Feature extraction for rolling element bearing fault diagnosis utilizing generalized S transform and two-dimensional non-negative matrix factorization

This paper presents a novel feature extraction scheme for roller bearing fault diagnosis utilizing generalized S transform and two-dimensional non-negative matrix factorization (2DNMF). The generalized S transform, which can make up the poor energy concentration of the standard S transform, is introduced to generate the time-frequency representation (TFR). Experiment results on simulated signal and vibration signals measured from rolling element bearings have revealed that the generalized S transform can obtain a more satisfactory TFR than other similar techniques. Furthermore, a new technique called two-dimensional non-negative matrix factorization (2DNMF), which can reduce the computation cost and preserve more structure information hiding in original 2D matrices compared to the NMF, is developed to extract more informative features from the time-frequency matrixes for accurate fault classification. Experimental results on bearing faults classification have demonstrated that the proposed feature extraction scheme has an advantage over other similar feature extraction approaches.     

Combine Harvester Bearing Fault-Diagnosis Method Based on SDAE-RCmvMSE

In the fault monitoring of rolling bearings, there is always loud noise, leading to poor signal stationariness. How to accurately and efficiently identify the fault type of rolling bearings is a challenge. Based on multivariate multiscale sample entropy (mvMSE), this paper introduces the refined composite mvMSE (RCmvMSE) into the fault extraction of the rolling bearing. A rolling bearing fault-diagnosis method based on stacked auto encoder and RCmvMSE (SDAE-RCmvMSE) is proposed. In the actual environment, the fault-diagnosis method use the multichannel vibration signals of the bearing as the input of stacked denoising autoencoders (SDAEs) to filter the noise of the vibration signals. The features of denoise signals are extracted by RCmvMSE and the rolling bearing operation-state diagnosis is completed with a support-vector machine (SVM) model. The results show that in the original test data, the accuracy rates of SDAE-RCmvMSE, RCmvMSE, and commonplace features of vibration signals combined with SVM (CFVS-SVM) methods are 99.5%, 100%, and 96% respectively. In the data with noise, the accuracy rates of RCmvMSE and CFVS-SVM are 97.75% and 93.08%, respectively, but the accuracy of SDAE-RCmvMSE is still 100%.     

A Bearing Fault Diagnosis Method Based on PAVME and MEDE

When rolling bearings have a local fault, the real bearing vibration signal related to the local fault is characterized by the properties of nonlinear and nonstationary. To extract the useful fault features from the collected nonlinear and nonstationary bearing vibration signals and improve diagnostic accuracy, this paper proposes a new bearing fault diagnosis method based on parameter adaptive variational mode extraction (PAVME) and multiscale envelope dispersion entropy (MEDE). Firstly, a new method hailed as parameter adaptive variational mode extraction (PAVME) is presented to process the collected original bearing vibration signal and obtain the frequency components related to bearing faults, where its two important parameters (i.e., the penalty factor and mode center-frequency) are automatically determined by whale optimization algorithm. Subsequently, based on the processed bearing vibration signal, an effective complexity evaluation approach named multiscale envelope dispersion entropy (MEDE) is calculated for conducting bearing fault feature extraction. Finally, the extracted fault features are fed into the k-nearest neighbor (KNN) to automatically identify different health conditions of rolling bearing. Case studies and contrastive analysis are performed to validate the effectiveness and superiority of the proposed method. Experimental results show that the proposed method can not only effectively extract bearing fault features, but also obtain a high identification accuracy for bearing fault patterns under single or variable speed.     

Hierarchical Amplitude-Aware Permutation Entropy-Based Fault Feature Extraction Method for Rolling Bearings

In order to detect the incipient fault of rolling bearings and to effectively identify fault characteristics, based on amplitude-aware permutation entropy (AAPE), an enhanced method named hierarchical amplitude-aware permutation entropy (HAAPE) is proposed in this paper to solve complex time series in a new dynamic change analysis. Firstly, hierarchical analysis and AAPE are combined to excavate multilevel fault information, both low-frequency and high-frequency components of the abnormal bearing vibration signal. Secondly, from the experimental analysis, it is found that HAAPE is sensitive to the early failure of rolling bearings, which makes it suitable to evaluate the performance degradation of a bearing in its run-to-failure life cycle. Finally, a fault feature selection strategy based on HAAPE is put forward to select the bearing fault characteristics after the application of the least common multiple in singular value decomposition (LCM-SVD) method to the fault vibration signal. Moreover, several other entropy-based methods are also introduced for a comparative analysis of the experimental data, and the results demonstrate that HAAPE can extract fault features more effectively and with a higher accuracy.     

Research on Remaining Useful Life Prediction Method of Rolling Bearing Based on Digital Twin

Bearing is a key part of rotating machinery. Accurate prediction of bearing life can avoid serious failures. To address the current problem of low accuracy and poor predictability of bearing life prediction, a bearing life prediction method based on digital twins is proposed. Firstly, the vibration signals of rolling bearings are collected, and the time-domain and frequency-domain features of the actual data set are extracted to construct the feature matrix. Then unsupervised classification and feature selection are carried out by improving the self-organizing feature mapping method. Using sensitive features to construct a twin dataset framework and using the integrated learning CatBoost method to supplement the missing data sets, a complete digital twin dataset is formed. Secondly, important information is extracted through macro and micro attention mechanisms to achieve weight amplification. The life prediction of rolling bearing is realized by using fusion features. Finally, the proposed method is verified by experiments. The experimental results show that this method can predict the bearing life with a limited amount of measured data, which is superior to other prediction methods and can provide a new idea for the health prediction and management of mechanical components.     

A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM

This paper proposes a novel fault diagnosis method for rolling bearing based on hierarchical refined composite multiscale fluctuation-based dispersion entropy (HRCMFDE) and particle swarm optimization-based extreme learning machine (PSO-ELM). First, HRCMFDE is used to extract fault features in the vibration signal at different time scales. By introducing the hierarchical theory algorithm into the vibration signal decomposition process, the problem of missing high-frequency signals in the coarse-grained process is solved. Fluctuation-based dispersion entropy (FDE) has the characteristics of insensitivity to noise interference and high computational efficiency based on the consideration of nonlinear time series fluctuations, which makes the extracted feature vectors more effective in describing the fault information embedded in each frequency band of the vibration signal. Then, PSO is used to optimize the input weights and hidden layer neuron thresholds of the ELM model to improve the fault identification capability of the ELM classifier. Finally, the performance of the proposed rolling bearing fault diagnosis method is verified and analyzed by using the CWRU dataset and MFPT dataset as experimental cases, respectively. The results show that the proposed method has high identification accuracy for the fault diagnosis of rolling bearings with varying loads and has a good load migration effect.     

Fault Recognition of Rolling Bearings Based on Parameter Optimized Multi-Scale Permutation Entropy and Gath-Geva

To extract fault features of rolling bearing vibration signals precisely, a fault diagnosis method based on parameter optimized multi-scale permutation entropy (MPE) and Gath-Geva (GG) clustering is proposed. The method can select the important parameters of MPE method adaptively, overcome the disadvantages of fixed MPE parameters and greatly improve the accuracy of fault identification. Firstly, aiming at the problem of parameter determination and considering the interaction among parameters comprehensively of MPE, taking skewness of MPE as fitness function, the time series length and embedding dimension were optimized respectively by particle swarm optimization (PSO) algorithm. Then the fault features of rolling bearing were extracted by parameter optimized MPE and the standard clustering centers is obtained with GG clustering. Finally, the samples are clustered with the Euclid nearness degree to obtain recognition rate. The validity of the parameter optimization is proved by calculating the partition coefficient and average fuzzy entropy. Compared with unoptimized MPE, the propose method has a higher fault recognition rate.     

Rolling Bearing Fault Diagnosis Based on VMD-MPE and PSO-SVM

The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).     

Low speed bearing fault diagnosis using acoustic emission sensors

In this paper, a new methodology for low speed bearing fault diagnosis is presented. This acoustic emission (AE) based technique starts with a heterodyne frequency reduction approach that samples AE signals at a rate comparable to vibration centered methodologies. Then, the sampled AE signal is time synchronously resampled to account for possible fluctuations in shaft speed and bearing slippage. The resampling approach is able to segment the AE signal according to shaft crossing times such that an even number of data points are available to compute a single spectral average which is used to extract features and evaluate numerous condition indicators (CIs) for bearing fault diagnosis. Unlike existing averaging based noise reduction approaches that require the computation of multiple averages for each bearing fault type, the presented approach computes only one average for all bearing fault types. The presented technique is validated using the AE signals of seeded fault steel bearings on a bearing test rig. The results in this paper have shown that the low sampled AE signals in combination with the presented approach can be utilized to effectively extract condition indicators to diagnose all four bearing fault types at multiple low shaft speeds below 10 Hz.     

Research on Fault Diagnosis of Rolling Bearings Based on Variational Mode Decomposition Improved by the Niche Genetic Algorithm

Due to the influence of signal-to-noise ratio in the early failure stage of rolling bearings in rotating machinery, it is difficult to effectively extract feature information. Variational Mode Decomposition (VMD) has been widely used to decompose vibration signals which can reflect more fault omens. In order to improve the efficiency and accuracy, a method to optimize VMD by using the Niche Genetic Algorithm (NGA) is proposed in this paper. In this method, the optimal Shannon entropy of modal components in a VMD algorithm is taken as the optimization objective, by using the NGA to constantly update and optimize the combination of influencing parameters composed of α and K so as to minimize the local minimum entropy. According to the obtained optimization results, the optimal input parameters of the VMD algorithm were set. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a rolling bearing. The decomposition process of the rolling-bearing fault signal was transferred to the variational frame by the NGA-VMD algorithm, and several eigenmode function components were obtained. The energy feature extracted from the modal component containing the main fault information was used as the input vector of a particle swarm optimized support vector machine (PSO-SVM) and used to identify the fault type of the rolling bearing. The analysis results of the simulation signal and measured signal show that: the NGA-VMD algorithm can decompose the vibration signal of a rolling bearing accurately and has a better robust performance and correct recognition rate than the VMD algorithm. It can highlight the local characteristics of the original sample data and reduce the interference of the parameters selected artificially in the VMD algorithm on the processing results, improving the fault-diagnosis efficiency of rolling bearings.     

滚动轴承声信号特征提取和诊断试验研究

为解决振动检测方法不能有效识别低速旋转机械滚动轴承故障问题,利用声发射检测方法,建立了滚动轴承低速声发射信号采集试验装置,对模拟人工缺陷滚动轴承声发射信号进行了采集,进而对滚动轴承声发射信号进行总体平均经验模式分解,结合能量矩及相关系数法综合判断分解后各模态分量的真伪,据此提取出特征信号并做出其局部Hilbert边际谱,最后对滚动轴承各种故障模式进行诊断。试验结果表明该诊断方法能准确识别滚动轴承声发射信号故障频率,依据特征频率及幅值大小可对低速滚动轴承故障进行有效诊断。     

基于粒子滤波状态估计的滚动轴承故障识别方法

提出了一种基于粒子滤波状态估计的滚动轴承故障识别方法,该方法主要包括故障模型建立和故障识别两个步骤。在故障模型建立部分,首先依据滚动轴承不同故障状态下的振动信号,建立对应的自回归模型,作为故障模型;在故障识别部分,将正常状态下对应的模型,转化为状态空间模型,设计粒子滤波器,然后对不同的故障状态进行估计,提取其残差的相关特征,并结合模型参数特征应用BP神经网络识别算法进行故障识别。最后以美国凯斯西储大学的滚动轴承振动数据为例,验证了该方法的有效性。     

Continuous-scale mathematical morphology-based optimal scale band demodulation of impulsive feature for bearing defect diagnosis

Integer-scale structuring element is usually used in the traditional mathematical morphology (MM) for signal processing. When applied for impulsive feature demodulation of vibration signal of rolling element bearings, the integer-scale MM (ISMM) may lead to low resolution result and thus undermines its defect diagnosis capability. For this reason, this paper proposes a continuous-scale MM (CSMM) scheme by interpolation and re-sampling to improve scale resolution for more reliable fault signature extraction. Based on the frequency domain kurtosis criterion, a narrowband merging operation is employed to locate the optimal scale band that best reflects the impulsive feature from the CSMM analysis results. The demodulated components in the optimal scale band are employed to detect the existence of the bearing fault. The proposed optimal CSMM demodulation technique is evaluated using both simulated and experimental bearing vibration signals. The results show that, the CSMM is capable of generating demodulation signals with higher resolution, and the optimal scale band demodulation based on the CSMM can reliably extract impulsive features for bearing defect diagnosis.     

A Rolling Bearing Fault Classification Scheme Based on k-Optimized Adaptive Local Iterative Filtering and Improved Multiscale Permutation Entropy

The health condition of the rolling bearing seriously affects the operation of the whole mechanical system. When the rolling bearing parts fail, the time series collected in the field generally shows strong nonlinearity and non-stationarity. To obtain the faulty characteristics of mechanical equipment accurately, a rolling bearing fault detection technique based on k-optimized adaptive local iterative filtering (ALIF), improved multiscale permutation entropy (improved MPE), and BP neural network was proposed. In the ALIF algorithm, a k-optimized ALIF method based on permutation entropy (PE) is presented to select the number of ALIF decomposition layers adaptively. The completely average coarse-graining method was proposed to excavate more hidden information. The performance analysis of the simulation signal shows that the improved MPE can more accurately dig out the depth information of the time series, and the entropy value obtained is more consistent and stable. In the research application, rolling bearing time series are decomposed by k-optimized ALIF to obtain a certain number of intrinsic mode functions (IMFs). Then the improved MPE value of effective IMF is calculated and input into backpropagation (BP) neural network as the feature vector for automatic fault identification. The comparative analysis of simulation signals shows that this method can extract fault information effectively. At the same time, the experimental part shows that this scheme not only effectively extracts the fault features, but also realizes the classification and identification of different fault modes and faults of different degrees, which has a certain application prospect in the research and application direction of rolling bearing fault identification.     

Reliable Fault Diagnosis of Bearings Using an Optimized Stacked Variational Denoising Auto-Encoder

Variational auto-encoders (VAE) have recently been successfully applied in the intelligent fault diagnosis of rolling bearings due to its self-learning ability and robustness. However, the hyper-parameters of VAEs depend, to a significant extent, on artificial settings, which is regarded as a common and key problem in existing deep learning models. Additionally, its anti-noise capability may face a decline when VAE is used to analyze bearing vibration data under loud environmental noise. Therefore, in order to improve the anti-noise performance of the VAE model and adaptively select its parameters, this paper proposes an optimized stacked variational denoising autoencoder (OSVDAE) for the reliable fault diagnosis of bearings. Within the proposed method, a robust network, named variational denoising auto-encoder (VDAE), is, first, designed by integrating VAE and a denoising auto-encoder (DAE). Subsequently, a stacked variational denoising auto-encoder (SVDAE) architecture is constructed to extract the robust and discriminative latent fault features via stacking VDAE networks layer on layer, wherein the important parameters of the SVDAE model are automatically determined by employing a novel meta-heuristic intelligent optimizer known as the seagull optimization algorithm (SOA). Finally, the extracted latent features are imported into a softmax classifier to obtain the results of fault recognition in rolling bearings. Experiments are conducted to validate the effectiveness of the proposed method. The results of analysis indicate that the proposed method not only can achieve a high identification accuracy for different bearing health conditions, but also outperforms some representative deep learning methods.     

Clustering diagnosis of rolling element bearing fault based on integrated Autoregressive/Autoregressive Conditional Heteroscedasticity model

Feature extraction plays an important role in the clustering analysis. In this paper an integrated Autoregressive (AR)/Autoregressive Conditional Heteroscedasticity (ARCH) model is proposed to characterize the vibration signal and the model coefficients are adopted as feature vectors to realize clustering diagnosis of rolling element bearings. The main characteristic is that the AR item and ARCH item are interrelated with each other so that it can depict the excess kurtosis and volatility clustering information in the vibration signal more accurately in comparison with two-stage AR/ARCH model. To testify the correctness, four kinds of bearing signals are adopted for parametric modeling by using the integrated and two-stage AR/ARCH model. The variance analysis of the model coefficients shows that the integrated AR/ARCH model can get more concentrated distribution. Taking these coefficients as feature vectors, K means based clustering is utilized to realize the automatic classification of bearing fault status. The results show that the proposed method can get more accurate results in comparison with two-stage model and discrete wavelet decomposition.     

Fault Diagnosis of Rolling Bearings Based on WPE by Wavelet Decomposition and ELM

The fault diagnosis classification method based on wavelet decomposition and weighted permutation entropy (WPE) by the extreme learning machine (ELM) is proposed to address the complexity and non-smoothness of rolling bearing vibration signals. The wavelet decomposition based on ‘db3’ is used to decompose the signal into four layers and extract the approximate and detailed components, respectively. Then, the WPE values of the approximate (CA) and detailed (CD) components of each layer are calculated and composed to be the feature vectors, which are finally fed into the extreme learning machine with optimal parameters for classification. The comparative study of the simulations based on WPE and permutation entropy (PE) shows that the classification method of seven kinds of signals of normal bearing signals and six types of fault states (7 mils and 14 mils) based on WPE (CA, CD) with the number of nodes in the hidden layers of ELM determined by the five-fold cross-validation has the best performances, the training accuracy can reach 100%, and the testing accuracy can reach 98.57% with 37 nodes of the hidden layer by ELM. The proposed method using WPE (CA, CD) by ELM provides guidance for the multi-classification of normal bearing signals.     

Identification of multiple transient faults based on the adaptive spectral kurtosis method

This paper proposes a multi-fault detection method based on the adaptive spectral kurtosis (ASK) analysis of the vibration signal from single sensor. A theoretical model of multiple bearing faults is established in this paper. Compared with the kurtogram and protrugram techniques, the proposed method can more effectively extract signatures of multiple bearing faults even in the presence of strong background noise. The performance of the proposed method in fault detection of the rolling element bearings is validated using simulation data and experimental signals from a bearing with multiple faults and two faulty bearings.     

小波包和GA-SVM在轴承故障诊断中的应用

为了解决傅里叶变换难以兼顾信号在时域和频域中的全貌和局部化特征以及支持向量机惩罚参数 和核函数参数 选取的问题,提出了基于小波包和GA-SVM的轴承故障诊断方法。首先通过实验采集多种工况下故障轴承和正常轴承的振动信号,从振动信号中提取能够表征轴承运行状态的时频域特征以及基于小波包分析的特征向量来作为GA-SVM的输入,然后在SVM的基础上,针对SVM的惩罚参数和核函数参数在不同应用场景下的取值难以确定的特性,采用了遗传算法对支持向量机进行参数优化的GA-SVM算法进行模式识别。实验结果显示,基于小波包和GA-SVM的轴承故障诊断方法比SVM和BP都具有更高的识别精度。     

Feature Enhancement Method of Rolling Bearing Based on K-Adaptive VMD and RBF-Fuzzy Entropy

The complex and harsh working environment of rolling bearings cause the fault characteristics in vibration signal contaminated by the noise, which make fault diagnosis difficult. In this paper, a feature enhancement method of rolling bearing signal based on variational mode decomposition with K determined adaptively (K-adaptive VMD), and radial based function fuzzy entropy (RBF-FuzzyEn), is proposed. Firstly, a phenomenon called abnormal decline of center frequency (ADCF) is defined in order to determine the parameter K of VMD adaptively. Then, the raw signal is separated into K intrinsic mode functions (IMFs). A coefficient En for selecting optimal IMFs is calculated based on the center frequency bands (CFBs) of all IMFs and frequency spectrum for original signal autocorrelation operation. After that, the optimal IMFs of which En are bigger than the threshold are selected to reconstruct signal. Secondly, RBF is introduced as an innovative fuzzy function to enhance the feature discrimination of fuzzy entropy between bearings in different states. A specific way for determination of parameter r in fuzzy function is also presented. Finally, RBF-FuzzyEn is used to extract features of reconstructed signal. Simulation and experiment results show that K-adaptive VMD can effectively reduce the noise and enhance the fault characteristics; RBF-FuzzyEn has strong feature differentiation, superior noise robustness, and low dependence on data length.