基于降维算法和Edgeworth级数的结构可靠性分析

Structural reliability analysis based on dimensionality reduction and Edgeworth series

针对工程实际中存在功能函数为隐式或高维非线性的复杂结构,本文提出了一种基于降维算法和Edgeworth级数的可靠性分析方法。利用降维算法将n维函数展开为n个一维函数,经变量转换后变量都相互独立且服从均值为0、方差为0.5的正态分布,再结合Gauss-Hermite积分方法计算出一维函数的原点矩,从而得到结构功能函数的中心矩,将所得的矩信息应用到Edgeworth级数展开式中,给出功能函数的累积分布函数表达式,计算得到结构的失效概率。该方法避免了功能函数对变量梯度的要求,仅需少量的确定性重分析计算。数值算例结果表明了本方法的有效性和正确性。

A reliability analysis method based on the dimension reduction algorithm and the Edgeworth series was proposed to treat the complicate structures with implicit and high dimensional nonlinear limit state functions in practical engineering. By utilizing the dimension reduction method,the n-dimensional function was expanded to n unidimensional functions and the random variable were made to subject to the independent normal distribution with mean value being zero and variance deviation being 0. 5 by means of the variable transformation. The origin moments of the unidimensional functions were obtained after the Gauss-Hermite integration. In this case,the central moments of the limit state function of the structure were achieved successfully and applied to the Edgeworth series expanding expressions,from which the cumulative distribution function of the limit state function could be generated and finally the probability of failure could be obtained. Avoiding gradient computation,the proposed method requires less definite reanalysis and is proved to be effective and correct via numerical examples.