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.

Measured load spectra of the bearing in high-speed train gearbox under different gear meshing conditions

The load spectrum is a crucial factor for assess-ing the fatigue reliability of in-service rolling element bear-ings in transmission systems.For a bearing in a high-speed train gearbox,a measurement technique based on strain detection of bearing outer ring was used to instrument the bearing and determine the time histories of the distributed load in the bearing under different gear meshing conditions.Accordingly,the load spectrum of the total radial load car-ried by the bearing was compiled.The mean value and class interval of the obtained load spectrum were found to vary non-monotonously with the speed and torque of gear mesh-ing,which was considered to be caused by the vibration of the shaft and the bearing cage.As the realistic service load input of bearing life assessment,the measured load spectrum under different gear meshing conditions can be used to pre-dict gearbox bearing life realistically based on the damage-equivalent principle and actual operating conditions.

Vibration-based bearing fault diagnosis of high-speed trains:A literature review

Due to the advantages of comfort and safety,high-speed trains are gradually becoming the mainstream public transport in China.Since the operating speed and mileage of high-speed trains have achieved rapid growth,it is more and more urgent to ensure their reliability and safety.As an important component in the bogies of highspeed trains,the health state of the bearing directly affects the operational safety of the trains.It is therefore necessary to diagnoze the faults of bearings in the bogies of high-speed trains as early as possible.In this paper,the bearing fault diagnostic methods for high-speed trains have been systematically summarized with their challenges and perspectives.First,it briefly introduces the structure of bearings in the bogies as well as the fault characteristic frequencies.Then,a brief review of the research on vibration-based signal processing methods and machine learning methods has been provided.Finally,the challenges and future developments of vibrationbased bearing fault diagnostic methods for high-speed trains have been analyzed.

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.

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.

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.

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%.

Frequency Loss and Recovery in Rolling Bearing Fault Detection

Rolling element bearings are key components of mechanical equipment. The bearing fault characteristics are a ected by the interaction in the vibration signals. The low harmonics of the bearing characteristic frequencies cannot be usually observed in the Fourier spectrum. The frequency loss in the bearing vibration signal is presented through two independent experiments in this paper. The existence of frequency loss phenomenon in the low frequencies, side band frequencies and resonant frequencies and revealed. It is demonstrated that the lost frequencies are actually suppressed by the internal action in the bearing fault signal rather than the external interference. The amplitude and distribution of the spectrum are changed due to the interaction of the bearing fault signal. The interaction mechanism of bearing fault signal is revealed through theoretical and practical analysis. Based on mathematical morphology, a new method is provided to recover the lost frequencies. The multi-resonant response signal of the defective bearing are decomposed into low frequency and high frequency response, and the lost frequencies are recovered by the combination morphological filter(CMF). The e ectiveness of the proposed method is validated on simulated and experimental data.

Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

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.

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.

Investigation on Skidding of Rolling Element Bearing in Loaded Zone

Skidding which occurs when rolling element entering into the loaded zone is prone to cause wear and incipient failure to the raceways and rolling elements. This paper presents a dynamic model to investigate the skidding of a rolling element bearing under radial load when the rolling element is entering into the load zone. In this dynamic model, the effects of the contact forces, friction forces on the rolling element-race and rolling element-cage interfaces, gravity, and the centrifugal forces of rolling elements are taken into consideration. The Hertzian contact theory is applied to calculate the non-linear contact forces. The Coulomb friction law is used to calculate the friction forces. The differential equations of rotational motion of the rolling element with regard to its central axis and the central axis of the outer ring are established respectively. The dynamic equations are then solved by using a fourth-order Runge-Kutta algorithm. The skidding characteristics of rolling element at the entry into the loaded zone are exposed, and the effects of the operating parameters on skidding behavior are carefully investigated.

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.

Bending stress of rolling element in elastic composite cylindrical roller bearing

A new structure design method of elastic composite cylindrical roller bearing is proposed, in which PTFE is embedded into a hollow cylindrical rolling element, according to the principle of creative combinations and through innovation research on cylindrical roller bearing structure. In order to systematically investigate the inner wall bending stress of the rolling element in elastic composite cylindrical roller bearing, finite element analysis on different elastic composite cylindrical rolling elements was conducted. The results show that, the bending stress of the elastic composite cylindrical rolling increases along with the increase of hollowness with the same filling material. The bending stress of the elastic composite cylindrical rolling element decreases along with the increase of the elasticity modulus of the material under the same physical dimension. Under the same load, on hollow cylindrical rolling element, the maximum bending tensile stress values of the elastic composite cylindrical rolling element after material filling at 0° and 180° are 8.2% and 9.5%, respectively, lower than those of the deep cavity hollow cylindrical rolling element. In addition, the maximum bending-compressive stress value at 90° is decreased by 6.1%.

Establishment of Dynamic Model for Axle Box Bearing of High-Speed Trains Under Variable Speed Conditions

In this study,a dynamic model for the bearing rotor system of a high-speed train under variable speed conditions is established.In contrast to previous studies,the contact stress is simplifed in the proposed model and the compensation balance excitation caused by the rotor mass eccentricity considered.The angle iteration method is used to overcome the challenge posed by the inability to determine the roller space position during bearing rotation.The simulation results show that the model accurately describes the dynamics of bearings under varying speed profles that contain acceleration,deceleration,and speed oscillation stages.The order ratio spectrum of the bearing vibration signal indicates that both the single and multiple frequencies in the simulation results are consistent with the theoretical results.Experiments on bearings with outer and inner ring faults under various operating conditions are performed to verify the developed model.

Analysis of the Temperature Characteristics of High-speed Train Bearings Based on a Dynamics Model and Thermal Network Method

High-speed trains often use temperature sensors to monitor the motion state of bearings.However,the temperature of bearings can be affected by factors such as weather and faults.Therefore,it is necessary to analyze in detail the relationship between the bearing temperature and influencing factors.In this study,a dynamics model of the axle box bearing of high-speed trains is established.The model can obtain the contact force between the rollers and raceway and its change law when the bearing contains outer-ring,inner-ring,and rolling-element faults.Based on the model,a thermal network method is introduced to study the temperature field distribution of the axle box bearings of high-speed trains.In this model,the heat generation,conduction,and dispersion of the isothermal nodes can be solved.The results show that the temperature of the contact point between the outer-ring raceway and rolling-elements is the highest.The relationships between the node temperature and the speed,fault type,and fault size are analyzed,finding that the higher the speed,the higher the node temperature.Under different fault types,the node temperature first increases and then decreases as the fault size increases.The effectiveness of the model is demonstrated using the actual temperature data of a high-speed train.This study proposes a thermal network model that can predict the temperature of each component of the bearings on a high-speed train under various speed and fault conditions.