A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables

This paper focuses on the hybrid reliability analysis with both random and interval variables (HRA-RI). It is determined that a metamodel only accurately approximating the projection outlines on the limit-state surface can precisely estimate the lower and upper bounds of failure probability in HRA-RI. According to this idea, a novel projection outline based active learning (POAL) method is proposed to sequentially update design of experiments (DoE). Then, a HRA-RI method combining POAL and Kriging metamodel (POAL-Kriging) is developed. In this method, Kriging metamodel is refined based on the update samples, which are sequentially chosen using POAL from the vicinity of the projection outlines on the limit-state surface. In the end, the lower and upper bounds of failure probability in HRA-RI are precisely estimated. Compared to the approximation of the whole limit-state surface, the proposed method only approximates the projection outlines on the limit-state surface, and therefore few DoE are needed to build a high quality metamodel. The accuracy, efficiency and robustness of the proposed method for HRA-RI are illustrated by four examples.