随机结构动力特征的统计矩及灵敏度分析研究  

Moment and sensitivity analysis for dynamic characteristic of stochastic structure

作　　者：宋述芳[1] 吕震宙[1] 乔红威[1] 

机构地区：[1]西北工业大学航空学院,陕西西安710072

出　　处：《振动工程学报》2011年第2期133-138,共6页Journal of Vibration Engineering

基　　金：国家自然科学基金(NSFC50875213);西北工业大学基础研究基金(NPU-FFR-JC20100201)资助项目

摘　　要：结构参数的不确定性会导致结构的动力特征(如自振频率、振型等)等具有不确定性,如果采用确定性分析方法进行结构设计可能会使结构处于比较危险的状态,因此对随机结构的动力特性分析是十分有必要的。由于统计矩反映了随机结构动力特征的统计特性,由这些统计矩就可以进一步掌握可靠性分析所需要的动力特征的分布规律。统计矩的灵敏度分析能够判别结构不确定性参数对结构动力特征的重要程度,从而为改进结构设计模型提供有效途径。建立了基于MCMC的分层抽样法,并采用该方法对结构动力特性进行统计矩的估计,并通过统计随机样本点信息进行统计矩的灵敏度分析,通过算例验证了所提方法的优越性。The uncertainty of structural parameters will lead to the uncertainty of structural dynamic characteristics（such as the natural frequency,mode shape）.If using the determinacy analysis for the designing may make the product in the dangerous state,then the dynamic characteristic analysis of the stochastic structure is very necessary.The statistic moments of dynamic characteristics of stochastic structure include the statistical properties of the dynamic characteristics.Through these statistical properties,the statistical information of reliability analysis and the distribution regularity of dynamic characteristic can be further obtained.And the sensitivity analysis of statistic moment can distinguish the degree of importance of random parameters with respect to the stochastic structure inherent properties,and then provide an effective way for improving the structural design model.In this work,MCMC based stratified sampling method is presented to estimate the statistics moment.And by collecting the information of random samples,the sensitivity of statistics moment is analyzed without increasing computing calculation.And the results of examples illustrate the advantages of the presented method.

关 键 词：随机结构 统计矩 灵敏度分析 动力特征 基于MCMC的分层抽样法 

分 类 号：TB114.3[理学—概率论与数理统计] TU311.3[理学—数学]