Abstract

This paper presents a hybrid reliability analysis method for structures involving random and interval variables. Firstly, the original performance function is approximated as the product of a series of univariate functions based on the multiplicative dimensional reduction method. Secondly, weight-point estimation is employed to calculate the first and second moments of all univariate functions with random variables. Thirdly, the second-order Taylor expansion is applied to the univariate functions involving interval variables for solving their maximum and minimum values. Lastly, the relationship between the upper and lower bounds of the failure probability and the upper and lower bounds of the product of the interval univariate function is derived. As the upper and lower bounds of the failure probability are derived analytically on the basis of the first two moments obtained by combining the multiplicative dimensional reduction model with the interval of the product of all interval univariate functions, the proposed method avoids the optimization analysis process completely and is very efficient. The accuracy and efficiency of the proposed method are verified by two numerical examples and a practical engineering problem involving finite element analysis.

中文翻译：

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一种包含随机变量和区间变量的结构的有效混合可靠性分析方法

摘要

本文提出了一种包含随机变量和区间变量的混合可靠性分析方法。首先，基于乘维约简方法，将原始性能函数近似为一系列单变量函数的乘积。其次，使用权重点估计来计算具有随机变量的所有单变量函数的第一矩和第二矩。第三，将二阶泰勒展开式应用于涉及区间变量的单变量函数，以求解其最大值和最小值。最后，推导了失效概率的上下限与区间单变量函数乘积的上下限之间的关系。由于在将乘维约简模型与所有间隔单变量函数的乘积的间隔相结合的前两个时刻的基础上，分析得出了故障概率的上限和下限，因此该方法完全避免了优化过程并且非常有效。通过两个数值例子和涉及有限元分析的实际工程问题验证了该方法的准确性和效率。