基于主成分分析的结构不确定性建模与传播研究

发布时间：2019-05-19 14:42

【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。
[Abstract]:Based on principal component analysis (PCA), a new modeling method of structural uncertainty is proposed. Firstly, the sample data of structural uncertainty parameters are analyzed by principal component analysis, and the orthogonal eigenvector is obtained. secondly, the sample data is projected to the new coordinate system with the direction of eigenvector as the new coordinate system. Finally, the boundary value of the sample in the new coordinate system is calculated, and the corresponding non-probabilistic interval model is established to realize the uncertainty modeling of structural parameters. The uncertainty model based on principal component analysis (PCA) is relatively compact, and the related parameters can be converted into unrelated parameters while modeling, which makes the uncertainty propagation problem easy and efficient to solve. Two examples and the uncertainty propagation comparison with the traditional interval model and parallel hexahedral model verify the correctness and effectiveness of the proposed method.
【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;
【基金】：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
【分类号】：TB12

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