Generalized hierarchical Bayesian inference for fatigue life prediction based on multi-parameter Weibull models

Abstract

This article proposes the use of generalized hierarchical Bayesian inference for fatigue life prediction based on general multi-parameter Weibull models. First, a five-parameter Weibull model for corrosion-stress-life (C-S-N) is introduced; neglecting the influence of corrosion, the model degenerates into a three-parameter Weibull model for stress-life (S-N). To predict the fatigue life based on the observation data, a three-layer hierarchical Bayesian structure for these Weibull models is established, and the posterior joint PDF of the parameters and hyperparameters in the generalized hierarchical Bayesian model (GHBM) is derived. Gibbs sampling is employed to obtain posterior samples for parameters and hyperparameters using their full conditional distribution, which is simplified using a Markov blanket based on the probabilistic dependences of the parameters and hyperparameters. Subsequently, three groups of fatigue data for steel wires with different corrosion degrees are used to validate the GHBM, considering both noninformative and informative priors. When considering conventional fatigue data (i.e., without corrosion), the fatigue life prediction obtained from the GHBM and the maximum likelihood estimation (MLE) are compared, along with the results obtained from traditional lognormal models. The results indicate that the scatter in fatigue life prediction for the corroded specimens using the GHBM becomes smaller when the informative priors for the parameters are considered in the Weibull model for C-S-N. For conventional fatigue data, the fatigue life predictions using the Weibull model for S-N are similar for both the GHBM with the noninformative priors and the MLE, which are more conservative when compared with the results obtained from the traditional lognormal models. The proposed method in this paper can be used as a general approach in fatigue life prediction.