高维小失效概率下的改进线抽样方法

 针对隐式极限状态方程的可靠性分析，提出了一种基于失效域样本模拟的高效线抽样法。该法采用马尔可夫链来快速得到失效域中的条件样本，利用这些失效域中的样本可以得到线抽样的重要方向，并且这些样本还可以作为线抽样的样本，来得到隐式极限状态方程失效概率的估计值。由于该法可以较准确地得到线抽样方法的重要方向，因此线抽样的效率可以得到提高，另外失效域的样本又可以作为线抽样的样本，从而进一步降低所提方法的计算工作量。算例表明所提算法的计算精度和效率均高于传统线抽样方法。

Improved Line Sampling Method for Structural Reliability with High Dimensionality and Small Failure Probability

For reliability analysis of implicit limit state function, an improved line sampling method is presented on the basis of sample simulation in the failure region. In the presented method, Markov chain is employed to simulate the samples located at the failure region, and the important direction of line sampling is obtained from these simulated samples. On the other hand, the simulated samples can be used as the samples for line sampling to evaluate the failure probability of implicit limit state function. Since the important direction is searched accurately and robustly by simulated samples in the failure region, the efficiency of line sampling is improved obviously. Farther, the computation cost of line sampling is reduced also, because the simulated samples can be used for line sampling. A few examples demonstrate the rationality and efficiency of the improved line sampling method.