Bayesian prediction for a jump diffusion process with application to crack growth in fatigue experiments
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Date
2015
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Abstract
In many felds of technological developments, understanding and controlling
material fatigue is an important point of interest. This article is concerned with
statistical modeling of the damage process of prestressed concrete under low cyclic
load. A crack width process is observed which exhibits jumps with increasing
frequency. Firstly, these jumps are modeled using a Poisson process where two
intensity functions are presented and compared. Secondly, based on the modeled
jump process, a stochastic process for the crack width is considered through a
stochastic differential equation (SDE). It turns out that this SDE has an explicit
solution. For both modeling steps, a Bayesian estimation and prediction procedure
is presented.
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Keywords
Nonhomogeneous Poisson process (NHPP), predictive distribution, Bayesian estimation, crack growth