An Adaptive Clustering-Based Active Learning Kriging Method Combining With Importance Sampling for Structural Reliability Analysis With Multiple Failure Regions

Reliability analysis of structures characterized by multiple failure regions remains a challenging task, especially when the computationally intensive numerical models are used to predict the system response. In order to address this problem, an adaptive clustering-based active learning Kriging method combining with importance sampling (abbreviated as AC-AK-IS) is proposed. The basic idea lies in the replacement of FORM stage of active learning and Kriging-based importance sampling (AK-IS) with a first stage adaptive Kriging to approximate the failure boundary. Then an adaptive clustering algorithm is proposed to automatically identify the failure regions, based on which a Gaussian mixture model (GMM) is fitted as the importance sampling density (ISD). With the fitted ISD, the second stage of AK-IS can be readily performed to estimate the failure probability. AC-AK-IS provides an effective way to identify the a-priori unknown multiple failure regions. It extends the application of AK-IS to cases with multiple failure regions while retaining the advantages of high efficiency and accuracy. Three examples are provided to demonstrate the application and efficiency of AC-AK-IS.