Novel reliability evaluation method combining active learning kriging and adaptive weighted importance sampling

To ensure the reliability of complex structures, a novel reliability assessment method combining an active learning kriging (ALK) model with adaptive weighted importance sampling (AWIS), the ALK-AIWS, was proposed in this work. The initial design of experiment (DoE) points were first generated using a modified Metropolis algorithm to construct a kriging metamodel. The Markov chain state seeds were then used as the centers for the importance sampling density function to simulate the training data in a given important region. Thus, the kriging surrogate model was updated using the revised DoE produced by the active learning function, and the failure probability can be evaluated using the entire training data set. An AWIS method was also introduced considering the contribution of the design point to the structural failure probability. Finally, the failure probabilities of several numerical examples and a complex engineering design case were evaluated verifying the efficiency, accuracy, and applicability of the proposed ALK-AWIS method, which provides an alternative approach to reliability evaluation in practical engineering applications.