Moving-zone renewal strategy combining adaptive Kriging and truncated importance sampling for rare event analysis

In practice, a vital challenge problem is how to accurately evaluate the failure probability of rare events with a minimum of samples. Although adaptive Kriging combined with truncated importance sampling (AK-TIS) provides a viable method to address this problem, unsatisfied samples are often added in Kriging modeling and thereby result in an unacceptable computing burden. To efficiently acquire best-desired samples and reduce the calls of real limit state function (LSF), a moving-zone renewal (MZR) strategy-based AK-TIS (MZR-AK-TIS) approach is proposed. By dividing the whole large candidate sampling pool into several small sub-candidate sampling pools, the MZR strategy can ceaselessly find desired samples and update the Kriging model as the moving of the sub-sampling pool. MZR-AK-TIS not only inherits the advantages of AK-TIS but also reduces its computing time in two aspects. One is the size reduction of the candidate sampling pool in each sub-zone, and the other is the reduction of the call number of real LSF since the samples outside the sub-sampling pool do not need to participate in Kriging updating. The proposed method is verified by several numerical cases and applied to the aeroengine variable stator vane mechanism. The analysis results demonstrate that MZR-AK-TIS holds the potential to reduce the computing cost while ensuring accuracy in rare event analysis.