Intelligent Fault Diagnosis Method of Rolling Bearings Based on Transfer Residual Swin Transformer with Shifted Windows

Due to their robust learning and expression ability for complex features,the deep learning(DL)model plays a vital role in bearing fault diagnosis.However,since there are fewer labeled samples in fault diagnosis,the depth of DL models in fault diagnosis is generally shallower than that of DL models in other fields,which limits the diagnostic performance.To solve this problem,a novel transfer residual Swin Transformer(RST)is proposed for rolling bearings in this paper.RST has 24 residual self-attention layers,which use the hierarchical design and the shifted window-based residual self-attention.Combined with transfer learning techniques,the transfer RST model uses pre-trained parameters from ImageNet.A new end-to-end method for fault diagnosis based on deep transfer RST is proposed.Firstly,wavelet transform transforms the vibration signal into a wavelet time-frequency diagram.The signal’s time-frequency domain representation can be represented simultaneously.Secondly,the wavelet time-frequency diagram is the input of the RST model to obtain the fault type.Finally,our method is verified on public and self-built datasets.Experimental results show the superior performance of our method by comparing it with a shallow neural network.

Predicting Reliability and Remaining Useful Life of Rolling Bearings Based on Optimized Neural Networks

In this study,an optimized long short-term memory(LSTM)network is proposed to predict the reliability and remaining useful life(RUL)of rolling bearings based on an improved whale-optimized algorithm(IWOA).The multi-domain features are extracted to construct the feature dataset because the single-domain features are difficult to characterize the performance degeneration of the rolling bearing.To provide covariates for reliability assessment,a kernel principal component analysis is used to reduce the dimensionality of the features.A Weibull distribution proportional hazard model(WPHM)is used for the reliability assessment of rolling bearing,and a beluga whale optimization(BWO)algorithm is combined with maximum likelihood estimation(MLE)to improve the estimation accuracy of the model parameters of the WPHM,which provides the data basis for predicting reliability.Considering the possible gradient explosion by training the rolling bearing lifetime data and the difficulties in selecting the key network parameters,an optimized LSTM network called the improved whale optimization algorithm-based long short-term memory(IWOA-LSTM)network is proposed.As IWOA better jumps out of the local optimization,the fitting and prediction accuracies of the network are correspondingly improved.The experimental results show that compared with the whale optimization algorithm-based long short-term memory(WOA-LSTM)network,the reliability prediction and RUL prediction accuracies of the rolling bearing are improved by the proposed IWOA-LSTM network.

Deep Residual Joint Transfer Strategy for Cross-Condition Fault Diagnosis of Rolling Bearings

Rolling bearings are key components of the drivetrain in wind turbines,and their health is critical to wind turbine operation.In practical diagnosis tasks,the vibration signal is usually interspersed with many disturbing components,and the variation of operating conditions leads to unbalanced data distribution among different conditions.Although intelligent diagnosis methods based on deep learning have been intensively studied,it is still challenging to diagnose rolling bearing faults with small amounts of samples.To address the above issue,we introduce the deep residual joint transfer strategy method for the cross-condition fault diagnosis of rolling bearings.One-dimensional vibration signals are pre-processed by overlapping feature extraction techniques to fully extract fault characteristics.The deep residual network is trained in training tasks with sufficient samples,for fault pattern classification.Subsequently,three transfer strategies are used to explore the generalizability and adaptability of the pre-trained models to the data distribution in target tasks.Among them,the feature transferability between different tasks is explored by model transfer,and it is validated that minimizing data differences of tasks through a dual-stream adaptation structure helps to enhance generalization of the models to the target tasks.In the experiments of rolling bearing faults with unbalanced data conditions,localized faults of motor bearings and planet bearings are successfully identified,and good fault classification results are achieved,which provide guidance for the cross-condition fault diagnosis of rolling bearings with small amounts of training data.

Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Quantitative Diagnosis of Fault Severity Trend of Rolling Element Bearings

The condition monitoring and fault diagnosis of rolling element bearings are particularly crucial in rotating mechanical applications in industry. A bearing fault signal contains information not only about fault condition and fault type but also the severity of the fault. This means fault severity quantitative analysis is one of most active and valid ways to realize proper maintenance decision. Aiming at the deficiency of the research in bearing single point pitting fault quantitative diagnosis, a new back-propagation neural network method based on wavelet packet decomposition coefficient entropy is proposed. The three levels of wavelet packet coefficient entropy（WPCE） is introduced as a characteristic input vector to the BPNN. Compared with the wavelet packet decomposition energy ratio input vector, WPCE shows more sensitive in distinguishing from the different fault severity degree of the measured signal. The engineering application results show that the quantitative trend fault diagnosis is realized in the different fault degree of the single point bearing pitting fault. The breakthrough attempt from quantitative to qualitative on the pattern recognition of rolling element bearings fault diagnosis is realized.

Fatigue Life Prediction of Rolling Bearings Based on Modified SWT Mean Stress Correction

The existing engineering empirical life analysis models are not capable of considering the constitutive behavior of materials under contact loads;as a consequence,these methods may not be accurate to predict fatigue lives of roll-ing bearings.In addition,the contact stress of bearing in operation is cyclically pulsating,it also means that the bear-ing undergo non-symmetrical fatigue loadings.Since the mean stress has great effects on fatigue life,in this work,a novel fatigue life prediction model based on the modified SWT mean stress correction is proposed as a basis of which to estimate the fatigue life of rolling bearings,in which,takes sensitivity of materials and mean stress into account.A compensation factor is introduced to overcome the inaccurate predictions resulted from the Smith,Watson,and Topper(SWT)model that considers the mean stress effect and sensitivity while assuming the sensitivity coefficient of all materials to be 0.5.Moreover,the validation of the model is finalized by several practical experimental data and the comparison to the conventional SWT model.The results show the better performance of the proposed model,especially in the accuracy than the existing SWT model.This research will shed light on a new direction for predicting the fatigue life of rolling bearings.

Influences on Generation of White Etching Crack Networks in Rolling Bearings

In rare cases rolling bearings fail by WEC （white etching crack） damage before reaching their calculated rating life, if so called additional loads are applied on the bearing in addition to the normal Hertzian stress （PHz）. A number of additional loads have been identified by means of tests with rolling bearings. These can be small direct currents as a result of electrostatic charge or large alternating currents from inverter-fed drives that unintentionally flow through the bearing. WEC damages can also be initiated by a pure mechanical additional load which is dependent on factors including the bearing kinematics but also on the dynamics of the drive train. The current state of knowledge on this subject is presented and taken as the basis for developing a hypothesis on the WEC damage mechanism. If load situations critical for WEC cannot be avoided, the risk of WEC can be considerably reduced by the selection of suitable materials and coatings as well as, in some cases, of suitable lubricants.

Bi-Modal Failure Mechanism of Rolling Contact Bearings

The theory of failure of rolling contact bearings is based on fluctuating high level loading and material fatigue. This theory is unimodal, considering only the solid components of the bearing, and ignoring the liquid phase, which is the lubricant. Bearing life is rather dispersed, reaching a ratio of 20 between the extreme values. Since this theory was established, several exceptional phenomena were detected that could not be explained by it, such as: 1) Pitting damage beyond the contact path;2) Detrimental effect of a minute quantity of water in the lubricant on bearing life. 25 ppm of water in the lubricant brought about shorter bearing life by over than 30%. The bimodal failure theory considers both solid and liquid bearing components. The damaging process of the lubricant evolves from its cavitation. During this process vapor filled cavities are formed in low pressure zones. When these cavities reach high pressure zones they implode exothermally. These implosions cause local high pressure pulses reaching 30,000 at accompanied by a temperature rise of about 2000 degrees K [1]. This paper includes cavitation erosion test results on stainless steel samples by vibratory and water tunnel test rigs. Various methods of lubricant dehydration are presented and evaluated. The main conclusion from this analysis is the use of water-free lubricants, for long life of RC bearings and more uniform service life thereof.

Influence of Lubrication Performance on the Service Life of Rolling Mill Bearings

In order to confirm the early failure cause of a four-row cylindrical roller bearing at the backup roll position of a six-high cold sheet mill, its lubrication behavior under harsh operating conditions is investigated. Through establishing and solving the Elastohydrodynamic Lubrication （EHL） model of the roller-inner raceway contact region, the minimum oil film thickness and the real lubrication performance are achieved. The results show the bearing failures come from the poor oil film thickness in the case of high temperature and low rotational speed, which leads to contact wear. So various approaches to improve bearing life via improving lubrication are compared. It has been proved decreasing surface roughness of both contact bodies is an effective way.

Fault Early Diagnosis of Rolling Element Bearings Combining Wavelet Filtering and Degree of Cyclostationarity Analysis

The vibration signals of rolling element bearing are produced by a combination of periodic and random processes due to the machine’s rotation cycle and interaction with the real world. The combination of such components can give rise to signals, which have periodically time-varying ensemble statistical and are best considered as cyclostationary. When the early fault occurs, the background noise is very heavy, it is difficult to disclose the latent periodic components successfully using cyclostationary analysis alone. In this paper the degree of cyclostationarity is combined with wavelet filtering for detection of rolling element bearing early faults. Using the proposed entropy minimization rule. The parameters of the wavelet filter are optimized. This method is shown to be effective in detecting rolling element bearing early fault when cyclostationary analysis by itself fails.

Ideal Failure Curve of Rolling Contact Bearings

The prevailing cumulative failure curves of Rolling Contact Bearings (RCB) have two main drawbacks: they begin at the origin and have a large dispersion. The purpose of this study is to develop an ideal failure curve and overcome the present drawbacks. The ideal failure curve of RC bearings is obtained by applying a water-free lubricant to the tested bearings. This eliminates the cavitation erosion from the Bimodal failure mechanism and the synergistic effect with the mechanical failure mode. This new concept considers the fatigue process involved in the failure mechanism and suggests decreasing the dispersion of bearing life.

RMA-CNN:A Residual Mixed Domain Attention CNN for Bearings Fault Diagnosis and Its Time-Frequency Domain Interpretability

Early fault diagnosis of bearings is crucial for ensuring safe and reliable operations.Convolutional neural networks(CNNs)have achieved significant breakthroughs in machinery fault diagnosis.However,complex and varying working conditions can lead to inter-class similarity and intra-class variability in datasets,making it more challenging for CNNs to learn discriminative features.Furthermore,CNNs are often considered“black boxes”and lack sufficient interpretability in the fault diagnosis field.To address these issues,this paper introduces a residual mixed domain attention CNN method,referred to as RMA-CNN.This method comprises multiple residual mixed domain attention modules(RMAMs),each employing one attention mechanism to emphasize meaningful features in both time and channel domains.This significantly enhances the network’s ability to learn fault-related features.Moreover,we conduct an in-depth analysis of the inherent feature learning mechanism of the attention module RMAM to improve the interpretability of CNNs in fault diagnosis applications.Experiments conducted on two datasets—a high-speed aeronautical bearing dataset and a motor bearing dataset—demonstrate that the RMA-CNN achieves remarkable results in diagnostic tasks.

Rolling Bearing Fault Diagnosis Based On Convolutional Capsule Network

Fault diagnosis technology has been widely applied and is an important part of ensuring the safe operation of mechanical equipment.In response to the problem of frequent faults in rolling bearings,this paper designs a rolling bearing fault diagnosis method based on convolutional capsule network(CCN).More specifically,the original vibration signal is converted into a two-dimensional time–frequency image using continuous wavelet transform(CWT),and the feature extraction is performed on the two-dimensional time–frequency image using the convolution layer at the front end of the network,and the extracted features are input into the capsule network.The capsule network converts the extracted features into vector neurons,and the dynamic routing algorithm is used to achieve feature transfer and output the results of fault diagnosis.Two different datasets are used to compare with other traditional deep learning models to verify the fault diagnosis capability of the method.The results show that the CCN has good diagnostic capability under different working conditions,even in the presence of noise and insufficient samples,compared to other models.This method contributes to the safe and reliable operation of mechanical equipment and is suitable for other rotating scenarios.

A fatigue life prediction method of rolling bearing under elliptical contact elastohydrodynamic lubrication

In order to more accurately predict the contact fatigue life of rolling bearing, a prediction method of fatigue life of rolling bearing is proposed based on elastohydrodynamic lubrication （EHL）, the 3-paameter Weibull distribution ad fatigue strength. First,the contact stress considering elliptical EHL is obtained by mapping film pressure onto the Hertz zone. Then,the basic strength model of rolling bearing based on the 3-parameter Weibull distribution is deduced by the series connection reliability theory. Considering the effect of the type of stress, variation of shape and fuctuation of load, the mathematical models of the 尸 -tS-TV curve of the minimum life and the characteristic life for rolling bearing are established, respectively, and thus the prediction model of fatigue life of rolling bearing based on the 3-paameter Weibull distribution and fatigue strength is further deduced. Finally, the contact fatigue life obtained by the proposed method ad the latest international standard （IS0281： 2007） about the fatigue life prediction of rolling bearing are compared with those obtained by the statistical method. Results show that the proposed prediction method is effective and its relative error is smaier than that of the latest international standard （IS0281： 2007） with reliability R 〉 0. 93.

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

Grey Relation between Nonlinear Characteristic and Dynamic Uncertainty of Rolling Bearing Friction Torque

The rolling bearing friction torque which is characterized by its uncertainty and nonlinearity affects heavily the dynamic performance of a system such as missiles, spacecrafts and radars, etc. It is difficult to use the classical statistical theory to evaluate the dynamic evaluation of the rolling bearing friction torque for the lack of prior information about both probability distribution and trends. For this reason, based on the information poor system theory and combined with the correlation dimension in chaos theory, the concepts about the mean of the dynamic fluctuant range （MDFR） and the grey relation are proposed to resolve the problem about evaluating the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque. Friction torque experiments are done for three types of the rolling bearings marked with HKTA, HKTB and HKTC separately; meantime, the correlation dimension and MDFR are calculated to describe the nonlinear characteristic and the dynamic uncertainty of the friction torque, respectively. And the experiments reveal that there is a certain grey relation between the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque, viz. MDFR will become the nonlinear increasing trend with the correlation dimension increasing. Under the condition of fewer characteristic data and the lack of prior information about both probability distribution and trends, the unitive evaluation for the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque is realized with the grey confidence level of 87.7%-96.3%.

Fault Analysis of Wind Power Rolling Bearing Based on EMD Feature Extraction

In a wind turbine,the rolling bearing is the critical component.However,it has a high failure rate.Therefore,the failure analysis and fault diagnosis of wind power rolling bearings are very important to ensure the high reliability and safety of wind power equipment.In this study,the failure form and the corresponding reason for the failure are discussed firstly.Then,the natural frequency and the characteristic frequency are analyzed.The Empirical Mode Decomposition(EMD)algorithm is used to extract the characteristics of the vibration signal of the rolling bearing.Moreover,the eigenmode function is obtained and then filtered by the kurtosis criterion.Consequently,the relationship between the actual fault frequency spectrum and the theoretical fault frequency can be obtained.Then the fault analysis is performed.To enhance the accuracy of fault diagnosis,based on the previous feature extraction and the time-frequency domain feature extraction of the data after EMD decomposition processing,four different classifiers are added to diagnose and classify the fault status of rolling bearings and compare them with four different classifiers.

Multi-view feature fusion for rolling bearing fault diagnosis using random forest and autoencoder

To improve the accuracy and robustness of rolling bearing fault diagnosis under complex conditions, a novel method based on multi-view feature fusion is proposed. Firstly, multi-view features from perspectives of the time domain, frequency domain and time-frequency domain are extracted through the Fourier transform, Hilbert transform and empirical mode decomposition (EMD).Then, the random forest model (RF) is applied to select features which are highly correlated with the bearing operating state. Subsequently, the selected features are fused via the autoencoder (AE) to further reduce the redundancy. Finally, the effectiveness of the fused features is evaluated by the support vector machine (SVM). The experimental results indicate that the proposed method based on the multi-view feature fusion can effectively reflect the difference in the state of the rolling bearing, and improve the accuracy of fault diagnosis.

An improved resampling algorithm for rolling element bearing fault diagnosis under variable rotational speeds

In order to address the issues of traditional resampling algorithms involving computational accuracy and efficiency in rolling element bearing fault diagnosis, an equal division impulse-based（EDI-based） resampling algorithm is proposed. First, the time marks of every rising edge of the rotating speed pulse and the corresponding amplitudes of faulty bearing vibration signal are determined. Then, every adjacent the rotating pulse is divided equally, and the time marks in every adjacent rotating speed pulses and the corresponding amplitudes of vibration signal are obtained by the interpolation algorithm. Finally, all the time marks and the corresponding amplitudes of vibration signal are arranged and the time marks are transformed into the angle domain to obtain the resampling signal. Speed-up and speed-down faulty bearing signals are employed to verify the validity of the proposed method, and experimental results show that the proposed method is effective for diagnosing faulty bearings. Furthermore, the traditional order tracking techniques are applied to the experimental bearing signals, and the results show that the proposed method produces higher accurate outcomes in less computation time.

Rolling element bearing instantaneous rotational frequency estimation based on EMD soft-thresholding denoising and instantaneous fault characteristic frequency

The accurate estimation of the rolling element bearing instantaneous rotational frequency(IRF) is the key capability of the order tracking method based on time-frequency analysis. The rolling element bearing IRF can be accurately estimated according to the instantaneous fault characteristic frequency(IFCF). However, in an environment with a low signal-to-noise ratio(SNR), e.g., an incipient fault or function at a low speed, the signal contains strong background noise that seriously affects the effectiveness of the aforementioned method. An algorithm of signal preprocessing based on empirical mode decomposition(EMD) and wavelet shrinkage was proposed in this work. Compared with EMD denoising by the cross-correlation coefficient and kurtosis(CCK) criterion, the method of EMD soft-thresholding(ST) denoising can ensure the integrity of the signal, improve the SNR, and highlight fault features. The effectiveness of the algorithm for rolling element bearing IRF estimation by EMD ST denoising and the IFCF was validated by both simulated and experimental bearing vibration signals at a low SNR.