Enhanced sequential directional importance sampling for structural reliability analysis

Abstract

Sequential directional importance sampling (SDIS) is an efficient adaptive simulation method for estimating failure probabilities. It expresses the failure probability as the product of a group of integrals that are easy to estimate, wherein the first one is estimated with Monte Carlo simulation (MCS), and all the subsequent ones are estimated with directional importance sampling. In this work, we propose an enhanced SDIS method for structural reliability analysis. We discuss the efficiency of MCS for estimating the first integral in standard SDIS and propose using Subset Simulation as an alternative method. Additionally, we propose a Kriging-based active learning algorithm tailored to identify multiple roots in certain important directions within a specificed search interval. The performance of the enhanced SDIS is demonstrated through various complex benchmark problems. The results show that the enhanced SDIS is a versatile reliability analysis method that can efficiently and robustly solve challenging reliability problems

Figures (9)

• Figure 1: Active learning Kriging model for finding root (one root case) in interval $[0.0362,8.0574]$.
• Figure 2: Active learning Kriging model for finding roots (two roots case) in interval $[0.0362,8.0574]$.
• Figure 3: Active learning Kriging model for finding roots (three roots case) in interval $[0.0362,8.0574]$.
• Figure 4: 1000 MCS samples drawn from standard normal PDF $\varphi_2(\boldsymbol{u})$ vs three types of limit states (left: linear; middle: concave; right: convex)
• Figure 5: 1000 samples drawn from standard normal PDF vs a special LSF with narrow failure domain. The probability of a sample to fall into the inflated failure domain $F=\{\boldsymbol{u}\in \mathbb{R}^{n} :G(3\boldsymbol{u})\leq 0\}$ is 0.014.

Theorems & Definitions (1)

• Remark 1