基于平稳非高斯结构响应前四阶矩的首次穿越概率计算

First passage probability assessment based on the first four moments of the stationary non-Gaussian structural responses

发展了一个平稳非高斯结构响应的首次穿越概率解析方法。在该方法中,基于已得到的平稳非高斯结构响应的前四阶矩(均值、标准差、偏度和峰度),分别利用Winterstein(1994)模型与Ding和Chen模型的等效高斯分位数,以及平稳非高斯结构响应的界限水平,将软化与硬化非高斯结构响应映射为标准高斯过程;进而利用考虑初始条件与群超效应的平稳高斯结构响应的Poisson模型来实现平稳非高斯结构响应的首次穿越概率计算。算例对比分析验证了该修正方法的有效性和准确性,同时相比蒙特卡洛模拟提高了计算效率,为计算平稳非高斯结构响应的首次穿越概率提供了高效合理的工具。

An analytical procedure was developed for estimating the first passage probability of stationary nonGaussian structural responses. In the procedure,based on the beforehand obtained first four moments of the stationary non-Gaussian structural responses, a stationary non-Gaussian response was mapped into stationary standard Gaussian processes by using the equivalent Gaussian fractile of translation model and the critical level. The equivalent Gaussian fractile of Winterstein＇s polynomial（ 1994） and Ding and Chen model were used for softening and hardening non-Gaussian responses,respectively. Then,the Poisson model based on stationary non-Gaussian structural responses was established considering the effects of clumping and initial conditions on the up-crossing rate. The accuracy and efficiency of the modified method were demonstrated through the comparison study of numerical examples. The results show that the computational efficiency is greatly improved compared with the Monte-Carlo simulation,which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian structural responses.