An Efficient Adaptive Reliability Analysis Method Based on Kriging and Weighted Average Misclassification Rate Improvement

In the past few years, the Kriging model based on the adaptive design of experiments (DoE) has attracted extensive attention in analyzing the reliability of structures involving time-consuming simulations or complicated implicit performance function. Although varieties of sampling strategies have been proposed, they update DoE mainly by selecting the sample at which its corresponding learning function value is the maximum or minimum. However, there are usually two drawbacks. First, the training samples in DoE are easily clustered or overlapped. Second, the existing strategies usually only consider the improvement of prediction accuracy at the new training sample rather than the accuracy improvement of the region near the new training sample. Unfortunately, these two drawbacks can cause some unnecessary performance function evaluations. Therefore, an efficient adaptive sampling strategy and reliability analysis algorithm based on Kriging model, weighted average misclassification rate, sampling uniformity and gradient of prediction uncertainty are proposed. Furthermore, an improved stopping criterion based on the relative error estimation of failure probability is also developed to further reduce iteration. Subsequently, two explicit examples from the literature are analyzed to verify the effectiveness and superiority of the proposed method. Finally, a truss structure subjected to six external loads is investigated to illustrate the feasibility of the proposed reliability analysis method in engineering applications.