An efficient adaptive importance samping method for structural reliability analysis
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摘要: 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.
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关键词:
- 快速高斯变换
Abstract: This study develops an efficient adaptive importancesampling method based on adaptive Markov chain Monte Carlo and fast Gausstransform technique for reliability analysis. In the proposed method, thesamples on the failure domain are generated by the adaptive Metropolisalgorithm, then the importance sampling density is constructed by means ofadaptive kernel density estimation method, and the fast Gauss transform arefinally adopted to accelerate the computation of the kernel function in theimportance sampling procedure. The adaptive Metropolis algorithm can obtainmore different samples on failure domain with the same computational effortwhen compared with the original Metropolis method. In another word, it caneffectively decrease the number of structural analyses and thereby canimprove the efficiency of the proposed method. The fast Gauss transform canconsiderably decrease the computational complexity of the kernel densityestimation method and avoid mounts of CPU time needed in the importancesampling procedure. Numerical examples illustrate that the proposed methodcan provide accurate and computationally efficient solutions of the problem.-
Key words:
- fast Gauss transform
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