Article | Proceedings of the 10<sup>th</sup> International Modelica Conference; March 10-12; 2014; Lund; Sweden | Modeling Parameter Sensitivities via Equation-based Algorithmic Differentiation Techniques: The ADMSL.Electrical.Analog Library
Göm menyn

Title:
Modeling Parameter Sensitivities via Equation-based Algorithmic Differentiation Techniques: The ADMSL.Electrical.Analog Library
Author:
Atiyah Elsheikh: Austrian Institute of Technology, Vienna, Austria
DOI:
10.3384/ecp14096557
Download:
Full text (pdf)
Year:
2014
Conference:
Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Issue:
096
Article no.:
059
Pages:
557-566
No. of pages:
10
Publication type:
Abstract and Fulltext
Published:
2014-03-10
ISBN:
978-91-7519-380-9
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

Parameter sensitivities of mathematical models play a vital rule in many applications of sensitivity analysis. The availability of algorithmic capabilities for representing and computing these quantities is surly advantageous. In this work it is shown how to systematically transform a Modelica library to another library that describes the desired models together with derivatives of model variables w.r.t. model parameters. The produced library remains with the same structure and the underlying models keep the same interface and outlook. The proposed approach relies on novel equation-based algorithmic differentiation techniques that are especially designed for Modelica. The illustration is rather done via a compact library; the opensource ADMSL library; but rich enough to facilitate a lot of representative Modelica language constructs. The ADMSL library is the algorithmically differentiated version of the standard Modelica library subpackage Modelica.Electrical.Analog.Basic.

Keywords: algorithmic differentiation; parameter Sensitivities; sensitivity analysis; ADMSL; AD of Modelica libraries

Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Author:
Atiyah Elsheikh
Title:
Modeling Parameter Sensitivities via Equation-based Algorithmic Differentiation Techniques: The ADMSL.Electrical.Analog Library
DOI:
http://dx.doi.org/10.3384/ecp14096557
References:

[1] The ADMSL library. https://github.com/AIT-CESLAB/ADMSL.


[2] Wolfram SystemModeler. http://www.wolfram.com/system-modeler/.


[3] J. Åkesson, K.-E. Årzén, M. Gäfvert, T. Bergdahl, and H. Tummescheit. Modeling and optimization with Optimica and JModelica.org—languages and tools for solving large-scale dynamic optimization problem. Computers and Chemical Engineering, 34(11):1737–1749, 2010.


[4] J. Andersson, B. Houska, and M. Diehl. Towards a computer algebra system with automatic differentiation for use with object-oriented modelling languages. In EOOLT’2010: The 3rd International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools, Oslo, Norway, Oct. 2010.


[5] I. Bauer, H. G. Bock, S. Körkel, and J. P. Schlöder. Numerical methods for optimum experimental design in DAE systems. Journal of Computational and Applied Mathematics, 120:1 – 25, 2000.


[6] C. H. Bischof, H. M. Bücker, W. Marquardt, M. Petera, and J. Wyes. Transforming equation-based models in process engineering. In H. M. Bücker, G. Corliss, P. Hovland, U. Naumann, and B. Norris, editors, Automatic Differentiation: Applications, Theory, and Implementations, Lect. Notes in Comp. Sc. and Eng., pages 189–198. Springer, 2005.


[7] W. Braun, L. Ochel, and B. Bachmann. Symbolically derived Jacobians using automatic differentiation - enhancement of the OpenModelica compiler. In odelica’
2011: The 8th International Modelica Conference, Dresden, Germany, Mar. 2011.


[8] R. Dickinson and R. Gelinas. Sensitivity analysis of ordinary differential equation systems - a direct method. Journal of Computational Physics, 21:123–143, 1976.


[9] A. Elsheikh. Modelica-based computational tools for sensitivity analysis via automatic differentiation. Dissertation, RWTH Aachen university, Aachen, Germany, 2011.


[10] A. Elsheikh. ADGenKinetics: An algorithmically differentiated library for biochemical networks modeling via simplified kinetics formats. In Modelica’2012:
The 9th International Modelica Conference, number 076 in Linköping Electronic Conference Proceedings, pages 915 – 926, Munich, Germany, Sep. 2012.


[11] A. Elsheikh. Assisting identifiability analysis of largescale dynamical models with decision trees: DecTrees and InteractiveMenus. In EuroSim’2013: The 8th UROSIM Congress on Modelling and Simulation, pages 300 – 305, Cardiff, Wales, UK, Sep. 2013.


[12] A. Elsheikh. Derivative-based hybrid heuristics for continuous-time simulation-optimization. Simulation Modelling Practice and Theory, 2013. In Press.


[13] A. Elsheikh. An equation-based algorithmic differentiation technique for differential algebraic equations. Computational and applied Mathematics, 201x. Submitted. Available online as a technical report.


[14] A. Elsheikh, S. Noack, and W. Wiechert. Sensitivity analysis of Modelica applications via automatic differentiation. In Modelica’2008: The 6th International Modelica Conference, volume 2, pages 669–675, Bielefeld, Germany, March 2008.


[15] A. Elsheikh and W. Wiechert. Automatic sensitivity analysis of DAE-systems generated from equationbased modeling languages. In C. H. Bischof, H. M. Bücker, P. D. Hovland, U. Naumann, and J. Utke, editors, Advances in Automatic Differentiation, pages 235–246. Springer, 2008.


[16] A. Elsheikh and W. Wiechert. Accuracy of parameter sensitivities of DAE systems using finite difference methods. Mathematical Modelling, IFAC Papers Online, 7(1):136 – 142, Feb. 2012. Presented in MATHMOD’ 2012, The 7th Vienna International Conference on Mathematical Modelling, Vienna, Austria.


[17] A. Elsheikh and W. Wiechert. A structure-preserving approach for sensitivity analysis of higher index differential algebraic equations. Mathematics and Computers in Simulation, 201x. Submitted.


[18] S. Galán, W. F. Feehery, and P. I. Barton. Parametric sensitivity functions for hybrid discrete/continuous systems. Applied Numerical Mathematics, 31(1):17– 47, 1999.


[19] A. Griewank and A.Walther. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Number 105 in Other titles in Applied Mathematics. SIAM, Philadelphia, PA, 2nd edition, 2008.


[20] A. K. Gupta and S. A. Forth. An AD-enabled optimization toolxbox in LabVIEWTM. In S. Forth, P. Hovland, E. Phipps, J. Utke, and A. Walther, editors, Recent Advances in Algorithmic Differentiation, volume 87 of Lecture Notes in Computational Science and Engineering, pages 285–295. Springer-Verlag Berlin Heidelberg, 2012.


[21] A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward. Sundials: Suite of nonlinear and differential/algebraic
equation solvers. ACM Trans. Math. Softw., 31(3):363–396, Sept. 2005.


[22] X. Ke. Tools for sensitivity analysis of modelica models. Master’s thesis, Siegen University, Germany, 2009.


[23] S. Li, L. Petzold, and W. Zhu. Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem. Applied Numerical Mathematics: Transactions of IMACS, 32(2):161–174, Feb. 2000.


[24] U. Naumann. The art of Differentiating Computer Programs, an Introduction to Algorithmic Differentiation. SIAM, 2012.


[25] H. Olsson, H. Tummescheit, and H. Elmqvist. Using automatic differentiation for partial derivatives of functions in Modelica. In Modelica’2005: The 4th International Modelica Conference, Hamburg, Germany, 2005.


[26] M. Sjölund and P. Fritzson. An openmodelica java external function interface supporting metaprogramming. In Modelica’2009: The 7th International Modelica Conference, Como, Italy, 2009.


[27] W. Wiechert and R. Takors. Validation of Metabolic Models: Concepts, Tools, and Problems. Taylor& Francis, 2004.

Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Author:
Atiyah Elsheikh
Title:
Modeling Parameter Sensitivities via Equation-based Algorithmic Differentiation Techniques: The ADMSL.Electrical.Analog Library
DOI:
http://dx.doi.org/10.3384/ecp14096557
Note: the following are taken directly from CrossRef
Citations:
No citations available at the moment


Responsible for this page: Peter Berkesand
Last updated: 2017-02-21