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.

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.

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.

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.

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.

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.

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.

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.

THE OPERATIONAL PROPERTY ANALYSES OF THE COMPOSITE ROLLING BEARING

This paper deals with the test research on noise and fatigue life of the composite rolling bearings which have been developed recently. The test results show that the-composite rolling bearings have remarkable advantages of low noise and great load-bearing capacity over plastic ones.

Weak Fault Diagnosis of Rolling Bearing Based on Improved Stochastic Resonance

Stochastic resonance can use noise to enhance weak signals,effectively reducing the effect of noise signals on feature extraction.In order to improve the early fault recognition rate of rolling bearings,and to overcome the shortcomings of lack of interaction in the selection of SR(Stochastic Resonance)method parameters and the lack of validation of the extracted features,an adaptive genetic random resonance early fault diagnosis method for rolling bearings was proposed.compared with the existing methods,the AGSR(Adaptive Genetic Stochastic Resonance)method uses genetic algorithms to optimize the system parameters,and further optimizes the parameters while considering the interaction between the parameters.This method can effectively extract the weak fault features of the bearing.In order to verify the effect of feature extraction,the feature signal extracted by AGSR method was input into the Fully connected neural network for fault diagnosis.the practicality of the algorithm is verified by simulation data and rolling bearing experimental data.the results show that the proposed method can effectively detect the early weak features of rolling bearings,and the fault diagnosis effect is better than the existing methods.

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.

Rolling Bearing Remaining Useful Life Prediction Based on Wiener Process

Rolling bearing is the key part of mechanical system.Accurate prediction of bearing life can reduce maintenance costs,improve availability,and prevent catastrophic consequences,aiming at solving the problem of the nonlinear,random and small sample problems faced by rolling bearings in actual operating conditions.In this work,the nonlinearWiener process with random effect and unbiased estimation of unknown parameters is used to predict the remaining useful life of rolling bearings.Firstly,random effects and nonlinear parameters are added to the traditional Wiener process,and a parameter unbiased estimation method is used to estimate the positional parameters of the constructed Wiener model.Finally,the model is validated using a common set of bearing datasets.Experimental results show that compared with the traditional maximum likelihood function estimation method,the parameter unbiased estimation method can effectively improve the accuracy and stability of the parameter estimation results.The model has a good fitting effect,which can accurately predict the remaining useful life of rolling bearing.

Long-Range Dependencies Learning Based on Nonlocal 1D-Convolutional Neural Network for Rolling Bearing Fault Diagnosis

In the field of data-driven bearing fault diagnosis,convolutional neural network(CNN)has been widely researched and applied due to its superior feature extraction and classification ability.However,the convolutional operation could only process a local neighborhood at a time and thus lack the ability of capturing long-range dependencies.Therefore,building an efficient learning method for long-range dependencies is crucial to comprehend and express signal features considering that the vibration signals obtained in a real industrial environment always have strong instability,periodicity,and temporal correlation.This paper introduces nonlocal mean to the CNN and presents a 1D nonlocal block(1D-NLB)to extract long-range dependencies.The 1D-NLB computes the response at a position as a weighted average value of the features at all positions.Based on it,we propose a nonlocal 1D convolutional neural network(NL-1DCNN)aiming at rolling bearing fault diagnosis.Furthermore,the 1D-NLB could be simply plugged into most existing deep learning architecture to improve their fault diagnosis ability.Under multiple noise conditions,the 1D-NLB improves the performance of the CNN on the wheelset bearing data set of high-speed train and the Case Western Reserve University bearing data set.The experiment results show that the NL-1DCNN exhibits superior results compared with six state-of-the-art fault diagnosis methods.

Rolling Bearing Condition Monitoring Technique Based on Cage Rotation Analysis and Acoustic Emission

In this paper,we present an alternative technique for detecting changes in the operating conditions of rolling element bearings(REBs)that can lead to premature failure.The developed technique is based on measuring the kinematics of the bearing cage.The rotational motion of the cage is driven by traction forces generated in the contacts of the rolling elements with the races.It is known that the cage angular frequency relative to shaft angular frequency depends on the bearing load,the bearing speed,and the lubrication condition since these factors determine the lubricant film thickness and the associated traction forces.Since a large percentage of REB failures are due to misalignment or lubrication problems,any evidence of these conditions should be interpreted as an incipient fault.In this paper,a novel method for the measurement of the instantaneous angular speed(IAS)of the cage is developed.The method is evaluated in a deep groove ball bearing test rig equipped with a cage IAS sensor,as well as a custom acoustic emission(AE)transducer and a piezoelectric accelerometer.The IAS of the cage is analyzed under different bearing loads and shaft speeds,showing the dependence of the cage angular speed with the calculated lubricant film thickness.Typical bearing faulty operating conditions(mixed lubrication regime,lubricant depletion,and misalignment)are recreated.It is shown that the cage IAS is dependent on the lubrication regime and is sensitive to misalignment.The AE signal is also used to evaluate the lubrication regime.Experimental results suggest that the proposed technique can be used as a condition monitoring tool in industrial environments to detect abnormal REB conditions that may lead to premature failure.

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.

A Regularized LSTM Method for Predicting Remaining Useful Life of Rolling Bearings

Rotating machinery is important to industrial production. Any failure of rotating machinery, especially the failure of rolling bearings, can lead to equipment shutdown and even more serious incidents. Therefore, accurate residual life prediction plays a crucial role in guaranteeing machine operation safety and reliability and reducing maintenance cost. In order to increase the forecasting precision of the remaining useful life(RUL) of the rolling bearing, an advanced approach combining elastic net with long short-time memory network(LSTM) is proposed, and the new approach is referred to as E-LSTM. The E-LSTM algorithm consists of an elastic mesh and LSTM, taking temporal-spatial correlation into consideration to forecast the RUL through the LSTM. To solve the over-fitting problem of the LSTM neural network during the training process, the elastic net based regularization term is introduced to the LSTM structure.In this way, the change of the output can be well characterized to express the bearing degradation mode. Experimental results from the real-world data demonstrate that the proposed E-LSTM method can obtain higher stability and relevant values that are useful for the RUL forecasting of bearing. Furthermore, these results also indicate that E-LSTM can achieve better performance.

An adaptive data-driven method for accurate prediction of remaining useful life of rolling bearings

A novel data-driven method based on Gaussian mixture model （GMM） and distance evaluation technique （DET） is proposed to predict the remaining useful life （RUL） of rolling bearings. The data sets are clustered by GMM to divide all data sets into several health states adaptively and reasonably. The number of clusters is determined by the minimum description length principle. Thus, either the health state of the data sets or the number of the states is obtained automatically. Meanwhile, the abnormal data sets can be recognized during the clustering process and removed from the training data sets. After obtaining the health states, appropriate features are selected by DET for increasing the classification and prediction accuracy. In the prediction process, each vibration signal is decomposed into several components by empirical mode decomposition. Some common statis- tical parameters of the components are calculated first and then the features are clustered using GMM to divide the data sets into several health states and remove the abnormal data sets. Thereafter, appropriate statistical parameters of the generated components are selected using DET. Finally, least squares support vector machine is utilized to predict the RUL of rolling bearings.Experimental results indicate that the proposed method reliably predicts the RUL of rolling bearings.

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.