A novel structural reliability analysis method via improved maximum entropy method based on nonlinear mapping and sparse grid numerical integration

摘要

This paper proposes an improved maximum entropy method for reliability analysis (i-MEM), in which the limit state function is transformed by a nonlinear mapping to predict the failure probability accurately. Through the nonlinear mapping, more statistical information can be obtained by the first-four statistical moments, and the truncation error originating from numerical integration is solved by the bounded limit state function after the nonlinear mapping, therefore the i-MEM can capture the tail information of the real probability distribution. In order to calculate the statistical moments in i-MEM with accuracy and efficiency, an improved sparse grid numerical integration method (i-SGNI) is developed on the basis of the normalized moment-based quadrature rule. Combining the i-MEM and i-SGNl, a novel reliability analysis method is proposed. To illustrate the accuracy, efficiency and numerical stability of the proposed method, six numerical examples and one engineering example are presented, compared with some common reliability analysis methods. The results show that the proposed method, with the combination of i-MEM and i-SGNI, can achieve a good balance between accuracy and efficiency for structural reliability analysis.