基于改进svd及参数优化vmd的轴承故障诊断
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依据frobeious范数意义下矩阵最佳逼近定理可得前r个较大的奇异值反映有用信号较小的奇异值反映噪声信号去掉噪声信号只需将较小奇异值置为0则信号中的噪声成分被去除再利用svd的逆过程得矩阵h?m其秩为r则矩阵h?m是hm的最佳逼近矩阵此时噪声被大大地压缩
第 40 卷 第 1 期 2020 年 2 月
噪声与振动控制 NOISE AND VIBRATION CONTROL
Vol 40 No.1 Feb. 2020
文章编号：1006-1355(2020)01-0051-08
基于改进 SVD 及参数优化 VMD 的轴承故障诊断
张 莹，殷 红，彭珍瑞
（ 兰州交通大学 机电工程学院，兰州 730070 ）
Keywords : fault diagnosis; singular value decomposition ; variational mode decomposition ; ensemble kurtosis; parameter optimization
轴承是旋转机械中重要的零部件，易损坏、故障 率高。若在轴承发生故障的早期有效识别出故障特 征信息，准确判断出轴承的运行状态，并及时维修或
Bearing Fault Diagnosis Method Based on Improved SVD and ParametIN Hong , PENG Zhenrui
( School of Mechatronics Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China )
摘 要：为解决轴承早期故障特征难以提取的问题，提出一种基于改进奇异值分解(SVD)及参数优化变分模态分解
(VMD)的轴承故障诊断方法。首先，对原始故障信号进行 SVD 降噪、微弱故障信号的分离，通过包络熵最小、峭度最大
原则对其重构矩阵的秩进行优化。其次，对改进 SVD 降噪后所得信号进行 VMD 分解，将包络谱幅值峭度和峭度构成
新的指标（合成峭度），通过所有本征模态分量(Intrinsic Mode Function，IMF)的合成峭度均值最大原则对 VMD 的参数
进行优化，获得若干的 IMFs。最后，根据峭度-欧氏距离指标筛选出含故障信息丰富的 IMF，进行包络解调运算，分析
信号的包络谱判断轴承故障类型。通过对仿真信号和实测信号进行分析，可成功提取出微弱特征频率信息。由此表
明，基于改进 SVD 及参数优化 VMD 的轴承故障诊断方法可有效地实现轴承早期故障诊断，具有一定的可靠性和实
用性。
关键词：故障诊断；奇异值分解；变分模态分解；合成峭度；参数优化
中图分类号：TH165.3
文献标志码：A
DOI 编码：10.3969/j.issn.1006-1355.2020.01.011
Abstract : In order to solve the difficulty of extracting the fault feature of bearings in early failure period, a bearing fault diagnosis method based on improved singular value decomposition (SVD) and parameter optimized variational mode decomposition (VMD) is proposed. Firstly, the original fault signal is denoised by SVD, and the weak fault signal is enhanced. The rank of the reconstruction matrix is optimized according to the principles of minimum envelope entropy and maximum kurtosis. Secondly, the signal denoised by the improved SVD is decomposed by VMD, and a new index, called ensemble kurtosis, is constructed by combining the kurtosis with the envelope spectrum kurtosis. The parameters of VMD are optimized by the principle of the maximum mean value of all intrinsic mode functions (IMFs), and several IMFs are obtained. Finally, according to the kurtosis-Euclidean distance index, the IMF with rich fault information is screened out, and the envelope demodulation operation is carried out. The envelope spectrum of the signal is analyzed to determine the type of bearing faults. By analyzing the simulated signal and the measured data, the weak characteristic frequency information can be extracted successfully. The results show that this bearing fault diagnosis method based on improved SVD and parameter optimization VMD can effectively realize the early fault diagnosis of bearings, and has certain reliability and practicability.
第 40 卷 第 1 期 2020 年 2 月
噪声与振动控制 NOISE AND VIBRATION CONTROL
Vol 40 No.1 Feb. 2020
文章编号：1006-1355(2020)01-0051-08
基于改进 SVD 及参数优化 VMD 的轴承故障诊断
张 莹，殷 红，彭珍瑞
（ 兰州交通大学 机电工程学院，兰州 730070 ）
Keywords : fault diagnosis; singular value decomposition ; variational mode decomposition ; ensemble kurtosis; parameter optimization
轴承是旋转机械中重要的零部件，易损坏、故障 率高。若在轴承发生故障的早期有效识别出故障特 征信息，准确判断出轴承的运行状态，并及时维修或
Bearing Fault Diagnosis Method Based on Improved SVD and ParametIN Hong , PENG Zhenrui
( School of Mechatronics Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China )
摘 要：为解决轴承早期故障特征难以提取的问题，提出一种基于改进奇异值分解(SVD)及参数优化变分模态分解
(VMD)的轴承故障诊断方法。首先，对原始故障信号进行 SVD 降噪、微弱故障信号的分离，通过包络熵最小、峭度最大
原则对其重构矩阵的秩进行优化。其次，对改进 SVD 降噪后所得信号进行 VMD 分解，将包络谱幅值峭度和峭度构成
新的指标（合成峭度），通过所有本征模态分量(Intrinsic Mode Function，IMF)的合成峭度均值最大原则对 VMD 的参数
进行优化，获得若干的 IMFs。最后，根据峭度-欧氏距离指标筛选出含故障信息丰富的 IMF，进行包络解调运算，分析
信号的包络谱判断轴承故障类型。通过对仿真信号和实测信号进行分析，可成功提取出微弱特征频率信息。由此表
明，基于改进 SVD 及参数优化 VMD 的轴承故障诊断方法可有效地实现轴承早期故障诊断，具有一定的可靠性和实
用性。
关键词：故障诊断；奇异值分解；变分模态分解；合成峭度；参数优化
中图分类号：TH165.3
文献标志码：A
DOI 编码：10.3969/j.issn.1006-1355.2020.01.011
Abstract : In order to solve the difficulty of extracting the fault feature of bearings in early failure period, a bearing fault diagnosis method based on improved singular value decomposition (SVD) and parameter optimized variational mode decomposition (VMD) is proposed. Firstly, the original fault signal is denoised by SVD, and the weak fault signal is enhanced. The rank of the reconstruction matrix is optimized according to the principles of minimum envelope entropy and maximum kurtosis. Secondly, the signal denoised by the improved SVD is decomposed by VMD, and a new index, called ensemble kurtosis, is constructed by combining the kurtosis with the envelope spectrum kurtosis. The parameters of VMD are optimized by the principle of the maximum mean value of all intrinsic mode functions (IMFs), and several IMFs are obtained. Finally, according to the kurtosis-Euclidean distance index, the IMF with rich fault information is screened out, and the envelope demodulation operation is carried out. The envelope spectrum of the signal is analyzed to determine the type of bearing faults. By analyzing the simulated signal and the measured data, the weak characteristic frequency information can be extracted successfully. The results show that this bearing fault diagnosis method based on improved SVD and parameter optimization VMD can effectively realize the early fault diagnosis of bearings, and has certain reliability and practicability.