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

发布时间：2018-05-07 15:10

本文选题：奇异值分解 + 降噪　；参考：《振动与冲击》2017年03期

【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。
[Abstract]:In order to improve the signal-to-noise ratio (SNR) of fault vibration signals of rotating machinery, the principle of singular value decomposition (SVD) denoising is studied, and a new method for determining the effective rank order of SVD denoising is proposed. Firstly, the vibration signal is reconstructed in phase space, and singular value decomposition is carried out on the track matrix of the attractor. Then, the singular value is divided into signal group and noise group according to different order, and the order of each group is taken as the independent variable. Taking singular value as dependent variable, the characteristic singular value curve and noise characteristic singular value curve of quasi-synthetic signal are used, and the fitting error is obtained. Finally, the order of singular value corresponding to the minimum value of fitting error is determined to be the order of effective rank. Singular value decomposition is used to reduce noise. Numerical simulation and actual gear fault data analysis show that this method can effectively improve the signal-to-noise ratio of the signal and create favorable conditions for the later fault feature extraction.
【作者单位】：海军航空工程学院飞行器工程系;海军航空工程学院飞行器检测与应用研究所;
【基金】：国家部委预研基金资助(9140A27020214JB1446)
【分类号】：TH17

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