结构可靠性分析高效自适应重要抽样方法

AN EFFICIENT ADAPTIVE IMPORTANCE SAMPING METHOD FOR STRUCTURAL RELIABILITY ANALYSIS

提出了一种基于自适应Metropolis算法和快速高斯变换技术的结构可靠性分析高效自适应重要抽样方法.该方法首先利用自适应Metropolis算法高效生成结构失效域样本,然后运用自适应宽核密度估计方法构造重要抽样密度函数,最后采用快速高斯变换加速重要抽样过程中核函数的计算.与传统方法相比,自适应Metropolis算法能够在相同计算量下提供更多结构失效域信息从而改善计算精度,即为求得给定精度问题的解,可有效减少样本生成过程中的结构分析次数,提高方法的计算效率;快速高斯(Gauss)变换大幅降低核密度估计的计算复杂度从而大幅缩减重要抽样的计算耗时.通过数值算例可以看出该方法具有较高的计算精度和效率.

This study develops an efficient adaptive importance sampling method based on adaptive Markov chain Monte Carlo and fast Gauss transform technique for reliability analysis. In the proposed method, the samples on the failure domain are generated by the adaptive Metropolis algorithm, then the importance sampling density is constructed by means of adaptive kernel density estimation method, and the fast Gauss transform are finally adopted to accelerate the computation of the kernel function in the importance sampling procedure. The adaptive Metropolis algorithm can obtain more different samples on failure domain with the same computational effort when compared with the original Metropolis method. In another word, it can effectively decrease the number of structural analyses and thereby can improve the efficiency of the proposed method. The fast Gauss transform can considerably decrease the computational complexity of the kernel density estimation method and avoid mounts of CPU time needed in the importance sampling procedure. Numerical examples illustrate that the proposed method can provide accurate and computationally efficient solutions of the problem.