Nonlinear Chaotic Time Series Feature Extraction And Parameter Calculation

The ubiquity of chaos makes the feature recognition of chaotic time series be research hotspot. Based on discussion of multi-feature recognition method for chaotic time series, the paper studies feature extraction of chaotic time series and its application in multi-variable phase space reconstruction under certain noise background. Include:1) Multi-feature recognition method of chaotic time series. Phase space reconstruction, the largest Lyapunov exponent and other existing methods are integrated to describe the characteristics of chaotic sequences from different aspects, such as qualitative and quantitative, time and space, etc. The results are applied in tool wear detection using acoustic emission signals. And a method to monitor the tool damage state is built through computing chaotic characteristics of the acoustic emission signal in different periods of tool cutting, and analyzing the trends of them. The results show that there are chaotic phenomena existing in the acoustic emission signals, the correlation dimension and the largest Lyapunov exponent have relationship with tool damage state. Therefore a new idea is provided for online monitoring and prediction of tool damage.2) Applying the noise robustness of high-order cumulant, calculation of fractal dimension by the third-order cumulant is proposed, that is algorithm of local intrinsic dimension based on the third-order cumulant (HC3LID). Aiming at multivariate chaotic time series, a noisy multi-variable phase reconstruction method is established. First, HC3LID of time series is calculated according to different sections, and the results are analyzed based on an evaluation function to select the best slice of the third-order cumulant. Then, the embedding delay window of the sequence is determined by the linear correlation and nonlinear correlation of the time series, and the phase space can be reconstructed. Typical chaotic sequences with additive noise are calculated and simulated. The results show that the method proposed in the paper have a good robustness in the embedded dimension calculation of the noisy chaotic sequences, and the reconstructed strange attractors get good extension in the phase space, which better reflects the phase space properties of the multivariate chaotic sequence.