Bayesian prediction of crack growth based on a hierarchical diffusion model
Séminaire Probabilités & Statistique
18/06/2015 - 14:00 Simone Hermann (Technische Universität Dortmund (Allemagne)) Salle 1 - Tour IRMA
In many research areas of engineering it is of particular interest to understand the process of material fatigue and to predict the failure time. Experiments are often very expensive because they take a long time and the constructions are costly. To extract as much information as possible from the available experiments and to predict fatigue, statistical models are a valuable tool. A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide prediction 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 compared. 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 the increments have additive errors. While Bayesian prediction is known for the hierarchical model based on nonlinear regression, we propose a new Bayesian prediction method for the hierarchical diffusion model. The presented methods are applied on the degradation data set of Virkler et al. (1979) where sixty-eight replicate constant amplitude tests in aluminum alloy were carried out to investigate the fatigue crack propagation.