Article | Proceedings of the 10<sup>th</sup> International Modelica Conference; March 10-12; 2014; Lund; Sweden | Efficient Monte Carlo simulation of stochastic hybrid systems
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Title:
Efficient Monte Carlo simulation of stochastic hybrid systems
Author:
Marc Bouissou: EDF R&D, Clamart, France/Ecole Centrale Paris, Ch√Ętenay Malabry, France Hilding Elmqvist: Dassault Syst√®mes 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
DOI:
10.3384/ecp14096715
Download:
Full text (pdf)
Year:
2014
Conference:
Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Issue:
096
Article no.:
075
Pages:
715-725
No. of pages:
11
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


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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.

Keywords: Stochastic hybrid system; PDMP; dynamic reliability; state-dependent hazard rate; continuous time state-machine; Monte Carlo Simulation

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

Author:
Marc Bouissou, Hilding Elmqvist, Martin Otter, Albert Benveniste
Title:
Efficient Monte Carlo simulation of stochastic hybrid systems
DOI:
http://dx.doi.org/10.3384/ecp14096715
References:

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

Author:
Marc Bouissou, Hilding Elmqvist, Martin Otter, Albert Benveniste
Title:
Efficient Monte Carlo simulation of stochastic hybrid systems
DOI:
http://dx.doi.org/10.3384/ecp14096715
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