Line sampling for time-variant failure probability estimation using an adaptive combination approach

An efficient sampling approach 'Adaptive Combined Line Sampling' is proposed for evaluating the 'time-variant failure probability function' (TFPF) of structures. Line Sampling is implemented in an adaptive and iterative way, where each individual Line Sampling run is carried out based on adaptively selected important directions, in order to ensure a sufficiently precise estimation of the TFPF over the whole time interval of analysis. An adaptive strategy and an optimal combination algorithm are developed for the practical implementation of the Line Sampling process. The adaptive strategy allows to determine the optimal important direction which is then used in the next Line Sampling run. The combination strategy allows to collect all these adaptive sampling runs together in an optimal way, which aims at minimising the coefficient of variation (C.o.V.) of the TFPF estimate. Due to these strategies, the proposed approach can estimate the TFPF in a more efficient way than the traditional Line Sampling, while guaranteeing that the C.o.V. of the estimate remains below a prescribed threshold over the whole time of analysis. Thus it can be seen as an extended version of classical Line Sampling specially tailored for time-variant reliability analysis. Examples are given to illustrate the performance of the proposed approach.