Novel Kriging-Based Variance Reduction Sampling Method for Hybrid Reliability Analysis with Small Failure Probability

For hybrid reliability analysis under random and multi-super-ellipsoidal variables (HRA-RM) with small failure probability, a combination of kriging and subset simulation importance sampling (SSIS) was proposed in this paper. Firstly, to quantify epistemic uncertainties more accurately, the super-ellipsoidal model was used to replace interval/ellipsoid ones. Besides, the real performance function was replaced by a kriging metamodel, which can be updated sequentially by selecting candidate samples from the first and last levels of SSIS. Due to the differences between hybrid reliability analysis (HRA) and probability reliability analysis, an expected modified risk function was adopted to obtain the next updated point. Two varying convergence conditions corresponding to the first and last levels of SSIS were employed in this paper to further improve the efficiency. Under the final kriging metamodel, the maximum failure probability of HRA-RM with small failure probability was calculated by the samples in all levels of SSIS. Finally, four validation examples were applied to demonstrate the accuracy and efficiency of the proposed method.