Locally Linear Embedding on Grassmann Manifold for Performance Degradation Assessment of Bearings

Abstract

In recent years, a significant amount of research work has been undertaken to address the problem about prognostic and health management (PHM) systems. Performance degradation assessment, an essential part of PHM systems, is still a challenge. Subspaces, forming a non-Euclidean and curved manifold that is known as Grassmann manifold, are able to capture dynamic behaviors and accommodate the effects of variations. In this paper, we propose a novel local subspace model for performance degradation assessment termed locally linear embedding on Grassmann manifold (GM-LLE), where subspaces are treated as points on Grassmann manifold. Due to the nonstationary property of vibration signal, second generation wavelet package is used to decompose the vibration signal into different levels. Subspaces are modeled by optimal statistical features of different frequency bands, and then GM-LLE is used to assess bearing performance degradation by embedding the subspaces into reproducing kernel Hilbert spaces. Finally, simulated and experimental vibration signals are used to validate the effectiveness of the proposed method. The results show that the proposed method can assess the bearing's degradation effectively, and performs better compared with locally linear embedding.