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)).     

Application of Adaptive MOMEDA with Iterative Autocorrelation to Enhance Weak Features of Hoist Bearings

Low-speed hoist bearings are characterized by fault features that are weak and difficult to extract. Multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) is an effective method for extracting periodic pulses in a signal. However, the decomposition effect of MOMEDA largely depends on the selected pulse period and filter length. To address these drawbacks of MOMEDA and accurately extract features from the vibration signal of a hoist bearing, an adaptive feature extraction method is proposed based on iterative autocorrelation (IAC) and MOMEDA. To automatically identify the pulse period, a new evaluation index named autocorrelation kurtosis entropy (AKE) was constructed to select the optimal IAC. To eliminate the influence of the filter length on the decomposition effect, an iterative MOMEDA strategy was designed to gradually enhance signal impulse features. The Case Western Reserve University bearing dataset and bearing data from a self-made hoisting test setup were used to verify the effectiveness of IAC-MOMEDA in extracting weak features. Moreover, the capability of IAC-MOMEDA for features extraction of normal bearing vibration signal was further confirmed by field test data.     

Application of Generalized Composite Multiscale Lempel–Ziv Complexity in Identifying Wind Turbine Gearbox Faults

Wind turbine gearboxes operate in harsh environments; therefore, the resulting gear vibration signal has characteristics of strong nonlinearity, is non-stationary, and has a low signal-to-noise ratio, which indicates that it is difficult to identify wind turbine gearbox faults effectively by the traditional methods. To solve this problem, this paper proposes a new fault diagnosis method for wind turbine gearboxes based on generalized composite multiscale Lempel–Ziv complexity (GCMLZC). Within the proposed method, an effective technique named multiscale morphological-hat convolution operator (MHCO) is firstly presented to remove the noise interference information of the original gear vibration signal. Then, the GCMLZC of the filtered signal was calculated to extract gear fault features. Finally, the extracted fault features were input into softmax classifier for automatically identifying different health conditions of wind turbine gearboxes. The effectiveness of the proposed method was validated by the experimental and engineering data analysis. The results of the analysis indicate that the proposed method can identify accurately different gear health conditions. Moreover, the identification accuracy of the proposed method is higher than that of traditional multiscale Lempel–Ziv complexity (MLZC) and several representative multiscale entropies (e.g., multiscale dispersion entropy (MDE), multiscale permutation entropy (MPE) and multiscale sample entropy (MSE)).     

A Novel Feature Extraction Method for Power Transformer Vibration Signal Based on CEEMDAN and Multi-Scale Dispersion Entropy

Effective diagnosis of vibration fault is of practical significance to ensure the safe and stable operation of power transformers. Aiming at the traditional problems of transformer vibration fault diagnosis, a novel feature extraction method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and multi-scale dispersion entropy (MDE) was proposed. In this paper, CEEMDAN method is used to decompose the original transformer vibration signal. Additionally, then MDE is used to capture multi-scale fault features in the decomposed intrinsic mode functions (IMFs). Next, the principal component analysis (PCA) method is employed to reduce the feature dimension and extract the effective information in vibration signals. Finally, the simplified features are sent into density peak clustering (DPC) to get the fault diagnosis results. The experimental data analysis shows that CEEMDAN-MDE can effectively extract the information of the original vibration signals and DPC can accurately diagnose the types of transformer faults. By comparing different algorithms, the practicability and superiority of this proposed method are verified.     

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.     

Intelligent Fault Identification for Rolling Bearings Fusing Average Refined Composite Multiscale Dispersion Entropy-Assisted Feature Extraction and SVM with Multi-Strategy Enhanced Swarm Optimization

Rolling bearings act as key parts in many items of mechanical equipment and any abnormality will affect the normal operation of the entire apparatus. To diagnose the faults of rolling bearings effectively, a novel fault identification method is proposed by merging variational mode decomposition (VMD), average refined composite multiscale dispersion entropy (ARCMDE) and support vector machine (SVM) optimized by multistrategy enhanced swarm optimization in this paper. Firstly, the vibration signals are decomposed into different series of intrinsic mode functions (IMFs) based on VMD with the center frequency observation method. Subsequently, the proposed ARCMDE, fusing the superiorities of DE and average refined composite multiscale procedure, is employed to enhance the ability of the multiscale fault-feature extraction from the IMFs. Afterwards, grey wolf optimization (GWO), enhanced by multistrategy including levy flight, cosine factor and polynomial mutation strategies (LCPGWO), is proposed to optimize the penalty factor C and kernel parameter g of SVM. Then, the optimized SVM model is trained to identify the fault type of samples based on features extracted by ARCMDE. Finally, the application experiment and contrastive analysis verify the effectiveness of the proposed VMD-ARCMDE-LCPGWO-SVM method.     

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.     

Bearing Fault Diagnosis Using Refined Composite Generalized Multiscale Dispersion Entropy-Based Skewness and Variance and Multiclass FCM-ANFIS

Bearing vibration signals typically have nonlinear components due to their interaction and coupling effects, friction, damping, and nonlinear stiffness. Bearing faults affect the signal complexity at various scales. Hence, measuring signal complexity at different scales is helpful to diagnosis of bearing faults. Numerous studies have investigated multiscale algorithms; nevertheless, multiscale algorithms using the first moment lose important complexity data. Accordingly, generalized multiscale algorithms have been recently introduced. The present research examined the use of refined composite generalized multiscale dispersion entropy (RCGMDispEn) based on the second moment (variance) and third moment (skewness) along with refined composite multiscale dispersion entropy (RCMDispEn) in bearing fault diagnosis. Moreover, multiclass FCM-ANFIS, which is a combination of adaptive network-based fuzzy inference systems (ANFIS), was developed to improve the efficiency of rotating machinery fault classification. According to the results, it is recommended that generalized multiscale algorithms based on variance and skewness be examined for diagnosis, along with multiscale algorithms, and be used to achieve an improvement in the results. The simultaneous usage of the multiscale algorithm and generalized multiscale algorithms improved the results in all three real datasets used in this study.     

A New Method Based on Time-Varying Filtering Intrinsic Time-Scale Decomposition and General Refined Composite Multiscale Sample Entropy for Rolling-Bearing Feature Extraction

The early fault diagnosis of rolling bearings has always been a difficult problem due to the interference of strong noise. This paper proposes a new method of early fault diagnosis for rolling bearings with entropy participation. First, a new signal decomposition method is proposed in this paper: intrinsic time-scale decomposition based on time-varying filtering. It is introduced into the framework of complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN). Compared with traditional intrinsic time-scale decomposition, intrinsic time-scale decomposition based on time-varying filtering can improve frequency-separation performance. It has strong robustness in the presence of noise interference. However, decomposition parameters (the bandwidth threshold and B-spline order) have significant impacts on the decomposition results of this method, and they need to be artificially set. Aiming to address this problem, this paper proposes rolling-bearing fault diagnosis optimization based on an improved coyote optimization algorithm (COA). First, the minimal generalized refined composite multiscale sample entropy parameter was used as the objective function. Through the improved COA algorithm, optimal intrinsic time-scale decomposition parameters based on time-varying filtering that match the input signal are obtained. By analyzing generalized refined composite multiscale sample entropy (GRCMSE), whether the mode component is dominated by the fault signal is determined. The signal is reconstructed and decomposed again. Finally, the mode component with the highest energy in the central frequency band is selected for envelope spectrum variation for fault diagnosis. Lastly, simulated and experimental signals were used to verify the effectiveness of the proposed method.     

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.     

Envelope extraction based dimension reduction for independent component analysis in fault diagnosis of rolling element bearing

A robust feature extraction scheme for the rolling element bearing (REB) fault diagnosis is proposed by combining the envelope extraction and the independent component analysis (ICA). In the present approach, the envelope extraction is not only utilized to obtain the impulsive component corresponding to the faults from the REB, but also to reduce the dimension of vibration sources included in the sensor-picked signals. Consequently, the difficulty for applying the ICA algorithm under the conditions that the sensor number is limited and the source number is unknown can be successfully eliminated. Then, the ICA algorithm is employed to separate the envelopes according to the independence of vibration sources. Finally, the vibration features related to the REB faults can be separated from disturbances and clearly exposed by the envelope spectrum. Simulations and experimental tests are conducted to validate the proposed method.     

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.     

Envelope order tracking for fault detection in rolling element bearings

An envelope order tracking analysis scheme is proposed in the paper for the fault detection of rolling element bearing (REB) under varying-speed running condition. The developed method takes the advantages of order tracking, envelope analysis and spectral kurtosis. The fast kurtogram algorithm is utilized to obtain both optimal center frequency and bandwidth of the band-pass filter based on the maximum spectral kurtosis. The envelope containing vibration features of the incipient REB fault can be extracted adaptively. The envelope is re-sampled by the even-angle sampling scheme, and thus the non-stationary signal in the time domain is represented as a quasi-stationary signal in the angular domain. As a result, the frequency-smear problem can be eliminated in order spectrum and the fault diagnosis of REB in the varying-speed running condition of the rotating machinery is achieved. Experiments are conducted to verify the validity of the proposed method.     

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。     

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.     

Infrared small target detection based on modified local entropy and EMD

Image entropy and empirical mode decomposition （EMD） are effective methods for target detection. EMD algorithm is a powerful tool for adaptive multiscale analysis of nonstationary signals. A new technique based on EMD and modified local entropy is proposed in small target detection under sea-sky background. With the EMD algorithm, it is valid to estimate the background and get the target image by removing the background from the original image and segmenting the target based on the modified local entropy method. The data analysis and experiments show the validity of the proposed algorithm.     

基于MCKD-EEMD近似熵和TWSVM的齿轮箱故障诊断

在复杂环境下齿轮箱信号往往会淹没在噪声信号中,特征向量难以提取;为了有效地进行故障诊断,提出了基于最大相关反褶积(MCKD)总体平均经验模态分解(EEMD)近似熵和双子支持向量机(TWSVM)的齿轮箱故障诊断方法;首先采用MCKD方法对强噪声信号进行滤波处理,在采用EEMD方法对齿轮箱信号进行分解,分解后得到本征模函数(IMF)分量进行近似熵求解,得到齿轮特征向量,最后将其输入到TWSVM分类器中进行故障识别;仿真实验表明,采用MCKD-EEMD方法能够有效地提取原始信号,与其他分类器相比,TWSVM的计算时间短,分类效果好等优点。     

仿生鳍条姿态测量及其误差分析

在复杂环境下齿轮箱信号往往会淹没在噪声信号中,特征向量难以提取。为了有效的进行故障诊断,提出了基于最大相关反褶积(MCKD)总体平均经验模态分解(EEMD)近似熵和双子支持向量机(TWSVM)的齿轮箱故障诊断方法。首先采用MCKD方法对强噪声信号进行滤波处理,在采用EEMD方法对齿轮箱信号进行分解,分解后得到本征模函数(IMF)分量进行近似熵求解,得到齿轮特征向量,最后将其输入到TWSVM分类器中进行故障识别。仿真实验表明,采用MCKD-EEMD方法能够有效的提取原始信号,与其他分类器相比,TWSVM的计算时间短,分类效果好等优点。     

Rolling bearing diagnosing method based on Empirical Mode Decomposition of machine vibration signal

Rolling bearing faults are one of the major reasons for breakdown of industrial machinery and bearing diagnosing is one of the most important topics in machine condition monitoring.The main problem in industrial application of bearing vibration diagnostics is the masking of informative bearing signal by machine noise. The vibration signal of the rolling bearing is often covered or concealed by other structural vibrations sources, such as gears. Although a number of vibration diagnostic techniques have been developed over the last several years, in many cases these methods are quite complicated in use or only effective at later stages of damage development. This paper presents an EMD-based rolling bearing diagnosing method that shows potential for bearing damage detection at a much earlier stage of damage development.By using EMD a raw vibration signal is decomposed into a number of Intrinsic Mode Functions (IMFs). Then, a new method of IMFs aggregation into three Combined Mode Functions (CMFs) is applied and finally the vibration signal is divided into three parts of signal: noise-only part, signal-only part and trend-only part. To further bearing fault-related feature extraction from resultant signals, the spectral analysis of the empirically determined local amplitude is used. To validate the proposed method, raw vibration signals generated by complex mechanical systems employed in the industry (driving units of belt conveyors), including normal and fault bearing vibration data, are used in two case studies. The results show that the proposed rolling bearing diagnosing method can identify bearing faults at early stages of their development.     

Matching pursuit of an adaptive impulse dictionary for bearing fault diagnosis

The sparse decomposition based on matching pursuit is an adaptive sparse expression of the signals. An adaptive matching pursuit algorithm that uses an impulse dictionary is introduced in this article for rolling bearing vibration signal processing and fault diagnosis. First, a new dictionary model is established according to the characteristics and mechanism of rolling bearing faults. The new model incorporates the rotational speed of the bearing, the dimensions of the bearing and the bearing fault status, among other parameters. The model can simulate the impulse experienced by the bearing at different bearing fault levels. A simulation experiment suggests that a new impulse dictionary used in a matching pursuit algorithm combined with a genetic algorithm has a more accurate effect on bearing fault diagnosis than using a traditional impulse dictionary. However, those two methods have some weak points, namely, poor stability, rapidity and controllability. Each key parameter in the dictionary model and its influence on the analysis results are systematically studied, and the impulse location is determined as the primary model parameter. The adaptive impulse dictionary is established by changing characteristic parameters progressively. The dictionary built by this method has a lower redundancy and a higher relevance between each dictionary atom and the analyzed vibration signal. The matching pursuit algorithm of an adaptive impulse dictionary is adopted to analyze the simulated signals. The results indicate that the characteristic fault components could be accurately extracted from the noisy simulation fault signals by this algorithm, and the result exhibited a higher efficiency in addition to an improved stability, rapidity and controllability when compared with a matching pursuit approach that was based on a genetic algorithm. We experimentally analyze the early-stage fault signals and composite fault signals of the bearing. The results further demonstrate the effectiveness and superiority of the matching pursuit algorithm that uses the adaptive impulse dictionary. Finally, this algorithm is applied to the analysis of engineering data, and good results are achieved.