Application of Hermitian wavelet to crack fault detection in gearbox

The continuous wavelet transform enables one to look at the evolution in the time scale joint representation plane. This advantage makes it very suitable for the detection of singularity generated by localized defects in the mechanical system. However, most of the applications of the continuous wavelet transform have widely focused on the use of Morlet wavelet transform. The complex Hermitian wavelet is constructed based on the first and the second derivatives of the Gaussian function to detect signal singularities. The Fourier spectrum of Hermitian wavelet is real; therefore, Hermitian wavelet does not affect the phase of a signal in the complex domain. This gives a desirable ability to extract the singularity characteristic of a signal precisely. In this study, Hermitian wavelet is used to diagnose the gear localized crack fault. The simulative and experimental results show that Hermitian wavelet can extract the transients from strong noise signals and can effectively diagnose the localized gear fault.     

基于多尺度Hermitian小波包络谱的轴承故障诊断

提出了一种基于多尺度Hermitian小波包络谱的轴承故障诊断方法。该方法综合利用了Hermitian小波和包络谱分析技术的优点,首先对轴承故障振动信号进行Hermitian连续小波变换,得到小波分解的实部和虚部,然后计算振动信号的多尺度包络谱。对齿轮箱轴承故障振动信号的分析表明,该方法在强噪声环境下能有效识别轴承内圈故障和外圈故障。     

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.     

基于小波分析的旋转机械故障诊断技术及其试验研究

通过把转子试验台裂纹故障信号与小波变换的多分辨率方法以及奇异性理论相结合进行研究,发现小波分析便于对信号的总体和局部进行刻画;利用小波变换对信号的分解和重构特性,可有针对性地选取有关频带的信息以及降低噪声干扰,通过对重构信号的频谱分析能更有效地提取裂纹故障的典型特征,为计算机自动识别或专家系统的建立奠定了基础,从而达到了诊断的目的。结果表明,对于旋转机械的非平稳信号来说,利用小波变换方法进行故障诊断是行之有效的。     

基于改进经验小波变换的行星齿轮箱故障诊断

行星齿轮箱振动信号具有复杂多分量和调幅-调频的特点。幅值解调和频率解调方法能够避免传统Fourier频谱中的复杂边带分析,有效识别故障特征频率。经验小波变换通过对信号Fourier频谱的分割构造一组正交滤波器组,能提取具有紧支撑Fourier频谱的单分量成分,再对单分量成分运用Hilbert变换即可实现信号的解调分析。经验小波变换能够有效分离出调幅-调频成分,不存在模态混叠现象,具有完备的理论基础,自适应性好、算法简单、计算速度快。将改进的经验小波变换应用于行星齿轮箱振动信号的解调分析;提出了一种单分量个数的估算方法,解决了经验小波变换中的Fourier频谱划分问题;给出了对故障敏感的信号分量的选取方法,提高了分析的针对性。将改进方法应用于行星齿轮箱振动仿真信号和实验信号分析,验证了该方法的有效性。     

基于幅值与相角小波映射的裂纹转子故障诊断

建立了基于简单铰链裂纹模型和局部柔度理论的裂纹转子动力学模型,得到了裂纹转子与无裂纹转子的数值仿真解及其傅里叶变换的相角;利用连续小波变换研究了裂纹转子与无裂纹转子的幅值与相角小波映射特性,提出了利用幅值与相角小波映射识别裂纹的新方法。数值仿真研究了尺度因子对幅值与相角小波映射准确性和有效性的影响,给出了建议的尺度因子。试验研究验证了该方法在工程实际中的有效性和实用性。     

连续小波变换的滚动轴承故障诊断

提出了用连续小波变换与傅立叶变换相结合进行轴承故障识别的新方法。先通过Morlet连续小波变换对故障轴承信号进行不同尺度的分解,然后进行小波尺度一能量谱统计,再在有可能体现故障频率的尺度上对其获得的小波系数进行快速傅立叶变换来识别故障特征频率。对于非常微弱的内圈故障提出了通过共振解调法对特定尺度系数进行Hilbert包络提取故障频率的新方法。优点在于能够在强噪声背景下较为精确的识别故障。实际测试验证了新方法的正确性。     

Precise measurement of defect width in tapered roller bearing using vibration signal

The present experimental investigation is focused on establishing a robust signal processing technique to measure the width of the defect present on the outer or inner race of a tapered roller bearing. An experiment has been designed with roller bearings having various widths of seeded faults, on outer and inner races, respectively. The corresponding vibration signals have been investigated with the proposed method. This method initially denoises the vibration signal using un-decimated wavelet transform. The approximation signal has been shown to be effective for further time–frequency analysis using continuous wavelet transform (CWT). It is not only difficult but ambiguous as well to detect the entry and the exit points of the defect. The ambiguity gets reduced by using Symlet wavelet due to its linear phase nature which maintains sharpness in the signal even when there is a sudden change in signal. In the first phase of the measurement, the scalogram generated from CWT is used to measure the time duration that the roller takes to roll over the defect. However, measurement process is dramatically enhanced with the proposed ridge spectrum, which is generated from the CWT scalogram. The vertical strips drawn on the ridge spectrum corroborates well with defect width. Summarizing, the proposed method can be reckoned suitable and reliable in measuring bearing defect width in real-time from vibration signal.     

基于IEWT和MCKD的滚动轴承故障诊断方法

针对经验小波变换（Empirical wavelet transform,EWT）对强噪声环境中滚动轴承微弱故障诊断的不足,主要是傅里叶频谱分段不当的问题。提出一种基于最大相关峭度解卷积（Maximum correlated kurtosis deconvolution,MCKD）降噪与改进EWT相结合的滚动轴承早期故障识别方法。首先采用最大相关峭度解卷积算法以包络谱的相关峭度最大化为目标对原信号进行降噪处理、检测信号中的周期性冲击成分,然后根据信号Fourier频谱的包络极大值进行分段,通过分析各频段平方包络谱中明显的频率成分来诊断故障。新方法能有效降噪、增强信号中周期性冲击特征、降低单次偶然冲击的影响、抑制非冲击成分。通过对含外圈、内圈故障的滚动轴承进行试验分析,结果表明,相比于快速谱峭度图和小波包络分析方法,该方法提取出的特征更加明显,能有效实现滚动轴承早期微弱故障的识别。     

Identification of faults through wavelet transform vis-à-vis fast Fourier transform of noisy vibration signals emanated from defective rolling element bearings

Fault diagnosis of rolling element bearings requires efficient signal processing techniques. For this purpose, the performances of envelope detection with fast Fourier transform (FFT) and continuous wavelet transform (CWT) of vibration signals produced from a bearing with defects on inner race and rolling element, have been examined at low signal to noise ratio. Both simulated and experimental signals from identical bearings have been considered for the purpose of analysis. The bearings have been modeled as spring-mass-dashpot systems and the simulated signals have been obtained considering transfer functions for the bearing systems subjected to impulsive loads due to the defects. Frequency B spline wavelets have been applied for CWT and a discussion on wavelet selection has been presented for better effectiveness. Results show that use of CWT with the proposed wavelets overcomes the short coming of FFT while processing a noisy vibration signals for defect detection of bearings.     

S变换用于滚动轴承故障信号冲击特征提取

为从低信噪比的滚动轴承故障信号中提取出冲击特征,以便于进行轴承故障诊断,引入S变换的信号处理方法。以短时傅里叶变换（short time Fourier transform,简称STFT）以及连续小波变换（continuous wavelet transform,简称CWT）为理论基础,分别推导得出了连续S变换的定义式,并利用快速傅里叶变换（fast Fourier transform,简称FFT）实现S变换离散化计算。S变换克服了STFT时频分辨率固定的缺点,弥补了CWT缺乏相位信息的不足。仿真信号研究表明,S变换在信号整个频带上具有良好的时频分辨率和时频聚集性,能够提取低信噪比信号中的冲击特征,且性能优于STFT和CWT。最后对一组实际的滚动球轴承故障振动信号进行S变换处理,结果表明,S变换能够方便有效地从中提取出周期性的冲击特征,从而指导滚动轴承相关故障的诊断。     

基于余弦调频小波变换的滚动轴承故障研究

针对滚动轴承故障振动信号的特点，构造余玄调频小波，采用连续小波变换的方法来提取滚动轴承故障振动信号的特征，在此基础上提出了一种滚动轴承故障诊断方法：时间一小波能量谱自相关分析法。通过对滚动轴承具有缺陷的情况下振动信号的分析，说明时间一小波能量谱自相关分析法不仅能检测到滚动轴承故障的存在，而且能有效地识别滚动轴承的故障模式。     

基于DT-CWT自适应Teager能量谱的轴承早期故障诊断

针对滚动轴承早期故障特征信息难以识别以及带通滤波器参数设置依赖使用者经验等造成共振带不能有效确定并自适应提取的问题,提出了频带幅值熵的概念。在此基础上,将双树复小波变换和Teager能量谱结合,提出了基于双树复小波自适应Teager能量谱的早期故障诊断方法。首先,利用双树复小波将采集到的振动信号分解为不同频带的子信号,并计算各子带的频带幅值熵;然后,将熵值按升序排列后依次作为阈值,提取频带幅值熵大于阈值的子带,依据峭度指标确定最佳阈值,从而自适应并且有效地提取出共振带;最后,对共振带进行Teager能量谱分析,即可从中准确地识别出轴承的故障特征频率。通过信号仿真与实验数据分析验证了该方法的有效性。     

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.     

Application of an impulse response wavelet to fault diagnosis of rolling bearings

To target the characteristic of roller bearing fault vibration signals, the impulse response wavelet is constructed by using continuous wavelet transform to extract the feature of fault vibration signals, based on which two methods namely scale-wavelet power spectrum comparison and auto-correlation analysis of time-wavelet power spectrum are proposed. The analysis results from roller bearing vibration signals with out-race or inner-race fault show that the two proposed methods can detect the faults of roller bearing and identify fault patterns successfully.     

FFT+FT离散频谱校正法参数估计精度

研究用FFT谱连续细化傅里叶变换分析法进行离散频谱校正时的参数估计误差。分析无噪声情况下频率﹑相位﹑幅值的估计误差随细化倍数的变化规律,估计精度随细化倍数的增大而提高,当细化倍数大于40时,最大估计误差几乎可忽略不计。在高斯白噪声的影响下,细化后频谱序列最大值找错的概率随细化倍数的增加而增加,综合考虑频率分辨率对频率估计精度的影响及频谱序列最大值找错的概率,提出用归一化频率估计综合误差和归一化频率估计最大可能误差两个指标评价此校正法对频率的估计精度,并基于此给出不同信噪比条件下的最优细化倍数。采用非线性最小二乘拟合法对噪声影响下的FFT谱连续细化傅里叶变换分析校正法进行改进,通过仿真模拟验证改进后该校正方法具备更高的校正精度和抗噪能力。     

基于奇异值分解的突变信息检测新方法及其应用

提出了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。利用该方法对任选的一数值信号和旋转机械静动件早期碰摩故障数值仿真信号进行了检测,并将检测结果与信号的小波变换结果进行了比较,结果表明,该方法是可行的,能够有效地应用于信号的奇异性检测。另外,还分析了噪声信号对该方法与小波变换方法所得结果的影响。最后,将该方法应用于旋转机械静动件早期碰摩故障试验信号的检测,获得了满意的结果。     

基于改进双树复小波变换的轴承多故障诊断

针对双树复小波变换产生频率混叠的缺陷,提出了改进双树复小波变换的轴承多故障诊断方法,该方法综合利用了双树复小波包变换和经验模态分解技术。首先,利用双树复小波变换将振动信号分解成不同频带的分量;然后,将各小波分量进行经验模态分解,获得各小波分量的主频率分量信号;最后,计算各小波分量的主频率分量信号的包络谱,根据包络谱识别齿轮箱轴承的故障部位和类型。通过仿真信号和齿轮箱轴承多故障振动实验信号的研究结果表明,该方法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,而且提高了从强噪声环境中提取瞬态冲击特征的能力,能有效识别轴承的故障类型。     

小波降噪技术在柴油机故障诊断中的应用

在柴油机的故障诊断中,对其振动信号的分析是柴油机故障诊断的重要手段,但是由于噪声的干扰而使诊断的精度大打折扣,而传统的傅里叶低通滤波降噪方法对于柴油机这样的非平衡复杂振动信号不能起到好的降噪作用。本文采用小波降噪技术,将柴油机缸盖振动信号进行小波多尺度分解,然后分别进行阈值处理,最后进行小波重构,剔除柴油机的噪声信号,提高信号的信噪比,获得了比较理想的效果。     

二进离散小波能量谱及其对微弱信号的检测

提出了二进离散小波的能量谱的分析方法 ,给出了实用的计算公式 ,论述了其可行性。导出了二进离散小波的能量频谱与离散信号频谱之间的关系。应用该分析方法有效地检测出了时域微弱奇异信号和频域微弱特征信号。能量时谱使二进离散小波分析得到的时域奇异信号更加突出 ,能量频谱发现了 Fourier分析不能得到的某些能量集中的特征信号。实例验证了该分析方法的优良特性 ,为设备运行状态检测和故障预报提供了一种新的手段。