Rolling element bearing fault detection based on optimal antisymmetric real Laplace wavelet

The presence of periodical impulses in vibration signals usually indicates the occurrence of rolling element bearing faults. Unfortunately, detecting the impulses of incipient faults is a difficult job because they are rather weak and often interfered by heavy noise and higher-level macro-structural vibrations. Therefore, a proper signal processing method is necessary. We proposed a differential evolution (DE) optimization and antisymmetric real Laplace wavelet (ARLW) filter-based method to extract the impulsive features buried in noisy vibration signals. The wavelet used in paper is developed from the fault characteristic signal model based on the idea of sparse representation in time-frequency domain. We first filter the original vibration signal using DE-optimized ARLW filter to eliminate the interferential vibrations and suppress random noise, then, demodulate the filtered signal and calculate its envelope spectrum. The analysis results of the simulation signals and real fault bearing vibration signals showed that the proposed method can effectively extract weak fault features.     

Detection of Bearing Faults Using a Novel Adaptive Morphological Update Lifting Wavelet

The current morphological wavelet technologies utilize a fixed filter or a linear decomposition algorithm, which cannot cope with the sudden changes, such as impulses or edges in a signal effectively. This paper presents a novel signal processing scheme, adaptive morphological update lifting wavelet (AMULW), for rolling element bearing fault detection. In contrast with the widely used morphological wavelet, the filters in AMULW are no longer fixed. Instead, the AMULW adaptively uses a morphological dilation-erosion filter or an average filter as the update lifting filter to modify the approximation signal. Moreover, the nonlinear morphological filter is utilized to substitute the traditional linear filter in AMULW. The effectiveness of the proposed AMULW is evaluated using a simulated vibration signal and experimental vibration signals collected from a bearing test rig. Results show that the proposed method has a superior performance in extracting fault features of defective rolling element bearings.     

Bearing fault diagnosis based on an improved morphological filter

The extraction of repetitive impacts from vibration signals plays an essential role in bearing fault detection. Among different signal processing algorithms, morphological filter (MF) has attracted lots of attention because it could directly extract the geometric structure of the impulsive feature and only needs little computation. However, the conventional MF and some current improvements are based on the local optima of the raw signal to de-noise the noisy signal and its faulty feature extracting capability would be greatly affected by the noise. In this paper, a new improved MF algorithm is proposed to overcome such deficiency. Firstly, morphological gradient (MG) operator is selected in this paper due to its capability of picking up both positive and negative impulses. Then, based on the relationship between the defect induced impulse and a harmonic function with the resonant frequency, the harmonic waveform in a period is adopted to instruct the construction of structuring element (SE). The improved MF can obtain the fault feature from low SNR signals. The processing results of a simulation signal and two sets of experimental signals and a set of comparisons verify the effectiveness and robustness of the proposed method.     

An optimal selection method for morphological filter’s parameters and its application in bearing fault diagnosis

The Mathematical morphological filter (MMF) is widely applied in vibration signal processing for fault diagnosis. The Structure element (SE) and the cutoff frequency of filter have important impacts on the filtering effect, but there is no selection principle of these parameters for vibration signal processing in fault diagnosis. In this paper, the working mechanism of the MMF is studied, and a novel technique with filter characteristics and selection criterion of the MMF is proposed. The filter characteristics of morphological filter are described through frequency response analysis. The relationship between the SE length and the cutoff frequency of MMF is put forward, and the quantitative selection method of SE in engineering is proposed to effectively remove the noise and detect the impulses. The method is evaluated using both simulated signal and experimental bearing vibration signal. The results show that quantized selection method can make MMF have the better filtering effect, and can reliably extract impulsive features for bearing defect diagnosis. The study provides a theoretical basis for the application of MMF in vibration signal processing.     

Faulty bearing signal recovery from large noise using a hybrid method based on spectral kurtosis and ensemble empirical mode decomposition

Time–frequency analyses are commonly used to diagnose the health of bearings by processing vibration signals captured from the bearings. However, these analyses cannot be guaranteed to be robust if the bearing signals are overwhelmed by large noise. Ensemble empirical mode decomposition (EEMD) was developed from the popular empirical mode decomposition (EMD). However, if there is large noise, it may be difficult to recover impulses from large noise. In this paper, we develop a hybrid signal processing method that combines spectral kurtosis (SK) with EEMD. First, the raw vibration signal is filtered using an optimal band-pass filter based on SK. EEMD method is then applied to decompose the filtered signal. Various bearing signals are used to validate the efficiency of the proposed method. The results demonstrate that the hybrid signal processing method can successfully recover the impulses generated by bearing faults from the raw signal, even when overwhelmed by large noise.     

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.     

Construction of customized redundant multiwavelet via increasing multiplicity for fault detection of rotating machinery

Fault detection from the vibration measurement data of rotating machinery is significant for avoiding serious accidents. However, non-stationary vibration signal with a large amount of noise makes this task challenging. Multiwavelet not only owns the advantage on multi-resolution analysis but also can offer multiple wavelet basis functions. So it has the possibility of detecting various fault features preferably. However, the fixed basis functions which are not related to the given signal may lower the accuracy of fault detection. Moreover, another major intrinsic deficiency of multiwavelet lies in its critically sampled filter-bank, which causes shift-variance and is harmful to extract the feature of periodical impulses. To overcome these deficiencies, a new method called customized redundant multiwavelet (CRM) is constructed via increasing multiplicity (IM). IM is a simple method to design a series of changeable multiwavelet which are available for the subsequent optimization process. By the rule of the envelope spectrum entropy minimum principle, optimal multiwavelet is searched for. Based on the customized multiwavelet filters, the filters of CRM can be calculated by inserting zeros. The proposed method is applied to analyze the simulation, gearbox and rolling element bearing vibration signals. Compared with some other conventional methods, the results demonstrate that the proposed method possesses robust performance in detecting fault features of rotating machinery.     

非凸罚正则化稀疏低秩矩阵的大型减速机圆锥滚子轴承微弱故障诊断

在强烈外界噪声下或轴承故障早期发展阶段,从轴承非平稳故障信号中提取微弱冲击成分是一个难点,针对这一问题,提出了一种新的基于非凸罚正则化稀疏低秩矩阵（Non-convex penalty regularization sparse low-rank matrix,NPRSLM）的轴承微弱故障特征提取方法。该方法不依赖振动信号结构的先验知识,也无需采集大量的样本信号来训练字典,避免了传统稀疏表示设计冗余字典带来的缺乏物理意义,通用性差等缺陷。该方法的核心思想是把采集的振动信号与待提取的故障脉冲看作一维矩阵（向量）,通过求解稀疏正则化的反问题得到故障脉冲信号。在建模上,通过引入非凸罚函数代替了传统最小化L1-norm融合套索算法,建立非凸罚正则化稀疏低秩矩阵模型,理论推导了所建立模型的严格凸性,并利用交替方向乘子法（Alternating direction method of multipliers,ADMM）对模型进行求解,同时讨论了模型参数对模型算法的收敛性问题、凸性与非凸性边界取值问题等。仿真算例与大型减速机圆锥滚子轴承诊断实例表明：该方法不仅能提取隐藏在强烈外界噪声中的微弱冲击特征,而且改善了传统最小化L1-norm融合套索算法在提取微弱故障冲击时产生的脉冲能量大幅衰减与脉冲数目丢失问题。     

基于粒子群优化的形态学滤波器消噪方法

为了有效地消除信号的噪声,提出了基于粒子群优化的数学形态滤波器构造方法。首先,根据数学形态学算法的特性构造了形态学滤波器;然后,对于形态学滤波运算中的重要参数形态结构算子,采用具有全局优化性能的粒子群算法自适应选取,以最大信噪比作为整个优化过程的判定标准,从而实现了最优滤波器的构造;最后,通过仿真实验和轴承故障信号的分析表明,该形态学滤波器能够实现较好的滤波效果,可以有效地对机械设备的故障信号进行消噪。     

A weighted multi-scale morphological gradient filter for rolling element bearing fault detection

This paper presents a novel signal processing scheme, named the weighted multi-scale morphological gradient filter (WMMG), for rolling element bearing fault detection. The WMMG can depress the noise at large scale and preserve the impulsive shape details at small scale. Both a simulated signal and vibration signals from a bearing test rig are employed to evaluate the performance of the proposed technique. The traditional envelope analysis and a multi-scale enveloping spectrogram algorithm combining continuous wavelet transform and envelope analysis (WT-EA) are also studied and compared with the presented WMMG. Experimental results have demonstrated the effectiveness of the WMMG to extract the impulsive components from the raw vibration signal with strong background noise. We also investigated the classification performance on identifying bearing faults based on the WMMG and statistical parameters with varied noise levels. Application results reveal that the WMMG achieves the same or better performance as EA and WT-EA. Meanwhile, the WMMG requires low computation cost and is very suitable for on-line condition monitoring of bearing operating states.     

Early fault detection method for rolling bearing based on multiscale morphological filtering of information-entropy threshold

The scale of structure element is especially important to obtain good filtering results in multiscale morphological filtering (MMF) method. In general, the optimal scale of structure element is set to be a fixed value in traditional morphological filter, therefore it is difficult to extract the fault feature from rolling bearing vibration signal effectively. A novel multiscale morphological filtering algorithm is proposed based on information-entropy threshold (IET-MMF) for early fault detection of rolling bearing. Compared with traditional MMF method, several optimal scales of structure elements are achieved according to the energy distribution characteristic of different vibration signals. The information entropy theory is applied to quantify the analyzed signals, and the optimal threshold of information entropy is obtained by iterative algorithm to ensure integrity of useful information. The simulation and rolling bearing experimental analysis results show that the IET-MMF method can extract fault features of vibration signals effectively.

     

基于形态滤波和Laplace小波的轴承故障诊断

针对强噪声背景下,轴承故障冲击响应的提取易被周围噪声干扰的问题,提出了一种基于数学形态学滤波和Laplace小波的包络谱分析方法。首先通过形态学滤波来滤除信号中的复杂噪声,增强信号的冲击特征,然后采用Laplace小波相关滤波法提取信号的冲击响应,最后对提取的冲击相关系数进行包络谱分析,即可诊断出故障。该方法结合了数学形态滤波和Laplace小波两者的优点,可以准确地捕捉到强噪声下的故障脉冲。将该方法应用于轴承内圈、外圈的故障诊断,与传统包络谱分析方法的对比结果很好地验证了所提方法的有效性。     

参数优化的组合形态-hat变换及其在风力发电机组故障诊断中的应用

开闭-闭开组合形态滤波(Combination morphological filter,CMF)可以有效剔除振动信号中的脉冲干扰,顶帽(Top-hat,TH)变换充分反映出信号周期性的冲击特征,借鉴此两种形态算子的理论思想,提出一种新的数学形态算子——组合形态-hat变换。为准确描述形态学算子在振动检测应用中的理论依据,通过非线性滤波器频响特性的分析方法考察形态学算子的滤波性质。此外,针对数学形态算子中结构元素的尺度按经验选择的问题,采用粒子群优化算法(Particle swarm optimization,PSO)对组合形态-hat变换的结构元素尺度进行参数优化,提高数学形态算子在振动信号处理中的精确度。通过仿真信号和实测风力发电机组振动信号的分析结果表明,参数优化的组合形态-hat变换在抑制背景噪声和提取冲击特征方面具备优良的性能,并能够准确高效地识别出风力发电机组齿轮箱高速轴齿轮的磨损故障,具有一定的实际工程应用价值。     

GEARBOX FAULT DIAGNOSIS USING ADAPTIVE WAVELET FILTER

Vibration signals from a gearbox are usually noisy. As a result, it is difficult to find early symptoms of a potential failure in a gearbox. Wavelet transform is a powerful tool to disclose transient information in signals. An adaptive wavelet filter based on Morlet wavelet is introduced in this paper. The parameters in the Morlet wavelet function are optimised based on the kurtosis maximisation principle. The wavelet used is adaptive because the parameters are not fixed. The adaptive wavelet filter is found to be very effective in detection of symptoms from vibration signals of a gearbox with early fatigue tooth crack. Two types of discrete wavelet transform (DWT), the decimated with DB4 wavelet and the undecimated with harmonic wavelet, are also used to analyse the same signals for comparison. No periodic impulses appear on any scale in either DWT decomposition.     

NEW METHOD OF EXTRACTING WEAK FAILURE INFORMATION IN GEARBOX BY COMPLEX WAVELET DENOISING

Because the extract of the weak failure information is always the difficulty and focus of fault detection. Aiming for specific statistical properties of complex wavelet coefficients of gearbox vibration signals, a new signal-denoising method which uses local adaptive algorithm based on dual-tree complex wavelet transform （DT-CWT） is introduced to extract weak failure information in gear, especially to extract impulse components. By taking into account the non-Gaussian probability distribution and the statistical dependencies among wavelet coefficients of some signals, and by taking the advantage of near shift-invariance of DT-CWT, the higher signal-to-noise ratio （SNR） than common wavelet denoising methods can be obtained. Experiments of extracting periodic impulses in gearbox vibration signals indicate that the method can extract incipient fault feature and hidden information from heavy noise, and it has an excellent effect on identifying weak feature signals in gearbox vibration signals.     

Quantitative diagnosis for bearing faults by improving ensemble empirical mode decomposition

In the bearing health assessment issues, using the adaptive nonstationary vibration signal processing methods in the time-frequency domain, lead to improving of early fault detection. On the other hand, the noise and random impulses which contaminates the input data, are a major challenge in extracting fault-related features. The main goal of this paper is to improve the Ensemble Empirical mode decomposition (EEMD) algorithm and combine it with a new proposed denoising process and the higher order spectra to increase the accuracy and speed of the fault severity and type detection. The main approach is to use statistical features without using any dimension reduction and data training. To eliminate unrelated components from faulty condition, the best combination of denoising parameters based on the wavelet transform, is determined by a proposed performance index. In order to enhance the efficiency of the EEMD algorithm, a systematic method is presented to determine the proper amplitude of the additive noise and the Intrinsic Mode Functions (IMFs) selection scheme. The fault occurrence detection and the fault severity level identification are performed by the Fault Severity Index (FSI) definition based on the energy level of the Combined Fault-Sensitive IMF (CFSIMF) envelope using the central limit theorem. Also, taking the advantages of a bispectrum analysis of CFSIMF envelope, fault type recognition can be achieved by Fault Type Index (FTI) quantification. Finally, the proposed method is validated using experimental data set from two different test rigs. Also, the role of the optimum denoising process and the algorithm of systematic selection of the EEMD parameters are described regardless of its type and estimating the consistent degradation pattern.     

Maximum kurtosis principle for the parameter selection of Gabor wavelet and its application to ultrasonic signal processing

The noise suppression techniques with wavelet transform (WT) are widely used in nondestructive testing and evaluation (NDT&E), especially in ultrasonics. But the wavelet based filter has the property of equal Q-factor, so, it is impossible to choose the central frequency and the bandwidth arbitrarily at the same time. This paper develops a new technique using WT to eliminate this drawback. In this paper, a weak ultrasonic signals identification method by using the optimal parameter Gabor wavelet transform is proposed. We address the choice of the optimal central frequency and bandwidth of the Gabor wavelet using the kurtosis maximization algorithm. The central frequency and bandwidth of the optimal parameter Gabor wavelet matched that of the ultrasonic signal very well. Numerical and experimental results have been presented to evaluate the effectiveness of the optimal parameter Gabor wavelet transform on ultrasonic flaw detection. This technique is a simpler and effective technique for processing heavy noised ultrasonic signals.     

基于小波变换的机器人腕力传感器滤波算法

在对机器人腕力传感器信号特点分析基础上，提出了应用小波变换对腕力传感器信号进行滤波的方法，讨论了小波滤波算法，研究了机器人腕力传感器信号滤波方案，并针对抛光机器人作业实验数据进行滤波。仿真实验表明方法有效。     

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.     

小波变换的流体压力信号自适应滤波方法研究

为了有效地消除流体压力信号中的噪声,提出了一种基于小波变换的自适应滤波算法,该算法针对信号和噪声经小波变换后在不同尺度上的特征不同,先对信号进行小波多尺度分解,然后对各尺度分解的信号分别选用不同的滤波参数,进行自适应滤波处理,并用该方法对液压系统运行中采集的压力信号进行降噪处理.试验结果表明,该方法比普通的自适应滤波方法能更有效地消除流体压力信号中的噪声.