Subset simulation interpolation - A new approach to compute effects of model-dynamics in structural reliability

To evaluate failure probabilities in structural reliability analysis, one often uses Monte Carlo methods such as Subset Simulation. However, when distributions of the relevant quantities lack certainty or are known to change over time, such as by deterioration or inspection, failure probabilities need to be calculated for every relevant constellation. In this paper, we show how to reduce the then required, often tremendous, computational effort by a new algorithm which avoids the need for repetitive expensive reliability evaluations. The algorithm couples Subset Simulation with interpolation methods and requires the probabilistic model to satisfy a natural monotonicity assumption as well as an independence assumption which suits many relevant settings. Regarding computation time, our simulations give evidence for high efficiency of the algorithm, even challenging the performance of the original Subset Simulation in a static reliability evaluation. For demonstration of utility, we present an application in reliability analysis of concrete structures where one benefits from the additional information provided by our algorithm.