Bayesian inference and model comparison for metallic fatigue data

TL;DR

This paper develops a comprehensive statistical framework for modeling, comparing, and ranking fatigue life data of aluminum alloys using both classical and Bayesian methods, accommodating censored data and providing robust uncertainty quantification.

Contribution

It introduces a systematic approach combining maximum likelihood and Bayesian techniques for fatigue data analysis, including model calibration, selection, and ranking with new Bayesian model comparison methods.

Findings

Bayesian methods effectively rank fatigue models.

Bootstrap confidence bands assess quantile estimation robustness.

Model comparison via information criteria identifies the best fit.

Abstract

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.