Li Hua, Liu Tao, Wu Xing, Li Shaobo
IEEE Trans Neural Netw Learn Syst. 2023 Jan;34(1):355-365. doi: 10.1109/TNNLS.2021.3094799. Epub 2023 Jan 5.
The singular value decomposition (SVD) based on the Hankel matrix is commonly used in signal processing and fault diagnosis. The noise reduction performance of SVD based on the Hankel matrix is affected by three factors: the reconstruction component(s), the structure of the Hankel matrix, and the point number of the analysis data. In this article, the three influencing factors are systematically studied, and a method based on correlated SVD (C-SVD) is proposed and successfully applied to bearing fault diagnosis. First, perform SVD analysis on the collected original signal. Then, the reconstructed component(s) determination method of SVD based on the combination of singular value ratio (SVR) and correlation coefficient is proposed. Then, based on the SVR, using the envelope kurtosis as the indicator, the optimal structure of the Hankel matrix (number of rows and columns) is studied. Then, the number of data points of the analysis signal is discussed, and the constraint range is given. Finally, the envelope power spectrum analysis is performed on the reconstructed signal to extract the fault features. The proposed C-SVD method is compared with the existing typical methods and applied to the simulated signal and the actual bearing fault signal, and its superiority is verified.
基于汉克尔矩阵的奇异值分解（SVD）常用于信号处理和故障诊断。基于汉克尔矩阵的SVD降噪性能受三个因素影响：重构分量、汉克尔矩阵结构以及分析数据的点数。本文系统研究了这三个影响因素，提出了一种基于相关奇异值分解（C-SVD）的方法，并成功应用于轴承故障诊断。首先，对采集到的原始信号进行SVD分析。然后，提出了基于奇异值比（SVR）和相关系数相结合的SVD重构分量确定方法。接着，基于SVR，以包络峭度为指标，研究了汉克尔矩阵的最优结构（行数和列数）。然后，讨论了分析信号的数据点数，并给出了约束范围。最后，对重构信号进行包络功率谱分析以提取故障特征。将所提出的C-SVD方法与现有的典型方法进行比较，并应用于模拟信号和实际轴承故障信号，验证了其优越性。
