1,569 research outputs found
Numerical method for impulse control of Piecewise Deterministic Markov Processes
This paper presents a numerical method to calculate the value function for a
general discounted impulse control problem for piecewise deterministic Markov
processes. Our approach is based on a quantization technique for the underlying
Markov chain defined by the post jump location and inter-arrival time.
Convergence results are obtained and more importantly we are able to give a
convergence rate of the algorithm. The paper is illustrated by a numerical
example.Comment: This work was supported by ARPEGE program of the French National
Agency of Research (ANR), project "FAUTOCOES", number ANR-09-SEGI-00
Numerical method for impulse control of Piecewise Deterministic Markov Processes - application to maintenance optimization
International audienc
Maintenance optimization with piecewise deterministic Markov processes
International audienc
Predictive maintenance for the heated hold-up tank
We present a numerical method to compute an optimal maintenance date for the
test case of the heated hold-up tank. The system consists of a tank containing
a fluid whose level is controlled by three components: two inlet pumps and one
outlet valve. A thermal power source heats up the fluid. The failure rates of
the components depends on the temperature, the position of the three components
monitors the liquid level in the tank and the liquid level determines the
temperature. Therefore, this system can be modeled by a hybrid process where
the discrete (components) and continuous (level, temperature) parts interact in
a closed loop. We model the system by a piecewise deterministic Markov process,
propose and implement a numerical method to compute the optimal maintenance
date to repair the components before the total failure of the system.Comment: arXiv admin note: text overlap with arXiv:1101.174
Piecewise deterministic Markov process for condition-based imperfect maintenance models
In this paper, a condition-based imperfect maintenance model based on
piecewise deterministic Markov process (PDMP) is constructed. The degradation
of the system includes two types: natural degradation and random shocks. The
natural degradation is deterministic and can be nonlinear. The damage increment
caused by a random shock follows a certain distribution, and its parameters are
related to the degradation state. Maintenance methods include corrective
maintenance and imperfect maintenance. Imperfect maintenance reduces the
degradation degree of the system according to a random proportion. The
maintenance action is delayed, and the system will suffer natural degradations
and random shocks while waiting for maintenance. At each inspection time, the
decision-maker needs to make a choice among planning no maintenance, imperfect
maintenance and perfect maintenance, so as to minimize the total discounted
cost of the system. The impulse optimal control theory of PDMP is used to
determine the optimal maintenance strategy. A numerical study dealing with
component coating maintenance problem is presented. Relationship with optimal
threshold strategy is discussed. Sensitivity analyses on the influences of
discount factor, observation interval and maintenance cost to the discounted
cost and optimal actions are presented.Comment: 34 pages, 28 figure
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