Uncertain reliability index in finite element reliability analysis

Finite Element Reliability Analysis (FERA) has been devised to obtain the probability of structural response events based on random material, geometry and loading parameters. Previously, such analysis has not distinguished between the uncertainties rising from inherent randomness, and from model errors and insufficient knowledge about the probability distribution parameters. In this paper, we argue that this distinction is imperative for meaningful interpretation of the resulting reliability and to provide confidence in reliability assessments among practicing engineers. To this end, we identify sources of epistemic uncertainty and explicitly include them in the analysis. The quantification, representation and propagation of epistemic uncertainty by the Bayesian probabilistic approach and the fuzzy randomness approach are explored. Consequently, measures of confidence in the reliability index are obtained. We also emphasise the utilisation of importance measures to identify where data gathering or model improvement has the greatest influence. Another novelty is the implementations in the rapidly advancing OpenSees software. The extended software produces an uncertain reliability index from which point estimates or confidence bounds are extracted. A numerical example involving a non-linear finite element model of a reinforced concrete building with approximately one hundred random variables is employed to demonstrate the implementations.