The unstable movement of the cage will lead to frequent collisions between rolling elements and cage, which inevitably results in wear and failure of the cage or the rolling element bearing. However, most studies assume that the rolling elements move under pure rolling conditions. Hence, this study abandons the assumption of pure rolling, and the thermal elastohydrodynamic lubrication, cage flexibility and pocket clearance are considered to establish a multi-DOF skidding dynamic model of rolling element bearings based on time-varying comprehensive stiffness and damping. The intrinsic relationship between thermal elastohydrodynamic lubrication and oil film thickness, contact damping, and stiffness is studied. Considering the viscous resistance and centrifugal force acting on the rolling elements, a flexible cage model is established, and the effects of pocket clearance, radial clearance, and the rolling element deformation on interaction force between the cage and rolling elements are analyzed. The influence of operational conditions and bearing parameters on skidding characteristics is explored, and the model is validated using an existing model and experiment. The results indicate that thermal elastohydrodynamic lubrication has a significant impact on oil thickness, pressure, and temperature. The skidding speed and rate increase with the increase of the rotational speed, and decrease with the increase of the radial load. As the cage pocket clearance and equivalent stiffness increase, the skidding speed and rate are decreased. This study can provide support for the optimization design, friction reduction, and early failure prevention of rolling element bearings.

High-fidelity modeling of rolling bearings (RBs) is essential for accurately mapping their nonlinear vibration characteristics and supporting digital twin (DT)-assisted intelligent fault diagnosis (IFD). However, traditional dynamic models (DMs) often suffer from limited accuracy due to oversimplified assumptions and imprecise parameter identification. To address these limitations, a DT framework for high-fidelity dynamic modeling of RBs is proposed by inverse parameter identification with an improved egret swarm optimization (IESO) algorithm and time-frequency feature fusion in this study. The proposed IESO algorithm is enhanced with chaotic initialization, an adaptive balance factor, and Lévy-flight local search to improve population diversity, global exploration, and convergence accuracy. Subsequently, a nonlinear DM of RBs is built by comprehensively considering key factors, including contact stiffness, damping, clearance, flexible deformation of the cage, elastohydrodynamic lubrication (EHL), and fault geometry. The IESO algorithm is then employed for global inverse identification of model parameters through a hybrid objective function that integrates time-frequency-domain features. The experimental results show that the proposed modeling framework achieves high consistency between simulated and measured vibration responses and can effectively reproduce various fault types under different operating conditions. This study can provide a robust theoretical foundation and a validated high-fidelity modeling methodology for the DT-driven IFD of RBs.

Accurate diagnosis of compound faults in rolling bearings remains a major challenge due to nonlinear signal coupling, nonstationary interference, and strong noise that conceals weak fault characteristics. A targeted diagnostic method SIAgram to address these issues is proposed in this paper, which integrates the square envelope unbiased autocorrelation kurtosis (SEACK) selection with an improved multipoint optimal minimum entropy deconvolution adjusted and adaptive maximal overlap discrete wavelet packet transform. The method employs an improved minimum entropy deconvolution to suppress irrelevant noise and highlight fault impulsive components, while an adaptive wavelet basis index with dynamic coefficient of variation weighting is employed to select the most suitable basis under varying operating conditions. The SEACK index is then applied for frequency band selection and the process of characteristic extraction. Experimental validation on private and public datasets shows that SIAgram achieves higher diagnostic accuracy, faster computational convergence, and effectively identifies multiple fault characteristics even under complex conditions. Compared with existing blind and target diagnostic methods, the proposed method provides reliable, comprehensive, and efficient fault identification, making it well suited for fault diagnosis in rotating machinery.

In small-sample intelligent fault diagnosis (IFD) scenarios for rolling bearings (RBs), simplifying noise modeling in digital twin (DT) signals reduces fidelity and introduces uncertainty, resulting in insufficient consistency between simulated and measured data. Meanwhile, distribution discrepancies between the DT-generated source domain and measured target domain significantly degrade generalization performance, which constitutes two key bottlenecks in IFD of RBs. To address these challenges, a unified learning framework is constructed, and a DT-driven dual-alignment domain-adaptive multi-scale CNN–BiMamba network (DDAMCBN) is proposed. The improved Egret Swarm Optimization (IESO) algorithm is employed for inverse parameter identification to build a high-fidelity DT model. Subsequently, IESO-VMD is used to adaptively extract real industrial noise components from measured signals and fuse them with simulated signals under physics-consistency constraints, generating high-fidelity DT samples and narrowing the simulation–reality gap. Based on this, a dual-alignment domain adaptation strategy is developed by integrating maximum mean discrepancy (MMD) and adversarial domain adaptation, achieving global distribution alignment and domain-invariant feature learning to further reduce residual cross-domain discrepancies not eliminated by data fusion. Furthermore, a feature-coupled multi-scale CNN–BiMamba backbone is designed, where multi-scale convolutional features dynamically regulate the state transition parameters of the bidirectional Mamba module, enabling joint extraction of local impulsive features and long-term temporal dependencies. Experimental results conducted on a self-developed MFS dataset and the public CWRU dataset demonstrate that the proposed method achieves 98.84% accuracy under noisy small-sample conditions and 93.15% in virtual–real fusion scenarios, outperforming the existing methods and showing strong transferability and adaptability for rotating machinery IFD.

Ball bearings (BBs) are widely used support components in rotating machinery, and their performance under complex operating conditions directly affects system stability. In actual service, rotational velocity and load fluctuations can significantly alter internal contact states and disrupt the dynamic equilibrium of bearing components. However, classical dynamic models suffer from oversimplified configurations, calculated contact-lubrication effects and limited fluctuation simulation capacity, leading to the lack of an effective approach to capture transient motion variations and energy transmission of BB components under fluctuating conditions. To address this issue, a complete dynamic model of BBs considering oil lubrication is developed, featuring full degrees of freedom, coupling of Hertz contact and fluid dynamic pressure theories, and flexible multi-type fluctuation simulation. This model enables accurate analysis of transient relative displacements, velocities and contact forces of key BB components, and its accuracy is validated by comparing the numerically calculated cage dynamic response with published results. The motion characteristics of the inner ring, cage and balls, as well as the variation of their interactive forces, are investigated under steady-state conditions and typical velocity/load fluctuation patterns. The results show that compared with steady-state conditions, fluctuations in velocity and load reduce cage stability, expand the vibration range of inner ring, increase inter-component collision frequency and amplify impact forces. Notably, velocity fluctuations exert a more pronounced destabilizing effect on cage and ball motion, while ball-race contact forces are more susceptible to load fluctuations. This study provides a solid theoretical basis for maintaining the stability of rotating systems and analyzing BB failure mechanisms.

In practical industrial applications, fault samples of critical components such as rolling bearings are often scarce, thereby limiting the diagnostic performance of deep learning models under small samples scenarios. To address this issue, a graph feature-enhanced denoising diffusion probabilistic model (GF-DDPM) is proposed to generate high-quality fault samples and improve the accuracy of intelligent fault diagnosis. The proposed method utilizes a dynamic graph feature construction strategy to transform time-frequency representations into undirected graphs, enabling explicit modeling of spatial-frequency correlations among pixels. Furthermore, a residual block (GF-RB) is incorporated into the diffusion process to effectively fuse local spatial features extracted by convolutional neural network with global structural information captured by graph convolutional network, while gated feature fusion mechanisms are employed to enhance feature representation. Finally, high-quality fault samples are generated using the improved residual U-Net architecture, and a multidimensional comprehensive evaluation is performed based on the constructed comprehensive quality index QFSP. Experimental results on public and private datasets demonstrate that the proposed GF-DDPM significantly enhances sample diversity and diagnostic accuracy, offering an efficient and feasible solution for intelligent fault diagnosis with small samples scenarios.

High-fidelity modeling of rolling bearings (RBs) is essential for accurately mapping their nonlinear vibration characteristics and supporting digital twin (DT)-assisted intelligent fault diagnosis (IFD). However, traditional dynamic models (DMs) often suffer from limited accuracy due to oversimplified assumptions and imprecise parameter identification. To address these limitations, a DT framework for high-fidelity dynamic modeling of RBs is proposed by inverse parameter identification with an improved egret swarm optimization (IESO) algorithm and time-frequency feature fusion in this study. The proposed IESO algorithm is enhanced with chaotic initialization, an adaptive balance factor, and Lévy-flight local search to improve population diversity, global exploration, and convergence accuracy. Subsequently, a nonlinear DM of RBs is built by comprehensively considering key factors, including contact stiffness, damping, clearance, and fault geometry. The IESO algorithm is then employed for global inverse identification of model parameters through a hybrid objective function that integrates time-frequency-domain features. In addition, validation experiments are conducted on both the self-built MFS test rig and the publicly available CWRU dataset. The experimental results show that the proposed modeling framework achieves high consistency between simulated and measured vibration responses and can effectively reproduce various fault types under different operating conditions. This study can provide a robust theoretical foundation and a validated high-fidelity modeling methodology for the DT-driven IFD of RBs.

The dynamic interaction among multiple defective rollers in cylindrical roller bearings (CRBs) would lead to the complex vibrations of bearings and slip behavior of rollers. Compared with raceway defects, roller defects involve a more intricate contact process, which has often been oversimplified in previous studies. However, the characteristics of roller defects contacting with raceways are closely related to both the motion behavior of the rollers and the geometric features of the defects. To accurately capture the complex dynamic interactions between the defective regions of the rollers and the raceways, a dynamic model for CRBs with multiple defective rollers under elastohydrodynamic lubrication conditions is developed by introducing a time-varying displacement excitation function. Furthermore, accounting for both the number and relative position of defective rollers, a comprehensive dynamic model is proposed to investigate the vibration mechanisms in various multi-defect scenarios. Experimental results confirm the simulated response of roller bearings. The effects of the number and relative positions of defective rollers on bearing vibration characteristics and slipping behavior are further investigated, as well as their influence on the motion of the cage and healthy rollers. The results indicate that with increasing quantity of defective rollers, the vibration amplitude and cage slip ratio of the bearing would increase correspondingly. Moreover, reducing the spacing between defective rollers intensifies the vibration and slipping behavior of the bearing.

Domain adaptation-based methods are extensively applied to predict the Remaining Useful Life (RUL) of rolling bearings under complex operating conditions. However, the nonlinear degradation process of bearings gives rise to markedly non-stationary characteristics in vibration signals throughout the full life cycle. Although significant differences in fault features arise across different degradation stages, clearly identifying the critical degradation information remains a challenge. In this paper, a Signal Knowledge-enhanced Domain Adaptation Network (SKDAN) is proposed to learn domain-invariant features from non-stationary degradation processes, thereby improving cross-domain RUL prediction. Specifically, an adaptive short-time Fourier transform layer with a variable window is introduced to analyze the raw vibration signals in the time domain. This differentiable layer extracts time-frequency physical information with high energy concentration, which enhances the representation of degradation features. Subsequently, a novel discrepancy metric, termed Multi-Stage Maximum Mean Discrepancy (MSMMD), is proposed to replace the global average discrepancy with multiple local discrepancies. The MSMMD metric effectively increases the inter-class distance between cluster centers, which enables crossdomain feature alignment. Finally, an uncertainty measurement mechanism is constructed via a step-by-step training strategy, with the objective of quantifying the uncertainty in RUL results by calculating confidence intervals for prediction points. Comparative tests with other methods are conducted on two different bearing datasets, and the results demonstrate that SKDAN achieves superior performance and reliability in cross-domain RUL prediction.

The fault characteristic frequency of rolling bearing (RB) is widely used in fault diagnosis, and the theoretical values of fault characteristic frequencies currently used for studying local defect on rolling element (LDRE) are derived based on the self-rotation speed of the rolling element (RE). However, particularly in the case of supporting bearings, the inner raceway is rotated with the shaft while the outer raceway is fixed. This results in different kinematic properties of different raceways in contact with LDRE. Therefore, based on the different types of kinematic characteristics, fault characteristic frequencies of RE contacting with the different raceways have been derived respectively. The proposed frequencies are proved by experiment results and the benchmark data sets of bearing. Because the transmission path generated by LDRE contacting with the outer raceway is shorter than that generated by the inner raceway, the vibration response generated by LDRE contacting the outer raceway are more obvious. Therefore, combining the characteristic frequency of LDRE contacting with the inner raceway(fFRCI) with that of LDRE contacting with the outer raceway(fFRCO) can reduce misdiagnosis rate. The proposed fFRCO and fFRCI will provide a theoretical foundation for the fault diagnosis and condition monitoring of RBs.

The utilization of wind energy can provide auxiliary thrust and hence reduce the fuel consumption as well as carbon dioxide (CO2) emissions of wind-assisted ship. However, the use of sails would deviate main engine (ME) from its optimal operating point, which would reduce the engine fuel efficiency. The adoption of the shaft generator (SG) can maintain the ME running at the optimal fuel efficiency point in this condition. However, it is crucial to achieve the integrated optimization of the sailing speed, route, sails' angle of attack, and SG output power (SG-OP) to enhance the wind-assisted ship energy efficiency. Therefore, an integrated energy efficiency optimization method is proposed for reducing the ship fuel consumption. The results reveal that this method can effectively increase the energy efficiency of the wind-assisted hybrid ship, decreasing fuel consumption and energy efficiency operational index (EEOI) by about 5.25 % and 7.36 %, respectively.

In the rotor-bearing system (RBS), the dynamic behaviors of the supporting bearing will be influenced by the changes of vibration interaction between the supporting bearings. When a localized defect occurs in one of the supporting bearings, the abnormal vibration generated by faulty bearing is transmitted to the healthy bearing due to vibration interaction. The raceway of the healthy bearing will generate a new localized fault under this cyclic impact and variation in operating conditions, resulting in a transition from unidirectional to bidirectional vibration interaction. To investigate the dynamic behavior of supporting bearing under both types of vibration interaction, a comprehensive dynamic model of RBS was established by using Lagrange equations. The proposed model was validated through the experimental results, demonstrating that it effectively satisfies with the characteristics of vibration interaction. The results show that the dynamic behavior of healthy bearing is influenced by the faulty bearing due to unidirectional vibration interaction. The healthy bearing undergoes further transformation into a faulty bearing, and its dynamic behavior will enter chaos faster due to the co-variation of rotating speed and defect size under the influence of bidirectional vibration interaction. The sequential occurrence of multiple time-varying factors in the time series will result in significant alterations to the dynamic behavior of the supporting bearing. These results are expected to enhance the comprehension of dynamic behavior in supporting bearings.

Efficient and accurate diagnosis of rolling bearing fault is essential to prevent equipment damage. However, Intelligent Fault Diagnosis (IFD) methods are mostly data-dependent and lack interpretability, especially in the face of complex working conditions and multi-fault coupling environment, it is difficult to deal with the feature discrepancy between different distribution domains. To solve these issues, an interpretable Physics-Informed Subdomain Moment-Enhanced Adaptation Network (PISMEAN) is proposed, which aims to alleviate sub-domain shift and enhance the interpretability of diagnosis process through physical convolution kernel mapping and high-order moment discrepancy metric. Firstly, the wavelet basis function is utilized for time-frequency analysis of local signal, and multiple of adaptive bandpass filtering structures are designed based on the frequency response set, thus the Physics-Informed Dynamic Convolution (PIDConv) layer is constructed, which effectively improves the correlation between the feature mapping and physical prior information. In addition, a new Local Multi-Order Moment discrepancy metric (LMOMD) is proposed, which overcomes the limitations of traditional first-order moment in low-dimensional space and ignores local nonlinear differences, bridges the center distance of sub-clusters, and further enhances the accuracy of cross-domain distribution discrepancy calculation. The fault diagnosis test is carried out on Paderborn University (PU) and Mechanical Fault Simulation ( (MFS) datasets, and the results show that PISMEAN has good transfer generalization performance under varying working or mixed faults conditions.

Intelligent fault diagnosis of rolling bearings under data imbalance remains a critical challenge in industrial environments. A lightweight physical information diffusion model (LPIDM) is proposed to address the scarcity and imbalanced distribution of fault samples. Firstly, a region-adaptive noise schedule is introduced to replace the conventional linear schedule, enabling targeted augmentation of fault-relevant regions. Secondly, a depthwise separable residual (DSR) structure is incorporated into the U-Net architecture to reduce model complexity and number of parameters. Finally, a multi-objective, collaborative optimization loss function is designed to improve time-frequency fidelity of generated signals. The performance of the proposed method is evaluated through experiments on public and laboratory bearing datasets. The results demonstrate that LPIDM can generate high-quality fault samples, improve diagnostic accuracy and effectiveness under imbalanced conditions, and offer a practical solution for intelligent fault diagnosis in actual industrial scenarios.

Multiple local defects on races can alter the skidding behavior and lubrication performance of bearings. Dynamic modeling is necessary for the investigation of the vibration mechanism and the operating characteristics of faulty bearings. In the development of a dynamic bearing model with multiple defects, the effects of self-rotation and rotation of the ball, friction force, skidding, and thermal elastohydrodynamic lubrication (TEHL) are taken into account. Experiment results on machinery test tig confirmed the model. The effect of multiple defects on the lubrication characteristics and skidding characteristics of bearings is analyzed. When compared to single faults, multiple faults reduce not only the thickness and load-carrying capacity of the lubrication film but also exacerbate the skidding behavior of the bearing and the thermal effect in the contact area. The proposed model can comprehensively simulate the actual condition of a bearing with multiple defects.

Rolling bearing compound faults (RBCF) always interact and couple with each other, which makes it tremendously challenging to accurately diagnose them by processing the collected vibration signals. For the sake of separating and extracting fault features in RBCF, a novel method based on enhanced minimum entropy deconvolution (EMED) with adaptive periodized symplectic geometry mode decomposition (APSGMD) is proposed. First, weighted unbiased autocorrelation kurtosis is established as the new objective function to determine the optimal inverse filter coefficients of EMED method, which can enhance periodic impulse components of weak fault and eliminate background noise in RBCF signal. Second, for proposed APSGMD method, the termination condition based on cosine difference factor and kurtosis criterion are employed to adaptively select symplectic geometry components (SGCs), and a criterion for selecting singular value pairs is established to enhance the periodic impulse components of each SGC obtained. Finally, hierarchical clustering is leveraged to classify and reconstruct SGCs with different fault periods. A comprehensive simulation model is developed for RBCF to testify this method. The experimental results show that inner ring and outer ring faults, inner ring and ball faults, outer ring and ball faults, and inner–outer ring and ball faults can be accurately diagnosed by the proposed method.

Slipping and local defects are significant causes of abnormal vibration and instability in rolling element bearings (REBs). In particular, the secondary slipping of rolling elements (REs) triggered by local defects on the raceway would exacerbate the vibration and reduce rotational precision of the bearing system. Therefore, to more accurately reveal the characteristics of local slipping and the vibration response mechanisms in defective bearings, a comprehensive 4Nb + 4 degrees of freedom dynamic model of defective REB with flexible cage is proposed. This model based on the consideration of time-varying displacement excitation, cage stiffness and damping, pocket clearance, and isothermal elastohydrodynamic lubrication. Through comparisons the simulation results with both experimental and reference results, the proposed model is verified. The study investigated variations in contact forces between REs and overall raceways in detail, especially the trend of changes within the local defect area as the defect width increases. Furthermore, the effects of flexible cage stiffness, radial load, and speed on bearing slipping behavior are explored, along with the secondary slipping phenomenon triggered by local raceway defects. The results indicate that with increase of flexible cage stiffness and load, the REs slipping speed and cage slipping rate would decrease. Conversely, as rotational speed increases, both slipping speed and cage slipping rate would also increase.

Faults that occur in rolling bearings during operation are complex and variable. While extensive research has been conducted on compound faults involving multiple components, studies on multiple faults in single component are relatively scarce. However, the occurrence of multiple faults in single component is a common phenomenon. To address the issues of difficulty in feature extraction, numerous network parameters, and slow computational speed, a multi-scale dynamic snake convolution with fast spatial pyramid pooling attention (FSPPA) and lightweight comprehensive feature fusion (LCFF) network is proposed for multipoint fault diagnosis of rolling bearings. Firstly, multi-scale shallow feature extraction module is applied to extract the features from the original signals. Then, dynamic snake convolution (DSC) with FSPPA module is used to refine these features deeply. Subsequently, LCFF module is employed to reduce network parameters while still fully extracting fault features. Additionally, fault identification is obtained through the softmax function. Finally, the t-distributed stochastic neighbor embedding method is utilized to visually demonstrate the fault classification performance of the proposed method. The experimental evaluation conducted on bearing datasets indicates that the proposed network exhibits excellent performance of multipoint fault diagnosis in rolling bearings.

Resumo Objetivo Avaliar os efeitos do modelo de enfermagem de Newman na qualidade de vida e recuperação muscular do assoalho pélvico em pacientes com disfunção do assoalho pélvico pós-parto. Métodos Oitenta e oito pacientes com disfunção do assoalho pélvico pós-parto tratadas de janeiro a abril de 2023 foram divididas em grupo Observação e Controle (n=44) por meio de tabela de números aleatórios. O grupo Controle recebeu enfermagem de rotina e o grupo Observação recebeu cuidados de enfermagem de Newman. A qualidade de vida foi avaliada pelo Short Form-36 Health Status Questionnaire. A função do assoalho pélvico foi avaliada por meio do Pelvic Floor Impact Questionnaire-7 (PFIQ7) e da Pelvic Organ Prolapse Quantification (POPQ). Resultados Após a intervenção, as pontuações de aspectos físico, emocional, capacidade funcional, social e motor do grupo Observação foram superiores às do grupo Controle (P<0,05). As pontuações da Escala de Autoavaliação de Ansiedade e da Escala de Autoavaliação de Depressão do grupo Observação foram inferiores às do grupo Controle. O nível de conhecimento sobre a doença foi maior no grupo Observação do que no grupo Controle (P<0,05). O grupo Observação apresentou maior força das fibras musculares tipo I e II, e menores graus de fadiga das fibras musculares tipo I e II do que o grupo Controle (P<0,05). As pontuações PEIQ7 e POPQ do grupo Observação foram inferiores às do grupo Controle (P<0,05). Conclusão O modelo de enfermagem de Newman ajuda a melhorar a função do assoalho pélvico, a qualidade de vida e o conhecimento sobre a doença, além de aliviar a ansiedade, a depressão e outras emoções adversas.