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.

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.

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.

An Inter-Shaft Bearing Fault Diagnosis Dataset from an Aero-Engine System

In this paper,the aero-engine test with inter-shaft bearing fault is carried out,and a dataset is proposed for the first time based on the vibration signal of rotors and casings.First,a test rig based on a real aero-engine is established,driven by motors and equipped with a lubricating system.Then,the aero-engine is disassembled and assembled following the specification process,and the inter-shaft bearing with artificial fault is replaced.Next,the aero-engine test is conducted at 28 groups of high-and low-pressure speeds.Six measuring points are arranged,including two displacement sensors to test the displacement vibration signals of the low-pressure rotor and four acceleration sensors to test the acceleration vibration signals of the casing.The test results are integrated into an inter-shaft bearing fault dataset.Finally,based on the dataset in this paper,frequency spectrum,envelope spectrum,CNN,LSTM,and TST are used for fault diagnosis,and the results are compared with those of CWRU and XJTU datasets.The results show that the characteristic fault frequency cannot be found directly in the spectrum and envelope spectrum corresponding to this paper’s dataset but in CWRU and XJTU datasets.Using CNN,LSTM,and TST for fault diagnosis of the dataset in this paper,the accuracy is 83.13%,85.41%,and 71.07%,respectively,much lower than the diagnosis results of CWRU and XJTU datasets.It can be seen that the dataset in this paper is closer to the actual fault diagnosis situation and is a more challenging dataset.This dataset provides a new benchmark for the validation of fault diagnosis methods.Mendeley data:https://github.com/HouLeiHIT/HIT-dataset.

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.

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.

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.

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.

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.

Fractional Envelope Analysis for Rolling Element Bearing Weak Fault Feature Extraction

The bearing weak fault feature extraction is crucial to mechanical fault diagnosis and machine condition monitoring.Envelope analysis based on Hilbert transform has been widely used in bearing fault feature extraction. A generalization of the Hilbert transform, the fractional Hilbert transform is defined in the frequency domain, it is based upon the modification of spatial filter with a fractional parameter, and it can be used to construct a new kind of fractional analytic signal. By performing spectrum analysis on the fractional envelope signal, the fractional envelope spectrum can be obtained. When weak faults occur in a bearing, some of the characteristic frequencies will clearly appear in the fractional envelope spectrum. These characteristic frequencies can be used for bearing weak fault feature extraction.The effectiveness of the proposed method is verified through simulation signal and experiment data.

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.

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.

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.

Remaining Useful Life Prediction of Rolling Element Bearings Based on Different Degradation Stages and Particle Filter

A method is proposed to improve the accuracy of remaining useful life prediction for rolling element bearings,based on a state space model(SSM)with different degradation stages and a particle filter.The model is improved by a method based on the Paris formula and the Foreman formula allowing the establishment of different degradation stages.The remaining useful life of rolling element bearings can be predicted by the adjusted model with inputs of physical data and operating status information.The late operating trend is predicted by the use of the particle filter algorithm.The rolling bearing full life experimental data validate the proposed method.Further,the prediction result is compared with the single SSM and the Gamma model,and the results indicate that the predicted accuracy of the proposed method is higher with better practicability.

Reliability Based Design Optimization of Aero-Engine Spindle Ball Bearings

Aero-engine spindle ball bearings work in harsh conditions which are affected by relatively complex stresses. One of the key factors which affects bearing performance is its structure. In this paper,we used reliability based design optimization method to solve the structure design problem of aero-engine spindle ball bearings.Compared with the optimization design method, the value of equivalent dynamic load using reliability optimization design method was the least by MATLAB simulation. Also the design solutions show that the optimized structure possesses higher reliability than the original solution.

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.

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.