Reliability analysis becomes increasingly complex when facing the complicated expensive-to-evaluate engineering applications, especially problems involve the implicit finite element models. In order to balance the accuracy and efficiency of implementing reliability analysis, an advanced Kriging method is proposed for efficiently analyzing the structural reliability. The method starts with an incipient Kriging model built from a very small number of samples generated by the simple random sampling method, then determines the most probable region in the probabilistic viewpoint and chooses the subsequent samples located in this region by employing the probabilistic classification function. Besides, the leave-one-out technique is used to update the current model. By locating samples in the probabilistic most probable region, only a small number of samples are used to build a precise surrogate model in the end, and only a few actual limit state function evaluations are required correspondingly. After the high quality surrogate of the implicit limit state is available by the advanced Kriging model, the Monte Carlo simulation method is employed to implement reliability analysis. Some engineering examples are introduced to demonstrate the accuracy and efficiency of the proposed method.
Zhang, L., Lu, Z., & Wang, P. (2015). Efficient structural reliability analysis method based on advanced Kriging model. Applied Mathematical Modelling, 39(2), 781–793. https://doi.org/10.1016/j.apm.2014.07.008