Prediction of crack growth based on a hierarchical diffusion model
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Date
2015
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Abstract
A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the
growth process. To improve the prediction, the information of other crack growth
processes is used in a hierarchical (mixed-effects) model. Two stochastic versions of a
deterministic growth model are considered. One is a nonlinear regression setup where
the trajectory is assumed to be the solution of an ordinary differential equation with
additive errors. The other is a diffusion model defined by a stochastic differential
equation (SDE) where increments have additive errors. Six growth models in the two
versions are compared with respect to their ability to predict the crack propagation in
a large data example. Two of them are based on the classical Paris-Erdogan law for
crack growth, and four are other widely used growth models. It turned out that the
three-parameter Paris-Erdogan model and the Weibull model provide the best results
followed by the logistic model. Suprisingly, the SDE approach has no advantage for
the prediction compared with the nonlinear regression setup.
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Keywords
fatigue propagation, Bayesian estimation and prediction, Euler-Maruyama approximation, stochastic differential equation, Paris-Erdogan equation