基于小波阈值密度的自适应重要抽样方法

戴鸿哲; 薛国峰; 王伟

doi:10.6052/0459-1879-13-303

基于小波阈值密度的自适应重要抽样方法

哈尔滨工业大学, 哈尔滨 150090
结构工程灾变与控制教育部重点实验室(哈尔滨工业大学), 哈尔滨 150090

基金项目: 高等学校博士学科点专项科研基金资助项目（20122302110058）.

详细信息

作者简介:
戴鸿哲，副教授，主要研究方向：结构随机振动、随机有限元及结构可靠性理论.E-mail：hzdai@hit.edu.cn

中图分类号: TB114;TU311
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出版历程
- 收稿日期: 2013-11-17
- 修回日期: 2013-12-09
- 刊出日期: 2014-05-17

A WAVELET THRESHOLDING DENSITY-BASED ADAPTIVE IMPORTANCE SAMPING METHOD

School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
Key Lab of Structures Dynamic Behavior and Control (Harbin Institute of Technology), Ministry of Education, Harbin 150090, China

Funds: The project was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (20122302110058).

摘要

摘要: 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.
- 结构可靠性 /
- 重要抽样 /
- 小波阈值密度 /
- 核密度 /
- 马尔可夫链模拟
Abstract: 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.
- structural reliability /
- importance sampling /
- wavelet thresholding density /
- kernel density /
- Markov chain simulation

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参考文献(14)

Balesdent M, Morio J, Marzat J. Kriging-based adaptive importance sampling algorithms for rare event estimation. Structural Safety, 2013, 44: 1-10

Yuan XK, Lu ZZ, Zhou CC, et al. A novel adaptive importance sampling algorithm based on Markov chain and low-discrepancy sequence. Aerospace Science and Technology, 2013, 29: 253-261

Ang GL, Ang AH-S, Tang WH. Optimal importance-sampling density estimator. Journal of Engineering Mechanics ASCE, 1992, 118: 1146-1163

Au SK, Beck JL. A new adaptive importance sampling scheme for reliability calculations. Structural Safety, 1999, 21: 135-158

Kurtz N, Song JH. Cross-entropy-based adaptive importance sampling using Gaussian mixture. Structural Safety, 2013, 42: 35-44

袁修开,吕震宙,池巧君. 基于核密度估计的自适应重要抽样. 西北工业大学学报,2008,26(3):297-302 (Yuan Xiukai, Lü Zhenzhou, Chi Qiaojun. Achieving efficient estimation of reliability sensitivity of a multi-model system without requiring knowledge of design point. Journal of Northwestern Polytechnical University, 2008,26(3):297-302 (in Chinese))

Silverman BW. Density Estimation for Statistic and Data Analysis. London New York: Chapman and Hall, 1986

Hardle W, Kerkyacharian G, Picard D. Wavelets, Approximation and Statistical Application. Berlin-Paris: Chapman and Hall, 1997

Walter GG, Shen XP. Wavelets and Other Orthogonal Systems. Boca Raton: CRC Press, 1994

Mallat S. Multiresolution approximations and wavelet orthonormal bases of L²(R). Transactions of American Mathematics Society, 1989, 315: 69-87

Donobo DL, Johnstane IM, Kerkyacharian G, et al. Density estimation by wavelet thresholding. Annual Statistics, 1996, 24: 508-539

Tribouley K. Practical estimation of multivariate densities using wavelet methods. Statistica Neerlandica, 1995, 49: 41-62

Pinheiro A, Vidakovic B. Estimating the Square Root of a Density Via Compactly Supported Wavelets. ISDS, Duke University, 1995

Dubourg V, Sudret B, Deheeger F. Metamodel-based importance sampling for structural reliability analysis. Probabilistic Engineering Mechanics, 2013, 33: 47-57