As a single-task classification method, support matrix machine (SMM) is widely used in mechanical equipment fault diagnosis. However, when diagnosing multi-objective tasks, it is difficult to fully utilize the common information between multiple tasks, resulting in limited information contained in the model. Meanwhile, SMM is extremely sensitive to abnormal samples, which is not conducive to model construction. To address the aforementioned issues, a novel multiple restriction cross-border matrix machine (MRCBMM) is proposed. In MRCBMM, a weighted constraint group (WCG) is firstly designed to adjust the influence of different abnormal samples on the hyperplane, thereby determining the optimal position of the hyperplane. Meanwhile, MRCBMM defines a matrix kernel expansion (MKE) that maps matrix samples to high-dimensional space to fully utilize the structural information of the original signal. In addition, to achieve cross-border diagnosis of MRCBMM, a regularized multi-task learning framework is constructed to complete the features and parameters. Two sets of multi-objective rotating mechanical fault datasets are used for validation, and the results show that MRCBMM improves diagnostic accuracy by approximately 2% in scenarios containing abnormal samples compared with existing methods, and consistently achieves over 98% accuracy on clean datasets.

Mechanical fault diagnosis faces significant challenges due to the susceptibility of traditional matrix classifiers to abnormal samples and their inability to leverage cross domain information. To address these limitations, this paper introduces a novel fuzzy cross domain matrix machine (FCDMM), which integrates fuzzy membership modeling with multi-task learning to enhance robustness and enable knowledge transfer across related tasks. FCDMM constructs fuzzy-based decision hyperplanes and designs adaptive boundary factors to mitigate the influence of outliers. Extensive experiments on multiple domain fault datasets demonstrate that FCDMM achieves remarkable accuracy rates of 98.86 % for bearing faults and 99.57 % for gear faults, significantly outperforming state-of-the-art methods.

The development of spectral analysis methods is very rapid, but these methods rarely take into account the difference of feature extraction under strong and weak random noise. In this article, a new adaptive spectral analysis method called enhanced Ramanujan spectrum (ERS) is proposed to strengthen the ability of feature extraction and noise robustness. First, hybrid Ramanujan Fourier transform is used to improve the calculation accuracy and period recognition ability of discrete Fourier transform. Second, generalized Ramanujan spectrum (GRS) is used to obtain features in the frequency domain. Finally, the ERS can be adaptively constructed by the optimal GRSs in each segment to reduce the influence of random noise. The analysis results of rolling bearing fault signals show that ERS is an effective feature extraction method and can be used in fault diagnosis field.

Support matrix machine (SMM) based methods have revolutionized the field of state identification by effectively mining correlations between fault features. However, some flaws limit its ability to handle interfered and limited samples, deriving from the purely focus on the closer samples nearing classify boundary and the thin design of binary classification nature, thus resulting SMM ignores the correlations between different samples and cannot align with the reality on the limited multiclass fault data. To address this issue, a novel approach called multiclass graph embedding support matrix machine (MGESMM) is proposed in this article. First, similarity matrix composed of similarity coefficient between each two samples are calculated by cosine distance. This similarity matrix is then used in manifold regularization-based graph embedding model, which can eliminate the negative impact of interfered and limited samples. Second, hamming loss-based predict error evaluation and multiclass loss-based boundary constraint is designed to form a direct multiclass classification constraint, thus the drawbacks of one-versus-one or one-versus-rest strategies for multiclass classification are prevented. Finally, to evaluate the efficacy of MGESMM, two roller bearing damage identification experiments are analyzed, and the results demonstrate that MGESMM achieves superior performance under different operating conditions.

In this article, a new deconvolution method, named maximum Ramanujan spectrum signal-to-noise ratio deconvolution (MRSD) method is proposed. MRSD updates the filter by maximizing the index ofv-Ramanujan spectrum signal-to-noise ratio (v-RSSNR) to improve the noise reduction effect and the performance of feature enhancement. On the one hand, the concept of generalized envelope is introduced into the MRSD method, and flexible envelopes are used to enhance the weak state features, and thev-Ramanujan spectrum of the signal is analyzed by using the mixed Ramanujan Fourier transform, so as to provide an optimal plane for the evaluation of weak state features. On the other hand, the MRSD method designs the filter by maximizing thev-RSSNR index, and optimizes the objective function by gradient descent. The simulation and experimental analysis results show that MRSD method is an effective noise reduction method and can accurately extract weak state features.

Federated learning has emerged as a promising approach for fault diagnosis, as its ability to learn from decentralized data while preserving client privacy for industry. Yet, it also brings the problem of nonidentically and independently distributed (Non-IID) data, which can result in model convergence delay and performance degradation. Recent research aims to alleviate the problem caused by cross-domain without considering by cross-location. However, it is common in industrial production to have devices across different monitoring locations. Furthermore, experimental results indicate that the diagnostic models' performance of the latest techniques is significantly affected. To address the cross-location Non-IID data problem, we propose DecFFD, a personalized federated fault diagnosis framework that decouples global and personalized features. In DecFFD, we design a reconstructor for each client that acts as a supervisor and decoupler to disentangle global and personalized features. We then present a client alignment algorithm to eliminate the differences in global features among clients. In addition, we provide a theoretical analysis of fairness and generalization capability, offering a theoretical guarantee for model convergence. Finally, extensive experiments are conducted on two real-world datasets. Experimental results show that the accuracy of DecFFD outperforms the accuracy that of the state-of-the-art approach by 14.67% and converges at a faster rate.

Exploring historical measurement data-driven health monitoring schemes for roller bearings is a current research hotspot. In engineering practice, the type of fault data obtained is often unknown and requires expensive costs to be annotated. However, most current intelligent diagnostic methods are based on the assumption that the labeled fault data is sufficient, so as to effectively establish the nonlinear mapping relationship between monitoring signals and health status. For this issue, a newly intelligent diagnosis method based on semi-supervised matrixized graph embedding machine (SMGEM) is proposed. In SMGEM, the geometric similarity relationship of unlabeled and labeled samples is obtained, which is subsequently embedded by incorporating a manifold regularization into the SMGEM model, so that SMGEM can use the structure information of unlabeled samples to assist modeling. Meanwhile, a weighted nuclear norm is used to highlight the importance of large singular values, so that a more accurate weight matrix can be constructed. The proposed method is verified by several roller bearing fault datasets, and experimental results demonstrate that the proposed semi-supervised diagnosis method can use a few labeled samples to obtain a better identification accuracy.