Efficient procedure for failure probability function estimation in augmented space

• Published in: Structural safety 2021-09, Vol.92, p.102104, Article 102104
• Main Authors: Yuan, Xiukai, Liu, Shaolong, Valdebenito, M.A., Gu, Jian, Beer, Michael
• Format: Article
• Language: English
• Subjects: Bayesian theory; Coefficient of variation; Design; Failure probability function; Importance sampling; Monte Carlo simulation; Random variables; Reliability analysis; Reliability-based optimization; Sampling; Simulation
• ISSN: 0167-4730; 1879-3355
• DOI: 10.1016/j.strusafe.2021.102104

•The failure probability function is estimated by an expression based on samples.•The target posterior distribution of design variables is expressed as an integral.•Implementations with Monte Carlo simulation, Importance Sampling and Subset Simulation are investigated.•Applications to a turbine disk and a dynamic steel frame are presented. An efficient procedure is proposed to estimate the failure probability function (FPF) with respect to design variables, which correspond to distribution parameters of basic structural random variables. The proposed procedure is based on the concept of an augmented reliability problem, which assumes the design variables as uncertain by assigning a prior distribution, transforming the FPF into an expression that includes the posterior distribution of those design variables. The novel contribution of this work consists of expressing this target posterior distribution as an integral, allowing it to be estimated by means of sampling, and no distribution fitting is needed, leading to an efficient estimation of FPF. The proposed procedure is implemented within three different simulation strategies: Monte Carlo simulation, importance sampling and subset simulation; for each of these cases, expressions for the coefficient of variation of the FPF estimate are derived. Numerical examples illustrate performance of the proposed approaches.