基于多项式混沌展开的结构动力特性高阶统计矩计算  

Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion

作　　者：万华平 邰永敢 钟剑[1] 任伟新[1] WAN Huaping;TAI Yonggan;ZHONG Jian;REN Weixin(College of Civil Engineering,Hefei University of Technology, Hefei 230009,P.R.China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《应用数学和力学》2018年第12期1331-1342,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51878235; 51508144);香江学者计划(XJ2016039);中国博士后科学基金(2015M581981);安徽省自然科学基金(1608085QE118)~~

摘　　要：结构参数的不确定性会导致其动力特性的不确定性,量化动力特性的不确定性能为结构动力设计分析提供准确的动力信息.统计矩是表征结构动力特性不确定性非常重要的统计量,比如均值和方差.传统的Monte-Carlo(蒙特-卡洛)模拟方法需要大量次数的模型运算来保证结果的收敛,其用于复杂结构的动力特性统计矩计算因耗时太高而使用受限.该文采用多项式混沌展开替代模型来取代计算花费高的有限元模型,然后在替代模型框架下快速有效地计算结构动力特性的统计矩.该方法在建立替代模型之初只需要少量次数有限元分析,后续的统计矩计算无需有限元模型,因此从根本上解决了动力特性统计矩计算花费高的难题.该文的多项式混沌展开方法适用于参数服从任意概率分布,能够有效地计算高阶统计矩,为量化结构动力特性不确定性提供更多统计矩信息.最后通过平铝板算例验证了此方法的有效性.Uncertainty of structural parameters leads to uncertainty of structural dynamic characteristics.Quantification of uncertainty of dynamic characteristics provides accurate dynamic information for structural dynamic analysis.Statistical moments (e.g.,mean and variance) mainly represent the uncertainty of structural dynamic properties.The Monte-Carlo simulation (MCS)requires a large number of model evaluations to ensure the convergence of the results, which hinders its application to the large-scale,complex engineering structures.The polynomial chaos expansion (PCE)surrogate model was used to replace the computationally expensive finite element model (FEM),and then the statistical moments of structural dynamic characteristics were efficiently calculated.The presented PCE-based method only needs a small set of model runs before the model formulation and subsequently does not require the FEM for calculations of the statistical moments.Therefore,the issue of the high computational cost associated with the computations of dynamic characteristic statistical moments was solved.The method is suitable for parameters with arbitrary probability distribution and has high computational efficiency in calculating the high-order statistical moments.Finally,the effectiveness of the developed method was verified through an example of an aluminum plate.

关 键 词：不确定性 动力特性 高阶统计矩 多项式混沌展开 

分 类 号：O324[理学—一般力学与力学基础]