Multimodel Bayesian estimation of total uncertainty and its application to modeling the yield strength of structural aluminum at elevated temperature

In the multimodel approach, inference is based on an ensemble of model classes. Uncertainties in the model probabilities and parameter values are estimated from data using Bayesian inference. While the epistemic uncertainty in the estimates of parameter values and model form are accounted for in literature on Bayesian multimodel inference, the epistemic uncertainty in the estimates of model probabilities is often ignored. When working with small data sets, however, there might be large epistemic uncertainty in the model probabilities. This thesis presents a Bayesian multimodel approach to quantifying the total uncertainty in random variables, which often serve as inputs to models of engineering systems, from limited data. The novelty of this approach is that it builds on existing Bayesian multimodel methods by integrating into them the treatment of epistemic uncertainty in model probabilities. In this approach, model probabilities are treated as random variables and their posterior distribution is obtained by Bayesian inference. The mode of this posterior distribution quantifies the epistemic uncertainty in the model form, and the marginals quantify the epistemic uncertainty in the model probabilities. The quantified uncertainty is propagated through models of engineering systems using samples drawn from the posterior predictive distribution, which incorporates the aleatory uncertainty as well as the epistemic uncertainty in the model probabilities, model form, and parameters of the set of input model classes. Then, importance sampling is employed to explicitly quantify the uncertainty in the outputs due to each kind of input uncertainty, by post-processing the outputs. The proposed approach was applied to the estimation of total uncertainty in the yield strength of aluminum 6061-T6 at elevated temperatures, using data derived from an extensive testing program. A total of 100 steady-state uniaxial tension tests were conducted at six temperatures using material sourced off-the-shelf from nine different batches to study the variability in the stress-strain response of aluminum 6061-T6. Multimodel inference is employed using this data to estimate the design value and reduction factor for tensile yield strength incorporating epistemic uncertainty in the model probability, model form, and parameters used to model the variability in the yield strength