Reliability Estimation Using Markov Chain Monte Carlo–Based Tail Modeling

Abstract

Tail modeling is an efficient method used in reliability estimation of highly safe structures. Classical tail modeling is based on performing limit-state function evaluations through a sampling scheme, selecting a threshold value to specify the tail part of the cumulative distribution function, fitting a proper model to the tail part, and estimating the reliability. In this approach, limit-state function calculations that do not belong to the tail part are mostly discarded, and so majority of limit-state evaluations are wasted. In this paper, Markov chain Monte Carlo 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. A commonly used proposal distribution formula is modified by using a scale parameter. The optimal value of this scale parameter is obtained for various numerical example problems with a varying number of random variables, and an approximate relationship is obtained between the optimal value of the scale parameter and the number of random variables. The approximate relationship is tested on the reliability prediction of a horizontal axis wind turbine and observed to work well. It is also found that the proposed approach is more accurate than the classical tail modeling when the number of variables is less than or equal to four. For a larger number of random variables, none of the two approaches are found to be superior to another.