Quaternion singular spectrum analysis using convex optimization and its application to fault diagnosis of rolling bearing
Quaternion singular spectrum analysis using convex optimization and its application to fault diagnosis of rolling bearing
复制标题
基于凸优化的四元数奇异谱分析及其在滚动轴承故障诊断中的应用
DOI：
10.1016/j.measurement.2017.02.047
复制
发表时间：
2017-06-01
期刊：
影响因子：
5.6
通讯作者：
Yu, Xun
中科院分区：
文献类型：
--
作者：
Yi, Cancan;Lv, Yong;Yu, Xun
随着多源信息融合和多维传感器技术的迅速发展，基于多通道信号的信号处理技术在消除噪声和信号重构方面具有明显的优势。利用四元数域描述四通道信号的相关性，提出了一种基于凸优化的四元数奇异谱分析方法。利用轨迹矩阵的不同奇异谱特征，在相空间中对单通道振动信号进行奇异谱分析。对于四元数域的信号处理，通过四通道嵌入过程形成的轨迹矩阵被用来生成增广轨迹矩阵。然后，通过对增广轨迹矩阵进行四元数奇异值分解（QSVD），区分有用信号和噪声等无用信号。还应该注意的是，QSVD的非凸罚函数的凸优化被用来精确地估计非零奇异值，其可以被设置为矩阵低秩近似中的正则化项。通过数值仿真信号和实验信号验证了该方法的有效性。通过与信号通道快速傅里叶变换（FFT）、SSA和多元经验模态分解（MEMD）的结果比较，发现该模型能更好地提取机械故障诊断中的特征频率。(C)2017爱思唯尔有限公司版权所有
With the rapid development of multi-source information fusion and multi-dimensional sensor technologies, the signal processing technology based on multi-channel signal has obvious advantages in noise elimination and signal reconstruction. In this paper, the correlation of four-channel signals is described by the quaternion domain, and a quaternion singular spectrum analysis method based on the convex optimization is proposed. Singular spectrum analysis (SSA) is used to analyze a single channel vibration signal in the phase space, which is performed by different singular spectrum characteristics of the trajectory matrix. For the signal processing in the quaternion domain, the trajectory matrixes developed by embedding procedure of four channels are employed to generate the augmented trajectory matrix. Then, the useful signal and unwanted signal such as noise can be distinguished by quaternion singular value decomposition (QSVD) to augmented trajectory matrix. It should also be noted that the convex optimization with non-convex penalty functions for QSVD is utilized to accurately estimate non-zero singular value, which can be set as regularization item in the matrix low-rank approximation. The proposed method is validated through numerical simulation signal and experimental signal. By comparing the results obtained from the proposed method, signal channel Fast Fourier Transform (FFT), SSA and multivariate empirical mode decomposition (MEMD), it is found that the application of the proposed model leads to a better solution to extract the feature frequency in mechanical fault diagnosis. (C) 2017 Elsevier Ltd. All rights reserved.