不确定性传播的混沌多项式方法研究进展  

Recent advances in polynomial chaos method for uncertainty propagation

作　　者：熊芬芬[1] 陈江涛[2] 任成坤 张立 李泽贤 XIONG Fenfen;CHEN Jiangtao;REN Chengkun;ZHANG Li;LI Zexian(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]中国空气动力研究与发展中心,四川绵阳621000

出　　处：《中国舰船研究》2021年第4期19-36,共18页Chinese Journal of Ship Research

基　　金：国家数值风洞项目(NNW2020ZT7-B31);国防基础科研科学挑战专题资助项目(TZ2018001)。

摘　　要：不确定性在工程设计中广泛存在,作为工程设计中的核心内容之一,不确定性传播和量化一直都是工程设计领域重要的理论课题之一。混沌多项式作为一种高效的不确定性传播方法近年来得到了广泛研究和应用,具有较大的工程应用潜力。为此,对混沌多项式方法的研究进展进行综述。首先,介绍该方法的应用场景和基本原理;其次,针对混沌多项式应用中面临的“维数灾难”、计算量大等难题,介绍基截断、稀疏重构、稀疏网格、多可信度建模等诸多解决策略;然后,对基于混沌多项式的全局和局部灵敏度分析方法进行介绍;最后,对混沌多项式的研究进行展望。Uncertainty exists widely in engineering design.As one of the key components of engineering design,uncertainty propagation and quantification has always been an important research topic.Polynomial chaos(PC)is a highly efficient uncertainty propagation method which has been widely studied and applied.Therefore,this paper reviews recent advances in the PC method.First,the fundamentals of PC are introduced,including the construction of an orthogonal polynomial basis and the calculation of PC coefficients.Second,strategies such as basis truncation,sparse reconstruction,sparse grid and multi-fidelity modeling are described to address the"curse of dimensionality"issue of PC.Local and global sensitivity analyses based on PC are then introduced.Finally,the research prospects of PC are given.

关 键 词：不确定性传播 混沌多项式 维数灾难 多可信度建模 灵敏度分析 

分 类 号：U662.2[交通运输工程—船舶及航道工程]