2015 QPRC

Uncertainty analysis for importance sampling estimators with stochastic simulations

Abstract:

Recently, stochastic simulations are becoming more widely used to model real-world stochastic systems and to evaluate the reliability of the systems. Yet, the reliability evaluation or computer experiment involving many replications of simulations can take significant computational resources as the simulator becomes more realistic. To speed up these experiments, stochastic importance sampling (SIS) was proposed in our prior study, which efficiently estimates the probability associated with the stochastic system output by optimally allocating the sampling efforts of random system inputs. In this study, we establish the central limit theorem for the SIS probability estimator under mild assumptions and construct an asymptotically valid confidence interval. The proposed method further alleviates the computational burden by eliminating the need for expensive repetitions of the experiment in quantifying the uncertainty of the SIS probability estimator. We apply the proposed approach to the structural reliability evaluation of a wind turbine and the associated uncertainty analysis.