A novel adaptive Kriging method combining Hessian matrix and an efficient F-scoreβ-based stopping criterion for structural reliability analysis

Abstract

Reliability analysis of complex structures or highly nonlinear performance functions generate an enormous computational burden and affects computational efficiency. It is crucial to accurately assess structural reliability. However, current methods do not meet the accuracy and efficiency requirements as the complexity and nonlinearity of the model gradually increase. To address these problems, a novel active learning Kriging method combined with a Hessian matrix was proposed for efficient structural reliability analysis. The predicted mean of the Kriging model was used as an element of the Hessian matrix to describe the degree of nonlinearity of the model. Based on the fact that the iterative process is greatly influenced dramatically by the sample points in proximity to the limit state surface (LSS), a candidate sample pool (CSP) is generated, where the sample points located in the vicinity of the LSS with a larger curvature are chosen to add to the design of experiments (DoE). A stopping criterion about F-scoreβ based on the number of the misclassified points is proposed to judge the model fitting effect, which can be used to effectively identify the LSS. Two mathematical cases and two finite element cases were used to illustrate the high accuracy and efficiency of the method, which a novel manner of the nonlinear reliability calculation is provided.