An adaptive Kriging-based bi-objective optimization method for reliability assessment using combined information gain

Reliability Analysis (RA) is essential for assessing the safety and performance of engineering structures under uncertainty. However, the computational demands of high-fidelity models and complex limit state functions pose significant challenges. This study introduces a novel active learning Kriging-based method that addresses these challenges by integrating global uncertainty reduction and boundary position information into a unified bi-objective optimization framework. Firstly, we propose a new metric for evaluating the potential of candidate samples to reduce global information entropy through a hypothetical Kriging update technique. Secondly, we develop another function for quantifying boundary position information in candidate samples. By formulating a bi-objective optimization problem that simultaneously considers these two aspects, the information gain from sampling is maximized. Finally, the proposed method was tested and compared through six typical examples. Numerical results show its accuracy and efficiency in guiding the adaptive learning process across diverse scenarios. This method offers an effective solution for RA and provides valuable insights for related research.