Adaptive subset simulation for time-dependent small failure probability incorporating first failure time and single-loop surrogate model

High-precision time-dependent reliability analysis (TDRA) is essential for small failure probability estimation and life-cycle design and maintenance for engineering structures of high importance. However, existing small failure probability estimation methods, e.g., subset simulation (SS) and importance sampling (IS), might face challenges in accurate TDRA with relatively low computational costs. Thus, this paper presents a novel TDRA method for small failure probability based on point evolution kernel density (PKDE) and adaptive SS. To efficiently reduce the computational burden, single-loop surrogate modeling (SLSM) is employed, and TDRA is implemented by capturing the cumulative density function (CDF) of the first failure time. The proposed method is called First-failure-Time-PKDE-Adaptive-Surrogate-modeling-based-SS (FT-PASS). In FT-PASS, good-lattice-point-set-Partially-Stratified-Sampling (GLP-PSS) is performed to select uniform initial points and achieve the initial TDRA by PKDE. Subsequently, a Kriging model is built and trained by an advanced learning function to obtain the distribution of the first failure time with SS and revise the initial TDRA. Four different cases, a numerical case, a corroded steel beam, a turbine blade subject to stochastic loads, and a planar steel truss subject to stochastic load and corrosion effect, are used to validate FT-PASS. The results indicate that FT-PASS can accurately estimate time-dependent small failure probability and strike a balance between computational efficiency and accuracy compared with conventional TDRA methods.