Multivariate phase space reconstruction by nearest neighbor embedding with different time delays

Abstract Several pairs of algorithms were used to determine the phase space reconstruction parameters to analyze the dynamic characteristics of chaotic time series. The reconstructed phase trajectories were compared with the original phase trajectories of the Lorenz attractor, Rössler attractor, and Chens attractor to obtain the optimum method for determining the phase space reconstruction parameters with high precision and efficiency. The research results show that the false nearest neighbor method and the complex auto-correlation method provided the best results. The saturated embedding dimension method based on the saturated correlation dimension method is proposed to calculate the time delay. Different time delays are obtained by changing the embedding dimension parameters of the complex auto-correlation method. The optimum time delay occurs at the point where the time delay is stable. The validity of the method is verified through combing the application of correlation dimension, showing that the proposed method is suitable for the effective determination of the phase space reconstruction parameters.

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High-dimensional time delays selection for phase space reconstruction with information theory

2012 2nd International Conference on Uncertainty Reasoning and Knowledge Engineering ◽

10.1109/urke.2012.6319545 ◽

2012 ◽

Author(s):

Chuntao Zhang ◽

Jialiang Xu ◽

Xiaofeng Chen ◽

Jiao Guo

Keyword(s):

Information Theory ◽

Phase Space ◽

Time Delays ◽

Phase Space Reconstruction ◽

High Dimensional ◽

Selection For

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Application of Time Series Analysis and Neural Networks to the Modeling and Analysis of Forced Vibrating Mechanical Systems

Design Engineering, Volumes 1 and 2 ◽

10.1115/imece2003-55519 ◽

2003 ◽

Cited By ~ 1

Author(s):

John Zolock ◽

Robert Greif

Keyword(s):

Neural Networks ◽

Time Series ◽

Phase Space ◽

Time Series Analysis ◽

Nearest Neighbor ◽

Mechanical Systems ◽

Phase Space Reconstruction ◽

Response Measurement ◽

Modeling And Analysis ◽

Series Analysis

A theoretical and mathematical based methodogy is discussed that utilizes time series analysis techniques and neural networks to model forced vibrating mechanical systems using measured input-output data. A technique in nonlinear time series analysis known as phase space reconstruction may be used to extend our understanding of the active dynamics recorded in a single time series measurement. Using a recorded output (response) measurement phase space reconstruction parameters are calculated; the embedding dimension is estimated using the method of false nearest neighbor, and the time delay is estimated from the first minimum of the mutual information. The phase space reconstruction characteristics are then used to fully shape the architecture of a time delayed neural network model for the dynamical system. The modeling methodology is applied to several forced vibrating systems common to many fields of engineering. The neural models are then used to analyze new input, demonstrating the usefulness and importance of the methodology.

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