A wavelet approach to fault diagnosis of a gearbox under varying load conditions

Varying load can cause changes in a measured gearbox vibration signal. However, conventional techniques for fault diagnosis are based on the assumption that changes in vibration signal are only caused by deterioration of the gearbox. There is a need to develop a technique to provide accurate state indicator of gearbox under fluctuating load conditions. This paper presents an approach to gear fault diagnosis based on complex Morlet continuous wavelet transform under this condition. Gear motion residual signal, which represents the departure of time synchronously averaged signal from the average tooth-meshing vibration, is analyzed as source data due to its lower sensitiveness to the alternating load condition. A fault growth parameter based on the amplitude of wavelet transform is proposed to evaluate gear fault advancement quantitatively. We found that this parameter is insensitive to varying load and can correctly indicate early gear fault. For a comparison, the advantages and disadvantages of other measures such as kurtosis, mean, variance, form factor and crest factor, both of residual signal and mean amplitude of continuous wavelet transform waveform, are also discussed. The effectiveness of the proposed fault indicator is demonstrated using a full lifetime vibration data history obtained under sinusoidal varying load.     

A time domain approach to diagnose gearbox fault based on measured vibration signals

Spectral analysis techniques to process vibration measurements have been widely studied to characterize the state of gearboxes. However, in practice, the modulated sidebands resulting from the local gear fault are often difficult to extract accurately from an ambiguous/blurred measured vibration spectrum due to the limited frequency resolution and small fluctuations in the operating speed of the machine that often occurs in an industrial environment. To address this issue, a new time-domain diagnostic algorithm is developed and presented herein for monitoring of gear faults, which shows an improved fault extraction capability from such measured vibration signals. This new time-domain fault detection method combines the fast dynamic time warping (Fast DTW) as well as the correlated kurtosis (CK) techniques to characterize the local gear fault, and identify the corresponding faulty gear and its position. Fast DTW is employed to extract the periodic impulse excitations caused from the faulty gear tooth using an estimated reference signal that has the same frequency as the nominal gear mesh harmonic and is built using vibration characteristics of the gearbox operation under presumed healthy conditions. This technique is beneficial in practical analysis to highlight sideband patterns in situations where data is often contaminated by process/measurement noises and small fluctuations in operating speeds that occur even at otherwise presumed steady-state conditions. The extracted signal is then resampled for subsequent diagnostic analysis using CK technique. CK takes advantages of the periodicity of the geared faults; it is used to identify the position of the local gear fault in the gearbox. Based on simulated gear vibration signals, the Fast DTW and CK based approach is shown to be useful for condition monitoring in both fixed axis as well as epicyclic gearboxes. Finally the effectiveness of the proposed method in fault detection of gears is validated using experimental signals from a planetary gearbox test rig. For fault detection in planetary gear-sets, a window function is introduced to account for the planet motion with respect to the fixed sensor, which is experimentally determined and is later employed for the estimation of reference signal used in Fast DTW algorithm.     

ARX model-based gearbox fault detection and localization under varying load conditions

The development of the fault detection schemes for gearbox systems has received considerable attention in recent years. Both time series modeling and feature extraction based on wavelet methods have been considered, mostly under constant load. Constant load assumption implies that changes in vibration data are caused only by deterioration of the gearbox. However, most real gearbox systems operate under varying load and speed which affect the vibration signature of the system and in general make it difficult to recognize the occurrence of an impending fault.This paper presents a novel approach to detect and localize the gear failure occurrence for a gearbox operating under varying load conditions. First, residual signal is calculated using an autoregressive model with exogenous variables (ARX) fitted to the time-synchronously averaged (TSA) vibration data and filtered TSA envelopes when the gearbox operated under various load conditions in the healthy state. The gear of interest is divided into several sections so that each section includes the same number of adjacent teeth. Then, the fault detection and localization indicator is calculated by applying F-test to the residual signal of the ARX model. The proposed fault detection scheme indicates not only when the gear fault occurs, but also in which section of the gear. Finally, the performance of the fault detection scheme is checked using full lifetime vibration data obtained from the gearbox operating from a new condition to a breakdown under varying load.     

基于激光自混合传感器的齿轮局部故障振动信号分析

建立了齿圈局部故障调频现象模型,分析了故障轮齿啮合频率及其倍频两侧边频带的产生机理,给出了齿圈局部故障特征频率的计算公式,建立了倒频谱分析模型。采用激光自混合传感器,分别从径向和轴向两个方向采集齿轮箱振动信号波形。在齿轮箱1Hz和2Hz两种不同输出转频下,分别研究了无故障齿轮箱和故障齿轮箱的振动信号特征。通过实验研究验证了理论推导结果。     

Condition monitoring of a single-stage gearbox with artificially induced gear cracks utilizing on-line vibration and acoustic emission measurements

The condition monitoring of a lab-scale, single stage, gearbox using different non-destructive inspection methodologies and the processing of the acquired waveforms with advanced signal processing techniques is the aim of the present work. Acoustic emission (AE) and vibration measurements were utilized for this purpose. The experimental setup and the instrumentation of each monitoring methodology are presented in detail. Emphasis is given on the signal processing of the acquired vibration and acoustic emission signals in order to extract conventional as well as novel parameters-features of potential diagnostic value from the monitored waveforms. Innovative wavelet-based parameters-features are proposed utilizing the discrete wavelet transform. The evolution of selected parameters/features versus test time is provided, evaluated and the parameters with the most interesting diagnostic behaviour are highlighted. The differences in the parameters evolution of each NDT technique are discussed and the superiority of AE over vibration recordings for the early diagnosis of natural wear in gear systems is concluded.     

Vibration signal models for fault diagnosis of planetary gearboxes

A thorough understanding of the spectral structure of planetary gear system vibration signals is helpful to fault diagnosis of planetary gearboxes. Considering both the amplitude modulation and the frequency modulation effects due to gear damage and periodically time variant working condition, as well as the effect of vibration transfer path, signal models of gear damage for fault diagnosis of planetary gearboxes are given and the spectral characteristics are summarized in closed form. Meanwhile, explicit equations for calculating the characteristic frequency of local and distributed gear fault are deduced. The theoretical derivations are validated using both experimental and industrial signals. According to the theoretical basis derived, manually created local gear damage of different levels and naturally developed gear damage in a planetary gearbox can be detected and located.     

环境卫星多光谱图像压缩算法

基于环境卫星多光谱图像特点的分析,提出了一种新的基于三维等级树集合划分算法(3D-SPI HT)和感兴趣区域(ROI)编码相结合的多光谱图像压缩算法。首先在谱间采用两种小波基相结合的三维离散小波变换(3D-DWT),去除多光谱图像在空间和谱间的冗余信息,减少恢复光谱的误差值,然后采用部分三维等级树集合划分算法和小波系数提升的感兴趣区域编码相结合的方法。该方法对小波系数从空间方向树上按对恢复光谱信息的重要性不同进行合理的码率分配,使得恢复光谱具有更好的分辨率,并依据比特平面层中重要系数的统计概率来自适应地进行3种编码模式的选择,提高了编码效率。实验数据结果表明,该算法比传统算法更好地保护了多光谱图像中的光谱信息,在压缩比为8∶1的情况下,满足了环境卫星多光谱图像压缩系统的要求。     

提升小波加权自相关函数的基音检测算法*

随着计算机技术的发展,语音信号处理作为人机交互的重要渠道,其在复杂噪声环境下的特征值检测算法直接关系到计算机的运算效率。基音周期是语音特征值提取的重要参数之一。针对传统基音检测算法在噪声环境下检测精度低的问题,提出了一种基于自适应提升小波变换加权线性预测误差自相关函数的基音检测算法。该方法用多级提升小波近似系数加权求和的方法来弥补自相关函数随着时间延迟量的增加幅值衰减的缺陷;用线性预测误差自相关函数的方法来抑制共振峰的干扰,然后将两种方法结合来突出基音周期处的峰值。实验结果表明,与传统的自相关函数法和小波加权法相比,该方法能有效减弱共振峰的影响,突出基音周期处的峰值,提高基音周期检测精度,鲁棒性更好。     

Research on dynamics and fault mechanism of spur gear pair with spalling defect

This study focuses on the nonlinear dynamic and vibration characteristics of spur gear pair with local spalling defect to explore the spalling mechanism. The dynamic model of the gear pair with spalling defect and time-variant mesh stiffness is established to investigate the effect of spalling defect on mesh stiffness and dynamic response. The analytical solutions of the system which is deduced into four different stages of the gear with the time-variant stiffness in a mesh period are obtained. The dynamic responses with the evolvement of sapll are analyzed by using time history, phase contrail, Poincaré section and spectrum analysis. The spalling characteristics are also evaluated by employing statistical techniques, which shows that the spalling failure is suitable to be detected under low velocity and small excitation. The gearbox with spalling defect is designed and the experiments are carried out to get the dynamic characteristics of the spalling vibration signals. The results obtained herein show the good agreement qualitatively with the theoretical analysis, which provides a theoretical basis to spalling fault diagnosis of gearbox.     

Optical image compression based on adaptive directional prediction discrete wavelet transform

The traditional lifting wavelet transform cannot effectively reconstruct the nonhorizontal and nonvertical high-frequency information of an image. In this paper, we present a new image compression method based on adaptive directional prediction discrete wavelet transform (ADP-DWT). We first design a directional prediction model to obtain the optimal transform direction of the lifting wavelet. Then, we execute the directional lifting transform along the optimal transform direction. The edge and texture energy can be reduced in the nonhorizontal and nonvertical directions of the high-frequency sub-bands. Finally, the wavelet coefficients are coded with the set partitioning in hierarchical trees (SPIHT) algorithm. The new method holds the advantages of both adaptive directional lifting (ADL) and direction-adaptive discrete wavelet transform (DA-DWT), and the computational complexity is far lower than that in these methods. For the images containing regular and fine textures or edges, the coding preformance of ADP-DWT is better than that of ADL and DA-DWT.     

基于灰色预测的直升机齿轮箱状态预测方法

作为直升机上重要的关键部件,直升机齿轮箱能够将动力转换为动力输出形式,从而满足不同形式下动力的需要。针对直升机齿轮箱状态无法准确预测的技术难题,本文将灰色系统理论中的灰色预测方法运用到直升机齿轮箱中,有效解决了齿轮箱使用状态难以准确预测的技术难题。首先对采集到的直升机齿轮箱的不同的振动信号进行特征提取,然后采用信息融合技术,将不同振动信号的特征值进行融合,最后运用灰色预测方法对直升机齿轮箱的使用状态进行预测。文中对所提出的方法进行了试验验证,结果表明,所提出的基于灰色预测的直升机齿轮箱状态预测方法能够实现对直升机齿轮箱的状态准确预测的效能,并对其他航空设备以及机械设备的状态预测具有一定的借鉴意义。     

Vibro-acoustic propagation of gear dynamics in a gear-bearing-housing system

This work developed a computational process to predict noise radiation from gearboxes. It developed a system-level vibro-acoustic model of an actual gearbox, including gears, bearings, shafts, and housing structure, and compared the results to experiments. The meshing action of gear teeth causes vibrations to propagate through shafts and bearings to the housing radiating noise. The vibration excitation from the gear mesh and the system response were predicted using finite element and lumped-parameter models. From these results, the radiated noise was calculated using a boundary element model of the housing. Experimental vibration and noise measurements from the gearbox confirmed the computational predictions. The developed tool was used to investigate the influence of standard rolling element and modified journal bearings on gearbox radiated noise.     

噪声模态单元预判的经验模态分解脉冲星信号消噪

为了改善脉冲星辐射脉冲信号的消噪效果, 提出了一种基于噪声模态单元预判的经验模态分解(EMD) 消噪声方法. 该方法首先利用EMD将含噪辐射脉冲信号分解为一组内蕴模态函数(IMF), 根据IMF系数的统计特性采用局部均方误差准则进行噪声模态单元预判, 并将噪声模态单元置零; 然后对噪声模态单元预判处理后的IMF以模态单元为基本单位进行最优比例萎缩消噪, 从而达到抑制噪声、保留信号的目的. 实验结果表明: 与Sure Shrink小波阈值法、Bayes Shrink小波阈值法和EMD模态单元比例萎缩法相比, 基于噪声模态单元预判的EMD消噪方法可以更有效地去除脉冲辐射信号中的噪声, 同时更好地保留信号突变处的细节信息特征, 在信噪比、 均方误差、峰值相对误差、峰位误差和相位误差等方面都有一定程度的改善. 关键词： 脉冲星信号消噪 经验模态分解 噪声模态单元预判 局部均方误差     

Complex signal analysis for wind turbine planetary gearbox fault diagnosis via iterative atomic decomposition thresholding

The vibration signals from complex structures such as wind turbine (WT) planetary gearboxes are intricate. Reliable analysis of such signals is the key to success in fault detection and diagnosis for complex structures. The recently proposed iterative atomic decomposition thresholding (IADT) method has shown to be effective in extracting true constituent components of complicated signals and in suppressing background noise interferences. In this study, such properties of the IADT are exploited to analyze and extract the target signal components from complex signals with a focus on WT planetary gearboxes under constant running conditions. Fault diagnosis for WT planetary gearboxes has been a very important yet challenging issue due to their harsh working conditions and complex structures. Planetary gearbox fault diagnosis relies on detecting the presence of gear characteristic frequencies or monitoring their magnitude changes. However, a planetary gearbox vibration signal is a mixture of multiple complex components due to the unique structure, complex kinetics and background noise. As such, the IADT is applied to enhance the gear characteristic frequencies of interest, and thereby diagnose gear faults. Considering the spectral properties of planetary gearbox vibration signals, we propose to use Fourier dictionary in the IADT so as to match the harmonic waves in frequency domain and pinpoint the gear fault characteristic frequency. To reduce computing time and better target at more relevant signal components, we also suggest a criterion to estimate the number of sparse components to be used by the IADT. The performance of the proposed approach in planetary gearbox fault diagnosis has been evaluated through analyzing the numerically simulated, lab experimental and on-site collected signals. The results show that both localized and distributed gear faults, both the sun and planet gear faults, can be diagnosed successfully.     

A Simplified Formulation to Estimate Influence of Gearbox Parameters on the Rattle Noise

Occurrence of gear rattle in transmission systems can result in severe vibration and noise, which in applications such as automobiles is an important source of user discomfort. As a result , the reduction of the rattling noise has attracted lot of concerns. The rattling noise level is affected by several gearbox parameters, an understanding of which is essential to prevent the expensive design modifications at later stages of product development. To develop such understanding at the gearbox design stage, this paper analytically evaluates the gear parameters’ effect on the root mean square of the wheel gear acceleration under idling condition, which is known to be linearly correlated to the rattling noise level. Therefore, this evaluation allows for an investigation of the gear parameters’ influence on the rattling noise as well. This method is then verified by comparing the analytical results with the simulation results from a dynamic model built in SIMPACK as well as previously published experimental results. Thus, the proposed analytical evaluation method can optimize the gearbox specifications at the design stage to reduce the gear rattle noise level.     

基于非采样提升小波-Contourlet变换的图像融合算法

为克服非采样Contourlet变换中金字塔分解的不足,首先在提升小波变换的基础上,通过取消其奇偶分裂环节得到具有平移不变性的非采样提升小波变换,然后用此变换来取代非采样Contourlet变换中的金字塔分解,得到新的非采样提升小波-Contourlet变换。将此变换与一定的融合规则相结合,提出了一种基于非采样提升小波-Contourlet变换的图像融合算法。实验表明,该算法相对于非采样Contourlet变换能从源图像中提取更多有用信息注入到融合图像中,可得到更高性能的融合图像。     

空间外差光谱仪光谱降噪方法研究

空间外差光谱仪是一种新式的超高分辨率光谱仪,可用于大气监测、卫星遥感等领域。为了减少空间外差光谱信号中的噪声,提出基于提升小波变换结合中值滤波方法来实现信号的降噪。改进的提升小波变换融合了一种双因子的阈值函数、分层阈值选取。与小波变换的软、硬阈值对比发现,它能提取空间外差光谱,减小峰宽和保留重要的细节特征,降噪效果优于小波变换的软、硬阈值法。最后用信噪比和均方误差两项定量指标来衡量算法的效果。实验结果表明:该算法比软阈值法在处理氙灯和积分球时信噪比提高了24.6%和31%,均方误差减少了43.2%和51.5%;与硬阈值法相比信噪比提高了21.5%和30.6%,均方误差减少了40.2%和51.2%。因此,算法在空间外差光谱降噪方面具有可行性。     

Comparisons of MFDFA,EMD and WT by Neural Network,Mahalanobis Distance and SVM in Fault Diagnosis of Gearboxes

A method for gearbox fault diagnosis consists of feature extraction and fault identification. Many methods for feature extraction have been devised for exposing nature of vibration data of a defective gearbox. In addition, features extracted from gearbox vibration data are identified by various classifiers. However, existing literatures leave much to be desired in assessing performance of different combinatorial methods for gearbox fault diagnosis. To this end, this paper evaluated performance of several typical combinatorial methods for gearbox fault diagnosis by associating each of multifractal detrended fluctuation analysis (MFDFA), empirical mode decomposition (EMD) and wavelet transform (WT) with each of neural network (NN), Mahalanobis distance decision rules (MDDR) and support vector machine (SVM). Following this, performance of different combinatorial methods was compared using a group of gearbox vibration data containing slightly different fault patterns. The results indicate that MFDFA performs better in feature extraction of gearbox vibration data and SVM does the same in fault identification. Naturally, the method associating MFDFA with SVM shows huge potential for fault diagnosis of gearboxes. As a result, this paper can provide some useful information on construction of a method for gearbox fault diagnosis.     

二维提升的CDF(1,3)小波结合改进的SPIHT的渐进性无损图像压缩方法

针对传统小波变换计算复杂的缺点和多级树集合分裂算法(SPIHT)编码过程重复运算、存储量大的问题,提出了一种二维提升的CDF(1,3)小波结合改进的SPIHT的渐进性无损图像压缩方法。对整数CDF(1,3)双正交小波变换实现二维提升,利用提升的小波对图像做变换,提高了运算速度、便于硬件实现。对SPIHT算法加以改进,根据各个子图像的不同特点,改变扫描路线,采用四路并行分块处理的方法,提高了编码速度,降低了编解码过程的运算复杂度和时间消耗。利用提升的CDF(1,3)小波变换结合改进的SPIHT实现了渐进性无损图像压缩,证明了二维提升方案的有效性。     

An adaptive OPD and dislocation prediction used characteristic of interference pattern for interference hyperspectral image compression

According to the imaging principle and characteristic of LASIS (Large Aperture Static Interference Imaging Spectrometer), we discovered that the 3D (three dimensional) image sequences formed by different interference pattern frames, which were formed in the imaging process of LASIS Interference hyperspectral image, had much stronger correlation than the original interference hyperspectral image sequences, either in 2D (two dimensional) spatial domain or in the spectral domain. We put this characteristic into image compression and proposed an adaptive OPD (optical path difference) and dislocation prediction algorithm for interference hyperspectral image compression. Compared the new algorithm proposed in this paper with Dual-Direction Prediction [1] proposed in 2009, lots of experimental results showed that the prediction error entropy of the new algorithm was much smaller. In the prediction step of lifting wavelet transform, this characteristic would also reduce the entropy of coefficients in high frequency significantly, which would be more advantageous for quantification coding [2].