Random and multi-super-ellipsoidal variables hybrid reliability analysis based on a novel active learning Kriging model

In this paper, based on the Kriging, an efficient minimum limit-state-surface search strategy is proposed for hybrid reliability analysis with both random and multi-super-ellipsoidal variables. The super-ellipsoidal model can represent the commonly used convex model (like ellipsoidal and interval models) in uncertainty analysis, which is a wise choice to represent the uncertainty for the available experimental data. For furtherly improving the approximation accuracy near the minimum limit state surface, a minimum limit-state-surface search strategy based on the active learning Kriging is proposed, where the separate sampling method for different uncertain variables is applied during the sequential sampling process. Combined with the constructed Kriging metamodel, the Monte Carlo Sampling is performed for the hybrid reliability problem with random and multi-super-ellipsoidal variables to evaluate the maximum failure probability. Finally, the effectiveness and precision of the proposed method are validated by four practical applications. •A multi-super-ellipsoidal model is introduced to quantify the epistemic uncertainties.•A minimum limit-state-surface search strategy is proposed for hybrid reliability analysis.•The significance of the separate sampling method for random and multi-super-ellipsoidal variables is determined.•The proposed method can well balance the computational efficiency and accuracy.