随机结构动力可靠度分析的极值概率密度方法

The extreme value probability density function based method for dynamic reliability assessment of stochastic structures

提出了随机结构动力可靠度分析的极值概率密度方法。基于概率密度演化的基本思想,构造一个虚拟随机过程,使得随机结构动力反应的极值为该虚拟随机过程的截口随机变量。进而,采用概率密度演化方法,建立概率密度演化方程并求解给出随机结构动力反应的极值分布。在安全域内积分即可给出结构动力可靠度。当安全界限为随机变量时,采用这一方法几乎不增加额外的工作量。与随机模拟结果的比较表明,本文建议方法具有良好的精度和效率。

The extreme value probability density function based method for dynamic reliability assessment of stochastic structures is presented. To obtain the probability density of the extreme value of the stochastic structural response, a virtual stochastic process, of which the extreme value response is the sectioned random variable, is firstly constructed. The probability density evolution equation is then set up and numerically solved to acquire the probability density function of the extreme value response. The integration over the safe domain will lead to the dynamic reliability. No essential additional workload is needed when the threshold is a random variable. The comparison with the Monte Carlo simulation demonstrates that the proposed method is of high accuracy and efficiency.