Article | Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany | Derivative-free Parameter Optimization of Functional Mock-up Units

Title:
Derivative-free Parameter Optimization of Functional Mock-up Units
Author:
Sofia Gedda: Centre for Mathematical Sciences, Lund University/Modelon AB, Sweden Christian Andersson: Centre for Mathematical Sciences, Lund University/Modelon AB, Sweden Johan Åkesson: Department of Automatic Control, Lund University/Modelon AB, Sweden Stefan Diehl: Centre for Mathematical Sciences, Lund University/Modelon AB, Sweden
DOI:
10.3384/ecp12076819
Download:
Full text (pdf)
Year:
2012
Conference:
Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany
Issue:
076
Article no.:
084
Pages:
819-828
No. of pages:
10
Publication type:
Abstract and Fulltext
Published:
2012-11-19
ISBN:
978-91-7519-826-2
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


Representing a physical system with a mathematical model requires knowledge not only about the physical laws governing the dynamics but also about the parameter values of the system. The parameters can sometimes be measured or calculated; however some of them are often difficult or impossible to obtain in these ways. Finding accurate parameter values is crucial for the accuracy of the mathematical model.

Estimating the parameters using optimization algorithms which attempt to minimize the error between the response from the mathematical model and the physical system is a common approach for improving the accuracy of the model.

Optimization algorithms usually require information about the derivatives which may not always be easily available or which may be difficult to compute due to; e.g.; hybrid dynamics. In such cases; derivative-free optimization algorithms offer an alternative for design and parameter optimization.

In this paper; we present an implementation of derivative-free optimization algorithms for parameter estimation in the JModelica.org platform. The implementation allows the underlying dynamic system to be represented as a Functional Mock-up Unit (FMU); thus enables parameter estimation of models designed in modeling tools following the standardized interface; the Functional Mock-up Interface (FMI); such as Dymola.

Keywords: Derivative-free optimization; Parameter Estimation; JModelica.org; FMI; Assimulo

Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Author:
Sofia Gedda, Christian Andersson, Johan Åkesson, Stefan Diehl
Title:
Derivative-free Parameter Optimization of Functional Mock-up Units
DOI:
10.3384/ecp12076819
References:
[1] Functional Mock-up Interface for Model Exchange. Interface specification; MODELISAR; January 2010.
[2] C. Andersson; J. Åkesson; C. Führer; and M. Gäfvert. Import and export of Functional Mock-up Units in JModelica.org. In In 8th International Modelica Conference 2011. Modelica Association; 2011.
[3] C. Andersson; J. Andreasson; C. FĂĽhrer; and J. Ă…kesson. A workbench for multibody systems ODE and DAE solvers. In The Second Joint International Conference on Multibody System Dynamics; 2012.
[4] J. Andersson; J. Åkesson; and M. Diehl. CasADi—A symbolic package for automatic differentiation and optimal control. In S. Forth; P. Hovland; E. Phipps; J. Utke; and A. Walther; editors; Proc. 6th International Conference on Automatic Differentiation; Lecture Notes in Computational Science and Engineering. Springer; 2012.
[5] Joel Andersson; Johan Ă…kesson; Francesco Casella; and Moritz Diehl. Integration of casadi and jmodelica.org. In 8th International Modelica Conference; March 2011.
[6] T. Binder; L. Blank; H.G. Bock; R. Bulirsch; W. Dahmen; M. Diehl; T. Kronseder; W Marquardt; J.P. Schlöder; and O. v. Stryk. Online Optimization of Large Scale Systems; chapter Introduction to model based optimization of chemical processes on moving horizons; pages 295–339. Springer-Verlag; Berlin Heidelberg; 2001.
[7] A.R. Conn; K. Scheinberg; and L.N. Vicente. Introduction to Derivative-Free Optimization. Mps-siam Series on Optimization. Society for Industrial and Applied Mathematics/Mathematical Programming Society; 2009.
[8] J. Dahl and D. Andersson. Gas exchange and exhaust condition modeling of a diesel engine using the Engine Dynamics Library. In In 9th International Modelica Conference 2012. Modelica Association; 2012.
[9] Dassault Systèmes. Dymola Home Page; 2012. http://www.3ds.com/products/catia/portfolio/dymola.
[10] Dassault Systèmes. iSIGHT Home Page; 2012. http://www.3ds.com/products/simulia/portfolio/isight-simulia-execution-engine/overview/.
[11] H. Elmqvist; H. Olsson; S.E. Mattsson; D. BrĂĽck; C. Schweiger; D. Joos; and M. Otter. Optimization for design and parameter estimation. In In 4th International Modelica Conference 2005. Modelica Association; 2005.
[12] ESTECO. modeFRONTIER Home Page; 2012. http://www.esteco.com/.
[13] Sofia Gedda. Calibration of Modelica models using derivative-free optimization. Master’s thesis; Lund University; August 2011.
[14] E. Hairer and G. Wanner. Solving Ordinary Differential Equations: Stiff and differentialalgebraic problems. Springer series in computational mathematics. Springer-Verlag; 1993.
[15] Alan C. Hindmarsh; Peter N. Brown; Keith E. Grant; Steven L. Lee; Radu Serban; Dan E. Shumaker; and Carol S. Woodward. Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw.; 31(3):363–396; September 2005.
[16] John H. Holland. Adaptation in natural and artificial systems. MIT Press; Cambridge; MA; USA; 1992.
[17] Y.D. Lang and L.T. Biegler. A software environment for simultaneous dynamic optimization. Computers and Chemical Engineering; 31(8):931–942; 2007. doi: 10.1016/j.compchemeng.2006.10.017.
[18] Linköping University. OMOptim Home Page; 2012. https://openmodelica.org/index.php/developer/tools/176.
[19] Numerica Technology. Jacobian; 2012. http://www.numericatech.com/jacobian.htm.
[20] H. Olsson; J. Eborn; S.E. Mattsson; and H. Elmqvist. Calibration of static models using Dymola. In In 5th International Modelica Conference 2006. Modelica Association; 2006.
[21] OPTEC K.U. Leuven. ACADO Home Page; 2012. http://www.acadotoolkit.org/.
[22] OptiY. OptiY Home Page; 2012. http://www.optiy.de/.
[23] Phoenix Integration. ModelCenter Home Page; 2012. http://www.phoenix-int.com/software/phx_modelcenter.php.
[24] Process Systems Enterprise. gPROMS Home Page; 2012. http://www.psenterprise.com/gproms/index.html.
[25] Johan Åkesson. Optimica—an extension of modelica supporting dynamic optimization. In In 6th International Modelica Conference 2008. Modelica Association; March 2008.
[26] Johan Åkesson; Karl-Erik Årzén; Magnus Gäfvert; Tove Bergdahl; and Hubertus 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; November 2010. doi: 10.1016/j.compchemeng.2009.11.011
[27] Rainer Storn and Kenneth Price. Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. of Global Optimization; 11(4):341–359; December 1997. doi: 10.1023/A:1008202821328.
[28] University of Heidelberg. MUSCOD-II Home Page; 2009. http://www.iwr.uni-heidelberg.de/~agbock/RESEARCH/muscod.php.

Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Author:
Sofia Gedda, Christian Andersson, Johan Åkesson, Stefan Diehl
Title:
Derivative-free Parameter Optimization of Functional Mock-up Units
DOI:
10.3384/ecp12076819
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