A Study On Methods for Determining Phase Space Reconstruction Parameters

2021 ◽  
Author(s):  
Shihui Lang ◽  
Zhu Hua ◽  
Guodong Sun ◽  
Yu Jiang ◽  
Chunling Wei
Keyword(s):  
Time Delay ◽  
Phase Space ◽  
Correlation Dimension ◽  
Nearest Neighbor ◽  
Correlation Method ◽  
Phase Space Reconstruction ◽  
Lorenz Attractor ◽  
Embedding Dimension ◽  
Phase Trajectories ◽  
Auto Correlation

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.

scholarly journals Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 221
Author(s):  
Mariano Matilla-García ◽  
Isidro Morales ◽  
Jose Miguel Rodríguez ◽  
Manuel Ruiz Marín
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Mutual Information ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Optimal Time ◽  
Embedding Dimension ◽  
Simple Method ◽  
Correlation Integral

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes

Dynamics of stainless steel corrosion based on the theory of phase space reconstruction and chaos

2016 ◽  
Vol 63 (3) ◽  
pp. 214-225 ◽  
Author(s):  
Hong Men ◽  
Bin Sun ◽  
Xiao Zhao ◽  
Xiujie Li ◽  
Jingjing Liu ◽  
...  
Keyword(s):  
Phase Space ◽  
Correlation Dimension ◽  
Design Methodology ◽  
Electrochemical Noise ◽  
Steel Corrosion ◽  
Time Domain Analysis ◽  
Phase Space Reconstruction ◽  
Content Type ◽  
Information Method ◽  
Novel Method

Purpose The purpose of this study is to analyze the corrosion behavior of 304SS in three kinds of solution, 3.5 per cent NaCl, 5 per cent H2SO4 and 1 M (1 mol/L) NaOH, using electrochemical noise. Design/methodology/approach Corrosion types and rates were characterized by spectrum and time-domain analysis. EN signals were evaluated using a novel method of phase space reconstruction and chaos theory. To evaluate the chaotic characteristics of corrosion systems, the delay time was obtained by the mutual information method and the embedding dimension was obtained by the average false neighbors method. Findings The varying degrees of chaos in the corrosion systems were indicated by positive largest Lyapunov exponents of the electrochemical potential noise. Originality/value The change of correlation dimension in three kinds of solution demonstrated significant differences, clearly differentiating various types of corrosion.

An optimal global projection denoising algorithm and its application to shaft orbit purification

2011 ◽  
Vol 10 (6) ◽  
pp. 603-616 ◽  
Author(s):  
Shumin Hou ◽  
Ming Liang ◽  
Yourong Li
Keyword(s):  
Fault Diagnosis ◽  
Time Delay ◽  
Phase Space ◽  
Rotating Machinery ◽  
The Other ◽  
Optimal Time ◽  
Main Step ◽  
Signal Denoising ◽  
Embedding Dimension ◽  
Fault Features

Noise reduction is a main step in fault diagnosis of the rotating machinery. However, it is not effective enough to purify the nonlinear fault features from the vibration shaft orbits using the traditional signal denoising techniques. This article improved the global projection denoising algorithm via calculating the optimal time delay τ and embedding dimension m, which can be regarded as an extension of the global phase space reconstruction. The de-noising effects of Lorenz signal and the experiment cases illustrated the optimal global projection method is very effective and reliable in reducing the noise and reconstructing the signals. Consequently, it is heavily recommended for use in fault diagnosis of large rotating machinery as well as in the other kinds of machinery.

scholarly journals Parameter Selection for Phase Space Reconstruction in Hydrological Series and Rationality Analysis of its Chaotic Characteristics

10.29007/2fb8 ◽  
2018 ◽  
Author(s):  
Hongyan Li ◽  
Shanshan Bao ◽  
Yunqing Xuan
Keyword(s):  
Time Series ◽  
Phase Space ◽  
River Basin ◽  
Delay Time ◽  
Phase Space Reconstruction ◽  
Sequence Length ◽  
Rainfall Time Series ◽  
Embedding Dimension ◽  
Characteristic Index ◽  
Runoff Series

This study performed a rationality analysis of the delay time and embedding dimension value during phase space reconstruction in hydrological series and the effect on their chaotic characteristics. Using a monthly average runoff time series from the Ayanqian station (upstream) and the Jiangqiao station (midstream) in the Nen River Basin, we reached the following regularity conclusions. 1 Based on the flood season (4 months) in the Nen River Basin, we can deduce that the correlation sequence length for the runoff is 4~5 months, i.e., the delay time =3 or 4 is a reasonable choice. 2 Learn from the predictability experiment results for the monthly rainfall time series, we know that the calculation results of the G-P algorithm for the dimension of runoff series for the Nen River Basin are reasonable, i.e., the embedding dimension is no more than seven. 3 the most suitable parameters for the phase space reconstruction and its chaotic characteristic index in the Nen River Basin are as follows: delay time = 3~4, embedding dimension = 6~7, correlation dimension = 2.90~3.00, maximum Lyapunov index = 0.24~0.32, and the forecast time is 3~4 months.

Selection of proper embedding dimension in phase space reconstruction of speech signals

2000 ◽  
Vol 17 (2) ◽  
pp. 161-169 ◽  
Author(s):  
Jiayu Lin ◽  
Zhiping Huang ◽  
Yueke Wang ◽  
Zhenken Shen
Keyword(s):  
Phase Space ◽  
Phase Space Reconstruction ◽  
Speech Signals ◽  
Embedding Dimension ◽  
Selection Of

A Method of Fault Diagnosis for Reciprocating Compressor Based on Phase Space Reconstruction (PSR) and Empirical Mode Decomposition (EMD)

2012 ◽  
Vol 151 ◽  
pp. 83-86
Author(s):  
Yan Liu ◽  
Wen Yuan ◽  
Shi Gang Wang
Keyword(s):  
Phase Space ◽  
Empirical Mode Decomposition ◽  
Correlation Dimension ◽  
Lorenz System ◽  
Simulation Analysis ◽  
Vibration Signal ◽  
Reciprocating Compressor ◽  
Embedding Dimension ◽  
Mode Decomposition ◽  
Emd Method

Extract correlation dimension of vibration signal of reciprocating compressor based on G-P algorithm and empirical mode decomposition（EMD）technology, with found mode of EMD de-noise, with the incorporation of method of self-interrelated function and method of pseudo-phase portrait ensure delay-time and calculate embedding dimension by EMD method. Through simulation analysis of Lorenz system, Apply the method to identify valve faults of reciprocating compressor, the result indicate that the modeling method is effective.

FRACTURE IN COMPOSITES IN A NONLINEAR DYNAMIC SCHEME

1999 ◽  
Vol 09 (12) ◽  
pp. 2363-2367
Author(s):  
ROBERTO TONELLI ◽  
FRANCO MELONI ◽  
FRANCESCO AYMERICH
Keyword(s):  
Phase Space ◽  
Critical Points ◽  
Nonlinear Dynamic ◽  
Correlation Dimension ◽  
Tensile Loading ◽  
Embedding Dimension ◽  
Time Diagram ◽  
Temporal Series ◽  
Engineering Approach

We consider the fracture of a fibre reinforced graphite peek polymer when an axial periodical fatigue is applied. The energy-time diagram shows various critical points during the cyclic tensile loading. An analysis of the temporal series in the representative phase space, in terms of fractal and embedding dimension, enhances some properties not revealed by the standard engineering approach. In particular, variation of the correlation dimension before fracture may be used as a useful indicator for the subsequent breakdown.

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