Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study

Abstract

This paper addresses a benchmark study designed to evaluate the performance of various methods in calculating the reliability of large systems. In particular, this paper focuses on evaluating two reliability methods recently proposed by the authors, referred to as spherical subset simulation (S3) and auxiliary domain method (ADM). S3 is based on dividing the failure domain into a number of appropriately selected subregions and calculating the failure probability as a sum of the probabilities associated with each of these subregions. The probability of each subregion is calculated as a product of factors. These factors can be estimated accurately by a relatively small number of samples generated according to the conditional distribution corresponding to the particular subregion. The generation of such samples is achieved through Markov Chain Monte Carlo (MCMC) simulations using a MCMC algorithm proposed by the authors. The proposed method is very robust and is suitable for treating general high-dimensional problems such as the given benchmark problems. ADM is applicable to reliability problems involving deterministic dynamic systems subjected to stochastic excitation. The first step in ADM involves the determination of an auxiliary failure domain (AFD). The choice of the AFD is based on preliminary MCMC simulations in the target failure domain. It must be noted that although the AFD is chosen to be specified as a union of linear failure domains, the method does not assume any restriction with respect to the target failure domain, which is assumed to be generally non-linear. Once the AFD is determined, the ADM proceeds with a modified subset simulation procedure where the first step involves the direct simulation of points in the AFD. This is in contrast to standard subset simulation (SSM) where the first step involves standard Monte Carlo Simulations. The number of steps and the computational effort required by ADM, assuming an appropriate AFD is chosen, can be smaller than that required by SSM. Results for the benchmark problems show that both S3 and ADM are efficient for treating high dimensional reliability problems. © 2006 Elsevier Ltd. All rights reserved.