基于概率密度演化方法的随机结构可靠度分析

Reliability analysis of stochastic structures based on probability density evolution method

随机结构反应的概率密度演化方法能够给出随机荷载作用下随机结构反应的概率密度函数。在此基础上,根据给定的正常使用位移限值要求,直接进行积分给出了随机结构的正常使用可靠度及其失效概率。在实例分析中,与一类情况下的精确解答及基于反应正态分布假定的二阶矩方法分析结果进行了比较。研究表明:基于密度演化方法的随机结构可靠度分析具有很高的精度,而二阶矩方法的可靠度分析结果则往往具有一定的偏差,在失效概率较低时可能给出虚假的失效概率。

The probability density function of the stochastic structural response can be obtained by the probability density evolution method. The service reliability and failure probability of the stochastic structure are evaluated by direct integral according to the limit state condition. In the examples, the results obtained by the proposed method are compared with the exact solution and the results obtained by the second-moment method. The investigations illustrate that the proposed method is of high accuracy whereas the widely applied second-moment method usually has deviation from the true solution and may even obtain misleading results particularly in the occasion that the failure probability is low.