Combining Bayesian active learning and conditional Gaussian process simulation for propagating mixed uncertainties through expensive computer simulators

Resulted from the limited information on both parameters and excitation at the early design stage of aerospace structures, evaluating the reliability with high accuracy has been recognized as a challenging task. Imprecise probability models have been widely developed and accepted due to their flexibility in separating the aleatory and epistemic uncertainties, and then the potential of estimating the reliability with high confidence. However, the propagation of these models through expensive-to-evaluate simulators remains to be a challenge due to the hierarchical model structure. To fill this gap, a new Bayesian active learning method is devised for efficiently learning the functional behavior of the failure probability and response variance over the epistemic input parameters. This information is especially useful for evaluating the safety of structures and for managing the uncertainties during the design process. The proposed method is based on training/updating a Gaussian Process Regression (GPR) model in the augmented space of aleatory and epistemic parameters, with the training data actively produced using two well-designed acquisition functions. The induced posterior features of the quantities of interest are inferred numerically based on efficient simulation of the GPR model. Benefiting from the decoupling scheme and the Bayesian adaptive design strategy, the proposed method is extremely efficient and provides accuracy guarantee for the numerical results. The effectiveness and superiority of the proposed method are demonstrated with numerical and engineering benchmarks, including the dynamic reliability analysis of a satellite structure.