基于重要抽样马尔可夫链模拟的可靠性灵敏度分析新方法

重要抽样法是一种计算效率高而应用广泛的可靠性分析方法.在采用重要抽样法计算失效概率的前提下,文中基于重要抽样马尔可夫链模拟提出一种可靠性灵敏度分析新方法.所提方法根据计算失效概率积分表达式,将失效概率对基本变量分布参数的偏导数表征的可靠性灵敏度转化为一个特征函数的条件数学期望形式,该数学期望是以基本变量在失效域中的条件概率密度函数为基础的.然后利用重要抽样马尔可夫链模拟,将计算失效概率的重要抽样样本转化为基本变量落在失效域中的条件样本.最后用特征函数在这些条件样本点处的样本均值估计数学期望,进而完成可靠性灵敏度分析.文中方法的主要优点是效率高,只需要在计算失效概率重要抽样法的基础上增加很少的工作量,即可完成可靠性灵敏度分析.另外,由于该方法未引入线性假设,因此它可以较好地考虑极限状态方程非线性对可靠性灵敏度的影响,大量的算例结果充分证明所提方法的这些优点.

NEW IMPORTANCE SAMPLING MARKOV CHAIN SIMULATION BASED RELIABILITY SENSITIVITY METHOD

Importance sampling has wide application as an efficient reliability analysis approach. On condition that the failure probability is analyzed by the importance sampling, a new method for the reliability sensitivity is presented on the basis of the importance sampling Markov Chain simulation. According to the integration form of the failure probability, the reliability sensitivity, measured by the partial differential of the failure probability with respect to the distribution parameter of the basic random variable, is transformed into an expectation of a feature function. Then, the importance sampling Markov Chain simulation is employed to generate the failure samples, called conditional samples, distributing as the conditional probability density function. At last, the average of the feature function values at these conditional samples is used to evaluate the conditional expectation and further complete the reliability sensitivity. Since a little computation cost is increased during the importance sampling procedure, the efficiency of the presented method is very high. Additionally, no hypothesis of the linear limit state equation is introduced in the construction of the presented method; hence, the effect of the non- linearity of the limit state equation can be accounted on the reliability sensitivity. A few examples illustrate the advantages of the presented method.