A density extrapolation approach to estimate failure probabilities

This paper proposes a novel approach called the Density Extrapolation Approach (DEA) for efficient reliability analysis. It builds on the Subset Simulation (SS) approach and integrates density estimation with SS. The proposed approach leverages the ability of SS to effectively move towards and generate samples in the tail regions and the ability of density estimation to extrapolate into the tail regions. Instead of running all the SS levels, only the first several SS levels are run, and then density estimation is used to calculate the failure probability. Kernel density estimation (KDE) with boundary correction is used to accurately capture the different shapes of the target distribution and also address the boundary bias of regular KDE. To establish a smooth estimation of the target distribution in the tail regions, KDE with adaptive bandwidth is used. Since density estimation requires i.i.d. samples, instead of using Markov Chain Monte Carlo (MCMC) that is typically used in SS, the modified rejection sampling algorithm with adaptive kernel sampling density (AKSD) is adopted to efficiently generate i.i.d. failure samples at each SS level. Results from illustrative examples validate the effectiveness of the proposed approach.