Efficient Monte Carlo simulation of stochastic hybrid systems

Abstract

International audienceThis paper 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. 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 by Davis (Davis 1993), 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 λ depends on continuous variables of the system model, 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

From Modelica models to dependability analysis

“…Both use the mechanisms given in Bouissou et al (2014) for the generation of random events and the Monte Carlo simulation.…”

“…It is organized as follows: the largest part of the article (sections 2 to 4) presents the connection that can be established between detailed simulation models in Modelica, and more abstract models written in Figaro, in order to generate fault trees or to perform probabilistic evaluations based on discrete models. Section 5 is an example of such a connection (for a telecom network), and Section 6 compares the method described in Bouissou et al (2014) to other techniques on a well-known benchmark.…”

“…This is why we looked for better solutions for hybrid systems, and investigated the use of Modelica. In Bouissou et al (2014) we showed that it is possible to add stochastic behaviour due to failures and repairs of components to a deterministic hybrid system described in Modelica. This paper explains how one can perform Monte Carlo simulations on such models, with a smart algorithm that minimizes the number of random numbers that must be generated.…”

“…An auxiliary contribution of the present paper is the application of the method described in Bouissou et al (2014) to a more complicated use case, which has served as a benchmark for numerous other methods. This application shows two things: the model is simple and "natural" with the proposed approach and the performances of the simulation are better than those of a recently published paper.…”

Reliability modelling of PEM fuel cells with hybrid Petri nets

“…Simulink was utilised for this purpose in (F. and Modelica (Modelica Association 2016) in (Bouissou et al 2014). Since the fuel cell submodel described by Equations 3-13 was initially implemented using Modelica, this language was chosen for development of current model.…”