基于拟合误差最小化原则的奇异值分解降噪有效秩阶次确定方法

摘要

为了最大限度地提高旋转机械设备故障振动信号的信噪比，研究了奇异值分解降噪的原理，提出了一种新的奇异值分解降噪有效秩阶次的确定方法。首先，对振动信号进行相空间重构，对吸引子轨迹矩阵进行奇异值分解；然后，按不同的阶数，将奇异值分成信号组和噪声组，对每次分组的结果，以阶数为自变量、以奇异值为因变量，拟合成信号特征奇异值曲线和噪声特征奇异值曲线，并求拟合误差；最后，将拟合误差最小值对应的奇异值阶数确定为有效秩阶次，并进行奇异值分解降噪。通过数值仿真和实际齿轮故障数据分析，表明该方法可以有效地提高信号的信噪比，为后期的故障特征提取创造有利条件。%In order to maximize the signal-to-noise ratio of a rotating mechanical equipment’s fault vibration signals,the singular value decomposition (SVD)de-noising method was studied,and a new method for determining its effective rank order was proposed.Firstly,a vibration signal was reconstructed in phase space,and the singular value decomposition of the attractor trajectory matrix was performed.Secondly,singular values were divided into a signal group and a noise group.For the results of each grouping,rank and singular value were taken as independent variable and dependent one,respectively.The feature singular value curve of signal and the feature singular value curve of noise were fitted,then the fitting errors were solved.At last,the singular value order corresponding to the minimum fitting error was taken as the effective rank order,and the SVD de-noising was performed.The results of numerical simulation and actual gear fault data analysis showed that the proposed method can effectively improve signal-to-noise ratios of signals,and create a beneficial condition for the subsequent fault feature extraction.