Efficient Monte Carlo simulation of stochastic hybrid systems

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

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp14096715

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

Linköping Electronic Conference Proceedings 96:75, s. 715-725

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Publicerad: 2014-03-10

ISBN: 978-91-7519-380-9

ISSN: 1650-3686 (tryckt), 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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