An adaptive importance sampling method with a Kriging metamodel to calculate failure probability

A Markov chain simulation was performed to extract points in a failure region. A Kriging metamodel was constructed to approximate a limit state based on the points extracted by the Markov chain simulation. A kernel sampling density was constructed to approximate the optimal importance sampling density. The points extracted in the failure region by the Markov chain simulation were assumed as a mean of each kernel. An importance sampling method was applied to calculate the failure probability. In the importance sampling method, points are extracted from the kernel in the vicinity of a limit state. Considering the statistical distance as well as the learning function, additional experimental points were selected for the kriging metamodel. A stable numerical calculation method was applied to find the parameters of the kernel sampling density. The completeness of the Kriging metamodel was evaluated on the basis of possible changes in failure probability.