Particle swarm optimization algorithm to solve the deconvolution problem for rolling element bearing fault diagnosis

Extraction of the fault related impulses from the raw vibration signal is important for rolling element bearing fault diagnosis. Deconvolution techniques, such as minimum entropy deconvolution (MED), MED adjusted (MEDA) and maximum correlated kurtosis deconvolution (MCKD), optimal MED adjusted (OMEDA) and multipoint optimal MED adjusted (MOMEDA), are typical techniques for enhancing the impulse-like component in the fault signal. This paper introduces the particle swarm optimization (PSO) algorithm to solve the filter of deconvolution problem. The proposed approaches solve the filter coefficients of the deconvolution problems by the PSO algorithm, assisted by a generalized spherical coordinate transformation. Compared with MED, MEDA, and OMEDA, the proposed PSO-MED and PSO-OMEDA can effectively overcome the influence of large random impulses and tend to deconvolve a series of periodic impulses rather than a signal impulse. Compared with MCKD and MOMEDA, the proposed PSO-MCKD and PSO-MOMEDA can achieve good performances even when the fault period is inaccurate. The effectiveness of the proposed methods is validated by the simulated signals. The study of experimental bearing fault signal shows that the PSO based deconvolution methods delivered better performance for rolling element bearing fault detection than the traditional deconvolution methods. Additionally, the proposed methods are compared with the following two popular signal processing methods: the ensemble empirical mode decomposition (EEMD) and fast kurtogram, which are used to highlight the improved performance of the proposed methods.     

基于改进最大相关峭度解卷积的滚动轴承复合故障诊断

强背景噪声环境下,多故障特征的准确分离是滚动轴承复合故障诊断的关键与难点。针对此问题,提出了一种改进最大相关峭度解卷积的滚动轴承复合故障诊断方法。该方法基于故障信号的特点,利用最大相关峭度解卷积实现信号中的多故障特征分离,借助改进的粒子群算法对参数进行优化选取;利用互相关谱进一步突出信号中的故障特征,提高信噪比。仿真信号和实测滚动轴承内、外圈复合故障信号的分析表明,所提方法能够准确提取出滚动轴承复合故障特征,借助互相关谱的噪声抑制能力,能实现比单一MCKD方法更为有效的故障特征提取。     

Diagnosis of compound faults of rolling bearings through adaptive maximum correlated kurtosis deconvolution

This paper proposes a new diagnosis method based on Adaptive maximum correlated kurtosis deconvolution (AMCKD) for accurate identification of compound faults of rolling bearings. The AMCKD method combines the powerful capability of cuckoo search algorithm for global optimization with the advantage of Maximum correlated kurtosis deconvolution (MCKD) for impact signal extraction. In contrast to traditional methods, such as direct envelop spectrum, Discrete wavelet transform (DWT), and empirical mode decomposition, the proposed method extracts each fault signal related to the single failed part from the compound fault signals and effectively separates the coupled fault features. First, the original signal is processed using AMCKD method. Demodulation operation is then performed on the obtained single fault signal, and the envelope spectrum is calculated to identify the characteristic frequency information. Verification is performed on simulated and experimental signals. Results show that the proposed method is more suitable for detecting compound faults in rolling bearings compared with traditional methods. This research provides a basis for improving the monitoring and diagnosis precision of rolling bearings.     

改进的共振稀疏分解方法及其在滚动轴承复合故障诊断中的应用

滚动轴承复合故障信号中各故障特征受到传输路径和其他干扰源的影响,在多缺陷共存条件下提取单个缺陷诱发的故障特征存在困难。提出一种基于双参数优化、子带重构改进的共振稀疏分解(RSSD)滚动轴承复合故障诊断方法：首先利用人工鱼群算法自适应选择RSSD的品质因子和分解层数以构造与故障特征匹配的最优小波基,获得包含瞬态冲击的低共振分量;然后依据提出的子带筛选准则选择并重构低共振分量中包含瞬态冲击成分的最佳子带;最后通过多点最优最小熵反卷积（MOMEDA）方法识别并提取重构信号中周期性故障冲击。仿真信号和轴承全寿命周期复合故障信号分析结果表明,与RSSD-MCKD方法相比,所提出方法能有效提取复合故障信号中各故障特征,精确实现轴承复合故障诊断。     

基于自适应最大相关峭度解卷积和频率切片小波变换的齿轮故障特征提取

针对最大相关峭度解卷积(MCKD)降噪效果受滤波器阶数影响的问题,提出了自适应MCKD方法。针对频率切片小波变换(FSWT)在强背景噪声中提取冲击故障特征的不足,提出了自适应MCKD和FSWT相结合的齿轮故障特征提取方法。首先用自适应MCKD对噪声齿轮信号进行降噪处理,然后对降噪后的信号进行频率切片小波变换和故障特征提取。齿轮故障诊断实例的分析结果验证了该方法的有效性。     

Impact fault detection of gearbox based on variational mode decomposition and coupled underdamped stochastic resonance

In the gear fault diagnosis, the emergence of periodic impulse components in vibration signals is an important symptom of gear failure. However, heavy background noise makes it difficult to extract the weak periodic impulse features. Therefore, the paper presents an impact fault detection method of gearbox by combining variational mode decomposition (VMD) with coupled underdamped stochastic resonance (CUSR) to extract the periodic impulse features. First, the adaptive VMD is presented to decompose the vibration signal into several intrinsic mode functions (IMFs), which can automatically determine the appropriate mode number according to the correlation kurtosis (CK) of decomposition results and extract the sensitive IMF component containing the main fault information. Next, the adaptive CUSR method is developed to analyze the selected sensitive IMF component, and the optimal system parameters are obtained by the genetic algorithm using the CK index as optimization objective function. Finally, the periodic impulse features are extracted by the output signal of CUSR system accurately. Experiments and engineering application verify the effectiveness and superiority of the proposed adaptive VMD-CUSR method for extracting the periodic impulse features in gear fault diagnosis compared to other methods.     

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。     

复选降噪自适应型MCKD方法研究

针对强噪声干扰下,最大相关峭度解卷积（Maximum correlation kurtosis deconvolution,MCKD）对于弱响应轴承滚动体故障信号指定周期冲击增强和辨识能力有限,无法自适应确定参数的问题,提出一种改进MCKD故障诊断方法。首先利用小波多尺度分解得到故障响应高频分量使冲击成份更加凸显;然后以峭度值最大准则复选出最优故障信号高频分量,降低噪音的干扰;最后结合小波方差自适应确定MCKD参数。轴承故障仿真、实验数据分析结果表明,该方法能够实现弱响应的轴承滚动体故障诊断,同时适用轴承内外圈故障诊断。     

基于最大相关峭度反褶积的轴承故障诊断方法

针对滚动轴承的故障信号是周期性冲击信号这一特性,提出了最大相关峭度反褶积(maximum correlated kurtosis deconvolution,简称MCKD)与谱峭度(spectral kurtosis,简称SK)结合的滚动轴承早期故障诊断方法,即MCKD-SK法。利用MCKD方法可以有效提取滚动轴承早期故障信号中被噪声淹没的周期冲击成分,抑制信号中的噪声,实现信号降噪,提升原信号的峭度。利用SK方法可以选择合理频带,将信号中的低频信息从高频信息中解调出来。通过仿真与实际监测数据的分析和验证,证明MCKD-SK方法可以准确有效地诊断滚动轴承的早期故障,可用于滚动轴承早期故障的在线监测。     

综合改进奇异谱分解和奇异值分解的齿轮故障特征提取方法

针对齿轮故障特征微弱，在强背景噪声下难以有效提取的问题，提出了一种改进奇异谱分解（ISSD）结合奇异值分解（SVD）的齿轮故障特征提取方法。针对奇异谱分解（SSD）算法中模态参数需凭经验选取的缺陷，基于散布熵优化算法对SSD算法进行了改进，在得到既定的一组奇异谱分量的基础上，根据峭度值最大准则筛选出了最佳奇异谱分量并进行了SVD处理，采用奇异值能量标准谱自适应地确定了信号重构阶数以还原信号和提高降噪效果。最后对信号进行包络解调以提取齿轮故障特征，将所提方法运用到仿真信号和齿轮实测信号中，并同传统包络谱、SSD包络谱以及经验模态分解结合SVD(EMD-SVD)方法进行了对比分析，结果表明，所提方法的降噪和特征提取效果更佳，能够更加有效地实现齿轮故障的判别。     

Sparsity-based signal extraction using dual Q-factors for gearbox fault detection

Early detection of faults developed in gearboxes is of great importance to prevent catastrophic accidents. In this paper, a sparsity-based feature extraction method using the tunable Q-factor wavelet transform with dual Q-factors is proposed for gearbox fault detection. Specifically, the proposed method addresses the problem of simultaneously extracting periodic transients and high-resonance component from noisy data for the gearboxes fault detection purpose. Firstly, a sparse optimization problem is formulated to jointly estimate the useful components from the noisy observation. In order to promote wavelet sparsity, non-convex regularizations are employed in the cost function of the optimization problem. Then, a fast converging, computationally efficient iterative algorithm which termed SpaEdualQA (the sparsity-based signal extraction algorithm using dual Q-factors) is developed to solve the formulated optimization problem. The derivation of the proposed fast algorithm combines the split augmented Lagrangian shrinkage algorithm (SALSA) with majorization–minimization (MM). Finally, the effectiveness of the proposed SpaEdualQA is validated by analyzing numerical signals and real data collected from engineering fields. The results demonstrated that the proposed SpaEdualQA can effectively extract periodic transients and high-resonance component from noisy vibration signals.     

Early fault feature extraction of bearings based on Teager energy operator and optimal VMD

As the fault shock component in vibration signals is extremely sparse and weak, it is difficult to extract the fault features when large-scale, low-speed and heavy-duty mechanical equipment is in the early stage of failure. To solve this problem, an early fault feature extraction method based on the Teager energy operator, combined with optimal variational mode decomposition (VMD) is presented in this study. First, the Teager energy operator was used to strengthen the weak shock component of the original signal. Next, a logistic–sine complex chaotic mapping with variable dimensions was constructed to enhance the global search ability and convergence speed of the pigeon-inspired optimization (PIO) algorithm, which is named the variable dimension chaotic pigeon-inspired optimization (VDCPIO) algorithm. Then, the VDCPIO algorithm is used to search for the optimal combination value of key parameters of VMD. The enhanced vibration signal is decomposed into a set of intrinsic mode functions (IMFs) by the optimized VMD, and then kurtosis for every IMF and mean kurtosis of all IMFs are extracted. According to the average kurtosis, several IMFs, whose kurtosis value is greater than the average kurtosis value, are selected to reconstruct a new signal. Then, envelope spectrum analysis of the reconstructed signal is carried out to extract the early fault features. Finally, experimental verification of the method was performed using the simulated signal and measured signal from a rolling bearing; the experimental results indicate that the method presented in this paper is more effective to extract the early fault features of this kind of mechanical equipment.     

基于MCKD和改进HHT多尺度模糊熵的齿轮故障诊断方法

针对齿轮故障信号常伴有大量噪声,故障特征难以提取的问题,提出一种基于最大相关峭度解卷积(MCKD)和改进希尔伯特-黄变换(HHT)多尺度模糊熵的故障诊断方法。首先采用MCKD算法对采集到的齿轮振动信号进行降噪处理,以提高信号的信噪比;然后利用自适应白噪声完备经验模态分解(CEEMDAN)对降噪后信号进行分解,获得一系列不同尺度的固有模态函数(IMF),并通过相关系数-能量的虚假IMF评价方法选取对故障敏感的模态分量;最后计算敏感IMF分量的模糊熵,将获得的原信号多尺度的模糊熵作为状态特征参数输入最小二乘支持向量机(LS-SVM)中,对齿轮的故障类型进行诊断。实测信号的诊断结果表明,该方法可实现齿轮故障的有效诊断。     

Virtual prototype and experimental research on gear multi-fault diagnosis using wavelet-autoregressive model and principal component analysis method

Gear systems are an essential element widely used in a variety of industrial applications. Since approximately 80% of the breakdowns in transmission machinery are caused by gear failure, the efficiency of early fault detection and accurate fault diagnosis are therefore critical to normal machinery operations. Reviewed literature indicates that only limited research has considered the gear multi-fault diagnosis, especially for single, coupled distributed and localized faults. Through virtual prototype simulation analysis and experimental study, a novel method for gear multi-fault diagnosis has been presented in this paper. This new method was developed based on the integration of Wavelet transform (WT) technique, Autoregressive (AR) model and Principal Component Analysis (PCA) for fault detection. The WT method was used in the study as the de-noising technique for processing raw vibration signals. Compared with the noise removing method based on the time synchronous average (TSA), the WT technique can be performed directly on the raw vibration signals without the need to calculate any ensemble average of the tested gear vibration signals. More importantly, the WT can deal with coupled faults of a gear pair in one operation while the TSA must be carried out several times for multiple fault detection. The analysis results of the virtual prototype simulation prove that the proposed method is a more time efficient and effective way to detect coupled fault than TSA, and the fault classification rate is superior to the TSA based approaches. In the experimental tests, the proposed method was compared with the Mahalanobis distance approach. However, the latter turns out to be inefficient for the gear multi-fault diagnosis. Its defect detection rate is below 60%, which is much less than that of the proposed method. Furthermore, the ability of the AR model to cope with localized as well as distributed gear faults is verified by both the virtual prototype simulation and experimental studies.     

基于电信号的改进VMD和DBN-DNN液压齿轮泵轮齿故障监测方法研究

液压系统电机电信号中包含丰富的系统运行状态信息,如何准确对电信号中的运行信息进行提取和分类是实现液压系统状态监测的关键。电机电流信号中蕴含的液压齿轮泵早期故障特征微弱,提取困难,用传统时频分析方法难以实现故障特征分离。本文提出基于相关系数和人工蜂群算法(Artificial bee colony,ABC)实现了对变分模态分解(Variational mode decomposition,VMD)参数的优化,同时以信号相关系数和峭度值最大为选取原则,确定有效的本征模态函数(Intrinsic mode function,IMF),并将IMF有效分量的排列熵和均方根值作为高维特征向量输入深度信念网络(Deep belief network,DBN-DNN),实现了对齿轮泵运行状态进行监测。结果表明,该方法能准确稳定地提取电流信号中携带的齿轮泵故障的微弱特征,进行齿轮泵运行状态监测,提高了齿轮故障诊断的准确性。     

基于蜂群优化投影寻踪的高光谱小目标检测

为了进一步提高高光谱遥感图像小目标无监督检测方法的运算速度,并降低其虚警率,提出了一种基于改进蜂群优化投影寻踪与K最近邻的检测方法。首先,采用核主成分分析法对原始高光谱遥感图像进行降维;然后,提出以邻域像元联合定义峰度与偏度的方法,并将两者结合作为投影指标,再以改进后的蜂群算法作为寻优方法,使用投影寻踪从高光谱图像中逐层获取投影图像,再根据其直方图提取小目标;最后,利用线性判别分析进一步提取像元特征,并结合加权K最近邻方法对小目标的检测结果进行提纯。大量实验结果表明,与RX方法、独立分量分析法、混沌粒子群优化投影寻踪法相比,本文方法不但可以更精确地检测出高光谱遥感图像中的小目标,而且具有更快的运算速度。     

基于WVD谱峭度法在轴承故障诊断中的应用

在对基于短时傅里叶变换(STFT)和基于小波变换的谱峭度法分析的基础上,提出了基于W igner Vil le分布的谱峭度法。将其作为检测工具,利用谱峭度构造最优滤波器提取轴承故障 信息。将这三种谱峭度法应用于滚动轴承故障诊断中进行对比分析。分析结果表明，时频分析方法对信号能量的集中程度和时窗与滤波器的选取是影响谱峭度法应用效果的主要因素。该结果对基于时频分析的谱峭度法理论体系的形成及其在故障诊断中的应用具有实际意义。     

PARAMETERS OPTIMIZATION OF CONTINUOUS WAVELET TRANSFORM AND ITS APPLICATION IN ACOUSTIC EMISSION SIGNAL ANALYSIS OF ROLLING BEARING

Morlet wavelet is suitable to extract the impulse components of mechanical fault signals. And thus its continuous wavelet transform (CWT) has been successfully used in the field of fault diagnosis. The principle of scale selection in CWT is discussed. Based on genetic algorithm,an opti-mization strategy for the waveform parameters of the mother wavelet is proposed with wavelet en-tropy as the optimization target. Based on the optimized waveform parameters,the wavelet scalogram is used to analyze the simulated acoustic emission (AE) signal and real AE signal of rolling bearing. The results indicate that the proposed method is useful and efficient to improve the quality of CWT.     

基于LCD的齿轮箱混合故障盲源分离研究

盲源分离是一种有效的混合故障诊断方法,而局部特征尺度分解（LCD）是非平稳信号的有效分析处理工具,综合两者的优点,提出了基于LCD的齿轮箱混合故障盲源分离方法。将源信号LCD分解,得到新的多维信号,采用Bayesian信息准则（BIC）估计盲源的数目并对多维信号进行重组。最后进行联合近似对角化处理,实现源信号的盲分离。仿真和实验结果表明,该方法能够有效地实现齿轮箱混合故障盲源分离。     

广义精细复合多尺度样本熵与流形学习相结合的滚动轴承故障诊断方法

针对滚动轴承故障特征提取困难的问题，提出了一种广义精细复合多尺度样本熵(GRCMSE)与流形学习相结合的特征提取方法。利用GRCMSE提取滚动轴承故障特征信息；采用判别式扩散映射分析(DDMA)方法对高维特征进行降维处理；将低维故障特征输入粒子群优化支持向量机多故障分类器中进行故障识别。滚动轴承故障实验分析结果表明：GRCMSE特征提取效果优于多尺度样本熵(MSE)、精细复合多尺度样本熵(RCMSE)和广义多尺度样本熵(GMSE)； DDMA降维效果优于等度规映射(Isomap)和局部切空间排列(LTSA)的降维效果；GRCMSE和DDMA相结合后的滚动轴承故障识别精度达到100%。