基于Beta分布的改进的一次可靠度法研究

Study of Modified First Order Reliability Method Based on Beta Distribution

为了提高一次可靠度方法的计算精度和计算效率,文章利用Beta分布拟合了功能函数中的随机变量的概率分布,利用VBA语言给出了将Beta分布和对数正态分布转化为标准正态分布的方法,采用蒙特卡洛模拟法比较了采用不同概率分布的一次可靠度计算精度。算例分析表明:当功能函数中随机变量服从对数正态分布时,失效概率被高估;当随机变量服从正态分布时失效概率被低估。利用本文提出的Beta分布拟合随机变量的概率不仅大大提高了计算精度,而且在保证迭代收敛的前提下提高了计算效率。

To improve the accuracy and efficiency of First Order Reliability Method （ FORM） , Beta distribution is firstly adopted to fit the probability distributions of the random variables. Afterward the procedures of the equivalent normal transformations for lognormal distribution and Beta distribution are presented using VBA （ Visual Basic for Applications ） program code. Monte Carlo simulations are performed to assess the accuracy of the results calculated using different probability distributions. The results from a numerical example indicate that FORM overestimates the probability of failure when the random variables are log-normally distributed and underestimates the probability of failure when the random variables are normally distributed. The accuracy of FORM has been highly promoted when the random variables follow Beta distribution adopted in this paper. Moreover, FORM for Beta distribution is not only time-consuming and meanwhile ensures convergence of iteration.