奇异值差分谱理论及其在车床主轴箱故障诊断中的应用

证明采用Hankel矩阵时奇异值分解(Singular value decomposition,SVD)可以将信号分解为一系列分量信号的简单线性叠加,为了确定其中的有用分量个数,提出奇异值差分谱的概念。差分谱可以有效地描述有用分量和噪声分量的奇异值性质差异,根据差分谱峰值位置可实现对有用分量个数的确定。研究结果表明,当差分谱最大峰值位于第一个坐标时,则表明原始信号存在较大的直流分量,此时根据第二最大峰值位置可以确定有用分量的个数,否则就根据最大峰值位置来确定分量个数。利用差分谱进一步研究Hankel矩阵的结构对SVD降噪效果的影响,指出矩阵列数和噪声去除量存在抛物线状的对称关系。利用基于差分谱的SVD方法对车削力信号进行处理,结果有效地分离出由于主轴箱故障齿轮的振动而引起的调制信号,并根据此信号可靠地定位了故障齿轮。     

基于变矩阵结构奇异值分解的信号分解算法

矩阵结构对奇异值分解的信号处理效果有重要影响,改变传统算法中矩阵结构固定的思想,提出在奇异值分解中采用变化的矩阵结构,每分解一次,矩阵结构就改变一次,以适应信号中不同的周期性分量。每次的分解都将上一层的信号分解为主、副两个分量,提取副分量,而对主分量再次进行变矩阵结构的奇异值分解,如此反复进行,最终将原始信号分解为一系列主、副分量。信号处理实例表明,这一方法具有良好的信号分离效果,能够实现信号中不同周期性分量的有效分离。     

变结构SVD算法及其在信号分离中的应用

利用奇异值分解（Singular value decomposition,SVD）进行信号处理的关键在于矩阵的构造,为利用SVD分离信号中的不同频率成分,提出一种变矩阵结构递推SVD算法,其思想是在SVD递推分解过程中逐次改变矩阵的结构,每进行一次SVD分解,矩阵的结构就规律性地变化一次,由此形成对信号中不同频率成分的适应性,从而达到将其分离出来的目的。推导出这种变结构SVD的信号分解算法,证明了这种算法可以将原始信号分解为一系列分量信号的线性组合。进一步从理论上分析了这种算法的信号分离机理,证明了对于一些特定的频率结构,这种变结构SVD算法可以实现对原信号中单个频率分量的逐次分离。最后通过对模拟信号和工程实际信号的分离实例证实了变结构SVD算法良好的信号分离效果,并与小波分析和多分辨SVD方法进行了比较,结果表明变结构SVD的信号分离结果优于这两种方法。     

基于奇异值分解的侵彻过载信号降噪方法

为解决硬目标侵彻过载信号的降噪问题,提出侵彻加速度信号的奇异值分解技术。首先,通过主体奇异值分量稳定原则确定信号的重构子矩阵;然后,利用前K次奇异值能量占优法则提取奇异值的有效阶次,在此基础上对实测信号进行奇异值分解;最后,利用分解出的有效奇异值完成信号的重构。实验证明,经此方法处理的侵彻过载信号可以有效剔除隐含在弹体加速度信号中的振动和噪声,重构后的加速度曲线具有比小波降噪效果更好的信噪比,积分得到的位移曲线能较好反映实际侵彻深度,是侵彻过载信号处理的一种新的可行方法。     

基于EWT_Hankel_SVD的矿山微震信号特征提取及分类方法

针对矿山微震与爆破振动信号自动识别难的问题,提出了基于经验小波变换_Hankel矩阵_奇异值分解(EWT_Hankel_SVD)的矿山微震信号特征提取及分类方法。首先,针对微震信号的瞬态性和多样性,对EWT频谱分割方法进行改进,并利用仿真信号表明了方法的有效性。其次利用改进EWT对实际矿山采取的微震和爆破振动信号进行分解,借助相关性分析筛选得到f1～f5 5个主分量,进而分别利用分量f1～f5构造Hankel矩阵,计算各Hankel矩阵的最大奇异值和奇异熵。最后利用遗传算法优化的支持向量机(GA-SVM)对微震和爆破信号进行分类识别。结果表明,爆破振动信号分量f1～f4的奇异熵要大于岩体微震信号分量f1～f4的奇异熵,爆破振动信号分量f1～f5的最大奇异值要大于岩体微震信号分量f1～f5的最大奇异值。改进EWT识别效果要优于传统EWT和经验模态分解,GA-SVM识别效果要优于支持向量机、逻辑回归和Bayes判别法,且基于EWT_Hankel_SVD和GA-SVM分类准确率达到94%。     

基于谐波小波奇异熵的轴承故障实时诊断

将谐波小波变换、奇异值分解理论和信息熵相结合,从揭示故障信号能量分布的复杂程度入手,提出一种轴承故障实时诊断的新方法。对轴承振动信号进行谐波小波分解,将分解得到的小波系数分别以尺度为行、时间为列构建谐波小波时频分布矩阵,并对该矩阵进行奇异值分解,以分解得到的奇异值为划分标准进行信息熵计算,通过信息的熵值来诊断轴承故障,给出了基于谐波小波奇异熵的轴承故障实时诊断的具体方法和模型。通过对轴承内圈故障、外圈故障大量的试验研究表明:该方法能有效地对轴承故障进行诊断,具有很高的实时性,能对采样频率低于68kHz的诊断系统进行实时诊断,适用性很好。     

复小波分解联合SVD提取振动信号非平稳特征

针对齿轮箱故障信号的多分量多频调制特点,提出了一种基于奇异值分解的最优小波解调技术。首先,采用小波变换的最小Shannon熵作为时间尺度分辨率的度量指标,将其应用到Morlet分析小波的参数优化选择中;其次,对常规小波参数选择方法进行了改进,利用奇异值分解技术对最优小波变化尺度进行了迭代搜索。该方法可以很好地降低噪声信号,有效提取信号中的周期成分,具有较好的瞬态信息提取能力。试验结果也表明了该方法在齿轮箱故障特征提取中的重要性以及降噪方法的有效性。     

自适应Morlet小波降噪方法及在轴承故障特征提取中的应用

分析了Morlet小波变换的滤波特性及其时频分辨率,利用Morlet小波良好的时域和频域特性及奇异值分解技术,提出了一种基于自适应Morlet小波和SVD的降噪方法。针对滚动轴承故障在振动信号中表现为冲击衰减波形的特点,采用修正的Shannon熵方法同时优化Morlet小波的中心频率与带宽参数,实现其与冲击特征成分的最优匹配;针对根据小波系数矩阵奇异值曲线的过渡阶段求取最佳变换尺度的方法存在着不够快捷方便的不足,将其与小波系数奇异值比方法相结合来快速方便地求得最佳变换尺度;最后对信号进行降噪处理提取故障特征。对仿真信号和实际轴承内外圈故障信号的应用分析表明,该方法具有良好的降噪性能,能有效地提取出滚动轴承的微弱故障特征。     

机械振动信号中突变信息检测的新方法研究

提出利用时间序列重构的吸引子轨迹矩阵奇异值分解的方法检测信号中的突变信息。针对２组数值信号,利用该方法进行检测,并将检测结果与小波变换结果进行比较。结果表明,该方法是可行的,从而为信号奇异性检测撮一种有效工具。     

奇异值小波降噪法在柱塞泵振动信号处理中的应用

针对小波阈值和奇异值分解降噪法的不足,研究一种新的小波阈值函数。提出一种基于改进阈值的奇异值小波降噪方法,该方法利用奇异值分解技术,将噪声非均匀分布的信号正交分解为噪声分布相对均匀的分量,并对每个分量进行小波阈值降噪,重构降噪后的分量,得到降噪信号。仿真实例证明,该方法与小波软、硬阈值及改进阈值法相比,不仅提高信噪比,而且能够更好地消除高斯噪声。利用该方法对柱塞泵不同状态振动信号进行降噪,结果表明,该方法能有效抑制噪声,为柱塞泵振动信号预处理提供一种更为有效的方法。     

Similarity of signal processing effect between Hankel matrix-based SVD and wavelet transform and its mechanism analysis

It is pointed out that signal processing effect of singular value decomposition (SVD) is very similar to that of wavelet transform when Hankel matrix is used. It is proved that a signal can be decomposed into the linear sum of a series of component signals by Hankel matrix-based SVD, and essentially what the component signals reflect are projections of original signal on the orthonormal bases of m-dimensional and n-dimensional vector spaces. The similarity mechanism of signal processing between SVD and wavelet transform is analyzed from the angle of basis of vector space and characteristic of Hankel matrix. The orthogonality of the component signals got by SVD and wavelet transform is also studied. It is discovered that singularity of signal can also be detected by Hankel matrix-based SVD, and compared with wavelet transform, there are two characteristics in SVD for singularity detection, one is that the order of vanishing moment of SVD component signals is increased progressively and the one of the nth SVD component signal is ‘n?1’, so singular points with different Lip index can all be detected, the other is that the width of impulse indicating the position of singularity will always keep the same throughout all SVD components and this width is determined by the column number of Hankel matrix.     

APPLICATION OF WAVELET TRANSFORM ON DIAGNOSIS AND PREDICTION OF MILLING CHATTER

In order to avoid the accuracy deterioration or tool damage caused by milling chatter, it is necessary to have an efficient and reliable diagnosis system that can on-line predict/detect the occur-rence of chatter. The diagnosis/predicting system proposed is to on-line process and analysis the vi-bration signals of the milling machine measured by accelerometers. According to the analysis results, the system will be able to detect/predict the occurrence of the chatter. The diagnosis algorithm is, first, collecting both the normal signals and chatter signals from milling processes, and then, converting the signals through wavelet transform and fast Fourier transform (FFT). Since the converted chatter sig-nals exhibit different characteristics from the normal signals, through defining the characteristic val-ues, such as root-mean-square value, max value, and ratio of peak value to root-mean-square value, etc, a diagnosis reference library that contains the distribution of these characteristic values is built for diagnosis. When a diagnosis is executing, the characteristic value of the measured signals is con-trasted with the diagnosis reference. The approach index which shows the possibility of occurrence of milling chatter will, then, be calculated through the diagnosis system. Cutting experiments are con-ducted to verify the proposed diagnosis system. The results show the success of early chatter detecting for the system.     

Haar wavelet for machine fault diagnosis

Continuous wavelet transform (CWT) is a kind of time–frequency analysis method commonly used in machine fault diagnosis. Unlike Fourier transform, the wavelet in CWT can be selected flexibly. In engineering application, there is a problem of how to select a suitable wavelet. At present, the selecting method mainly depends on the waveform similarity between the signal required to extract and the wavelet. This method is imperfect. For example, Haar wavelet possesses the rectangular waveform in its supporting field and dissimilarity to any component in the machine signal. It is rarely used in machine diagnosis. However, the time–frequency periodicity of Haar wavelet continuous wavelet transform (HCWT) should be useful in revealing the features in signals. In addition, Haar wavelets under different scales have good low-pass filter characteristic in frequency domain, particularly under larger scales, and that can allow HCWT to detect the lower frequency signal. These merits are presented in this paper and applied to diagnose three types of machine faults. Furthermore, in order to verify the effect of Haar wavelet, the diagnosis information obtained by HCWT is compared with that by Morlet wavelet continuous wavelet transform (MCWT), which is popular in machine diagnosis. The results demonstrate that Haar wavelet is also a feasible wavelet in machine fault diagnosis and HCWT can provide abundant graphic features for diagnosis than MCWT.     

基于小波—奇异值分解差分谱的弱故障特征提取方法

对于一些复杂信号中的弱故障特征信息,以往的两种小波—奇异值分解(Singular value decompositiom,SVD)组合模式的特征提取效果不佳,从小波的频率窗特性出发分析了出现这种问题的原因,进而对复杂信号的奇异值分布规律进行研究,据此提出一种新的小波-SVD差分谱组合模式。对原始信号做小波分解得到一系列细节信号后,不再将这些信号简单地排列成矩阵,而是利用每个细节信号构造特定结构的Hankel矩阵,再通过SVD对每个矩阵做正交化分解,并利用奇异值差分谱来选择特征奇异值进行SVD重构,由此实现对弱故障特征信息的提取。对一个轴承振动信号的处理结果证实该方法对复杂信号中的弱故障特征信息具有优良的提取效果,其获得的故障特征波形非常清晰,克服了以往小波-SVD组合模式对弱故障特征提取效果不佳的缺陷。     

基于小波包分析的铣刀状态监测方法研究

应用小波分析方法,通过对声发射信号的处理及分析判别铣刀状态.以三齿牛鼻铣刀为实验对象,分别以铣刀3种状态为例,采用不同的切削参数进行铣削实验,将采集到的AE信号进行小波分解后再进行时频域对比,结果表明:该方法可以比较准确的判断铣刀状态,并且有较好的理论基础、直观性与易操作性.     

自适应改进双树复小波变换的齿轮箱故障诊断

针对双树复小波变换存在频率混叠以及参数需自定义的缺陷,提出自适应改进双树复小波变换的齿轮箱故障诊断方法。首先,利用双树复小波变换将信号进行分解和单支重构,采用粒子群算法将分解后分量峭度值作为适应度函数,选择双树复小波的最优分解层数;其次,对重构出的低频信号进行频谱分析提取故障特征,将单支重构后的各高频分量进行变分模态分解,通过峭度值获得各高频分量经变分模态分解后的主频率分量信号;最后,分析各主频率分量信号的频谱,识别齿轮箱的故障特征。结果表明,该方法与双树复小波变换和变分模态分解相比,不仅消除了频率混叠现象,提高了信噪比和频带选择的正确性,而且还提高了从强噪声环境中提取瞬态冲击特征的能力。     

基于小波变换的盲信号分离的神经网络方法

提出一种新的盲信号分离的神经网络方法,该方法将小波变换和独立分量分析(ICA,Independent Component Analysis)相结合。利用小波变换的滤噪作用,将混合在原始信号中的部分高频噪声滤除后,再重构原始信号作为ICA的输入信号,有效地克服了现有ICA算法不能将噪声从源信号中分离的缺陷。实验结果表明,将该方法用于多通道脑电信号的盲分离是很有效的。     

SINGULARITY ANALYSIS USING CONTINUOUS WAVELET TRANSFORM FOR BEARING FAULT DIAGNOSIS

In this paper, wavelet transform is applied to detect abrupt changes in the vibration signals obtained from operating bearings being monitored. In particular, singularity analysis across all scales of the continuous wavelet transform is performed to identify the location (in time) of defect-induced bursts in the vibration signals. Through modifying the intensity of the wavelet transform modulus maxima, defect-related vibration signature is highlighted and can be easily associated with the bearing defect characteristic frequencies for diagnosis. Due to the fact that vibration characteristics of faulty bearings are complex and defect-related vibration signature is normally buried in the wideband noise and high frequency structural resonance, simple signal processing cannot be used to detect bearing fault. We show, through experimental results, that the proposed method has the ability to discriminate noise from the signal significantly and is robust to bearing operating conditions, such as load and speed, and severity of the bearing damage. These properties are desirable for automatic detection of machine faults.