基于聚类分析的核密度估计重要抽样方法
An Importance Sampling Method for Kernel Density Estimation Based on Cluster Analysis
邵俊虎 1冯渺 1陈小平 1周阳 1宋帅 2王芳芳1
作者信息
- 1. 成都大学建筑与土木工程学院,四川成都 610106
- 2. 成都理工大学工程技术学院,四川 乐山 614000
- 折叠
摘要
对于结构体系失效概率的计算,当其失效概率较小时,马尔科夫蒙特卡洛方法难以获取足够的失效样本点,且无法覆盖全部失效区域,导致采用核密度估计重要抽样方法计算失效概率精度较低.因此,提出一种基于聚类分析的核密度估计重要抽样方法.该方法首先利用拉丁超立方抽样得出第1次马尔科夫蒙特卡洛方法抽样的初始样本点,并通过抽样获得失效样本;然后将获得的失效样本进行聚类分析,获得结构失效模式的个数,并选取出具有代表性的失效样本作为初始失效样本点,进行第2次马尔科夫蒙特卡洛方法抽样;最后基于第2次抽样获得的失效样本点,采用核密度估计的重要抽样方法进行失效概率计算.算例分析表明,该方法针对小失效概率的体系可靠度问题具有良好的计算精度.
Abstract
For the calculation of the failure probability of structural system,when the failure probability is low,it is difficult to obtain sufficient failure sample points by using Markov Monte Carlo method,and cov-ering all failure areas is also impossible.Therefore,this leads to a low accuracy in calculating failure prob-ability by using importance sampling method for kernel density estimation.The proposed method uses Lat-in hypercube sampling to obtain the initial sample points,which is the same as the one obtained by using Markov Monte Carlo method and the failure samples are also obtained through sampling.Then,the number of structural failure modes are obtained by the cluster analysis of the failure samples,and representative failure samples are selected as the initial failure sample points for the second Markov Monte Carlo method sampling.Finally,based on the failure sample points obtained from the second sampling,the importance sampling method for kernel density estimation is used to calculate the failure probability.The analysis of numerical examples shows that the proposed method has good accuracy for the system reliability with small failure probability.
关键词
结构体系失效概率/马尔科夫蒙特卡洛方法/核密度估计/聚类分析/重要抽样方法Key words
failure probability of structural systems/Markov Monte Carlo method/kernel density estima-tion/cluster analysis/an importance sampling method引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据