Improved Adaptive Multipoint Optimal Minimum Entropy Deconvolution and Application on Bearing Fault Detection in Random Impulsive Noise Environments

Random impulsive noise is a special kind of noise, which has strong impact features and random disturbances with large amplitude, short duration, and long intervals. This type of noise often displays nonGaussianity, while common background noise obeys Gaussian distribution. Hence, random impulsive noise greatly differs from common background noise, which renders many commonly used approaches in bearing fault diagnosis inapplicable. In this work, we explore the challenge of bearing fault detection in the presence of random impulsive noise. To deal with this issue, an improved adaptive multipoint optimal minimum entropy deconvolution (IAMOMED) is introduced. In this IAMOMED, an envelope autocorrelation function is used to automatically estimate the cyclic impulse period instead of setting an approximate period range. Moreover, the target vector in the original MOMED is rearranged to enhance its practical applicability. Finally, particle swarm optimization is employed to determine the optimal filter length for selection purposes. According to these improvements, IAMOMED is more suitable for detecting bearing fault features in the case of random impulsive noise when compared to the original MOMED. The contrast experiments demonstrate that the proposed IAMOMED technique is capable of effectively identifying fault characteristics from the vibration signal with strong random impulsive noise and, in addition, it can accurately diagnose the fault types. Thus, the proposed method provides an alternative fault detection tool for rotating machinery in the presence of random impulsive noise.

Fault Diagnosis for Abnormal Wear of Rolling Element Bearing Fusing Oil Debris Monitoring

The abnormal wear of a rolling element bearing caused by early failures, such as pitting and spalling, will deteriorate the running state and reduce the life. This paper demonstrates the importance of oil debris monitoring and its effective feature extraction for bearing health assessment. In this paper, a rolling bearing-rotor test rig with forced lubrication is set up and the nonferrous contaminants with higher hardness were introduced artificially to accelerate the occurrence of pitting and spalling. The early failure and abnormal wear of rolling bearings cannot be effectively detected only through the vibration signal; the temperature and oil debris monitoring data are also collected synchronously. Two features regarding the ferrous particle size distribution are extracted and fused with vibration based-features to form a feature set. The sensitive features are extracted from the features set using the Neighborhood Component Analysis method to avoid feature redundancy. Finally, the importance of the oil debris based-features for the diagnosis of abnormal bearing wear is analyzed with different machine learning algorithms. Taking SVM classifier as an example, the experiment results show that the introduction of oil debris based-features increases the diagnostic accuracy by 15.7%.

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.

Feature Extraction Using Sparse Kernel Non-Negative Matrix Factorization for Rolling Element Bearing Diagnosis

For early fault detection of a bearing, the localized defect generally brings a complex vibration signal, so it is difficult to detect the periodic transient characteristics from the signal spectrum using conventional bearing fault diagnosis methods. Therefore, many matrix analysis technologies, such as singular value decomposition (SVD) and reweighted SVD (RSVD), were proposed recently to solve this problem. However, such technologies also face failure in bearing fault detection due to the poor interpretability of the obtained eigenvector. Non-negative Matrix Factorization (NMF), as a part-based representation algorithm, can extract low-rank basis spaces with natural sparsity from the time–frequency representation. It performs excellent interpretability of the factor matrices due to its non-negative constraints. By this virtue, NMF can extract the fault feature by separating the frequency bands of resonance regions from the amplitude spectrogram automatically. In this paper, a new feature extraction method based on sparse kernel NMF (KNMF) was proposed to extract the fault features from the amplitude spectrogram in greater depth. By decomposing the amplitude spectrogram using the kernel-based NMF model with L1 regularization, sparser spectral bases can be obtained. Using KNMF with the linear kernel function, the time–frequency distribution of the vibration signal can be decomposed into a subspace with different frequency bands. Thus, we can extract the fault features, a series of periodic impulses, from the decomposed subspace according to the sparse frequency bands in the spectral bases. As a result, the proposed method shows a very high performance in extracting fault features, which is verified by experimental investigations and benchmarked by the Fast Kurtogram, SVD and NMF-based methods.

A Novel Fault Detection Method for Rolling Bearings Based on Non-Stationary Vibration Signature Analysis

To realize the accurate fault detection of rolling element bearings, a novel fault detection method based on non-stationary vibration signal analysis using weighted average ensemble empirical mode decomposition (WAEEMD) and modulation signal bispectrum (MSB) is proposed in this paper. Bispectrum is a third-order statistic, which can not only effectively suppress Gaussian noise, but also help identify phase coupling. However, it cannot effectively decompose the modulation components which are inherent in vibration signals. To alleviate this issue, MSB based on the modulation characteristics of the signals is developed for demodulation and noise reduction. Still, the direct application of MSB has some interfering frequency components when extracting fault features from non-stationary signals. Ensemble empirical mode decomposition (EEMD) is an advanced nonlinear and non-stationary signal processing approach that can decompose the signal into a list of stationary intrinsic mode functions (IMFs). The proposed method takes advantage of WAEEMD and MSB for bearing fault diagnosis based on vibration signature analysis. Firstly, the vibration signal is decomposed into IMFs with a different frequency band using EEMD. Then, the IMFs are reconstructed into a new signal by the weighted average method, called WAEEMD, based on Teager energy kurtosis (TEK). Finally, MSB is applied to decompose the modulated components in the reconstructed signal and extract the fault characteristic frequencies for fault detection. Furthermore, the efficiency and performance of the proposed WAEEMD-MSB approach is demonstrated on the fault diagnosis for a motor bearing outer race fault and a gearbox bearing inner race fault. The experimental results verify that the WAEEMD-MSB has superior performance over conventional MSB and EEMD-MSB in extracting fault features and has precise and effective advantages for rolling element bearing fault detection.

Bearing Fault Diagnosis Based on a Hybrid Classifier Ensemble Approach and the Improved Dempster-Shafer Theory

Bearing fault diagnosis of a rotating machine plays an important role in reliable operation. A novel intelligent fault diagnosis method for roller bearings has been developed based on a proposed hybrid classifier ensemble approach and the improved Dempster-Shafer theory. The improved Dempster-Shafer theory well considered the combination of unreliable evidence sources, the uncertainty information of basic probability assignment, and the relative credibility of the evidence on the weights in the process of decision making under the framework of fuzzy preference relations, which can effectively deal with conflicts of the evidences and then well improve the diagnostic accuracy for the hybrid classifier ensemble. The effectiveness of the improved Dempster-Shafer theory has been verified via a numerical example. In addition, deep neural networks, a support vector machine, and extreme learning machine techniques have been utilized in the single-stage classification based on singular spectrum entropy, power spectrum entropy, time-frequency entropy, and wavelet packet energy spectrum entropy in this work. Performances of the proposed hybrid ensemble classifier has been demonstrated on a bearing test-rig, compared with the original Dempster-Shafer theory. It can be found that the overall error rate can be greatly reduced with the hybrid ensemble classifier and the improved Dempster-Shafer theory.

Research on rolling bearing fault diagnosis based on multi-dimensional feature extraction and evidence fusion theory

Rolling bearing failure is the main cause of failure of rotating machinery, and leads to huge economic losses. The demand of the technique on rolling bearing fault diagnosis in industrial applications is increasing. With the development of artificial intelligence, the procedure of rolling bearing fault diagnosis is more and more treated as a procedure of pattern recognition, and its effectiveness and reliability mainly depend on the selection of dominant characteristic vector of the fault features. In this paper, a novel diagnostic framework for rolling bearing faults based on multi-dimensional feature extraction and evidence fusion theory is proposed to fulfil the requirements for effective assessment of different fault types and severities with real-time computational performance. Firstly, a multi-dimensional feature extraction strategy on the basis of entropy characteristics, Holder coefficient characteristics and improved generalized box-counting dimension characteristics is executed for extracting health status feature vectors from vibration signals. And, secondly, a grey relation algorithm is used to calculate the basic belief assignments (BBAs) using the extracted feature vectors, and lastly, the BBAs are fused through the Yager algorithm for achieving bearing fault pattern recognition. The related experimental study has illustrated the proposed method can effectively and efficiently recognize various fault types and severities in comparison with the existing intelligent diagnostic methods based on a small number of training samples with good real-time performance, and may be used for online assessment.

Fault Diagnosis of Rolling Element Bearings with a Two-Step Scheme Based on Permutation Entropy and Random Forests

This study presents a two-step fault diagnosis scheme combined with statistical classification and random forests-based classification for rolling element bearings. Considering the inequality of features sensitivity in different diagnosis steps, the proposed method utilizes permutation entropy and variational mode decomposition to depict vibration signals under single scale and multiscale. In the first step, the permutation entropy features on the single scale of original signals are extracted and the statistical classification model based on Chebyshev’s inequality is constructed to detect the faults with a preliminary acquaintance of the bearing condition. In the second step, vibration signals with fault conditions are firstly decomposed into a collection of intrinsic mode functions by using variational mode decomposition and then multiscale permutation entropy features derived from each mono-component are extracted to identify the specific fault types. In order to improve the classification ability of the characteristic data, the out-of-bag estimation of random forests is firstly employed to reelect and refine the original multiscale permutation entropy features. Then the refined features are considered as the input data to train the random forests-based classification model. Finally, the condition data of bearings with different fault conditions are employed to evaluate the performance of the proposed method. The results indicate that the proposed method can effectively identify the working conditions and fault types of rolling element bearings.

Rolling Element Bearing Fault Diagnosis by Combining Adaptive Local Iterative Filtering, Modified Fuzzy Entropy and Support Vector Machine

A new fault feature extraction method for rolling element bearing is put forward in this paper based on the adaptive local iterative filtering (ALIF) algorithm and the modified fuzzy entropy. Due to the bearing vibration signals' non-stationary and nonlinear characteristics, the ALIF method, which is a new approach for the analysis of the non-stationary signals, is used to decompose the original vibration signals into a series of mode components. Fuzzy entropy (FuzzyEn) is a nonlinear dynamic parameter for measuring the signals' complexity. However, it only emphasizes the signals' local characteristics while neglecting its global fluctuation. Considering the global fluctuation of bearing vibration signals will change with the bearing working condition varying, we modified the FuzzyEn. The modified FuzzyEn (MFuzzyEn) of the first few modes obtained by the ALIF is utilized to form the fault feature vectors. Subsequently, the corresponding feature vectors are input into the multi-class SVM classifier to accomplish the bearing fault identification automatically. The experimental analysis demonstrates that the presented ALIF-MFuzzyEn-SVM approach can effectively recognize the different fault categories and different levels of bearing fault severity.

A Reliable Health Indicator for Fault Prognosis of Bearings

Estimation of the remaining useful life (RUL) of bearings is important to avoid abrupt shutdowns in rotary machines. An important task in RUL estimation is the construction of a suitable health indicator (HI) to infer the bearing condition. Conventional health indicators rely on features of the vibration acceleration signal and are predominantly calculated without considering its non-stationary nature. This often results in an HI with a trend that is difficult to model, as well as random fluctuations and poor correlation with bearing degradation. Therefore, this paper presents a method for constructing a bearing’s HI by considering the non-stationarity of the vibration acceleration signals. The proposed method employs the discrete wavelet packet transform (DWPT) to decompose the raw signal into different sub-bands. The HI is extracted from each sub-band signal, smoothened using locally weighted regression, and evaluated using a gradient-based method. The HIs showing the best trends among all the sub-bands are iteratively accumulated to construct an HI with the best trend over the entire life of the bearing. The proposed method is tested on two benchmark bearing datasets. The results show that the proposed method yields an HI that correlates well with bearing degradation and is relatively easy to model.

A Semi-Supervised Approach to Bearing Fault Diagnosis under Variable Conditions towards Imbalanced Unlabeled Data

Fault diagnosis of rolling element bearings is an effective technology to ensure the steadiness of rotating machineries. Most of the existing fault diagnosis algorithms are supervised methods and generally require sufficient labeled data for training. However, the acquisition of labeled samples is often laborious and costly in practice, whereas there are abundant unlabeled samples which also imply health information of bearings. Thus, it is worthwhile to develop semi-supervised methods of fault diagnosis to make effective use of the plentiful unlabeled samples. Nevertheless, considering the normal data are much more than the faulty ones, the problem of imbalanced data exists among unlabeled samples for fault diagnosis. Besides, in practice, bearings often work under uncertain and variable operation conditions, which would also have negative influence on fault diagnosis. To solve these issues, a novel hybrid method for bearing fault diagnosis is proposed in this paper: (1) Inspired by visibility graph, a novel fault feature extraction method named visibility graph feature (VGF) is proposed. The obtained features by VGF are natively insensitive to variable conditions, which has been validated by a simulation experiment in this paper; (2) On basis of VGF, to deal with imbalanced unlabeled data, graph-based rebalance semi-supervised learning (GRSSL) for fault diagnosis is proposed. In GRSSL, a graph based on a weighted sparse adjacency matrix is constructed by the k-nearest neighbors and Gaussian Kernel weighting algorithm by means of the samples. Then, a bivariate cost function over classification and normalized label variable is built up to rebalance the importance of labels. Finally, the proposed VGF-GRSSL method was verified by data collected from Case Western Reserve University Bearing Data Center. The experiment results show that the proposed method of bearing fault diagnosis performs effectively to deal with the imbalanced unlabeled data under variable conditions.

Multiband Envelope Spectra Extraction for Fault Diagnosis of Rolling Element Bearings

Bearing fault features are presented as repetitive transient impulses in vibration signals. Narrowband demodulation methods have been widely used to extract the repetitive transients in bearing fault diagnosis, for which the key factor is to accurately locate the optimal band. A multitude of criteria have been constructed to determine the optimal frequency band for demodulation. However, these criteria can only describe the strength of transient impulses, and cannot differentiate fault-related impulses and interference impulses that are cyclically generated in the signals. Additionally, these criteria are easily affected by the independent transitions and background noise in industrial locales. Therefore, the large values of the criteria may not appear in the optimal frequency band. To overcome these problems, a new method, referred to as multiband envelope spectra extraction (MESE), is proposed in this paper, which can extract all repetitive transient features in the signals. The novelty of MESE lies in the following aspects: (1) it can fuse envelope spectra at multiple narrow bands. The potential bands are selected based on Jarque-Bera statistics of narrowband envelope spectra; and (2) fast independent component analysis (fastICA) is introduced to extract the independent source spectra, which are fault- or interference-related. The multi-band strategy will preserve all impulse features and make the method more robust. Meanwhile, as a blind source separation technique, the fastICA can suppress some in-band noise and make the diagnosis more accurate. Several simulated and experimental signals are used to validate the efficiency of the proposed method. The results show that MESE is effective for enhanced fault diagnosis of rolling element bearings. Bearing faults can be detected even in a harsh environment.

Early Fault Diagnosis of Bearings Using an Improved Spectral Kurtosis by Maximum Correlated Kurtosis Deconvolution

The early fault characteristics of rolling element bearings carried by vibration signals are quite weak because the signals are generally masked by heavy background noise. To extract the weak fault characteristics of bearings from the signals, an improved spectral kurtosis (SK) method is proposed based on maximum correlated kurtosis deconvolution (MCKD). The proposed method combines the ability of MCKD in indicating the periodic fault transients and the ability of SK in locating these transients in the frequency domain. A simulation signal overwhelmed by heavy noise is used to demonstrate the effectiveness of the proposed method. The results show that MCKD is beneficial to clarify the periodic impulse components of the bearing signals, and the method is able to detect the resonant frequency band of the signal and extract its fault characteristic frequency. Through analyzing actual vibration signals collected from wind turbines and hot strip rolling mills, we confirm that by using the proposed method, it is possible to extract fault characteristics and diagnose early faults of rolling element bearings. Based on the comparisons with the SK method, it is verified that the proposed method is more suitable to diagnose early faults of rolling element bearings.