Aiming at the reliability-based design optimization problem of complex structural systems, an efficient optimization method based on subset simulation and Markov chain simulation in augmented space was proposed. Considering the reliability-based design optimization problem in which the design parameters were distributed parameters of basic random variables, the target failure probability was transformed into a posterior density function of the design parameters in the augmented space, obtained a set of initial failure samples in the whole design domain through subset simulation, and then adopted the efficient Markov chain simulation to generate more failure samples in the gradually smaller design domain under the sequential approximate optimization framework. The target posterior density function was estimated and updated, and the decoupling approach was used to solve the transformed optimization problem to finally obtain the optimum. Compared with the existing methods, the proposed method requires only one reliability analysis and can avoid local optimal solution, resulting in the global optimal solution. Examples were given to illustrate the applicability of the proposed method in engineering and its superiority in the accuracy and efficiency of analysis and calculation.

Assessment of imprecise time-variant reliability in engineering is a critical task when accounting for both the variability of structural properties and loads over time and the presence of uncertainties involved in the ambiguity of parameters simultaneously. To estimate the Imprecise Time-variant Failure Probability Function (ITFPF) and derive the imprecise reliability results as a byproduct, Adaptive Combination Augmented Line Sampling (ACALS) is proposed. It consists of three integrated features: Augmented Line Sampling (ALS), adaptive strategy, and the optimal combination. ALS is adopted as an efficient analysis tool to obtain the failure probability function w.r.t. imprecise parameters. Then, the adaptive strategy iteratively applies ALS while considering both imprecise parameters and time simultaneously. Finally, the optimal combination algorithm collects all result components in an optimal manner to minimize the Coefficient of Variance (C.o.V.) of the ITFPF estimate. Overall, the proposed ACALS method outperforms the original ALS method by efficiently estimating the ITFPF while guaranteeing a minimal C.o.V. Thus, the proposed approach can serve as an effective tool for imprecise time-variant reliability analysis in real engineering applications. Several examples are presented to demonstrate the superiority of the proposed approach in addressing the challenges of estimating the ITFPF.