多项式混沌展开和最大熵原理的结构动力特性不确定性量化  

Uncertainty quantification for structural dynamic characteristics using polynomial chaos expansion and maximum entropy principle

作　　者：万华平 邰永敢 钟剑[1] 任伟新[1] WAN Hua-ping;TAI Yong-gan;ZHONG Jian;REN We-xin(School of Civil and Hydraulic Engineering,Hefei University of Technology,Hefei 230009,China;College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310058,China)

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009 [2]浙江大学建筑工程学院,浙江杭州310058

出　　处：《振动工程学报》2019年第4期574-580,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51878235,51508144);香江学者计划资助项目(XJ2016039);中国博士后基金资助项目(2015M581981);安徽省自然科学基金资助项目(1608085QE118)

摘　　要：结构参数不可避免存在不确定性,参数不确定性必然会导致结构动力特性具有不确定性.量化动力特性不确定性能为结构分析与设计提供准确的动力信息,因此发展快速有效的不确定性量化方法非常必要.提出了一种基于多项式混沌展开和最大熵原理的不确定性量化方法,用于定量参数不确定性传递到结构动力特性不确定性的大小.具体是,多项式混沌展开替代模型用来取代耗时的结构有限元模型,并实现解析地计算出结构动力特性的高阶统计矩,然后利用统计矩信息并结合最大熵原理推断出结构动力特性的概率密度函数的解析表达式.最后以一简支钢桁架桥为例,验证多项式混沌展开和最大熵原理的结构动力特性不确定性量化方法的有效性.Structural parameters inevitably involve uncertainty, and the uncertainty of parameters will lead to the variability in the structural dynamic characteristics.Quantification of uncertainty in dynamic characteristics is able to provide accurate dy-namic information for structural analysis and design. Therefore,developing a rapid and effective uncertainty quantification (UQ) method is very necessary. This paper proposes an efficient UQ method with combination of polynomial chaos expansion (PCE) and maximum entropy principle (MEP) to measure the uncertainty in dynamic characteristics propagated from parame-ter uncertainty. Specifically, the PCE surrogate model is used to replace the time-consuming structural finite element model, and the high-order statistical moments of the structural dynamic characteristics are analytically calculated;the obtained statisti-cal moment information and the MEP are used to deduce the probability density function of structural dynamic characteristics. Finally,a simple-supported steel truss bridge is provided to verify the feasibility of the proposed method in UQ for structural dynamic characteristics.

关 键 词：动力特性 不确定性量化 多项式混沌展开 最大熵原理 统计矩 

分 类 号：O324[理学—一般力学与力学基础] TB123[理学—力学]