Hybrid active learning method for non-probabilistic reliability analysis with multi-super-ellipsoidal model

Non-probabilistic reliability analysis is of great importance in both reliability measure and reliability based design, the efficiency and precision of non-probabilistic reliability analysis, as well as uncertainty quantification, have attracted great attention currently. In this study, considering the coexistence of correlated and independent uncertain-but-bounded variables in engineering applications, a multi-super-ellipsoidal model is used to quantify the uncertainties. Furthermore, inspired by both "norm" based reliability index and "volume-ratio" based reliability index, a hybrid non-probabilistic reliability index is derived to measure the reliability extent more accurately and intuitively. To improve the accuracy and efficiency of solving the hybrid non-probabilistic reliability index, an effective Kriging based hybrid active learning method (HALM) is further developed. Finally, four examples are used to verify the effectiveness and robustness of the proposed HALM. The results show that the selection of multi-super-ellipsoidal model has a certain effect on the estimation of reliability index. Compared with the sampling-based analysis method, HALM presents better performance in terms of the trade-of between in computational efficiency and accuracy.