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基于主成分分析的结构不确定性建模与传播研究
引用本文:刘杰,谢凌,卿宏军,刘浩.基于主成分分析的结构不确定性建模与传播研究[J].计算力学学报,2017,34(4):411-416.
作者姓名:刘杰  谢凌  卿宏军  刘浩
作者单位:湖南大学 机械与运载工程学院 汽车车身先进设计制造国家重点实验室,长沙,410082
基金项目:国家自然科学基金(11572115);中央高校基本科研业务费;湖南大学汽车车身先进设计制造国家重点实验自主研究课题(51475003)资助项目.
摘    要:基于主成分分析提出一种新的结构不确定性建模方法。首先,对结构不确定性参数的样本数据进行主成分分析,获取正交化的特征向量;其次,以特征向量方向为新坐标系,将样本数据向其投影;最后,计算新坐标系下样本的边界值,并建立相应的非概率区间模型,从而实现结构参数不确定性建模。基于主成分分析建立的不确定性模型相对紧凑,且在建模的同时能将相关参数转换为互不相关参数,使得不确定性传播问题可以便捷高效求解。两个算例及与传统区间模型和平行六面体模型的不确定性传播比较,验证了本文方法的正确性和有效性。

关 键 词:不确定性建模  主成分分析  非概率凸模型  不确定性传播  区间模型  相关性
收稿时间:2016/4/18 0:00:00
修稿时间:2016/10/16 0:00:00

Structural uncertainty modeling and propagation based on principal component analysis
LIU Jie,XIE Ling,QING Hong-jun,LIU Hao.Structural uncertainty modeling and propagation based on principal component analysis[J].Chinese Journal of Computational Mechanics,2017,34(4):411-416.
Authors:LIU Jie  XIE Ling  QING Hong-jun  LIU Hao
Institution:State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, School of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China,State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, School of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China,State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, School of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China and State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, School of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
Abstract:This paper proposes a new structural uncertainty modeling method based on principal component analysis.First,the sample data of uncertain structure parameters are analyzed through principal component analysis method,and the corresponding orthogonal eigenvectors can be obtained.Then the sample data are projected to the new coordinate system which are established based on the eigenvector direction.Finally,the boundaries of uncertain parameters on the new coordinate system are calculated so that the non-probabilistic interval model for modeling the uncertainties of structure parameters is established.The uncertainty model based on principal component analysis is relatively compact,and it can transform the correlated parameters to uncorrelated parameters while the uncertainty model is established,which is convenient to efficiently solve uncertainty propagation problems.Two examples of uncertainty propagation that compared with the traditional interval model and parallelepiped model demonstrate the correctness and effectiveness of the proposed method.
Keywords:uncertainty modeling  principal component analysis  non-probabilistic convex model  uncertainty propagation  interval model  correlation
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