Piecewise deterministic Markov processes applied to fatigue crack growth modelling

被引：39

作者：

Chiquet, Julien ^{[1
]}

Limnios, Nikolaos ^{[1
]}

Eid, Mohamed ^{[2
]}

机构：

[1] Univ Technol Compiegne, F-60206 Compiegne, France

[2] Commissariat Energie Atom, Saclay, France

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2009年 / 139卷 / 05期

关键词：

Piecewise deterministic Markov process; Markov renewal process; Averaging principle; Maximum likelihood estimation; Fatigue crack growth; STOCHASTIC DYNAMICAL-SYSTEMS; RELIABILITY;

D O I：

10.1016/j.jspi.2008.05.034

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1657 / 1667

页数：11

共 23 条

[1] ESTIMATING INFINITESIMAL GENERATOR OF A CONTINUOUS-TIME, FINITE STATE MARKOV PROCESS [J].

ALBERT, A .

ANNALS OF MATHEMATICAL STATISTICS, 1962, 33 (02) :727-&

[2]

[Anonymous], 1985, Probabilistic Models of Cumulative Damage(Book)

[3]

Billingsley P., 1961, STAT INFERENCE MARKO

[4]

BOGOLYUBOV N, 1961, ASYMPTOTICS METHODS

[5]

CHIQUET J, 2007, STAT PROB L IN PRESS

[6]

Chiquet J, 2006, PROC MONOGR ENG WATE, P133

[7] Estimating stochastic dynamical systems driven by a continuous-time jump Markov process [J].

Chiquet, Julien ;

Limnios, Nikolaos .

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2006, 8 (04) :431-447

[8]

DAVIS MHA, 1984, J ROY STAT SOC B MET, V46, P353

[9]

Davis MHA., 1993, Markov models and optimization, Monographs on Statistics and Applied Probability

[10] MARKOV PROCESSES WITH HOMOGENEOUS SECOND COMPONENT .2. [J].

EZHOV, II ;

SKOROKHO.AV .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1969, 14 (04) :652-&

← 1 2 3 →