中文摘要：

提出一种基于增广四元数矩阵奇异值分解与流形学习正交邻域保持嵌入算法的多通道机械故障信号分类方法，通过引入四元数来耦合4个通道信号，并且利用四元数乘方的性质对数据进行增广处理，充分利用各通道信息并挖掘通道之间的相关性，从而减少因故障特征信息丢失对分类结果的影响。此外，针对传统奇异谱分析提取特征参数的分类效果受噪声影响较大的问题，引入正交邻域保持嵌入算法对奇异值序列进行雏数约简，最后使用分类器完成故障分类。对仿真信号的分类结果表明，在强噪声背景下，相较于单通道奇异谱分析方法和机械故障信号中常用的排列熵方法，本文提出的方法分类效果更好。将其应用于更为复杂的实测轴承故障信号的分类与识别中，同样有着较好的效果。

英文摘要：

A novel method for multi-channel mechanical fault signal classification based on augmented quaternion matrix singular value decomposition and orthogonal neighborhood preserving embedding algorithm of manifold learning is proposed. Quaternion is used to couple four channel signals, and the nature of the quaternion power is employed for augmented processing of the data. The correlation be- tween channels is made use of, and the information from each channel is employed to offset the nega- tive influence of loss of characteristic information of faults on classification. Considering that the tra- ditional classification method that uses singular spectrum analysis to extract characteristic parameters is seriously affected by noise, the orthogonal neighborhood preserving embedding algorithm is used to reduce the dimension of singular value sequence. Finally, the classifier is used to classify faults. The results show that, with the background of strong noise, the proposed method is superior to the tradi- tional single-channel singular spectrum analysis method and the method of permutation entropy in fault classification. Applied to the complex identification and classification of real bearing fault sig- nals, the proposed method shows good performance.