摘要
针对隐式非线性极限状态的复杂结构可靠性预测,提出了一种变量分解方法.该方法利用双变量分解法将求解功能函数统计矩的多维积分转化为多个低维积分,并利用高斯-埃尔米特数值积分对低维积分进行求积.在获得功能函数的统计矩后,应用最大熵原理确定用于可靠性分析的功能函数的最佳概率密度函数.该方法只需进行一次结构功能函数的概率密度函数求解,就能获得不同极限状态值的可靠度.算例分析结果表明,该方法的结果与Monte Carlo法100万次模拟结果相比,其相对误差不超过0.5%,具有很好的计算精度.
To predict the reliability of implicit and nonliear performance function for complex structures, a dimension-reduction method was presented. The multi-dimensional integration applied to calculate statistical moments of performance function is transformed into multiple low dimensional integrations using the bivariate dimension-reduction method, and the low dimensional integrations are then numerically calculated by the Gauss-Hermite integration. After obtaining the statistical moments, the maximum entropy principle （MEP） is used to determine the best probability density function of performance function for reliability analysis. The proposed method has the merit that the reliabilities at different limit-state values can be obtained readily by determining the probability density function of performance function simultaneously. The results of two examples show that the relative error of failure probability obtained by the proposed method is less than 0. 5% compared with that derived by one million times simulations of the Monte Carlo method.
出处
《西南交通大学学报》
EI
CSCD
北大核心
2014年第1期79-85,共7页
Journal of Southwest Jiaotong University
基金
中央高校基本科研业务费专项资金资助项目(CHD2009JC152
2013G3254015)
关键词
结构可靠性
双变量分解法
最大熵原理
概率密度函数
structural reliability
bivariate dimension-reduction method
maximum entropy principle
probability density function
