Reliability estimation using MCMC based tail modeling

Abstract

Tail modeling is an efficient method used in reliability estimation of highly safe structures. In classical tail modeling approach, first a relatively small number of limit-state function evaluations are performed through a sampling scheme (e. g., Monte Carlo simulations), then a proper threshold value (e. g., 90%) is selected that specifies the tail part of the cumulative distribution function, and finally a proper tail model is fitted (to the tail part) and reliability is estimated using the fitted model. In this approach, limit-state function calculations that do not belong to the tail part are mostly discarded, so majority of limit-state evaluations are wasted. In this paper, Markov chain Monte Carlo (MCMC) method with Metropolis-Hastings algorithm is used to draw samples from the tail part only, so that a more accurate reliability index prediction is achieved. Example problems with varying complexity are used to compare the accuracy of the proposed method to that of the classical tail modeling. For the example problems explored, the accuracy of the proposed tail modeling method is found to be better than that of the classical tail modeling method, provided that the proposal distribution scale parameter used in MCMC is selected properly. © 2016, American Institute of Aeronautics and Astronautics. All right reserved.