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 Linköping University Electronic Press Conference Proceedings
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Title:
Efficient Monte Carlo simulation of stochastic hybrid systems
Author:
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
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:

Aldemir T (1991): Utilization of the Cell-to-Cell Mapping Technique to Construct Markov Failure Models for Process Control Systems, PSAM Proceedings, Elsevier Publishing Company Co. Inc., NY, pp 1431-1436.

Bouissou M., Jankovic M. (2012): Critical comparison of two user friendly tools to study Piecewise Deterministic Markov Processes (PDMP). ESREL 2012, Helsinki.

Bouissou M., Chraibi H., Chubarova I. (2013): Critical comparison of two user friendly tools to study Piecewise Deterministic Markov Processes (PDMP): season 2.
ESREL 2013, Amsterdam. Davis M.H.A (1993): Markov Models and Optimization, Chapman& Hall

Elmqvist H., Gaucher F., Mattsson S.E., Dupont F. (2012): State Machines in Modelica. Modelica’2012 Conference, Munich, Germany, Sept. 3-5, 2012. Download:
http://www.ep.liu.se/ecp/076/003/ecp12076003.pdf

Elmqvist H., Mattsson S.E., Otter M. (2014): Modelica extensions for multi-mode DAE systems. Modelica’2014 Conference, Lund, Sweden, March 10-12.

Looye G., Joos H.D. (2006): Design of Autoland Controller Functions with Multi-objective Optimization. Journal of Guidance, Control, and Dynamics, Vol. 29, No. 2,
March-April, pp. 475 -484.

Marseguerra M. and E. Zio (1996): Monte Carlo Approach to PSA for dynamic process system. Reliability Engineering and System Safety, 52:227-241.

Sheldon M.R. (1990): A course in simulation. Mc Millan, ISBN 0-02-403891-1

Tuffin B., D. S. Chen, and K. Trivedi (2001): Comparison of hybrid systems and fluid stochastic Petri nets. Discrete Event Dynamic Systems, 11 (1/2):77-95.

Zhang H., Dufour F., Dutuit Y., and Gonzalez K. (2008): Piecewise deterministic Markov processes and dynamic reliability. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 222(4), 545–551.

Zhang H., Saporta B., Dufoura F., and Deleuzed G. (2013): Dynamic Reliability by Using Simulink and Stateflow. Chemical Engineering Transactions. Vol. 33, pp. 529-534

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:
https://doi.org10.3384/ecp14096715
Note: the following are taken directly from CrossRef
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  • F. Chiacchio, D. D’Urso, G. Mann & L. Compagno (2016). Stochastic hybrid automaton model of a multi-state system with aging: Reliability assessment and design consequences. Reliability Engineering & System Safety, 149: 1. DOI: 10.1016/j.ress.2015.12.007
  • M. Bouisso & X. de Bossoreille (2015). From Modelica models to dependability analysis. IFAC-PapersOnLine, 48(7): 37. DOI: 10.1016/j.ifacol.2015.06.470
  • Peter Fritzson, Adrian Pop, Karim Abdelhak, Adeel Ashgar, Bernhard Bachmann, Willi Braun, Daniel Bouskela, Robert Braun, Lena Buffoni, Francesco Casella, Rodrigo Castro, Rüdiger Franke, Dag Fritzson, Mahder Gebremedhin, Andreas Heuermann, Bernt Lie, Alachew Mengist, Lars Mikelsons, Kannan Moudgalya, Lennart Ochel, Arunkumar Palanisamy, Vitalij Ruge, Wladimir Schamai, Martin Sjölund, Bernhard Thiele, John Tinnerhol & Per Östlund (2020). The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development. Modeling, Identification and Control: A Norwegian Research Bulletin, 41(4): 241. DOI: 10.4173/mic.2020.4.1
  • Hindolo George-William & Edoardo Patelli (2017). Maintenance Strategy Optimization for Complex Power Systems Susceptible to Maintenance Delays and Operational Dynamics. IEEE Transactions on Reliability, 66(4): 1309. DOI: 10.1109/TR.2017.2738447


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