关键词: 结构可靠性, 降维算法, Taylor 展开, Edgeworth 级数, 矩方法

Abstract: In order to overcome the difficulties in structural numerical analysis caused by the high-dimension nonlinearity or the implicit performance functions in engineering practice,a numerical method to directly analyze the structural reliability is proposed.In this method,the n-dimension function is changed into n single-dimension functions via the dimension reduction,and the origin moment and the central moment of each single-dimension function are calculated through the variable transformation of the single-dimension functions and the Gauss-Hermite numerical integration.Then,the moment information is combined with the central moment of the structural performance function obtained by Taylor expansion,the cumulative distribution function of the structural performance function is deduced with the help of Edgeworth series,and the failure probability of the structural performance function is calculated based on the structural reliability theory.The proposed method avoids the multiple integrations for the statistical moment calculation of the performance function.Numerical examples show that this method is correct and feasible.

Key words: structural reliability, dimensionality reduction algorithm, Taylor expansion, Edgeworth series, moment method