2DUMAP: Two-Dimensional Uniform Manifold Approximation and Projection for Fault Diagnosis

With the continuous development of industry, the operational data of mechanical equipment has grown exponentially. High-dimensional fault data often contain a significant amount of noise signals and redundant information, severely impacting the performance of fault diagnosis methods. The currently popular manifold learning dimensionality reduction algorithm, Uniform Manifold Approximation and Projection (UMAP), effectively extract complex nonlinear relationships in fault diagnosis data while preserving both local and global structures. However, the UMAP has Out-of-Sample Problem, making it unable to directly map new samples to the learned low-dimensional space. To address this problem, a mapping matrix is learned to directly extend Out-of-Sample data, but this approach still faces the issue of the mapping matrix being too large. To tackle this challenge, the Two-Dimensional UMAP method is proposed, which transforms one-dimensional vector inputs into two-dimensional matrix representations. Subsequently, considering discriminant information, a Supervised Two-dimensional UMAP algorithm (2DSUMAP) is proposed. This study conducts fault diagnosis experiments on 7 datasets of bearings and gears to comprehensively evaluate the proposed methods. The experiments demonstrate that these methods solve the inherent Out-of-Sample Problem of the UMAP, effectively reduce algorithm complexity, and have superior classification performance and strong robustness in practical fault diagnosis applications.