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.

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.