一种基于马尔可夫链模拟样本的自适应重要样本法  

An Adaptive Important Sampling Method Based on Markov Chain Sample Simulation Algorithm

作　　者：吴建成[1] 吴剑国[1] 吴亚舸[1] 

机构地区：[1]华东船舶工业学院船舶与土木工程系,江苏镇江212003

出　　处：《华东船舶工业学院学报》2003年第3期8-12,共5页Journal of East China Shipbuilding Institute(Natural Science Edition)

基　　金：船舶行业基金项目(院编2000102)

摘　　要：在结构可靠性计算中,传统的重要样本法需要给出最大似然点即设计点。对于结构存在多个设计点的系统可靠性问题,重要样本法失去了普遍性,其效率和精度也随之降低。本文提出了一种适合于计算结构的系统可靠性的重要样本法,主要的改进在于根据Metropolis准则,构造马尔可夫链模拟样本,计算模拟样本的均值和标准方差,并结合重要抽样技术,计算结构的系统可靠性。此方法有效的改善了重要样本法在系统可靠性计算中的应用,并获得了较好的效率和精度。Importance sampling method,which is commonly used in the reliability analysis of structures and requires the socalled 'the most probable point'or design point'to be known before applyingimportance sampling techniqueto determine the failure probability, may cause difficulties and lose its conveniencein calculation when there are multidesign points existing in the failure region or applied to system reliability analysis, and will result in ludicrousdeviation from precise value. In this paper, an adaptive importance sampling method has been developedto overcome this drawback, which is mainly based on Markov chain samples simulation algorithm according to Metropolis criterionto populate the higher probability density zones in the failure region and get the distributioninformation of these areas, thena general importance sampling method is introduced to calculate the failure probability with the mean and standard deviation of priorsamples. For not needing to determine the multi-design points that are in system reliabilityanalysis,it is particularly suitable for structural system reliability calculation. Finally,this paper gives some examples, which take the failure modes of series and parallel systems into account, to verify itsaccuracy and efficiency.

关 键 词：重要样本法 马尔可夫链样本模拟 METROPOLIS准则 结构系统可靠性 

分 类 号：TU311.2[建筑科学—结构工程]