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As a vital mechanical sub-component, the health monitoring of rolling bearings is important. Vibration signal analysis is a commonly used approach for fault diagnosis of bearings. Nevertheless, the collected vibration signals cannot avoid interference from noises which has a negative influence on fault diagnosis. Thus, denoising needs to be utilized as an essential step of vibration signal processing. Traditional denoising methods need expert knowledge to select hyperparameters. And data-driven methods based on deep learning lack interpretability and a clear justification for the design of architecture in a "black-box" deep neural network. An approach to systematically design neural networks is by unrolling algorithms, such as learned iterative soft-thresholding (LISTA). In this paper, the multi-layer convolutional LISTA (ML-CLISTA) algorithm is derived by embedding a designed multi-layer sparse coder to the convolutional extension of LISTA. Then the multi-layer convolutional dictionary learning (ML-CDL) network for mechanical vibration signal denoising is proposed by unrolling ML-CLISTA. By combining ML-CDL network with a classifier, the proposed denoising method is applied to the explainable rolling bearing fault diagnosis. The experiments on two bearing datasets show the superiority of the ML-CDL network over other typical denoising methods. • The multi-layer convolutional LISTA (ML-CLISTA) algorithm is derived. • The multi-layer convolutional dictionary learning network is proposed. • The proposed method is applied to the explainable rolling bearing fault diagnosis. [ABSTRACT FROM AUTHOR]

Aiming at the problem of difficult fault diagnosis work caused by the difficulty of data acquisition of the bearing in the traction part of a coal mining machine, a method of ADAMS simulation and HHT feature extraction of the bearing fault of a coal mining machine is proposed. First of all, take the traction section bearing as the research object, use the virtual prototype in the establishment of the healthy state of coal mining machine traction section model based on the establishment of the bearing inner ring fault, rolling body fault, outer ring fault of the coal mining machine traction section dynamics model, and then after the EMD decomposition, each IMF component of the Hilbert transform, to obtain the signal in the time-frequency plane of the time-frequency joint characteristics, to get the HHT marginal spectra and to different Under different working conditions, the bearing vibration signal features are mined by quantitative feature extraction. Finally, a variety of mainstream machine learning algorithms are introduced to classify the features, and the results show that the feature extraction method in this paper is universal and provides valuable theoretical support and technical guidance for the field application of coal mining machine-bearing fault diagnosis. [ABSTRACT FROM AUTHOR]

To well extract the early fault characteristics of rotating machines, a new fast sparsity-enabled feature-energy-ratio method is investigated in this paper. This method includes two stages. In the first stage, the spectrum is adaptively segmented through a coarse-to-fine strategy based on the ordered local maximums. Thus, the fault characteristic band can be divided automatically. A novel index based on sparsity, energy ratio, and kurtosis, is constructed to evaluate periodic impulses in each sub-signal, and it can evaluate the periodic impulses from the globality and locality. In the second stage, the Fourier spectrum from the first stage are refined by an improved sparse coding shrinkage denoising (SCSD) method whose parameters can be dynamically determined for each point. Within the improved SCSD approach, the differential result of the amplitude spectrum is used as input to improve the sparsity. Moreover, the ratios between the SCSD output and its input are applied to weigh the Fourier spectrum and maintain the phase information. Finally, the inverse fast Fourier transform and squared envelope spectra are applied to detect the fault characteristics. Bearing and gearbox vibration signals are used to validate the proposed methodology. The experimental results show that the proposed method is superior to some typical methods and the proposed index are robust to the interferences from aperiodic impulses. Therefore, the proposed method has great potential in the fault diagnosis of rotating machine. • Frequency spectrum is adaptively segmented by a coarse-to-fine strategy. • Potential characteristic spectral lines are estimated by the harmonic product. • An improved SCSD is proposed to suppress the same frequency band interferences. • Prior about the fault type is not required in this method. [ABSTRACT FROM AUTHOR]

Domain adaptation has been widely used for knowledge transfer. However, the aligning targets of the existing domain adaptation mechanisms dynamically vary during the training, which leads to the loss oscillation, slow convergence, and poor robustness. To overcome this main problem, a novel domain adaptation mechanism named intermediate distribution alignment (IDA) is proposed. For implementing the end-to-end diagnostic tasks, a feature extractor based on deep convolutional neural network with wide first-layer kernel is first built to fit the posterior distributions of source and target domains. Then through the KL divergence, IDA maps the learned features from the source and target domains into a specific intermediate distribution. It is proved theoretically that IDA can align the prior distributions of two domains. The proposed IDA mechanism is successfully applied to the fault transfer diagnosis of planetary gearboxes without labeled target-domain samples. The comparative results show that the proposed IDA mechanism has higher diagnostic performance than the typical domain adaptation mechanisms. [ABSTRACT FROM AUTHOR]

The simulation signals generated by the bearing dynamics model have a big gap with the actual signals, which limits their efficacy in bearing fault diagnosis. Therefore, it is valuable to build an accurate digital twin model of faulty rolling bearing. Firstly, a multi-degree-of-freedom bearing fault dynamics model is constructed in the virtual space for generating the vibration responses of bearing parts. Then considering that the frequency spectrum contains more characteristic information than the time-domain signal, a frequency-domain bi-directional long short-term memory (Bi-LSTM) cycle generative adversarial network (CycleGAN) named FBC-GAN is proposed to construct the frequency-domain coupling mapping relationship between the multipart vibration responses and the measured signals. In the proposed network, Bi-LSTM is used for enhancing the feature extraction ability. Meantime, a new spectrum-constraint loss is proposed to ensure the frequency-domain mapping. Next, the simulated fault bearing signals close to the actual signals are generated by FBC-GAN and Fourier transform. Finally, the results of two experiments show the superiority of the proposed method over other advanced data augmentation methods in bearing fault diagnosis with the imbalanced samples. [ABSTRACT FROM AUTHOR]

In actual engineering, insufficient bearing samples for each fault category presents a substantial obstacle to the intelligent fault diagnosis of rolling bearings. To address sample imbalance, this work explores a novel bearing fault data–generation approach based on digital twin technique. First, an inverse physics–informed neural network (PINN) is built to recognize dynamic model parameters by embedding a bearing dynamic model into a neural network. In this network, a boundary loss is designed to quickly determine the approximate ranges of parameters that can accelerate network convergence, and a true value loss is constructed for the assessment of spectral discrepancy between simulated and actual data. Then, using an inverse PINN, a bearing fault dynamic model, and real vibration data, we propose a digital twin–based fault data–generation method for producing high-quality bearing fault samples under multiple working conditions and fault modes. Finally, the developed approach is applied to generate bearing fault vibration samples under a specific working condition. The samples are used for training the diagnostic network, thus solving the issue of sample imbalance. The comparison results of several experiments suggest that the developed data-generation method effectively improves the precision of cross-working-condition bearing fault diagnosis and surpasses multiple state-of-the-art methods. [ABSTRACT FROM AUTHOR]

To improve extraction accuracy of bearing fault feature, a novel index named weighted characteristic energy ratio (WCER) is proposed in this article. In WCER, the fault feature in squared envelope spectrum is enhanced through a square operation, and a series of decreasing weights are imposed on the increasing fault harmonics to highlight the low-order fault feature and suppress the noise around the high-order harmonics. For unknown fault types, including single and compound faults, another index named compound WCER (CWCER) is proposed on the basis of WCER. The optimal resonant frequency band is determined via maximizing WCER and CWCER, and the fault feature can be effectively extracted. WCER is applied to diagnose two single faults, whereas CWCER is employed to detect two single faults and a compound fault. Their superiority to traditional indices is demonstrated; they can be better applied to bearing fault diagnosis, especially for unknown faults. [ABSTRACT FROM AUTHOR]

The key of bearing fault feature extraction is to select the optimal resonant frequency band (ORFB) containing fault information with an appropriate index. However, the background noise and cyclostationary impulsive noise will seriously affect the location of ORFB. Moreover, traditional indexes may be ineffective for compound faults. Thus, a novel fault feature method for rolling bearings is explored to solve these problems. First, by evaluating the potential fault types with the designed relative local threshold, an adaptive harmonic kurtosis (AHK) is first proposed to locate the ORFB for an arbitrary fault or compound fault. Then, according to the index of AHK, an improved bat algorithm (IBA) is proposed to find the ORFB unlike fast kurtogram (FK). The proposed rolling bearing fault diagnosis method based on an adaptive harmonic kurtosis and IBA has been applied to two single faults and a compound fault. The comparative results indicate that the proposed method can more accurately extract the fault feature compared with the FK method, the method based on the ratio of cyclic content, discrete wavelet transform based on kurtosis, and ensemble empirical mode decomposition based on kurtosis. [ABSTRACT FROM AUTHOR]

The deep learning-based fault diagnosis approaches have achieved remarkable success in the field of rotating machinery condition monitoring. However, the basic intelligent fault diagnosis approaches require plenty of labeled samples to learn the strong feature representations in embedding feature space. Besides, it is time-consuming and laborious to collect sufficient labeled training samples in industrial occasions, which tremendously limits its performance in actual applications. To address the shortcoming, a relation-based semisupervised method is proposed in this article. In the proposed method, the sample relation discovering and pseudo label learning are integrated into an iterative framework, which is used to perform labeled sample augmentation in a progressive manner. Afterward, the supervised transfer training is introduced to reduce distribution discrepancy between the labeled and unlabeled samples, and eventually realize fault classification. Two gearbox fault diagnosis experiments are carried out to evaluate the effectiveness of the proposed method. The experimental results indicate that the proposed method obtains remarkable fault classification accuracy even only 5% of the labeled samples are available, which outperforms traditionally supervised and semisupervised fault diagnosis approaches. [ABSTRACT FROM AUTHOR]

Tanh is a sigmoidal activation function that suffers from vanishing gradient problem, so researchers have proposed some alternative functions including rectified linear unit (ReLU), however those vanishing-proof functions bring some other problem such as bias shift problem and noise-sensitiveness as well. Mainly for overcoming vanishing gradient problem as well as avoiding to introduce other problems, we propose a new activation function named Rectified Linear Tanh (ReLTanh) by improving traditional Tanh. ReLTanh is constructed by replacing Tanh 's saturated waveforms in positive and negative inactive regions with two straight lines, and the slopes of the lines are calculated by the Tanh 's derivatives at two learnable thresholds. The middle Tanh waveform provides ReLTanh with the ability of nonlinear fitting, and the linear parts contribute to the relief of vanishing gradient problem. Besides, thresholds of ReLTanh that determines the slopes of line parts are learnable, so it can tolerate the variation of inputs and help to minimize the cost function and maximize the data fitting performance. Theoretical proofs by mathematical derivations demonstrate that ReLTanh is available to diminish vanishing gradient problem and feasible to train thresholds. For verifying the practical feasibility and effectiveness of ReLTanh , fault diagnosis experiments for planetary gearboxes and rolling bearings are conducted by stacked autoencoder-based deep neural network (SAE-based DNNs). ReLTanh alleviates successfully vanishing gradient problem and the it learns faster, more steadily and precisely than Tanh , which is consistent with the theoretical analysis. Additionally, ReLTanh surpasses other popular activation functions such as ReLU family, Hexpo and Swish , which shows that ReLTanh has certain applying potential and researching value. [ABSTRACT FROM AUTHOR]

When the source domain has more fault types than the target domain, the traditional domain adaptation (DA) performance will degrade. Therefore, exploring partial domain adaptation to improve the accuracy of cross-domain fault diagnosis is significant. This work develops a novel adaptive manifold partial domain adaptation (AMPDA) approach for implementing the partial transfer fault diagnosis by decreasing the distribution discrepancy and adaptively learning global geometrical structures. Specifically, AMPDA first proposes the extraction method of the global geometrical structure by an affinity matrix. Then, the two domains are aligned by decreasing the maximum mean discrepancy (MMD) between two classes. AMPDA applies the manifold regularization to the objective function of partial domain adaptation, adaptively changing the weight of the geometrical structure according to the feature mapping within the process aligning two domains. AMPDA can adaptively learn the global geometrical structure to reduce the man-made interference in the K-nearest neighbor and restrain negative transfer learning caused by forcing to keep the structure. AMPDA is successfully applied to partial transfer fault diagnosis of rolling bearings and planetary gearboxes with unlabeled target domain samples. The experimental results demonstrate that the AMPDA performs better than typical DA methods based on machine learning. • Adaptive manifold partial domain adaptation framework is first constructed. • A new manifold regularization for partial domain adaptation is proposed. • The proposed method is verified by two faulty rotating machinery datasets. [ABSTRACT FROM AUTHOR]

Efficient and accurate planetary gearbox fault diagnosis is the key to enhance the reliability and security of wind turbines. Therefore, an intelligent and integrated approach based on deep belief networks (DBNs), improved logistic Sigmoid (Isigmoid) units, and impulsive features is proposed in this paper. The vanishing gradient problem is an inherent drawback of conventional Sigmoid units, and it usually occurs in the backpropagation process of DBNs, resulting in that the training is considerably slowed down and the classification rate is reduced. To solve this problem, Isigmoid units are designed to combine the merits of unsaturation from leaky rectified linear (LReL) units. The results of handwritten digit recognition experiments show the superiority of Isigmoid over Sigmoid on convergence speed and classification accuracy. Since impulses contain much useful fault information, especially for early failures, an integrated approach using the optimized Morlet wavelet transform, kurtosis index, and soft-thresholding is applied to extract impulse components from original signals to improve the diagnosis accuracy. Then, the features extracted from original signals and impulsive signals are employed to train and test the DBNs with Isigmoid, Sigmoid, and LReL units for comparison. Finally, the results of planetary gearbox fault diagnosis show that Isigmoid has higher comprehensive performance than conventional sigmoid and LReL. [ABSTRACT FROM AUTHOR]

An adaptive signal decomposition and selection (ASDS) method is proposed to estimate the rotation speed of a direct current (dc) motor. This paper contributes to order tracking (OT) and fault diagnosis of dc motor independent of a shaft encoder and under the condition of speed variation. Wavelet transform is first applied to the current signal, and the wavelet ridge is extracted from the time–frequency plane. Synchronous demodulation and smoothing spline fitting are subsequently applied to reconstruct and adaptively select the signal component related to rotation ripple. The ASDS method is used to estimate the rotation speed accurately from the extracted rotation ripple, which is interfered with the dominant dc fluctuation and current noises. The proposed method is applied to variable-speed bearing fault diagnosis by combining vibration signal analysis. The effectiveness and robustness of the method are verified by the current signals acquired from both constant and variable load conditions. This method, as a new tacholess OT technique, can be extended to fault diagnosis of other mechanical and electrical components in a dc motor under variable-speed condition. [ABSTRACT FROM AUTHOR]

A planetary gearbox is a crucial but failure-prone component in rotating machinery, therefore an intelligent and integrated approach based on impulsive signals, deep belief networks (DBNs) and feature uniformation is proposed in this paper to achieve real-time and accurate fault diagnosis. Since the gear faults usually generate the repetitive impulses, an integrated approach using the optimized Morlet wavelet transform, kurtosis index and soft-thresholding is applied to extract impulse components from original signals. Then time-domain features and frequency-domain features are calculated by both original signals and impulsive signals, and probability density functions are applied to study the sensitivities of the features to the faults. The extracted features are fed into DBNs to identify the fault types, and the results show that the DBN-based fault diagnosis method is feasible and the impulsive signals play a positive role to improve the accuracies. Finally, by the mean value of various signals under multiple load conditions, uniformed time-domain features are constructed to reduce the interference of loads, and the experimental results validate that feature uniformation can improve the accuracies and robustness of intelligent fault diagnosis approach. [ABSTRACT FROM AUTHOR]

The localized faults of rolling bearings can be diagnosed by the extraction of the impulsive feature. However, the approximately periodic impulses may be submerged in strong interferences generated by other components and the background noise. To address this issue, this paper explores a new impulsive feature extraction method based on the sparse representation. According to the vibration model of an impulse generated by the bearing fault, a novel impulsive wavelet is constructed, which satisfies the admissibility condition. As a result, this family of model-based impulsive wavelets can form a Parseval frame. With the model-based impulsive wavelet basis and Fourier basis, a convex optimization problem is formulated to extract the repetitive impulses. Based on the splitting idea, an iterative thresholding shrinkage algorithm is proposed to solve this problem, and it has a fast convergence rate. Via the simulated signal and real vibration signals with bearing fault information, the performance of the proposed approach for repetitive impulsive feature extraction is validated and compared with the noted spectral kurtosis method, the optimized spectral kurtosis method based on simulated annealing, and the resonance-based signal decomposition method. The results demonstrate its advantage and superiority in weak repetitive transient feature extraction. [ABSTRACT FROM PUBLISHER]

• Fast iteration filter is proposed to extract the spectrum trend curve. • A novel voting index is proposed to evaluate periodic impulses in noisy signal. • A novel variational model penalized by a frequency is built to extract impulses. • Impulses can be accurately extracted from signals with strong interference. A key step in rotating machinery fault diagnosis is extracting the subcomponent that best characterizes the fault features. To this end, a fault feature extraction methodology based on an adaptive spectrum segmentation method, a new voting index, and a new variational model is constructed in this paper. More specifically, the spectrum is divided into a series of sub-bands through a fast iteration filter by changing the width of the window. Then, by considering the amplitudes and locations of the fault feature spectral lines in squared envelope spectrum, a novel index based on voting mechanism is constructed to evaluate the periodic impulses in each sub-band. Finally, a new variational model penalized by a center frequency penalty item is proposed to extract the fault characteristics from the raw vibration signal by maximining the proposed index iteratively. The proposed methodology is applied to extract the fault characteristics from rolling bearing and planetary gearbox signals. The comparative results indicate the proposed method is superior to fast kurtogram, fast entrogram, and the proposed fault feature extraction methods based on other classical indices. [ABSTRACT FROM AUTHOR]

The existing fault diagnosis methods based on manifold learning assume that all the faults distribute on a single manifold, however the faults may distribute on different manifolds in practical applications. Aiming at this problem, rotating machinery fault diagnosis method based on multiple fault manifolds is proposed. Firstly, mixed-domain features are extracted from the vibration signals to characterize the property of the faults, and the vibration signals are also preprocessed by empirical model decomposition before feature extraction. Then, the corresponding fault manifold of each fault is extracted from the high-dimensional fault samples. In the method, linear local tangent space alignment is applied to solve the problem of low-dimensional manifold extraction, and immune genetic algorithm is used to select the intrinsic dimensionality of fault manifold. At last, the test samples are respectively projected to all the fault manifolds, and the projection errors are used as the criterion to determine the fault types of the test samples. In order to verify the effectiveness of the proposed fault diagnosis method, the method is applied to diagnose the faults of the gear box. The experimental results indicate that feature compression can remove the redundant information between features, and moreover fault diagnosis method based on multiple fault manifolds can obtain even better performance than those methods which project all the faults to a single low-dimensional manifold. [ABSTRACT FROM AUTHOR]

Abstract: Since the empirical mode decomposition (EMD) lacks strict orthogonality, a new method for multicomponent signal decomposition, orthogonal empirical mode decomposition (OEMD), is proposed by this paper. The essential principle of this method is to obtain the intrinsic mode functions (IMFs) and the residue by self-adaptive band-pass filtering. Firstly, the feasibility of OEMD is theoretically analyzed, then its strict orthogonality and completeness is proved, and the orthogonal basis used in OEMD is generated. Secondly, the method of analytical band-pass filtering which preserves perfect band-pass feature in the frequency domain is presented, then two fast algorithms to implement OEMD are proposed, i.e. IMF sequential searching (ISS) algorithm and IMF binary searching (IBS) algorithm. The speed of IBS is faster than that of ISS, whereas IBS algorithm may obtain much more false IMFs than ISS when signals are of complex spectral constitutions. Finally, OEMD is applied to both synthetic signals and mechanical vibration signals, the results show that compared with EMD, OEMD better solves mode aliasing, avoids the occurrence of false mode, is free of end extension, and can be effectively applied to mechanical fault diagnosis. [Copyright &y& Elsevier]

• A shared classifier is constructed to unify fault classifier and domain classifier. • The CORAL loss is added into adversarial training for promoting domain confusion. • An unbalanced adversarial training strategy is proposed for improving the accuracy. • PSADAN has higher and more stable diagnosis accuracies than traditional methods. The domain adaptation (DA) model, aiming to solve the task of unlabeled or less-labeled target domain fault classification through the training of labeled source domain fault data, is widely used in the transfer diagnosis task of mechanical faults by unsupervised learning. However, traditional transfer learning models such as deep domain confusion (DDC) and RevGrad still have the problems of high training cost and low classification accuracy. Therefore, this paper proposes a parameter sharing adversarial domain adaptation network (PSADAN). The proposed approach constructs a shared classifier to unify fault classifiers and domain classifiers to reduce the complexity of network structure (i.e. the number of hyperparameters), and adds the CORAL loss for adversarial training to enhance the domain confusion. Meanwhile, an unbalanced adversarial training strategy is proposed for improving the domain confusion ability of the feature extractor, so as to improve the accuracy of transfer diagnosis. The effectiveness and advantage of the proposed method is verified by the planetary gearbox fault transfer diagnosis experiments including several transfer tasks of load condition, speed condition, and measurement point. [ABSTRACT FROM AUTHOR]

Multicomponent AM–FM demodulation is an available method for machinery fault vibration signal analysis, so a new method for mechanical fault diagnosis based on iterated Hilbert transform (IHT) is proposed. The principle of computing the asymptotically exact multicomponent sinusoidal model for an arbitrary signal by iterating Hilbert transform is introduced, and some properties of IHT are analyzed. Theoretical analysis for the generic two-component signal shows that there are limitations in the direct estimation of instantaneous frequencies via the phase signals of the previously obtained model. Therefore, a smoothed instantaneous frequency estimation (SIFE) method based on difference operator and zero-phase digital low-pass filtering is proposed, and then the accuracy and validity of this method have been proved by the simulation results. The analysis results of the mechanical fault signals show that the weak features of these signals can be efficiently extracted with the proposed approach. [Copyright &y& Elsevier]

In recent years, various deep domain adaption (DDA) models, such as deep domain confusion (DDC) and deep adaption network (DAN), are proposed. These models can adapt a trained model in the source domain to new classification tasks in the target domain. However, these classical DDA models suffer from some inherent drawbacks. For example, traditional DDA models can output only one transfer feature (TF) with high dimension and fixed scales, thus possibly losing important information while performing domain confusion operation. Multiscale domain adaption (MSDA) is proposed in this paper to remold and improve the classical DDA models to solve the aforementioned problems. MSDA is a universally applicable strategy that can be embedded into most existing classical DDA models. An MSDA block is designed and constructed on the basis of multiscale convolution networks to replace the last convolutional layer of the original DDA model. The MSDA block has four parallel pipelines consisting of multiscale convolutional and global average pooling operations. Therefore, MSDA can extract more domain-invariant features than the original feature extractor, meanwhile the four low-dimension TFs can simplify the calculation of domain confusion losses. The four TFs are concatenated into a feature vector, and then it is input into the top classifier for fault identification. MSDA can be effectively applied to five classical DDA models and enhance their abilities of domain adaption. The effectiveness and advantage of the proposed MSDA are verified through 18 fault transfer diagnosis tasks of planetary gearboxes. [ABSTRACT FROM AUTHOR]

• CAE is first designed as the feature extractor to mine the fault features. • Both CORAL loss and domain classifier loss are integrated for domain adaptation. • A new fault transfer diagnosis model called CAE-DTLN is constructed. • The proposed model can be well applied to mechanical fault transfer diagnosis. Deep learning has gained a great achievement in the intelligent fault diagnosis of rotating machineries. However, the labeled data is scarce in actual engineering and the marginal distribution of data is discrepant under different conditions. Transfer learning provides a feasible way to overcome these difficulties. Considering the effect of noise on the transfer fault diagnosis, this work puts forward a new deep transfer learning network based on convolutional auto-encoder(CAE-DTLN) to implement the mechanical fault diagnosis in target domain without labeled data. In the proposed framework, CAE is used as the feature extractor as it has the ability of noise removal. Moreover, both CORrelation ALignment (CORAL) loss and domain classification loss are integrated to enhance the effect of domain confusion. The proposed model is applied to the fault transfer diagnosis of planetary gearboxes under different working loads and noise levels, and it is compared with other typical fault transfer diagnosis models. The experimental results show that CAE-DTLN has higher diagnosis accuracy and stronger generalization ability. The average diagnostic accuracy of CAE-DTLN is over 99%. Moreover, the proposed transfer learning model has better anti-noise performance. [ABSTRACT FROM AUTHOR]

• A multiple-degree-of-freedom dynamic model for high-speed bearing is constructed. • The influence of the local defect on cage and rolling element is first considered. • The dynamic responses under different working conditions and defects are analyzed. • The experiments on aero-engine spindle bearings are applied to validate the model. It is well known that the dynamic response of the rolling bearing would change especially in the acceleration vibration signal when the defects occur. To accurately simulate the dynamic response of a high-speed rolling bearing with a localized surface defect, we propose a new dynamic model for the faulty rolling bearing. The proposed model considers not only the high-speed effect of the rolling element, such as centrifugal force and gyroscopic moment, but also the degrees of freedom (DOFs) of all movable components, including five-DOF inner raceway, three-DOF balls and three-DOF the cage. Then the fourth order Runge-Kutta algorithm is used to solve the nonlinear differential equations of the model for obtaining the dynamic response of the bearing. Under different radial forces, rotational speeds and defect sizes, the acceleration vibration response of inner raceway and the motion of cage considering the effect of the localized surface defect are respectively analyzed. Finally, the correctness and effectiveness of the proposed model are proved by the measured signals of the faulty aero-engine spindle bearings. [ABSTRACT FROM AUTHOR]

• A new dynamic model of faulty high-speed angular contact ball bearings is set up. • A B-spline fitting excitation function is used to represent the fault excitation. • The dynamic responses under different fault sizes and speeds are compared. • Experiment on high-speed bearings was performed to verify the proposed model. Angular contact ball bearings (ACBBs) are widely used in rotary machines especially in high-speed rotating machines because of their excellent properties. However, the traditional dynamic model of a rolling bearing is mainly applied to simulate the dynamic response at low speed, and uses the simple displacement excitation function to characterize the fault, thus its accuracy will decrease under high speed condition. Aiming at the shortcomings of the traditional model, a new high-speed fault dynamic model of ACBB is proposed by considering the influences of centrifugal force, gyroscopic moment and time-varying contact angles on the rolling element under high-speed running and using a B-spline fitting displacement excitation method to represent the fault excitation. With this model, high-speed dynamic responses under different fault sizes and rotation speeds are calculated by the Runge–Kutta method and Newton– Raphson method. Then the corresponding time and frequency domain characteristics are analyzed. From the simulation results, it can be seen that all the simulated acceleration signals of ACBBs are more in line with the actual situation than the traditional model, especially for the shape of an impulse. Finally, the effectiveness and correctness of the proposed model are verified by the experiment on aero-engine spindle bearings. [ABSTRACT FROM AUTHOR]

• A M-band flexible wavelet transform with high frequency resolution is constructed. • The wavelet filter bank is designed by the frequency domain method. • The fast numeric implementation algorithm of the proposed transform is presented. • This method can be well applied to diagnose the faults of planetary gearboxes. The fault diagnosis of planetary gear transmission systems is crucial for the safety of machineries and equipment. To identify the underlying fault features in measured signals, a novel M-band flexible wavelet transform is constructed. This transform provides a denser sampling of the time–frequency plane and preserves tunable filter parameters and dilation factors. A perfect reconstruction condition of the proposed transform is established, and its corresponding wavelet filter bank is designed to satisfy the perfect reconstruction condition. A numerical implementation algorithm of M-band flexible wavelet transform is investigated using a multirate filter bank and fast Fourier transform. Denoising the simulation signals demonstrates that the proposed transform exhibits better performance than analytic flexible wavelet transform, orthogonal wavelet transform, and biorthogonal wavelet transform. A new fault diagnosis method for planetary gear transmission systems is proposed on the basis of M-band flexible wavelet transform and spectral negentropy. Experimental and comparative results show that the proposed method can be more effectively and accurately applied to the fault diagnosis of planetary gear transmission systems compared with typical fault diagnosis methods based on analytic flexible wavelet transform, Morlet wavelet transform, and infograms. [ABSTRACT FROM AUTHOR]

With the popularization of the intelligent manufacturing, much attention has been paid in such intelligent computing methods as deep learning ones for machinery fault diagnosis. Thanks to the development of deep learning models, the interference of the human experience can be greatly reduced, and the fault diagnosis accuracy can also be increased under certain conditions. To improve the generalization ability of the intelligent fault diagnostics, the deep transfer learning consisting of both transfer learning and deep learning components was accordingly developed. This paper reviews the research progress of the deep transfer learning for the machinery fault diagnosis in recently years. It is summarizing, classifying and explaining many publications on this topic with discussing various deep transfer architectures and related theories. On this basis, this review expounds main achievements, challenges and future research of the deep transfer learning. This provides clear directions for the selection, design or implementation of the deep transfer learning architecture in the field of the machinery fault diagnostics. [ABSTRACT FROM AUTHOR]

• A method combining semi-supervised learning and deep learning is proposed. • Layers lose correlation function have been used to avoid information loss. • The optimal wavelet basis is selected by the correlation coefficient. • The proposed method is trained and get higher accuracy with fewer labeled data. The vibration signal can effectively represent the equipment fault information and be utilized for fault diagnosis by further extracting sensitive features. However, traditional supervised diagnosis requires a huge amount of labeled samples, and the features extraction and selection are mainly done manually, which are costly and time consuming. Deep Learning (DL) can automatically extract fault-sensitive features and effectively improve the recognition rate of fault diagnosis, while Semi-Supervised Learning (SSL) trains a model together with labeled and unlabeled data to increase recognition accuracy. In this paper, a novel deep Semi-Supervised method of Multiple Association Layers Networks (SS-MALN) framework of planetary gearbox vibration-based fault diagnosis is proposed. The SS-MALN model has the advantages of SSL and DL simultaneously, which can reduce the amount of labeled samples and improve the accuracy of recognition. The wavelet packet transform was employed to highlight various impulse components and present time-frequency features of the original vibration signal. Then, the transformed samples were divided into two parts, a major part of which deletes the category information, i.e. the labels. After that, the labeled and unlabeled samples were employed to train the improved SS-MALN model. Validation by Drivetrain Diagnostic Simulator testbed data on several planetary gearbox fault datasets manifests that our SS-MALN semi-supervised method can deliver enhanced performance over other traditional deep networks of planetary gearbox fault classification with less labeled data. [ABSTRACT FROM AUTHOR]

Plenty of maximum mean discrepancy (MMD)-based domain adaptation models have been applied to the fault transfer diagnosis. MMD uses the mean statistic in Hilbert space to measure the distribution discrepancy, whereas it cannot precisely reflect the distribution relationship in some cases. Meanwhile, the working mechanism of MMD needs to be further investigated. To this end, a novel insight into MMD is provided, and its working principle from the perspective of space mapping is theoretically explored. A vibration characteristic-guided distribution alignment metric called variance discrepancy representation (VDR) that can express variance information is proposed to enhance the discrepancy representation ability. The biased and unbiased empirical VDR statistics are developed, and the error bounds between the two statistics and the real distribution discrepancy are derived to ensure the reliability of VDR. Furthermore, a new Student kernel is designed to guarantee the robustness and generalization ability of VDR. Ultimately, the VDR with Student kernel-based fault diagnosis model is constructed. The experimental results on three bearing datasets and the actual vibration signals of wind turbine gearbox show that the proposed method is superior to the typical and advanced fault transfer diagnosis methods, especially the proposed VDR outperforms the current distribution alignment metrics. The related code can be downloaded from https://qinyi-team.github.io/2024/05/Variance-discrepancy-representation. [ABSTRACT FROM AUTHOR]

The ocean surroundings are mostly complex and harsh, which make the faults of the unmanned underwater vehicles (UUVs) difficult to avoid. Fault diagnosis (FD) technologies for UUVs can assist in providing the damage states and are helpful for implementing the targeted fault-tolerant strategies with which further expansion of the losses could be prevented. In the past three decades, a lot of researches on UUV FD have been carried out, from which the findings are classified and analyzed in this paper to present a clear status of the development for the future studies. The task, capability, and component layers of FD are defined based on the specific control structure of the UUVs, where the task layer FD concerns the overall risks of the system operation and task execution, the capability layer FD describes the comprehensive effects on the motion and sensing features with multiple components, and the component layer FD pays attention to the physical information toward specific components. For each layer, the literatures are organized and briefly explained based on the similarities of solutions. Accordingly, some worthwhile issues to be solved are summarized. • The FD literatures of UUVs are reviewed in layers of task, capability, and component concerning the solution similarities. • The overall risks of the system operation and task execution are concerned in the task layer FD. • The comprehensive effects on the motion and sensing characteristics of the components are analyzed in the capability layer. • The comparison-based FD concerning the physical information is contained in the component layer. • Worthwhile issues concerning the adaptive fault threshold, active FD, multi-layer FD, and FD applications are summarized. [ABSTRACT FROM AUTHOR]

• The coupling fault evolution model of fatigue crack and wear is first established. • A new TVMS calculation method for the evolutive coupling fault is proposed. • An 8-DOF spur gear dynamics model with evolutive coupling fault is constructed. • Experimental results verify the effectiveness and accuracy of the proposed model. Parallel shaft spur gear system is widely used in various machineries because of its simple structure, high transmission efficiency and strong adaptability. The health status of spur gear greatly affects the safety and reliability of equipment in service, so it is quite necessary to reveal the evolution law of gear fault and clarify the fault dynamic response. Fatigue crack is a typical gear fault, and it is often accompanied by wear which is generally unavoidable in the life cycle of gear transmission system. The two typical gear faults reduce the meshing stiffness of the gear pair, whereupon a calculation approach of time-varying meshing stiffness for the coupling fault of fatigue crack and wear is proposed. First, the prediction models of fatigue crack and wear are respectively investigated, then a coupling fault evolution model is built by combining them. Using this model, a new approach for calculating the time-varying meshing stiffness is put forward. Via embedding the obtained meshing stiffness into the eight-degree-of-freedom dynamics model of spur gear transmission system as the fault excitation, an evolutive coupling fault dynamics model is constructed. Finally, the effectiveness and accuracy of the proposed evolutive fault dynamics model is verified by the experiment on a faulty single-stage gearbox. The proposed model has important guiding significance for the fault diagnosis and prognosis of spur gearbox. [ABSTRACT FROM AUTHOR]

Domain-adaptation technologies have been widely developed for mechanical fault diagnosis. Most related methods assume the same label space between the source and target domains, whereas the partial domain adaptation problem is more widespread and challenging. Moreover, most previous studies focused on data distribution alignment but failed to address fine-grained distributional differences of subdomains. Hence, this study proposes a novel duplex adversarial deep discriminative network (DADDN) for fault diagnosis in cross-domain partial transfer cases. First, a dual-domain adversarial attention mechanism is adopted in the DADDN to discriminate the label space and evaluate the transferability of the data samples. Second, a new metric function of the distribution difference is employed to learn both the fine-grained and discriminative features of the data samples and a weight-joint adaptive distribution mechanism is proposed to improve the domain confusion capability. Third, a center-of-balance weighting strategy is utilized to expand the categories of the target domain and reduce label space asymmetry. In addition, to avoid negative transfer, a weighting mechanism is designed to filter outlier categories, and a dynamic adaptive factor is introduced to weigh the importance of the marginal and conditional distributions. Finally, the effectiveness, robustness, and progressiveness of the proposed method are validated using several partial-transfer diagnostic tasks based on three rotating machinery datasets. [Display omitted] • A duplex domain adversarial attention module is given to improve model robustness. • A novel adaptive distribution mechanism is built to align the domain distribution. • A dynamic adaptive factor is given to balance inter-domain probability distribution. [ABSTRACT FROM AUTHOR]

Discrepancy representation metric completely determines the transfer diagnosis performance of deep domain adaptation methods. Maximum mean discrepancy (MMD) based on the mean statistic, as the commonly used metric, has poor discrepancy representation in some cases. MMD is generally known from the aspect of kernel function, but the inherent relationship between the two is unknown. To deal with these issues, the authors theoretically explore their relationship first. With the revealed relationship, a novel discrepancy representation metric named maximum mean square discrepancy (MMSD), which can comprehensively reflect the mean and variance information of data samples in the reproducing kernel Hilbert space, is constructed for enhancing domain confusion. Additionally, for the real application under limited samples and ensuring the effectiveness of MMSD, biased and unbiased empirical MMSD statistics are developed, and the error bounds between the two empirical statistics and the real distribution discrepancy are derived. The proposed MMSD is successfully applied to the end-to-end fault diagnosis of planetary gearbox of wind turbine without labeled target-domain samples. The experimental results on twelve cross-load transfer tasks validate that MMSD has a better ability of discrepancy representation and a higher diagnosis accuracy compared with other well-known discrepancy representation metrics. The related code can be downloaded from https://qinyi-team.github.io/2023/06/Maximum-mean-square-discrepancy. [ABSTRACT FROM AUTHOR]

As a crucial role in the prognostic and health management of mechanical equipment, fault diagnosis encounters serious challenges, such as the scarcity of fault samples, the high cost of sample labeling, the distribution discrepancy, and the data island between multiple users. Federated transfer learning (FTL)-based diagnosis methods provide a feasible and effective solution for such challenges, aiming to transfer and generalize models across domains by leveraging data from diverse sources under the preserving framework of data privacy. However, no dedicated research review comprehensively summarizes FTL-based fault diagnosis methods because its application in fault diagnosis is still in the preliminary exploration stage. Therefore, this paper develops a systematic literature review for the technique and application of FTL-based machinery fault diagnosis. This review introduces the related definition and diagnosis procedure of FTL. Then, detailed discussion and analysis are conducted on the three core elements of FTL, including privacy-preserving paradigm, federated communication framework, and distribution alignment mechanism; next, based on whether the data from the target client can be accessed during the training phase, relevant FTL-based diagnosis approaches are comprehensively discussed. Ultimately, this review is expected to help researchers better understand this intelligent diagnostic technology based on FTL, inspiring them to contribute. [ABSTRACT FROM AUTHOR]

• A powerful domain adaption method is proposed for bearing fault diagnosis. • This method deals with the feature misalignment problem in difficult transfer tasks. • Unknown target labels are reliably estimated by weak prior embedding. • The effectiveness and superiority of this method have been verified by challenging experiments. Transfer learning extends the application scope of deep intelligent fault diagnosis models. However, when operation conditions are significantly varied, existing transfer learning methods may encounter a bottleneck. The unsupervised methods will mismatch features, while supervised methods are constrained by insufficient target labeled instances. A weak prior embedding-based domain adaption network (WPEDAN) is proposed to resolve this problem. Specifically, the cluster ability of source data pre-trained network to target data is emphasized and enhanced directly and indirectly so as to obtain discriminative feature clusters. The target prior template samples are embedded and automatically delivered to the most relevant feature clusters, so the class information of target instances can be estimated based on similarity and supervised training on target is following. Moreover, an improved conditional maximum mean discrepancy (ICMMD) is developed to further align conditional distribution. Experiments on two challenging bearing datasets show that proposed method achieves more than 99% diagnosis accuracy in all tasks, and is significantly ahead of the comparison methods in complex transfer tasks. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of fault diagnosis, this article proposes a multi-fault diagnosis method for rotating machinery based on orthogonal supervised linear local tangent space alignment (OSLLTSA) and least square support vector machine (LS-SVM). First, the collected vibration signals are decomposed by empirical model decomposition (EMD), and a high-dimensional feature set is constructed by extracting statistical features, autoregressive (AR) coefficients and instantaneous amplitude Shannon entropy from those intrinsic model functions (IMFs) that contain most fault information. Then, the high-dimensional feature set is inputted into OSLLTSA for dimension reduction to yield more sensitive low-dimensional fault features, which not only achieves the combination of intrinsic structure information and class label information of dataset but also improves the discrimination of the low-dimensional fault features. Further, the low-dimensional fault features are inputted to LS-SVM to recognize machinery faults according to the LS-SVM parameters selected by enhanced particle swarm optimization (EPSO). Finally, the performance of the proposed method is verified by a fault diagnosis case in a rolling element bearing, and the results confirm the improved accuracy of fault diagnosis. [ABSTRACT FROM AUTHOR]

• An enhanced symplectic geometry mode decomposition method is proposed for harmonics decomposition and extraction. • Rotating speed harmonics can be adaptively extracted with high computational efficiency and accuracy. • The proposed method is reliable for instantaneous shaft phase estimation of rotating machineries. Tacholess order tracking (TLOT) has been one of the most powerful and applicable rotating machinery fault diagnosis methods. However, it is still a challenge to accurately estimate the instantaneous phase of the reference shaft under variable speed conditions. Although current available signal decomposition methods can deal with non-stationary vibration signal, they are probably interfered by some tough problems, such as prior knowledge requirement or heavy computational burden. In this paper, the aforementioned problems are addressed and an adaptive harmonic components extraction framework is proposed. Firstly, the vibration signal is low-pass filtered and down-sampled for computation speed acceleration. Harmonic components are subsequently extracted by enhanced symplectic geometry mode decomposition (ESGMD), which is based on Cramer-von Mises criterion. Secondly, surrogate data test is applied for pseudo components identification, thereby interferences induced by background noise can be filtered out adaptively. Finally, Hilbert transform is applied to obtain the instantaneous phase of the decomposed fundamental harmonic component, and thereby TLOT is conducted to realize fault diagnosis. The effectiveness of the proposed method has been validated by both simulated and experimental tests. The results exhibit that the proposed method outperforms conventional approaches in harmonic components extraction for rotating machinery fault diagnosis under variable speed conditions. [ABSTRACT FROM AUTHOR]

• A weakly supervised rotating machinery fault diagnosis method is proposed. • The weakly supervised fault diagnosis model is built upon non-local feature extraction and few-shot learning strategy. • The proposed method is effective for fault diagnosis when few labeled training samples are available. • The experimental results indicate the proposed method outperforms conventional fault diagnosis method. Despite the considerable success achieved by deep learning-based fault diagnosis methods, a powerful deep learning model must require a substantial set of training data to obtain a strong generalization ability in practical application. Focusing on the fault diagnosis case under small data sets, an enhanced non-local weakly supervised fault diagnosis method is proposed in this paper. In the proposed method, the few-shot learning strategy is presented to perform learning task augmentation to alleviate the overfitting problem caused by scarce training data, and the non-local operation is investigated to further enhance the feature extraction ability of convolutional neural network through capturing the long-range dependency. Two fault diagnosis experiments which were conducted on rolling bearing and bevel gear are carried out. The proposed method obtains 97.23% and 99.76% fault diagnosis accuracy in bearing data sets and gear data sets, which outperforms the traditional fault diagnosis methods. [ABSTRACT FROM AUTHOR]