Abstract: A new noise reduction method for nonlinear time series based on principal manifold learning is proposed. The one-dimensional time series is embedded into a high phase space in which the principal manifold of the dynamical system, in the form of a single global orthogonal coordinate system of low dimensionality, is identified by nonlinear dimensionality reduction method. The final noise reduction result is achieved after averaging of phase space data which are regenerated according to the principal manifold. The results of numerical experiment on Lorenz system illustrate that, compared with the existed nonlinear noise reduction methods such as singular value decomposition(SVD)-method, the method based on principal manifold learning is more effective to eliminate Gaussian white noise in chaotic time series. The new method is applied to fault analysis of a vibration signal from a defective gear box with a broken tooth. The denoised result shows that the impact features, which are overwhelmed by noise, can be successfully extracted via the new noise reduction scheme.

Key words: Principal manifold learning Nonlinear time series, Fault diagnosis, Noise reduction