Bayesian inference and model comparison for metallic fatigue data

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

Predictors of fatigue damage accumulation in the neighborhood of small notches

“…The definition of q given here is not the same as Peterson's notch sensitivity index discussed in Section 3. We retain this notation for the sake of consistency with the notation used in reference [20].…”

“…The parameters for the statistical models 1b and 2b were determined by an R-code 9 optimization routine called optim. Details are presented in [20]. The estimated parameters for Model 1 (resp.…”

“…In the following we will be concerned with Model 2a only. For a detailed investigation of models 1b, 2b and other statistical models we refer to [20].…”

“…Since the experiments were performed at various stress levels, the experimental data was normalized using the location and scale parameters of the unnotched data as indicated in equation (20). Therefore the standard normal CDF is the predicted CDF.…”

Bayesian inference to identify parameters in viscoelasticity

“…Some examples are the studies of Madireddy et al (2015) for hyperelastic constitutive models for tissue, Oden et al (2013) for phenomenological models for tumour growth, Chiachío et al (2015) for models of damage progression in composites due to fatigue, and Babuška et al (2016) for fatigue descriptions of metals. Model selection is however out of the scope of the current study.…”