Interval Monte Carlo methods for structural reliability

This paper considers structural reliability assessment when statistical parameters of distribution functions can not be determined precisely due to epistemic uncertainty. Uncertainties in parameter estimates are modeled by interval bounds constructed from confidence intervals. Reliability analysis needs to consider families of distributions whose parameters are within the intervals. Consequently, the probability of failure will vary in an interval itself. To estimate the interval failure probability, an interval Monte Carlo method has been developed which combines simulation process with the interval analysis. In this method, epistemic uncertainty and aleatory uncertainty are propagated separately through finite element-based reliability analysis. Interval finite element method is utilized to model the ranges of structural responses accurately. Examples are presented to compare the interval estimates of limit state probability obtained from the proposed method and the Bayesian approach.