Adaptive Monte Carlo Simulation Method and Its Applications to Reliability Analysis of Series Systems with a Large Number of Components

Abstract

It is not uncommon to encounter engineering structures that can be modeled as series systems with a large, even unlimited, number of correlated components (e.g., component number greater than 1,000). It can be a significant challenge to estimate the failure probability of a large-series system, at least partially, due to difficulties in quantifying correlation among components, nonlinear system responses, and high dimensionality of uncertain parameters. Direct Monte Carlo simulation (MCS) is a straightforward method to address these difficulties, but it may need prohibitive computational costs if the component number is large and the system failure event is rare. This study proposes an efficient method called adaptive MCS for reliability analysis of series systems with a large number of components. The proposed approach is a variant of direct MCS, and it estimates the system failure probability by iteratively identifying failure samples from all direct MCS random samples without the need to explore them exclusively. The performance (including convergence and computational efficiency) of the proposed method was systematically explored using a number of series system examples under various settings (e.g., component number, correlation among components, and component reliability). It is shown that the results from adaptive MCS converge to estimates from direct MCS with much lower computation effort. The proposed approach is applicable to series systems with a large number of components (say greater than 1,000) and assumes that different components are correlated to a certain degree so that they may share some failure samples. As the component number and the correlation coefficient among components increase, the improvement of computational efficiency by the adaptive MCS becomes more prominent, leading to significant computational savings in comparison with direct MCS. Finally, the proposed method was applied to efficiently evaluating the system failure probability of a two-layer slope with a large number of potential slip surfaces (i.e., components).