Piecewise deterministic Markov processes applied to fatigue crack growth modelling

Julien Chiquet; Nikolaos Limnios; Mohamed Eid

doi:10.1016/j.jspi.2008.05.034

Piecewise deterministic Markov processes applied to fatigue crack growth modelling

Julien Chiquet, Nikolaos Limnios, Mohamed Eid

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigue crack growth. We first derive some probability results on the stochastic dynamics with the help of Markov renewal theory: a closed-form solution for the transition function of the PDMP is given. Then, we investigate some methods to estimate the parameters of the dynamical system, involving Bogolyubov's averaging principle and maximum likelihood estimation for the infinitesimal generator of the underlying jump Markov process. Numerical applications on a real crack data set are given.

Original language	English
Pages (from-to)	1657-1667
Number of pages	11
Journal	Journal of Statistical Planning and Inference
Volume	139
Issue number	5
DOIs	https://doi.org/10.1016/j.jspi.2008.05.034
Publication status	Published - 1 May 2009
Externally published	Yes

Keywords

Averaging principle
Fatigue crack growth
Markov renewal process
Maximum likelihood estimation
Piecewise deterministic Markov process

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10.1016/j.jspi.2008.05.034

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title = "Piecewise deterministic Markov processes applied to fatigue crack growth modelling",

abstract = "In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigue crack growth. We first derive some probability results on the stochastic dynamics with the help of Markov renewal theory: a closed-form solution for the transition function of the PDMP is given. Then, we investigate some methods to estimate the parameters of the dynamical system, involving Bogolyubov's averaging principle and maximum likelihood estimation for the infinitesimal generator of the underlying jump Markov process. Numerical applications on a real crack data set are given.",

keywords = "Averaging principle, Fatigue crack growth, Markov renewal process, Maximum likelihood estimation, Piecewise deterministic Markov process",

author = "Julien Chiquet and Nikolaos Limnios and Mohamed Eid",

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T1 - Piecewise deterministic Markov processes applied to fatigue crack growth modelling

AU - Chiquet, Julien

AU - Limnios, Nikolaos

AU - Eid, Mohamed

PY - 2009/5/1

Y1 - 2009/5/1

N2 - In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigue crack growth. We first derive some probability results on the stochastic dynamics with the help of Markov renewal theory: a closed-form solution for the transition function of the PDMP is given. Then, we investigate some methods to estimate the parameters of the dynamical system, involving Bogolyubov's averaging principle and maximum likelihood estimation for the infinitesimal generator of the underlying jump Markov process. Numerical applications on a real crack data set are given.

AB - In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigue crack growth. We first derive some probability results on the stochastic dynamics with the help of Markov renewal theory: a closed-form solution for the transition function of the PDMP is given. Then, we investigate some methods to estimate the parameters of the dynamical system, involving Bogolyubov's averaging principle and maximum likelihood estimation for the infinitesimal generator of the underlying jump Markov process. Numerical applications on a real crack data set are given.

KW - Averaging principle

KW - Fatigue crack growth

KW - Markov renewal process

KW - Maximum likelihood estimation

KW - Piecewise deterministic Markov process

U2 - 10.1016/j.jspi.2008.05.034

DO - 10.1016/j.jspi.2008.05.034

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EP - 1667

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 5

ER -

Piecewise deterministic Markov processes applied to fatigue crack growth modelling

Abstract

Keywords

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