Ensemble of metamodels-assisted probability density evolution method for structural reliability analysis

An active-learning reliability method called the AEM-PDEM is proposed that combines adaptive ensemble of metamodels (EM) and the probability density evolution method (PDEM). Three critical aspects are addressed in this method. First, the ensemble of three diverse metamodels, i.e., the polynomial chaos Kriging (PCK), the low-rank approximation (LRA) and the support vector regression (SVR), is built by weighted combination according to their global error measures, which enables to provide both predicted value and variance. Second, the EM predictions at the training samples are replaced by the true computational model responses, so as to secure the accuracy of failure probability estimate. Third, according to the PDEM-oriented expected improvement function (PEIF), a multi-point enrichment process is developed based on the EM and the three component metamodels. Then, three numerical examples are investigated and comparisons are made between the AEM-PDEM and other existing reliability methods. Results demonstrate that, in comparison with the existing APCK-PDEM, the AEM-PDEM needs roughly 85-95% of the number of computational model evaluations. More importantly, it only requires approximately 30-45% of the number of iterations during the active-learning process. As a result, it just consumes nearly 35-50% of computational time of the APCK-PDEM, especially in high-dimensional dynamic problems and practical complex engineering problems.