Rare failure event analysis of structures under mixed uncertainties

Two challenges may exist in the reliability analysis of highly reliable structures in, e.g., aerospace engineering. The first one is that, the failure probability may be extremely small (typically, smaller than 1e-6), which commonly prevents us from generating accurate estimation with acceptable computational costs by using the available methods. The second one is that, the available information for the input variables may be subject to incompleteness (e.g., sparse data) and/or imprecision (e.g., measuring error), which, makes it impossible to generate precise probability models for the input variables. To address the above two challenges, this work proposes two effective algorithms based on combining the sampling techniques (i.e., extended Monte Carlo simulation and subset simulation), active learning techniques and high-dimensional model representation decomposition. The proposed methods can effectively estimate the failure probability function w.r.t. the uncertain distribution parameters of the input variables with small number of training samples even when the failure event is extremely rare. A numerical test example is introduced to illustrate the proposed methods.