AK-HRn: An efficient adaptive Kriging-based n-hypersphere rings method for structural reliability analysis

With increasing complexity of engineering problems, various traditional reliability analysis methods are facing rising challenges in terms of computational efficiency and accuracy. Surrogate models, especially Kriging model, have received growing attention and been widely used in reliability analyses by the virtue of their advantages for achieving high computational efficiency and ensuring high numerical accuracy. Nevertheless, there have been still two significant problems in the Kriging model-assisted reliability analyses due to the absence of prior knowledge: i.e. (1) the size of candidate sample pool tends to be quite large in order to ensure prediction of a convergent failure probability; and (2) local prediction accuracy of limiting state surface by Kriging model is generally excessive. These above two issues can often result in high computational cost for Kriging-based reliability analyses. To enhance computational efficiency, a new method that combines adaptive Kriging and n-hypersphere rings, named an AK-HRn method, is proposed in this study. First, the n-hypersphere rings, which can update its position and radius adaptively, is adopted to divide the design space into potential safety domains and potential failure domains. Second, these potential failure domains are used as the sampling domains for implementing importance sampling method to generate a suitably-sized candidate sample pool. Third, a novel learning function is presented to enrich the design of experiment (DoE), which avoids excessive local prediction accuracy of Kriging models by establishing the rejection domains. Finally, the efficiency and robustness of AK-HRn is compared with other Kriging-based reliability analysis methods through four illustrative numerical examples and one 6-DOF industrial robot case study. Comparison shows that the proposed AK-HRn method has high efficiency and robustness to solve complex reliability analysis problems.