基于小波阈值密度的自适应重要抽样方法

提出了一种基于小波阈值密度估计的结构可靠性分析高效自适应重要抽样方法.该方法利用非线性小波收缩方法对结构失效域样本进行密度估计，并以此作为重要抽样密度进行可靠性分析.与传统基于核密度估计的重要抽样方法比，由于非线性小波阈值密度估计具有较好局部适应性和最优收敛速度，且克服了核密度估计中计算精度严重依赖于参数选择的缺陷，因此以较少的预抽样样本就能获得与传统方法相当的精度，有效提高计算效率.数值算例表明所提方法对工程中常遇到的多设计点及噪音功能函数可靠性问题具有良好适应性. 

A WAVELET THRESHOLDING DENSITY-BASED ADAPTIVE IMPORTANCE SAMPING METHOD

This study develops an efficient adaptive importance sampling method based on nonlinear wavelet thresholding for reliability analysis. In the proposed method, the pre-sampling samples, which fall in the failure region, are used to estimate the density via the nonlinear wavelet thresholding estimator, and the density obtained is applied as the near-optimal sampling density to implement the importance sampling. Compared with the kernel density estimator, the nonlinear wavelet thresholding density estimator has a high degree of flexibility in terms of convergence rate and smoothness, moreover, the choice of the initial parameters slightly affects the accuracy of the method. Therefore, the proposed method can achieve comparable accuracy with fewer pre-sampling samples and improve the computational efficiency of the traditional method. Numerical examples show that the proposed method is applicable for wide-range reliability problems with multi-design points or noisy limit state functions.