改进PCA算法及其在转子特征提取中的应用
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TH113.2;TN911.72

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国家自然科学基金资助项目 (51875205,51875216);广东省自然科学基金资助项目(2018A030310017,2019A1515011780);广东省教育厅项目(2018KQNCX191);广州市科技计划资助项目(201904010133);广东省重大科技专项资助项目(2019B090918003)


Improved PCA Algorithm and Its Application in Rotor Feature Extraction
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    摘要:

    针对传统主成分分析(principal component analysis, 简称PCA)方法中有效主成分的选择依赖于先验知识的缺点,提出利用协方差矩阵特征值差分谱的概念来描述有效主成分与次要成分的特征值差异性。首先,通过理论推导得出奇异值与特征值之间关系,即奇异值与特征值之间存在平方关系;其次,利用差分谱理论进一步研究了Hankel矩阵方式下PCA信号处理原理;最后,提出一种基于差分谱理论的PCA算法,通过仿真信号验证该算法的有效性。研究结果表明,根据协方差矩阵特征值差分谱的最大峰值位置可自动选择有效主成分的个数,且通过不同谱峰之间的分量信号的组合可以提取出不同的频率成分。将此PCA算法用于大型滑动轴承试验台转子的轴心轨迹提纯,提纯效果优于传统PCA算法。

    Abstract:

    The traditional principal component analysis (PCA) method selects the primary components according to the prior knowledge. In light of this shortcoming, the covariance matrix eigenvalue difference spectrum is introduced to describe the differences between the primary and secondary components. First, a square relation between singular value and eigenvalue is discovered by theoretical deduction. Second, the principle of PCA signal processing with the Hankel matrix is further studied by difference spectrum theory. Finally, a PCA algorithm based on differential spectrum theory is proposed, and the effectiveness of the algorithm is verified by simulation. The results show that the number of active principal components can be selected automatically according to the maximum peak of the difference spectrum of the eigenvalues of the covariance matrix, and different frequency components can be extracted from the combination of the component signals between different spectral peaks. The PCA algorithm is used to purify the axis trajectory of the rotor of a large sliding bearing testbed and present better performance than that of the traditional PCA algorithm.

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  • 在线发布日期: 2020-07-02
  • 出版日期: 2020-06-30
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