A new direct second-order reliability analysis method
A new direct second-order reliability analysis method
复制标题
一种新的直接二阶可靠性分析方法
DOI：
10.1016/j.apm.2017.10.026
复制
发表时间：
2018-03-01
影响因子：
5
通讯作者：
Zhang, Xufang
中科院分区：
文献类型：
--
作者：
Huang, Xianzhen;Li, Yuxiong;Zhang, Xufang
在二阶可靠度方法中，任意分布随机变量的极限状态函数用标准正态变量的二次多项式近似。拟合的二次多项式然后用于计算极限状态的失效概率。然而，一般的二次多项式曲面的失效概率的封闭形式的解决方案是不可用的。因此，本文提出了一种新的二阶可靠性方法，用于可靠性分析的鞍点近似。极限状态函数的二阶近似是通过在最可几点处的二阶泰勒级数展开得到的。解析地导出了标准正态变量拟合二次多项式的累积量母函数。利用鞍点近似法，得到了极限状态的概率密度函数、累积分布函数和失效概率。最后，通过三个算例，将所提出的二阶可靠性方法与一阶可靠性方法、传统二阶可靠性方法以及Monte Carlo模拟方法进行了比较。比较表明，建议的二阶可靠性方法给出了准确的，收敛的，计算效率高的估计故障概率。(C)2017爱思唯尔公司All rights reserved.
In the second-order reliability method, the limit state function in arbitrarily distributed random variables is approximated by a quadratic polynomial of standard normal variables. The fitted quadratic polynomial is then used to calculate the probability of failure of the limit state. However, a closed-form solution for the probability of failure of a general quadratic polynomial surface is not available. As such, in this paper, a new second order reliability method for reliability analysis is presented using saddlepoint approximation. The second-order approximation of the limit state function is obtained by the second order Taylor series expansion at the most probable point. The cumulant generating function of the fitted quadratic polynomial of standard normal variables is derived analytically. The saddlepoint approximation is utilized to generate the, probability density function, cumulative distribution function and probability of failure of the limit state. Finally, three numerical examples are used to compare the performance of the proposed second-order reliability with that of the first-order reliability method, the conventional second-order reliability method, and Monte Carlo simulation. The comparisons show that the proposed second-order reliability method gives accurate, convergent, and computationally efficient estimates of the probability of failure. (C) 2017 Elsevier Inc. All rights reserved.