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.

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.

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

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

Rolling Element Bearing Diagnostics by Combination of Envelope Analysis and Wavelet Transform

Rolling element-bearing diagnostics has been studied over the last thirty years, and envelope analysis is widely recognized as being the best approach for detection and diagnosis of rolling element bearing incipient failure. But one of the on-going difficulties with envelope technique is to determine the best frequency band to envelop. Here, wavelet transform technique is introduced into envelope analysis to solve the problem by capturing bearing defects-sensory scales (i.e. frequency bands). A modulated Gaussian function is chosen to be the analytical wavelet because it coincides well with bearing defect-induced vibration signal patterns. Vibration signals measured from railway bearing tests were studied by the proposed method. Cases of bearings with single and multiple defects on inner and outer race under different testing conditions are presented. Experimental results showed that the proposed method allowed a more accurate local description and separation of transient signal part, which were caused by impacts between defects and the mating surfaces in the bearing. The combination method provides an effective signal detection technique for rolling element-bearing diagnostics.

Fault Diagnosis for Rolling Element Bearing in Dataset Bias Scenario

Recently, data-driven methods, especially deep learning, outperform other methods for rolling elementbearing (REB) fault diagnosis. Nevertheless, most research work assumes that REB dataset is unbiased. Inthe real industry applications, the dataset bias exists with REB owing to varying REB working conditions andnoise interference. Recently proposed adversarial discriminative domain adaptation (ADDA) is an increasinglypopular incarnation to solve dataset bias problem. However, it mainly devotes to realizing domain alignments, andignores class-level alignments;it can cause degradation of classification performance. In this study, we proposea new REB fault diagnosis model based on improved ADDA to address dataset bias. The proposed diagnosismodel realizes domain- and class-level alignments in dataset bias scenario;it consists of two feature extractors,a domain discriminator, and two label classifiers. The feature extractors and domain discriminator are trainedin an adversarial manner to minimize the domain difference in feature extractors. The domain discrepancy inlabel classifier is reduced by minimizing correlation alignment (CORAL) loss. We evaluate the proposed model onthe Case Western Reserve University (CWRU) bearing dataset and Paderborn University bearing dataset. Theproposed method yields better results than other methods and has good prospects for industrial applications.

Synchronous chirp mode extraction: A promising tool for fault diagnosis of rolling element bearings under varying speed conditions

As critical components in modern aerospace productions,rolling element bearings(REBs)generally work under varying speed conditions,which brings great challenges to their operating health monitoring.Some novel time–frequency decomposition(TFD)algorithms are established recently to extract nonlinear features from the non-stationary signals effectively,which are promising for realizing fault diagnosis of REBs under varying speed conditions.However,numerous personal experiences must be incorporated and the anti-noise performance of these methods needs to be further enhanced.Given these issues,a synchronous chirp mode extraction(SCME)-based REB fault diagnosis method is proposed for the health monitoring of REBs under varying speed conditions in this study.It mainly consists of following two parts.(a)The shaft rotational frequency(SRF)is initially estimated from the low-frequency band of the vibration signal.Simultaneously,an adaptive refining strategy is incorporated to obtain a suitable bandwidth parameter.(b)A cycle-one-step estimation frame is constructed to extract synchronous modes from the envelope waveform of the vibration signal.Meanwhile,a synchronous mode spectrum(SMS)is generated using the information of the extracted synchronous modes,which is a novel REBs fault diagnosis technique with tacholess and resampling-free.In contrast to the current TFD algorithms,the proposed method needs fewer input parameters and owns a well anti-noise performance because there is no iterative optimization in the procedure of construction of SMS.As a result,the health conditions of REBs are evaluated by detecting the exhibited features in the SMS.Simulations and experiments are conducted to validate the effectiveness of the proposed method in terms of REB fault diagnosis.Analysis results demonstrate that the proposed method outperforms the current TFD algorithm and the conventional order tracking technique for fault diagnosis of REB under varying speed conditions.

Fault Diagnosis of Rolling Element Bearing Using Multi-Scale Lempel-Ziv Complexity and Mahalanobis Distance Criterion

A new fault diagnosis technique for rolling element bearing using multi-scale Lempel-Ziv complexity(LZC) and Mahalanobis distance(MD) criterion is proposed in this study. A multi-scale coarse-graining process is used to extract fault features for various bearing fault conditions to overcome the limitation of the single stage coarse-graining process in the LZC algorithm. This is followed by the application of MD criterion to calculate the accuracy rate of LZC at different scales, and the best scale corresponding to the maximum accuracy rate is identified for fault pattern recognition. A comparison analysis with Euclidean distance(ED) criterion is also presented to verify the superiority of the proposed method. The result confirms that the fault diagnosis technique using a multi-scale LZC and MD criterion is more effective in distinguishing various fault conditions of rolling element bearings.

Improving Kinetic Energy Storage for Vehicles through the Combination of Rolling Element and Active Magnetic Bearing

The demand for short term energy storage providing high power for electric and hybrid-electric vehicles is increasing drastically. Stationary FESS （flywheel energy storage systems） is established as UPS （uninterruptible power supply） and represent an emerging market. In contrast, mobile FESSs are currently only used in a few application, e.g., in motor sports. To enable a wider use in personal and public transportation the life-span of the flywheel＇s bearings needs to be increased significantly. This paper presents an alternative approach to extend the lifespan of the flywheel＇s bearings significantly by using a CREAMB （combination of rolling element and active magnetic bearings）.

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.

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

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

Rolling Bearing 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.

Detection of Bearing Faults Using a Novel Adaptive Morphological Update Lifting Wavelet

The current morphological wavelet technologies utilize a fixed filter or a linear decomposition algorithm, which cannot cope with the sudden changes, such as impulses or edges in a signal effectively. This paper pre- sents a novel signal processing scheme, adaptive morpho- logical update lifting wavelet （AMULW）, for rolling element bearing fault detection. In contrast with the widely used morphological wavelet, the filters in AMULW are no longer fixed. Instead, the AMULW adaptively uses a morphological dilation-erosion filter or an average filter as the update lifting filter to modify the approximation signal. Moreover, the nonlinear morphological filter is utilized to substitute the traditional linear filter in AMULW. The effectiveness of the proposed AMULW is evaluated using a simulated vibration signal and experimental vibration sig- nals collected from a bearing test rig. Results show that the proposed method has a superior performance in extracting fault features of defective roiling element bearings.

An Overview of Bearing Candidates for the Next Generation of Reusable Liquid Rocket Turbopumps

There is a consensus in the aerospace field that the development of reusable liquid rockets can effectively reduce the launch expense.The pursuit of a long service life and reutilization highly depends on the bearing components.However,the rolling element bearings(REBs)used in the existing rocket turbopumps present obvious and increasing limitations due to their mechanical contacting mode.For REBs,high rotational speed and long service life are two performance indexes that mutually restrict each other.To go beyond the DN value(the product of the bearing bore and rotational speed)limit of REBs,the major space powers have conducted substantial explorations on the use of new types of bearings to replace the REB.This review discusses,first,the crucial role of bearings in rocket turbopumps and the related structural improvements of REBs.Then,with the prospect of application to the next generation of reusable liquid rocket turbopumps,the bearing candidates investigated by major space powers are summarized comprehensively.These promising alternatives to REBs include fluid-film,foil,and magnetic bearings,together with the novel superconducting compound bearings recently proposed by our team.Our more than ten years of relevant research on fluid-film and magnetic bearings are also introduced.This review is meaningful for the development of long-life and highly reliable bearings to be used in future reusable rocket turbopumps.

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

An Improved Dynamic Modelling for Exploring Ball Bearing Vibrations from Time-Varying Oil Film

Bearings are key components in rotating machinery,which is widely used in many fields,such as CNC machines,wind turbines and induction machines.The increasingly harsh operation environment can lead to wear and tear on raceways and reduce the precision and reliability of bearing or even machinery.Lubrication could relieve the wear to some degree,which is benefit to prolong the bearing’s life.Thus,investigation on the vibration responses under the influence of oil film is of great significance.However,for mechanism analysis,how to include the oil film into the bearing dynamic model affects the result and efficiency of solution.To address this problem,this study proposed a fast algorithm through load distribution and interpolation when calculating oil film stiffness and thickness during the solution of bearing vibration model.Analysis of oil film on vibration is carried out and a bearing test rig is designed to verify the proposed model.Numerical simulation result shows that rotational speed and load have vital effect on oil film and vibration.The experimental result is consistent with the simulation,which shows that the proposed model has a better performance on modeling bearing vibration and the method of considering oil film is reasonable.

Iterative HOEO fusion strategy:a promising tool for enhancing bearing fault feature

As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO techniques are subjected to the limited number of EOs,and they cannot reflect the non-linearity of the machinery dynamic systems and affect the noise reduction.As a result,the fault-related transients strengthened by these improved EO techniques are still subject to contamination of strong noises.To address these issues,this paper presents a novel EO fusion strategy for enhancing the bearing fault feature nonlinearly and effectively.Specifically,the proposed strategy is conducted through the following three steps.First,a multi-dimensional information matrix(MDIM)is constructed by performing the higher order energy operator(HOEO)on the analysis signal iteratively.MDIM is regarded as the fusion source of the proposed strategy with the properties of improving the signal-to-interference ratio and suppressing the noise in the low-frequency region.Second,an enhanced manifold learning algorithm is performed on the normalized MDIM to extract the intrinsic manifolds correlated with the fault-related impulses.Third,the intrinsic manifolds are weighted to recover the fault-related transients.Simulation studies and experimental verifications confirm that the proposed strategy is more effective for enhancing the bearing fault feature than the existing methods,including HOEOs,the weighting HOEO fusion,the fast Kurtogram,and the empirical mode decomposition.

Time-varying stiffness analysis of double-row tapered roller bearing based on the mapping structure of bearing stiffness matrix

Time-varying stiffness is one of the most important dynamic characteristics of rolling element bearings.The method of analyzing the elements in the bearing stiffness matrix is usually adopted to investigate the characteristics of bearing stiffness.Linear mapping structure of the bearing stiffness matrix is helpful to understand the varying compliance excitation and its influence on vibration transmission.In this study,a method to analyze the mapping structure of bearing stiffness matrix is proposed based on the singular value decomposition of block matrices in the stiffness matrix.Not only does this method have the advantages of coordinate transformation independence and unit independence,but also the analysis procedure involved is geometrically intuitive.The time-varying stiffness matrix of double-row tapered bearing is calculated and analyzed using the proposed method under two representative load cases.The principal stiffnesses and principal axes defined in the method together indicate the dominant and insignificant stiffness properties with the corresponding directions,and the vibration transmission properties are also revealed.Besides,the coupling behaviors between different shaft motions are found during the analysis of mapping structure.The mechanism of the generation of varying compliance excitation is also revealed.

New analysis model for rotor-bearing systems based on plate theory

The purpose of this work is to develop a new analysis model for angular-contact,ball-bearing systems on the basis of plate theory instead of commonly known approaches that utilize spring elements.Axial and radial stiffness on an annular plate are developed based on plate,Timoshenko beam,and plasticity theories.The model is developed using theoretical and inductive methods and validated through a numerical simulation with the finite element method.The new analysis model is suitable for static and modal analyses of rotor-bearing systems.Numerical examples are presented to reveal the effectiveness and applicability of the proposed approach.