Statistical models are formulated to explore the influences of various experimental variables on an ultrasonic axial fatigue setup. Model uncertainty is accounted for through a coherent Bayesian Model Averaging (BMA) mechanism to show that conditioning on a single statistical model ignores model uncertainty and can lead to underestimating uncertainty when making inferences of fatigue life. Motivation for this effort stems from the need to model high cycle fatigue (HCF) life that is critical for the structural assessment of turbine engine components. Bayesian statistical models infer the underlying probabilistic models of the fatigue life while accounting for uncertainties in model parameters. BMA then provides an estimate of specimen fatigue life that is an average of the posterior distributions of specimen fatigue life under each model considered, weighted by their posterior model probability. Nine experimental variables are included in a model composed of linear, quadratic, and interaction terms, providing a model space of 2~(54) models that is decomposed into subspaces of models using variable selection heredity principles. These subspaces are then sampled via Monte Carlo Model Composition (MC3) for determining the posterior model probabilities, variable posterior inclusion probabilities, and uncertain model parameter densities. This approach is found to identify important experimental variables, provide parameter and fatigue life estimates that account for model uncertainty, and suggest improvement over selecting any single model.
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