Article | Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany | Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler Linköping University Electronic Press Conference Proceedings
Göm menyn

Title:
Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler
Author:
Willi Braun: Bielefeld University of Applied Sciences, Department of engineering and mathematics, Germany Lennart Ochel: Bielefeld University of Applied Sciences, Department of engineering and mathematics, Germany Bernhard Bachmann: Bielefeld University of Applied Sciences, Department of engineering and mathematics, Germany
DOI:
10.3384/ecp11063495
Download:
Full text (pdf)
Year:
2011
Conference:
Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany
Issue:
063
Article no.:
056
Pages:
495-501
No. of pages:
7
Publication type:
Abstract and Fulltext
Published:
2011-06-30
ISBN:
978-91-7393-096-3
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


Export in BibTex, RIS or text

Jacobian matrices are used in a wide range of applications - from solving the original DAEs to sensitivity analysis. Using Automatic Differentiation the necessary partial derivatives can be provided efficiently within a Modelica-Tool. This paper describes the corresponding implementation work within the OpenModelica Compiler (OMC) to create a symbolic derivative module. This new OMC-feature generates symbolically partial derivatives in order to calculate Jacobian matrices with respect to different variables. Applications presented here; are the generation of linear models of non-linear Modelica models and the usage of the Jacobian matrix in DASSL for simulating a model.

Keywords: Symbolic Jacobian; Automatic Differentiation; Linearization; DASSL; OpenModelica

Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany

Author:
Willi Braun, Lennart Ochel, Bernhard Bachmann
Title:
Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler
DOI:
http://dx.doi.org/10.3384/ecp11063495
References:

[1] Elsheikh A.; Noack S. and Wiechert W.: Sensitivity analysis of Modelica applications via automatic differentiation; 6th International Modelica Conference; Bielefeld; 2008.

[2] MODELISAR: Functional Mockup Interface for Model Exchange; http://modelisar.org/specifications/FMI_for_ModelExchange_v1.0.pdf; Januar 2010.

[3] Fritzson P. et. al.: OpenModelica System Documentation; PELAB; Department of Computer and Information; Linköpings universitet; 2010.

[4] Imsland L.; Kittilsen P. and Schei T.: Using Modelica models in the real time dynamic optimization - gradient computation; Proceedings 7th Modelica Conference; Como; 2009. doi: 10.3384/ecp09430067.

[5] Lunze; J.: Regelungstechnik 2 – Beobachterentwurf; Springer-Lehrbuch; Springer Berlin Heidelberg; 2010. Proceedings 8th Modelica Conference; Dresden; Germany; March 20-22; 2011

[6] Modelica Association: Modelica – A unified Object-oriented Language for Physical Systems Modeling Language Specification – Version 3.2; 2010.

[7] Otter M.: Objektorientierte Modellierung Physikalischer Systeme (Teil 4) Transformationsalgorithmen; Automatisierungstechnik; Oldenbourg Verlag München; 1999.

[8] Petzold L. R.: A Description of DASSL: A Differential/Algebraic System Solver; Sandia National Laboratories Livermore; 1982.

[9] Rall L.B.: Automatic differentiation: Techniques and applications; vol. 120 of Lecture Notes in Computer Science; Springer; 1981.

Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany

Author:
Willi Braun, Lennart Ochel, Bernhard Bachmann
Title:
Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler
DOI:
https://doi.org10.3384/ecp11063495
Note: the following are taken directly from CrossRef
Citations:
  • Sabrina Pro & Bernhard Bachmann (2012). Hybrid Modelling and Process Optimization of Biological Systems. IFAC Proceedings Volumes, 45(2): 1041. DOI: 10.3182/20120215-3-AT-3016.00184
  • Atiyah Elsheikh (2015). An equation-based algorithmic differentiation technique for differential algebraic equations. Journal of Computational and Applied Mathematics, 281: 135. DOI: 10.1016/j.cam.2014.12.026


  • Responsible for this page: Peter Berkesand
    Last updated: 2019-11-06