An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability

The estimation of system failure probabilities may be a difficult task when the values involved are very small, so that sampling-based Monte Carlo methods may become computationally impractical, especially if the computer codes used to model the system response require large computational efforts, both in terms of time and memory. This paper proposes a modification of an algorithm proposed in literature for the efficient estimation of small failure probabilities, which combines FORM to an adaptive kriging-based importance sampling strategy (AK-IS). The modification allows overcoming an important limitation of the original AK-IS in that it provides the algorithm with the flexibility to deal with multiple failure regions characterized by complex, non-linear limit states. The modified algorithm is shown to offer satisfactory results with reference to four case studies of literature, outperforming in general several other alternative methods of literature.