AK-MCSi: A Kriging-based method to deal with small failure probabilities and time-consuming models

Abstract Reliability analyses still remain challenging today for many applications. First, assessing small failure probabilities is tedious because of the very large number of calculations required. Secondly, mechanical system models can require considerable numerical efforts. To deal with these problems, classical reliability analysis methods may be combined with those of meta-modeling, to enable the construction of a model like the former numerical model but with fewer time-consuming evaluations. Among these approaches, the Active Learning Reliability Method, combining Kriging and Monte Carlo Simulations, has received attention over the last few years. This method has several drawbacks, such as the difficulty to assess small failure probabilities and its inability to parallelize computations. The proposed paper focuses on the improvement of such a method to solve both these issues. It introduces a sequential Monte Carlo Simulation technique to deal with small failure probabilities. A multipoint enrichment technique is also proposed to allow parallelization and thus to reduce numerical efforts. Both these new techniques give rise to the proposal of a new, more conservative stopping condition for learning. The efficiency of this new method, called AK-MCSi, is then demonstrated using three examples for which the results show a significant reduction in the time required and/or the number of iterations needed for an accurate evaluation of the failure probability.