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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。
Aiming at the complex structure with implicit or high dimensional nonlinear function in engineering practice, this paper presents a reliability analysis method based on dimensionality reduction and Edgeworth series. Using the dimensionality reduction algorithm, the n-dimensional function is expanded into n one-dimensional functions. After the variables are transformed, the variables are independent of each other and obey a normal distribution with an average of 0 and a variance of 0.5. Combined with the Gauss-Hermite integral method, The moment of origin is obtained, and the center moment of the structural function function is obtained. The resulting moment information is applied to the Edgeworth series expansion. The cumulative distribution function expression of the function function is given, and the failure probability of the structure is calculated. This method avoids the requirement of function function on the variable gradient, only a small amount of deterministic reanalysis calculation. Numerical examples show the validity and correctness of the method.