Bi-Objective Adaptive Kriging for Reliability Analysis with Random and Evidence Variables

Random uncertainty and evidence uncertainty usually coexist in actual structures. For efficient reliability analysis of structure in presence of hybrid random and evidence uncertainties (RA-HRE), a single-layer sampling method (SLSM) is proposed. First, two equivalent expectation formulas are derived for the belief and the plausibility measures in RA-HRE. According to these formulas, the belief and the plausibility measures can be directly estimated by only one group of samples of the random variables and focal elements of the evidence variables that are generated at the same level. Second, for greatly reducing the computational cost in RA-HRE by SLSM, the SLSM-based bi-objective adaptive kriging (SLSM-BAK) is subsequently developed to simultaneously estimate the belief and the plausibility measures. Aiming at the two objectives in RA-HRE, that is, accurately estimating the belief and the plausibility measures, a new compound learning function is developed in SLSM-BAK. Based on the compound learning function, the kriging model is adaptively updated to accurately and efficiently recognize the sign of the maximum and minimum performance functions for each random sample over the corresponding sampled focal element. This training process continues until both the estimation precision of the belief and the plausibility measures satisfy the preset requirements.