Production Engineering; pages 85-93;
Springer International Publishing; 2015. ISBN/ISSN: 978-3-319-12624-1
DOI: 10.1007/978-3-319-12625-8_8.
@ARTICLE{LanSBetal15,
author = {{Lang}, N. and {Saak}, J. and {Benner}, P. and {Ihlenfeldt}, S. and {Nestmann}, S. and {Sch{\"a}dlich}, K.},
title = {Towards the identification of heat induction in chip removing processes via an optimal control approach},
issn = {0944-6524},
journal = {Production Engineering},
doi = {10.1007/s11740-015-0608-9},
publisher = {Springer Berlin Heidelberg},
year = 2015,
volume = {9},
number = {3},
pages = {343--349} }
Towards the Identification of Heat Induction in Chip Removing Processes via an Optimal Control Approach;
Norman Lang, Jens Saak, Peter Benner, Steffen Ihlenfeldt, Steffen Nestmann, Klaus Schädlich;
Production Engineering Research & Development  :  Volume 9, Issue 3, Pages 343-349;
Springer Berlin Heidelberg; 2015. ISBN/ISSN: 0944-6524, 1863-7353
DOI: 10.1007/s11740-015-0608-9.
@article{LanSS15,
title = {Towards Practical Implementations of Balanced Truncation for {LTV} Systems},
journal = {IFAC-PapersOnLine},
volume = {48},
number = {1},
pages = {7--8},
year = {2015},
issn = {2405-8963},
doi = {http://dx.doi.org/10.1016/j.ifacol.2015.05.135},
url = {http://www.sciencedirect.com/science/article/pii/S2405896315001366},
author = {N.~Lang and J.~Saak and T.~Stykel},
}
Towards Practical Implementations of Balanced Truncation for LTV Systems;
Norman Lang, Jens Saak, Tatjana Stykel;
IFAC-PapersOnLine  :  Volume 48, Issue 1, Pages: 7-8;
Elsevier; 2015. ISBN/ISSN: 2405-8963
DOI: 10.1016/j.ifacol.2015.05.135.
389Model Order Reduction for Coupled Problems;
P. Benner and L. Feng;
Applied and Computational Mathematics: an international journal  :  14(1):3-22;
2015.
@String{PAMM = \"Proc. Appl. Math. Mech.\" }
@String{WileyVCH = \"WILEY-VCH Verlag\" }
@Article{LanMS14,
title = {An {$LDL^T$} factorization based {ADI} algorithm for solving large scale differential matrix equations},
author = {N. Lang and H. Mena and J. Saak},
publisher = WileyVCH,
journal = PAMM,
volume = 14,
number = 1,
year = 2014,
url = {http://onlinelibrary.wiley.com/doi/10.1002/pamm.201410394/abstract},
doi = {10.1002/pamm.201410394},
pages = {827--828} }
An LDLT factorization based ADI algorithm for solving large-scale differential matrix equations;
Norman Lang, Hermann Mena, Jens Saak;
Proceedings in Applied Mathematics and Mechanics  :  Volume 14, Issue 1, Pages: 827–828;
WILEY-VCH Verlag; 2014.
DOI: 10.1002/pamm.201410394.
@Article{morLanSB14,
author = {Lang, Norman and Saak, Jens and Benner, Peter},
title = {Model Order Reduction for Systems with Moving Loads},
journal = {at-Automatisierungstechnik},
year = 2014,
volume = 62,
number = 7,
pages = {512--522},
month = {June},
publisher = {deGruyter},
doi = {10.1515/auto-2014-1095} }
Model Order Reduction for Systems with Moving Loads;
Norman Lang, Jens Saak, Peter Benner;
in De Gruyter Oldenbourg: at-Automatisierungstechnik  :  Volume 62, Issue 7, Pages 512-522;
2014. ISBN/ISSN: 0178-2312, 2196-677X
DOI: 10.1515/auto-2014-1095.
@ARTICLE{morBauBB14,
author = {U. Baur and C.~A. Beattie and P. Benner},
title = {Mapping parameters across system boundaries: parameterized model reduction with low-rank variability in dynamics},
journal = {Proc. Appl. Math. Mech.},
year = 2014,
publisher = {WILEY-VCH Verlag},
volume = 14,
pages = {19--22},
number = 1,
month = dec,
organization = {GAMM},
doi = {10.1002/pamm.201410006} }
Mapping parameters across system boundaries: parameterized model reduction with low rank variability in dynamics;
Ulrike Baur, Christopher Beattie and Peter Benner;
in P. Steinmann and G. Leugering: Proc. Appl. Math. Mech.  :  Vol. 14 ;
WILEY-VCH Verlag; 2014. ISBN/ISSN: 1617-7061
@INPROCEEDINGS{morBenLS13,
author = {Peter Benner,
orman Lang,
ens Saak},
title = {Modeling structural variability in reduced order models of machine tool assembly groups via parametric MOR},
journal = {Proceedings in Applied Mathematics and Mechanics},
publisher = {WILEY-VCH Verlag},
year = {2013},
volume = {13},
number = {1},
url = {http://dx.doi.org/10.1002/pamm.201310233},
doi = {10.1002/pamm.201310233},
pages = {481--482},
}
Modeling structural variability in reduced order models of machine tool assembly groups via parametric MOR;
Peter Benner, Norman Lang, Jens Saak;
Proceedings in Applied Mathematics and Mechanics  :  Volume 13, Issue 1, Pages: 481–482;
WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim; 2013.
DOI: 10.1002/pamm.201310233.
@INPROCEEDINGS{morBenLS13a,
author = {Peter Benner and Norman Lang and Jens Saak},
title = {Modellordnungsreduktion für geschaltete, gekoppelte thermo-elastische {S}ysteme},
booktitle= {Tagungsband des GMA-Fachausschusses 1.30 \glqq Modellbildung, Identifikation und Simulation in der Automatisierungstechnik\grqq},
pages = {215--227},
editor = {Oliver Sawodny and J\"urgen Adamy},
month = {November},
year = {2013},
publisher = {Technische Universit\"at Darmstadt, Institut f\"ur Automatisierungstechnik und Mechatronik},
isbn = {978-3-9815012-5-4},
}
Modellordnungsreduktion für geschaltete, gekoppelte thermo-elastische Systeme;
Peter Benner, Norman Lang, Jens Saak;
in Sawodny, Oliver; Adamy, Jürgen: Tagungsband des GMA-Fachausschusses 1.30 „Modellbildung, Identifikation und Simulation in der Automatisierungstechnik“  :  Pages 215 - 227;
Technische Universität Darmstadt, Institut für Automatisierungstechnik und Mechatronik; 2013. ISBN/ISSN: 978-3-9815012-5-4
@Article{BenKS13,
author = {Peter Benner and Patrick Kürschner and Jens Saak},
title = {An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems},
year = 2013,
journal = {Mathematical and Computer Modelling of Dynamical Systems},
volume=19,
number=6,
pages={593--615},
doi = {10.1080/13873954.2013.794363},
note = {Early Version available from \url{http://www.mpi-magdeburg.mpg.de/preprints/2012/20/}},
}
An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems;
Peter Benner, Patrick Kürschner, Jens Saak;
Mathematical and Computer Modelling of Dynamical Systems  :  Vol. 19(6), pages 593-615;
2013.
DOI:10.1080/13873954.2013.794363 Also available as Preprint MPIMD/12-20.
@INPROCEEDINGS{SaaUV13,
author = {Jens Saak and M. Monir Uddin and Matthias Voigt},
title = {Modellreduktion für strukturierte {I}ndex-3-{S}ysteme},
booktitle= {Tagungsband des GMA-Fachausschusses 1.30 \glqq Modellbildung, Identifikation und Simulation in der Automatisierungstechnik\grqq},
pages = {180--190},
editor = {Oliver Sawodny and J\"urgen Adamy},
month = {November},
year = {2013},
publisher = {Technische Universit\"at Darmstadt, Institut f\"ur Automatisierungstechnik und Mechatronik},
isbn = {978-3-9815012-5-4},
}
Modellreduktion für strukturierte Index-3-Systeme
Saak, Jens; Uddin, M. Monir; Voigt, Matthias;
in Sawodny, Oliver; Adamy, Jürgen: Tagungsband des GMA-Fachausschusses 1.30 „Modellbildung, Identifikation und Simulation in der Automatisierungstechnik“  :  pp. 180 - 190;
Technische Universität Darmstadt, Institut für Automatisierungstechnik und Mechatronik; 2013. ISBN/ISSN: 978-3-9815012-5-4

Related talks:

Towards a practical implementation of Balanced Truncation for linear time-varying systems, MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling
Vienna, February 18th 2015

Efficient solution of differential Riccati equations , GMA Workshop of FA 1.30
Salzburg (Anif), September 24th 2014

An LDL-factorization based ADI algorithm for large-scale matrix differential equations , GAMM 85th Annual meeting,
Erlangen, March 14th 2014

Modellordnungsreduktion für geschaltete, gekoppelte thermo-elastische Systeme , 3rd colloquium of the DFG Transregio SFB 96,
Aachen, October 30th 2013

Modellreduktion für gekoppelte thermo-elastische Systeme , GMA Workshop of FA 1.30
Salzburg (Anif), September 20th 2013

Modellreduktion für gekoppelte thermo-elastische Systeme , 3rd general assembly of the DFG Transregio SFB 96,
Dresden, July 10th 2013

Modelling structural variability in reduced order models of machine tool assembly groups via parametric MOR , GAMM 84th Annual meeting,
Novi Sad (Serbia), March 20th 2013

Parametererhaltende Modellordnungsreduktion für die Simulation thermo-elastischer Probleme an Werkzeugmaschinen , 2nd colloquium of the DFG Transregio SFB 96,
Fraunhofer IWU Chemnitz, October 25th 2012

Model Order Reduction for Thermo-Elastic Assembly Group Models , GAMM Workshop on Dynamics and Control,
Anif (Salzburg), September 19th 2012

AG Simulation und Parametrierung Bericht TP A06 SFB/Transregio 96 , 2nd general assembly of the DFG Transregio SFB 96,
Fraunhofer IWU Chemnitz, March 19-20th 2012




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Jens Saak, Norman Lang, saak@mpi-magdeburg.mpg.de, norman.lang@mpi-magdeburg.mpg.de