Symbolic Initialization of Over-determined Higher-index Models

Lennart Ochel
Bielefeld University of Applied Sciences, Department of Mathematics and Engineering, Bielefeld, Germany

Bernhard Bachmann
Bielefeld University of Applied Sciences, Department of Mathematics and Engineering, Bielefeld, Germany

Francesco Casella
Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Milano, Italy

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp140961179

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

Linköping Electronic Conference Proceedings 96:124, s. 1179-1187

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Publicerad: 2014-03-10

ISBN: 978-91-7519-380-9

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


The amount of needed initial equations in an object-oriented model can only be determined at system level. Because Modelica models are generally designed by components; it is hard to figure out all needed initial conditions at system level; even more when changes are applied to the model; e.g. by adding or removing components. Hence; it is more convenient to define initial equations at component level. Due to component connections; algebraic dependencies between states may be introduced; which eventually lead to the removal of states when symbolic index reduction algorithms are applied. In this process the corresponding initial equations are not automatically removed and an over-determined initial system ensues.

This paper describes an algorithm that detects such redundant equations and determines if they are consistent or not. Consistent redundant initial equations can thus be removed automatically; and inconsistent ones can be reported to the modeler. The algorithm is implemented in OpenModelica; tested on several representative cases; and compared to previously presented concepts.


Initialization; higher-index; simulation; over-constrained


[1] B. Bachmann, P. Aronsson, P. Fritzson, "Robust Initialization of Differential-Algebraic Equations", In Proceedings 5th International Modelica Conference, Vienna, Austria, Sep. 4-5, 2006, pp. 607-614

[2] L. Ochel, B. Bachmann, "Initialization of Equation-Based Hybrid Models within Open-Modelica", In EOOLT 2013 Proceedings, Nottingham, UK, April 19, 2013, pp. 97-103

[3] C.C. Pantelides, The Consistent Initialization of Differential-algebraic Systems. SIAM Journal on Scientific and Statistical Computing, Vol. 9, No. 2, 1988

[4] S.E. Mattsson, G. Söderlind, Index Reduction in Differential-algebraic Equations Using Dummy Derivatives. SIAM Journal on Scientific Computing, Vol. 14, No. 3, 1993

[5] R. Tarjan, Depth-first search and linear graph algorithms. SIAM Journal on Computation, Vol. 1, No. 2, 1972

[6] F.E. Cellier, E. Kofman, Continuous System Simulation, Springer, 2006

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