Metamodel-Guided Failure Sample Screening in Monte Carlo Simulations

Rare event simulation is a crucial task in risk assessment and engineering failure control. Although the crude Monte Carlo simulation (MCS) can provide accurate probability of failure estimation and enables comprehensive failure case analysis, its high computational cost makes it impractical for high-dimensional and low-probability events. This study proposes a novel metamodel-guided failure sample screening method that maintains comprehensive failure analysis capabilities while significantly reducing computational demands. Unlike existing approaches that rely entirely on either metamodels or performance functions, our proposed method strategically integrates both—using performance functions in the critical failure domain to ensure near-MCS level of accuracy while employing metamodels elsewhere for computational efficiency. To construct effective metamodels for high-dimensional problems, a statistics-based space-filling resampling strategy extracts representative samples from a predetermined MCS pool. Those samples in the failure domain and its vicinity are first screened using the metamodel, then corrected with the performance function to identify all failure samples for accurate reliability analysis. The proposed method can be implemented in both single-step and iterative manners with two distinct algorithms. A rigorous theoretical convergence proof for the single-step algorithm is derived. Three numerical examples of increasing complexity validate the method’s efficacy, including practical applications to slope stability analysis and insights gained from high-risk cases analysis.