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.

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.

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.

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.

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.

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.

A Novel Rolling Bearing Vibration Impulsive Signals Detection Approach Based on Dictionary Learning

The localized faults of rolling bearings can be diagnosed by its vibration impulsive signals.However,it is always a challenge to extract the impulsive feature under background noise and non-stationary conditions.This paper investigates impulsive signals detection of a single-point defect rolling bearing and presents a novel data-driven detection approach based on dictionary learning.To overcome the effects harmonic and noise components,we propose an autoregressive-minimum entropy deconvolution model to separate harmonic and deconvolve the effect of the transmission path.To address the shortcomings of conventional sparse representation under the changeable operation environment,we propose an approach that combines K-clustering with singular value decomposition(K-SVD)and split-Bregman to extract impulsive components precisely.Via experiments on synthetic signals and real run-to-failure signals,the excellent performance for different impulsive signals detection verifies the effectiveness and robustness of the proposed approach.Meanwhile,a comparison with the state-of-the-art methods is illustrated,which shows that the proposed approach can provide more accurate detected impulsive signals.

PARAMETERS OPTIMIZATION OF CONTINUOUS WAVELET TRANSFORM AND ITS APPLICATION IN ACOUSTIC EMISSION SIGNAL ANALYSIS OF ROLLING BEARING

Morlet wavelet is suitable to extract the impulse components of mechanical fault signals. And thus its continuous wavelet transform （CWT） has been successfully used in the field of fault diagnosis. The principle of scale selection in CWT is discussed. Based on genetic algorithm, an optimization strategy for the waveform parameters of the mother wavelet is proposed with wavelet entropy as the optimization target. Based on the optimized waveform parameters, the wavelet scalogram is used to analyze the simulated acoustic emission （AE） signal and real AE signal of rolling bearing. The results indicate that the proposed method is useful and efficient to improve the quality of CWT.

Demodulation spectrum analysis for multi-fault diagnosis of rolling bearing via chirplet path pursuit

The vibration signals of multi-fault rolling bearings under nonstationary conditions are characterized by intricate modulation features,making it difficult to identify the fault characteristic frequency.To remove the time-varying behavior caused by speed fluctuation,the phase function of target component is necessary.However,the frequency components induced by different faults interfere with each other.More importantly,the complex sideband clusters around the characteristic frequency further hinder the spectrum interpretation.As such,we propose a demodulation spectrum analysis method for multi-fault bearing detection via chirplet path pursuit.First,the envelope signal is obtained by applying Hilbert transform to the raw signal.Second,the characteristic frequency is extracted via chirplet path pursuit,and the other underlying components are calculated by the characteristic coefficient.Then,the energy factors of all components are determined according to the time-varying behavior of instantaneous frequency.Next,the final demodulated signal is obtained by iteratively applying generalized demodulation with tunable E-factor and then the band pass filter is designed to separate the demodulated component.Finally,the fault pattern can be identified by matching the prominent peaks in the demodulation spectrum with the theoretical characteristic frequencies.The method is validated by simulated and experimental signals.

Fault Feature Extraction of Rolling Bearing Based on an Improved Cyclical Spectrum Density Method

The traditional cyclical spectrum density（CSD） method is widely used to analyze the fault signals of rolling bearing. All modulation frequencies are demodulated in the cyclic frequency spectrum. Consequently, recognizing bearing fault type is difficult. Therefore, a new CSD method based on kurtosis（CSDK） is proposed. The kurtosis value of each cyclic frequency is used to measure the modulation capability of cyclic frequency. When the kurtosis value is large, the modulation capability is strong. Thus, the kurtosis value is regarded as the weight coefficient to accumulate all cyclic frequencies to extract fault features. Compared with the traditional method, CSDK can reduce the interference of harmonic frequency in fault frequency, which makes fault characteristics distinct from background noise. To validate the effectiveness of the method, experiments are performed on the simulation signal, the fault signal of the bearing outer race in the test bed, and the signal gathered from the bearing of the blast furnace belt cylinder. Experimental results show that the CSDK is better than the resonance demodulation method and the CSD in extracting fault features and recognizing degradation trends. The proposed method provides a new solution to fault diagnosis in bearings.

Fusion Fault Diagnosis Approach to Rolling Bearing with Vibrational and Acoustic Emission Signals

As the key component in aeroengine rotor systems,the health status of rolling bearings directly influences the reliability and safety of aeroengine rotor systems.In order to monitor rolling bearing conditions,a fusion fault diagnosis method,namely empirical mode decomposition(EMD)-Mahalanobis distance(E2MD)and improved wavelet threshold(IWT)(E2MD-IWT)for vibrational signals and acoustic emission(AE)signals is developed to improve the diagnostic accuracy of rolling bearings.The IWT method is proposed with a hard wavelet threshold and a soft wavelet threshold.Moreover,it is shown to be effective through numerical simulation.EMD is utilized to process the original AE signals for rolling bearings so as to generate a set of components called intrinsic modes functions(IMFs).The Mahalanobis distance(MD)approach is introduced in order to determine the smallest MD between the original AE signal and IMF components.Then,the IWT approach is employed to select the IMF components with the largest MD.It is demonstrated that the proposed E2MD-IWT method for vibrational and AE signals can improve rolling bearing fault diagnosis,beyond its ability to effectively eliminate noise signals.This study offers a promising approach to fault diagnosis for rolling bearings in aeroengines with regard to vibration signals and AE signals.

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.

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.

Finite element analysis of deformation characteristics in cold helical rolling of bearing steel-balls

Due to the complexity of investigating deformation mechanisms in helical rolling(HR) process with traditional analytical method, it is significant to develop a 3D finite element(FE) model of HR process. The key forming conditions of cold HR of bearing steel-balls were detailedly described. Then, by taking steel-ball rolling elements of the B7008 C angular contact ball bearing as an example, a completed 3D elastic-plastic FE model of cold HR forming process was established under SIMUFACT software environment. Furthermore, the deformation characteristics in HR process were discovered, including the forming process, evolution and distribution laws of strain, stress and damage based on Lemaitre relative damage model. The results reveal that the central loosening and cavity defects in HR process may have a combined effect of large negative hydrostatic pressure(positive mean stress)caused by multi-dimensional tensile stresses, high level transverse tensile stress, and circular-alternating shear stress in cross section.