Modified subset simulation method for reliability analysis of structural systems

► A modified Markov-chain based simulation method called “Regenerative Adaptive Subset Simulation (RASS)” is described. ► The proposed RASS provides improvements to the classical Subset Simulation (SS) by incorporating several new features. ► RASS reduces the correlation between the samples through a regeneration algorithm. ► Updating the variances of the proposal distribution function in an adaptive algorithm improves the overall efficiency. ► Univariate proposal distribution functions help optimize the computational effort for high-dimension problems. A “Regenerative Adaptive Subset Simulation” (RASS) method is proposed for performing the reliability analysis of complex structural systems. Proposed modifications to the classic subset simulation method include the implementation of advanced Markov Chain processes to combine the benefits of a Markov Chain regeneration process, a Delayed Rejection and Adaptive sample selection algorithms and a Componentwise sampling model. The proposed modifications help to overcome the limitations of the original Metropolis–Hasting algorithm used in the subset simulation which include the “burn-in problem” and the difficulty of the selection of the proposal probability function. Several illustrative examples are presented to demonstrate the efficiency of the proposed simulation and compare its results to those of other methods. The results show that RASS is robust and efficient in estimating the probability of failure of structural systems with complex failure regions, large numbers of random variables, and small probabilities of failure.