Model and Data Uncertainty Effects on Reliability Estimation

This paper proposes a probabilistic framework to include both aleatory and epistemic uncertainty within model-based reliability estimation of engineering systems. Epistemic uncertainty is considered due to both data and model sources. Sparse point and/or interval data regarding the input random variables leads to uncertainty regarding their distribution types, distribution parameters, and correlations; this statistical uncertainty is included in the reliability analysis through a combination of likelihood-based representation, Bayesian hypothesis testing and Bayesian model averaging techniques. Model errors, which include numerical solution errors and model form errors, are quantified through Gaussian process models and included in the reliability analysis. The probability integral transform helps to implement an auxiliary variable approach that facilitates a single-level representation of both aleatory and epistemic uncertainty. This strategy results in an efficient single-loop implementation of Monte Carlo simulation (MCS) and FORM/SORM techniques for reliability estimation under aleatory and epistemic uncertainty. An aeroelasticity example is used to demonstrate the proposed methodology.