High-order Statistic Feature Extraction And Third Analysis Of Nonlinear Time Series

Nonlinear time series is a common phenomenon in nature, and it is often difficult to getthe essential characteristics of the system by traditional linear analysis methods. Based on thephase space reconstruction theory, the paper has a good anti-noise property method whichdetermines the reconstruction parameters, analyzes the characteristics and evolution law ofnonlinear time series in the phase space. As follows:1. The higher-order statistics reflects the high-level nonlinear relation of the time series,and has the blind Gaussian noise characteristic. Based on the Takens embedding theorem andthe characteristics of higher-order statistics, this paper is used to establish a fractal dimensioncalculation method of strange attractors. To reduce the influence on dimension calculationcaused by different choices of the cumulant slice, the cumulant slice evaluation function isestablished. By comparing the calculated results, it could select a more robustness cumulantslice to noise and the change of reconstruction parameters such as embedding dimension, et al.Then, combining with embedding time window method, the reconstruction parameters arecalculated, and the phase space is reconstructed with clearer attractor trajectories.2. Applying the research method to the analysis procedure of cutting tool acousticemission siganls and rolling bearing vibration signal. In the reconstructed phase space, themaximum Lyapunov exponent and K entropy, two characteristic parameters are calculated andtheir evolution trends are analyzed. Simulation results show that the extractive characteristicsusing the method of this paper could effectively reflect the variation trendency of tool wearingthroughout the cutting process. It also could effectively diagnose the normal and faultbearings. Therefore, it offers an approach to on-line monitoring and system healthy diagnosisbased on the measured signal.