Inference and Updating of Probabilistic Structural Life Prediction Models
Cross, Richard J. (Richard John)
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Aerospace design requirements mandate acceptable levels of structural failure risk. Probabilistic fatigue models enable estimation of the likelihood of fatigue failure. A key step in the development of these models is the accurate inference of the probability distributions for dominant parameters. Since data sets for these inferences are of limited size, the fatigue model parameter distributions are themselves uncertain. A hierarchical Bayesian approach is adopted to account for the uncertainties in both the parameters and their distribution. Variables specifying the distribution of the fatigue model parameters are cast as hyperparameters whose uncertainty is modeled with a hyperprior distribution. Bayes' rule is used to determine the posterior hyperparameter distribution, given available data, thus specifying the probabilistic model. The Bayesian formulation provides an additional advantage by allowing the posterior distribution to be updated as new data becomes available through inspections. By updating the probabilistic model, uncertainty in the hyperparameters can be reduced, and the appropriate level of conservatism can be achieved. In this work, techniques for Bayesian inference and updating of probabilistic fatigue models for metallic components are developed. Both safe-life and damage-tolerant methods are considered. Uncertainty in damage rates, crack growth behavior, damage, and initial flaws are quantified. Efficient computational techniques are developed to perform the inference and updating analyses. The developed capabilities are demonstrated through a series of case studies.