Active Kriging-based conjugate first-order reliability method for highly efficient structural reliability analysis using resample strategy

•Accurate and robust approximate numerical differentiation methods for Kriging model.•Efficient conjugate analytical method for highly nonlinear structural reliability analysis problems.•Uniform sampling for global optimization and resampling strategy for local optimization.•Active Kriging-based CFORM for solving complex structural reliability analysis problems. Efficient structural reliability analysis method is crucial to solving reliability analysis of complex structural problems. High-computational cost and low-failure probability problems greatly limit the efficiency in structural reliability analysis problems, causing the safety and reliability of the structure to be questioned. In this work, a highly efficient structural reliability analysis method coupling active Kriging algorithm with conjugate first order reliability method (AK-CFORM) is proposed. Specifically, the resample strategy is considered to reduce the number of samples evaluated in each active learning process; the uniform sampling is used to better balance global and local optimal problems; the conjugate map is used to improve the robustness of analytical first order reliability method; and the approximate numerical differential formula is proposed to solve the problems of non-convergence when solving the gradient of the Kriging surrogate model. Finally, three numerical cases and four engineering cases are used to illustrate the effectiveness and robustness of the proposed method. The results show that the proposed AK-CFORM has greater advantages in the number of calling system response and surrogate model with robust and accurate performance.