Adaptive surrogate model-assisted radial-based line sampling for rare event evaluation

Evaluating rare events remains a challenge in structural and systems reliability analysis. While line sampling has emerged as a robust alternative to traditional Monte Carlo Simulation for rare event assessment, enhancements to conventional LS methodologies are actively sought. To address this, this study proposes a novel model-agnostic framework: Adaptive Surrogate Model-Assisted Radial-Based Line Sampling (AS-RBLS). The AS-RBLS approach offers three key advantages. Firstly, through the integration of LS with the radial-based partitioning mechanism, it effectively circumvents the limitation of algorithm efficiency resulting from an excessive number of samples falling into the safe domain during the execution of the line sampling algorithm. Second, a novel ‘Sequential Sorting’ algorithm is introduced. This non-intrusive algorithm, integrated with the adaptive surrogate model, efficiently determines the adaptive hypersphere radius and identifies important directions by performing merely two distance-sorting operations on candidate samples during surrogate model updating. Finally, the radial partitioning confines the failure domain exclusively outside the hypersphere, thereby enabling highly efficient short-range line searches along important directions solely within the outer hypersphere region. The proposed AS-RBLS method is systematically benchmarked against several existing approaches through five numerical case studies evaluating rare events. The results indicate that the proposed AS-RBLS notably enhances the efficiency of rare event estimation.