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Structural uncertainty modeling and propagation based on principal component analysis[J].计算力学学报,2017,(4):411~416

Structural uncertainty modeling and propagation based on principal component analysis
Structural uncertainty modeling and propagation based on principal component analysis

DOI：10.7511/jslx201704002

 作者 单位 E-mail 刘杰 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 liujie@hnu.edu.cn 谢凌 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 卿宏军 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 刘浩 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。

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.