Guided tail modelling for efficient and accurate reliability estimation of highly safe mechanical systems

Classical tail modelling is based on performing a relatively small number of limit-state calculations through Monte Carlo sampling, and then fitting a generalized Pareto distribution to the tail part of the data. The limit-state calculations that do not belong to the tail part are discarded. To reduce the amount of discarded data, this article proposes an efficient tail modelling procedure based on guiding the limit-state evaluations towards the sampling points that have high chances of yielding limit-state values falling into the tail region. The guidance of the limit-state evaluations is achieved through a procedure that utilizes limit-state approximation and distribution fitting. The accuracy of the proposed method is tested through a mathematical problem and four structural mechanics problems, and it is found that the accuracy of reliability estimations can be significantly increased compared to classical tail modelling techniques for the same number of limit-state function evaluations. In addition, it is also found that the improvement in accuracy can be traded off for reducing the number of limit-state evaluations.