Bayesian inference and model comparison for metallic fatigue data

• Published in: Computer methods in applied mechanics and engineering 2016-06, Vol.304, p.171-196
• Main Authors: Babuška, Ivo, Sawlan, Zaid, Scavino, Marco, Szabó, Barna, Tempone, Raúl
• Format: Article
• Language: English
• Subjects: Alloys; Bayesian analysis; Bayesian computational techniques for model calibration/ranking; Computer simulation; Confidence intervals; Criteria; Fatigue (materials); Fatigue life prediction; Mathematical models; Maximum likelihood methods; Metallic fatigue data; Predictive accuracy for Bayesian models; Random fatigue-limit models; Ranking
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.02.013

In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios. •Several models are calibrated to the 75S-T6 data set by means of the maximum likelihood method.•Classical measures of fit based on information criteria are used to compare and rank models.•Bayesian approach is considered to analyze some models under two different a priori scenarios.•Bayes factor and predictive information criteria are used to compare Bayesian models.