Marc Bouissou
EDF R&D, Clamart, France/Ecole Centrale Paris, Châtenay Malabry, France
Hilding Elmqvist
Dassault Systèmes AB, Ideon Science Park, Lund, Sweden
Martin Otter
DLR, Institute of System Dynamics and Control, Wessling, Germany
Albert Benveniste
IRISA/INRIA, Campus de Beaulieu, Rennes Cådex, France
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http://dx.doi.org/10.3384/ecp14096715Published in: Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Linköping Electronic Conference Proceedings 96:75, p. 715-725
Published: 2014-03-10
ISBN: 978-91-7519-380-9
ISSN: 1650-3686 (print), 1650-3740 (online)
This article proposes an efficient approach to model stochastic hybrid systems and to implement Monte Carlo simulation for such models; thus allowing the calculation of various probabilistic indicators: reliability; availability; average production; life cycle cost etc. First; we show that stochastic hybrid systems can be considered; most of the time; as Piecewise Deterministic Markov Processes (PDMP). Although PDMP have been long ago formalized and studied from a theoretical point of view; they are still difficult to use in real applications. The solution proposed here relies on a novel method to handle the case when the hazard rate of a transition depends on continuous variables; the use of an extension of Modelica 3.3 and on Monte Carlo simulation. We illustrate the approach with a simple example: a heating system subject to failures; for which we give the details of the modeling and some calculation results. We compare our ideas to other approaches reported in the literature.
Stochastic hybrid system; PDMP; dynamic reliability; state-dependent hazard rate; continuous time state-machine; Monte Carlo Simulation
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