An efficient method based on AK-MCS for estimating failure probability function

The function of failure probability varying with distribution parameters of random inputs is referred as failure probability function (FPF), it is often required in reliability-based design optimization. However, it is a computational challenging task since large number of expensive model evaluations are needed to estimate the failure probability at every distribution parameter. A method combining adaptive Kriging with Monte Carlo simulation is employed by this paper to efficiently estimate the FPF. Based on the augmented reliability theory and Bayes’ rule, the estimation of FPF is firstly transformed into that of the augmented failure probability and conditional joint probability density function (PDF) of distribution parameters on failure domain. Then, a Kriging model for the actual performance function is iteratively trained by the U-learning function until the stopping criterion is satisfied. The well-trained Kriging model can efficiently and accurately recognize the failure samples in the sample pool, on which the augmented failure probability and conditional joint PDF of distribution parameters on failure domain can be simultaneously estimated without extra model evaluations. The results of test examples illustrate that the method used in this work is more efficient than the existing methods, but its accuracy depends on the PDF approximation algorithms.