In this paper, two fixed-point iteration methods for solving the tensor absolute value equation (TAVE) are introduced and their convergence properties are discussed. The optimal value of the parameter for both methods is derived. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.

Recently, Lv and Miao (Appl Math Lett 154: 109109, 2024) presented a new inexact fixed point iteration method which is based on an inexact fixed point iteration method for solving the tensor absolute value equation (TAVE). In this paper, we give new convergent conditions of the inexact fixed point iteration method and the new inexact fixed point iteration method, respectively.

Rolling bearings are pivotal components within rotating mechanical systems, and accurately predicting their remaining service life holds significant practical importance. This paper addresses issues prevalent in common deep learning methods for predicting remaining useful life (RUL), notably inadequate feature extraction and low prediction accuracy resulting from reliance solely on short-term or long-term dependent features.In this paper, we introduce a residual useful life prediction method for bearings, named TcLstmNet-CBAM. Compared to conventional deep learning-based bearing life prediction methods, the proposed approach leverages a temporal convolutional network (TCN) to extract long-term temporal dependencies and higher-level spatial features from historical data, while employing a long short-term memory (LSTM) network to capture short-term temporal dependencies and sequence relationships. Additionally, a Convolutional Block Attention Module (CBAM) is incorporated to perform multi-dimensional weighting on the extracted features, assigning greater importance to critical features. Consequently, this method enables more comprehensive feature extraction and enhances RUL prediction accuracy by emphasizing key features. Finally, to validate the effectiveness of the proposed approach, we conducted experiments on the PHM2012 and XJTU-SY rolling bearing datasets, comparing its performance against several other prevalent deep learning prediction methods. Experimental results demonstrate that the proposed TcLstmNet-CBAM method can effectively predict the remaining useful life (RUL) of bearings, achieving a mean absolute error (MAE) of 2.287 and a root mean square error (RMSE) of 3.123. These results strongly validate the effectiveness and superiority of the proposed method.

Rolling bearings, as critical components of rotating machinery, support and reduce friction in mechanical systems. Failures in these bearings can not only disrupt project progress but also lead to substantial economic losses and potentially cause casualties. Consequently, research into rolling bearing fault diagnosis is of paramount importance. This paper addresses the problem of bearing failure by proposing a fault diagnosis method that combines wavelet packet energy spectrum analysis with an Extreme Learning Machine (ELM). To replicate real-world noisy operational environments, high-intensity noise is added to the collected signal samples. These samples undergo wavelet packet decomposition and reconstruction for energy feature extraction, with the band energy being selected via the wavelet packet energy spectrum. The extracted energy features are then used to construct a dataset that is input into the ELM model for multiple training iterations. The diagnostic accuracy of the model reached 95.1429±2.87%, demonstrating the method's effectiveness in bearing fault diagnosis and its ability to enhance the recognition and diagnosis capabilities of bearing fault signals.

As a vital component of rotating machinery, the accurate fault diagnosis of rolling bearings is crucial to maintaining project continuity, minimizing economic losses, and ensuring safety. This document introduces an innovative method for diagnosing faults in rolling bearings, utilizing a blend of multi-domain feature extraction and PSO Support Vector Machine (PSO-SVM).This method integrates the time domain, frequency domain, and wavelet packet energy features of vibration signals to construct a comprehensive feature library that enhances sensitivity and classification accuracy. The PSO-SVM model classifies these fault features, with the particle swarm algorithm optimizing the parameters automatically and the support vector machine providing robust interpretability. To validate the effectiveness of the proposed method, tests were conducted using both open-source and laboratory data. Gaussian noise was introduced to the vibration signals to replicate complex operational conditions. The diagnostic accuracy of this model was then benchmarked against traditional SVM and Genetic Algorithm-Back Propagation (GA-BP) models. Evidence shows the technique's high accuracy, sturdiness, sturdiness, and resilience, making it suitable for diagnosing faults in rolling bearings.

Recent research has demonstrated that various network architectures combined with Transformers exhibit outstanding performance, particularly in models integrating Transformers with CNNs, which have made significant strides in the field of fault diagnosis. However, existing models that combine Transformers and CNNs fail to effectively utilise multi-scale convolutions for feature extraction and suffer from channel weight information loss, which weakens the network's feature extraction capability. Therefore, this paper proposes an MK-ACFormer framework for mechanical fault diagnosis to address these issues. Firstly, a multi-scale convolutional attention module is designed to extract features with multiple local receptive fields from vibration signals and capture inter-channel correlations, thereby optimally distributing channel weights. Secondly, the ECA module is employed to fuse features extracted from different scale convolutions with those derived from the Transformer, adaptively adjusting feature channels to assign varying weights and reduce information redundancy. Experimental results indicate that the proposed method is more robust compared to recent Transformer-CNN integrated approaches and CNN-based improvements for fault diagnosis, further validating the model's effectiveness through performance analysis. Finally, transfer experiments on small sample data demonstrate the model's capability in employing transfer learning methods.

Rolling bearings are crucial components in mechanical systems, and accurately predicting their remaining service life holds significant practical importance. To tackle the shortcomings of conventional deep learning methods for predicting remaining useful life (RUL), which suffer from insufficient feature extraction and low prediction accuracy, especially regarding single short-term and single long-term dependent features. This paper introduces a residual remaining useful life prediction method for bearings, named TCN-LSTM-attention, which leverages CBAM attention alongside parallel Temporal Convolutional Network (TCN) and Long Short-Term Memory (LSTM) components. The method employs parallel TCN and LSTM network architectures for feature extraction, concurrently integrating the CBAM attention mechanism to weigh features across various dimensions. This approach not only captures a more comprehensive distribution of features but also amplifies the representation of critic al features, thereby significantly enhancing RUL prediction accuracy. Finally, to assess the efficacy of the proposed method, we conducted experiments using the PHM2012 rolling bearing datasets. The results demonstrate the method's robustness and generalization capabilities.

Rolling bearings are the core devices in the industrial field, widely used in machinery production and automation industry. Therefore, it is necessary to detect the fault of rolling bearing. In this paper, an improved VGG model based on Channel Attention mechanism (SENet) is proposed to extract the spatial features of multi-scale features after fault signal preprocessing. The BiGRU network model based on Global Attention optimization is proposed to extract the time domain features of multi-scale features after fault signal pretreatment. Excellent results are obtained by parallel fusion for fault detection.

Bearings are crucial components of modern mechanical equipment and their failure can lead to equipment downtime, economic losses, and potential threats personal safety. Therefore, it is essential to carry out fault diagnosis of bearings. In this paper, Multichannel Signal Transformer (MST) model is employed for diagnosing bearing faults. Initially, a single vibration signal and two motor current signals are collected and combined into a multichannel signal. This multichannel signal is then used to train and test the MST model. The performance of the MST model is subsequently compared with that of an established one-dimensional CNN. The feasibility of the method is verified by comparing the accuracy and loss function values of the two models in fault diagnosis. Finally, the confusion matrix of the MST model for fault classification is analyzed, and the t-SNE visualization is performed on the features of the fully-connected layer. The results demonstrate that the MST model has a higher accuracy in fault diagnosis.

To address the decline or failure in the autonomous learning capability of traditional transfer learning methods when training and test samples come from different machines, resulting in low cross-machine fault diagnosis rates, we propose a cross-domain manifold structure preservation (CDMSP) method for diagnosing rolling bearing faults across machines. The CDMSP method can induce the manifold space projection matrices of the source and target domains more effectively. This method maps high-dimensional features into a low-dimensional manifold, preserving non-linear relationships and aligning distribution differences while maintaining cross-domain manifold structure consistency. Additionally, highly confidently labeled target domain samples are selected from each mapping result and added to the training dataset to enhance subspace learning in subsequent iterations. The CDMSP method is both simple and effective at capturing the underlying structures and patterns in the data. The CWRU dataset and our self-built test platform dataset were used to validate this method. Experimental results show that CDMSP, as a non-deep domain adaptation method of transfer learning, outperforms similar methods in cross-machine fault identification, achieving a maximum fault identification accuracy of 100 % with excellent convergence performance. Furthermore, simulated diagnostic experiments under noise interference indicate that CDMSP maintains high fault identification accuracy, even in noisy environments. Overall, CDMSP is an efficient and reliable new method for diagnosing cross-machine bearing faults.

Background and purposeAtherosclerosis is a very complex process influenced by various systemic and local factors. Therefore, in patients with bilateral carotid plaques (BCPs), there may be differences in carotid plaque vulnerability between the sides. We aimed to investigate the differences in BCP characteristics in patients with BCPs using magnetic resonance vessel wall imaging (MR-VWI). MethodsParticipants with BCPs were selected for subanalysis from a multicentre study of Chinese Atherosclerosis Risk Evaluation II. We measured carotid plaque burden, identified each plaque component and measured their volume or area bilaterally on MR-VWI. Paired comparisons of the burden and components of BCPs were performed. ResultsIn all, 540 patients with BCPs were eligible for analysis. Compared with the right carotid artery (CA), larger mean lumen area (p<0.001), larger mean wall area (p=0.025), larger mean total vessel area (p<0.001) and smaller normalised wall index (p=0.006) were found in the left CA. Regarding plaque components, only the prevalence of lipid-rich necrotic core (LRNC) in the left CA was higher (p=0.026). For patients with a vulnerable plaque component coexisting on both sides, only the intraplaque haemorrhage (IPH) volume (p=0.011) was significantly greater in the left CA than in the right CA. ConclusionsThere were asymmetries in plaque growth and evolution between BCPs. The left carotid plaques were more likely to have larger plaque burden, higher prevalence of LRNC and greater IPH volume, which may contribute to the lateralisation of ischaemic stroke in the cerebral hemispheres.

Expert consensus recommends linear-combination modeling (LCM) of 1 H MR spectra with sequence-specific simulated metabolite basis function and experimentally derived macromolecular (MM) basis functions. Measured MM basis functions are usually derived from metabolite-nulled spectra averaged across a small cohort. The use of subject-specific instead of cohort-averaged measured MM basis functions has not been studied widely. Furthermore, measured MM basis functions are not widely available to non-expert users, who commonly rely on parameterized MM signals internally simulated by LCM software. To investigate the impact of the choice of MM modeling, this study, therefore, compares metabolite level estimates between different MM modeling strategies (cohort-mean measured; subject-specific measured; parameterized) in a lifespan cohort and characterizes its impact on metabolite-age associations. 100 conventional (TE = 30 ms) and metabolite-nulled (TI = 650 ms) PRESS datasets, acquired from the medial parietal lobe in a lifespan cohort (20-70 years of age), were analyzed in Osprey. Short-TE spectra were modeled in Osprey using six different strategies to consider the MM baseline. Fully tissue- and relaxation-corrected metabolite levels were compared between MM strategies. Model performance was evaluated by model residuals, the Akaike information criterion (AIC), and the impact on metabolite-age associations. The choice of MM strategy had a significant impact on the mean metabolite level estimates and no major impact on variance. Correlation analysis revealed moderate-to-strong agreement between different MM strategies (r > 0.6). The lowest relative model residuals and AIC values were found for the cohort-mean measured MM. Metabolite-age associations were consistently found for two major singlet signals (total creatine (tCr])and total choline (tCho)) for all MM strategies; however, findings for metabolites that are less distinguishable from the background signals associations depended on the MM strategy. A variance partition analysis indicated that up to 44% of the total variance was related to the choice of MM strategy. Additionally, the variance partition analysis reproduced the metabolite-age association for tCr and tCho found in the simpler correlation analysis. In summary, the inclusion of a single high signal-to-noise ratio MM basis function (cohort-mean) in the short-TE LCM leads to more lower model residuals and AIC values compared with MM strategies with more degrees of freedom (Gaussian parametrization) or subject-specific MM information. Integration of multiple LCM analyses into a single statistical model potentially allows to identify the robustness in the detection of underlying effects (e.g., metabolite vs. age), reduces algorithm-based bias, and estimates algorithm-related variance.

Expert consensus recommends linear-combination modeling (LCM) of 1 H MR spectra with sequence-specific simulated metabolite basis function and experimentally derived macromolecular (MM) basis functions. Measured MM basis functions have been derived from metabolite-nulled spectra averaged across a small cohort. The use of subject-specific instead of cohort-averaged measured MM basis functions has not been studied. Furthermore, measured MM basis functions are not widely available to non-expert users, who commonly rely on parameterized MM signals internally simulated by LCM software. To investigate the impact of the choice of MM modeling, this study, therefore, compares metabolite level estimates between different MM modeling strategies (cohort-mean measured; subject-specific measured; parameterized) in a lifespan cohort and characterizes its impact on metabolite-age associations. 100 conventional (TE = 30 ms) and metabolite-nulled (TI = 650 ms) PRESS datasets, acquired from the medial parietal lobe in a lifespan cohort (20-70 years of age), were analyzed in Osprey. Short-TE spectra were modeled in Osprey using six different strategies to consider the macromolecular baseline. Fully tissue- and relaxation-corrected metabolite levels were compared between MM strategies. Model performance was evaluated by model residuals, the Akaike information criterion (AIC), and the impact on metabolite-age associations. The choice of MM strategy had a significant impact on the mean metabolite level estimates and no major impact on variance. Correlation analysis revealed moderate-to-strong agreement between different MM strategies (r > 0.6). The lowest relative model residuals and AIC values were found for the cohort-mean measured MM. Metabolite-age associations were consistently found for two major singlet signals (tCr, tCho) for all MM strategies, however, findings for highly J-coupled metabolites it was depended on the MM strategy. A variance partition analysis indicated that up to 44% of the total variance was related to the choice of MM strategy. Additionally, the variance partition analysis reproduced the metabolite-age association for tCr and tCho found in the simpler correlation analysis. In summary, the inclusion of a single high-SNR MM basis function (cohort-mean) leads to more robust metabolite estimation (lower model residuals and AIC values) compared to MM strategies with more degrees of freedom (Gaussian parametrization) or subject-specific MM information. Integration of multiple LCM analyses into a single statistical model potentially improves the robustness in the detection of underlying effects (e.g. metabolite vs age), reduces algorithm-based bias, and estimates algorithm-related variance.

In this paper, we construct two-step tensor splitting iteration method for multi-linear systems. Moreover, we present convergence analysis of this method. Finally, we give two numerical examples to show that this new method is more ecient than the existing methods.

In this paper, new preconditioned GAOR methods are proposed for solving a class of 2 x 2 block structure linear systems arising from the weighted linear least squares problems. Comparison theorems are derived. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods in the previous literatures whenever these methods are convergent. A numerical example is given to confirm our theoretical results.

In this paper, we construct a two-step modulus-based multisplitting iteration method based on multiple splittings of the system matrix for the nonlinear complementarity problem. And we prove its convergence when the system matrix is an H-matrix with positive diagonal elements. Numerical experiments show that the proposed method is efficient.

为了快速求解一类来自加权线性最小二乘问题的2×2块线性系统,本文提出一类新的预处理子用以加速GAOR方法,也就是新的预处理GAOR方法.得到了一些比较结果,这些结果表明当GAOR方法收敛时,新方法比原GAOR方法和之前的一些预处理GAOR方法有更好的收敛性.而且,数值算例也验证了新预处理子的有效性.

In this paper, we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem. And we prove the convergence of the method when the system matrix is an $$H_+$$ -matrix. Finally, we give two numerical examples.

BackgroundThe development of a noninvasive, objective, and accurate method to assess peripheral nerve disorders in Guillain–Barre syndrome (GBS) is of clinical significance. Diffusion tensor imaging (DTI) has been used to evaluate some peripheral nerve disorders.PurposeTo investigate the feasibility of DTI in evaluating the peripheral nerve disorders in patients with GBS.Study TypeCase control.SubjectsTwenty GBS patients and 16 healthy volunteers.Field Strength/Sequence3.0T, T1WI‐SE, T2WI‐SPAIR, DTI; electrophysiology.AssessmentMRI data were analyzed by two radiologists blindly and independently. Fractional anisotropy (FA), apparent diffusion coefficient (ADC), axial diffusion coefficient (AD), and radial diffusion coefficient (RD) values of tibial nerve (TN) and common peroneal nerve (CPN) were recorded. Motor nerve conduction velocity (MCV) and motor nerve conduction amplitude of TN and CPN were recorded.Statistical TestsIntraclass correlation coefficient (ICC), t‐test, receiver‐operating characteristic (ROC), and area under the curve (AUC) analysis, Pearson correlation coefficient.ResultsThe FA and AD values of TN and CPN in the GBS group were significantly lower and the ADC and RD values were higher than those in the controls (P <0.05). The AUC of the FA values (0.970 for TN and 0.927 for CPN) were higher than that of the ADC, AD, and RD values. FA and AD values were positively correlated and ADC, RD values were negatively correlated with MCV and motor nerve conduction amplitude, respectively (P <0.05). The correlations between FA value and electrophysiology parameters were the highest.Data ConclusionDTI quantitative parameters could evaluate the disorders of peripheral nerves in patients with GBS. A moderate correlation was observed between DTI and electrophysiology parameters.Level of Evidence: 3Technical Efficacy: Stage 1J. Magn. Reson. Imaging 2019;49:1356–1364.

By multiple realignments of density matrices, we present a new separability criterion for the multipartite quantum state, which includes the computable cross-norm or realignment criterion and the multipartite partial realignment criterion as special cases. An example is used to show that the new criterion can be more efficient than the corresponding multipartite realignment criteria given in Horodecki et al. (Open Syst Inf Dyn 13:103–111, 2006) and Shen et al. (Phys Rev A 92:042332, 2015).