Abstract: A new trend analysis method based on the manifold evolution for the running state of machinery equipment is presented. A one-dimensional time series is embedded into a high dimensional phase space to reconstruct a dynamical manifold. The tangent direction of each phase point in the manifold is approximated by extracting the local geometric information within the neighborhood. Then the tangent direction matrix, which contains the information of the manifold evolution, is obtained. Finally the weight score of each state, which serves as a feature index of the trend analysis, is calculated by performing multi-way principal component analysis to all states in the form of tangent direction matrices. The method is validated by using data measured from chaotic system with additive GAUSSIAN white noise and periodical impacts with increasing amplitude. The experiments indicate that the new method has advantage over the traditional features such as LYAPUNOV exponents and approximate entropy in terms of the noise robustness. In addition, the method is applied to the analysis of vibration signals measured from a bearing test-bed. In the experiment, the outer races of the bearings are made with some pits on purpose, representing different levels of fault. The experimental results show that the proposed method based on the manifold evolution is able to reveal the fatigue deterioration trend of mechanical system.

Key words: High dimensional space, Manifold evolution, Multi-way principle component analysis, Trend analysis