DETECTING CHAOS TIME SERIES VIA COMPLEX NETWORK FEATURE

2011 ◽  
Vol 25 (23) ◽  
pp. 1889-1896 ◽  
Author(s):  
QIANG TANG ◽  
JUNCHAN ZHAO ◽  
TIESONG HU
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Complex Network ◽  
Stream Flow ◽  
Yangtze River ◽  
Random Series ◽  
Coordinate Method ◽  
Network Feature ◽  
Periodic Time Series

In this paper, an effective method from time series to complex network via phase space reconstruction is introduced. We reconstruct the phase space from a time series by the time-delay coordinate method. Each state vector of phase space is regarded as a vertex of network and the connection is based on the distance of the vertices in phase space. The networks corresponding to various time series, the x component of the chaotic Rössler system, noisy periodic time series and random series, display different topology feature. So we can determine whether a time series is chaotic series by the topology feature of corresponding network. Finally, the daily stream-flow series of Yangtze River is investigated to validate the effective of our method.

scholarly journals Traffic Flow Characteristics mining of Time Series Data Based on Phase Space Reconstruction Using Complex Networks

CONVERTER ◽  
2021 ◽  
pp. 146-161
Author(s):  
Xue Xing, Yaqi Zhai, Zhongtai Jiang, Xiaoyu LI
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Network Analysis ◽  
Traffic Flow ◽  
Complex Network ◽  
Degree Distribution ◽  
Data Flow ◽  
Flow Time ◽  
Phase Space Reconstruction ◽  
Traffic Data

Traffic flow time series is vital for mining the traditional statistical characteristics by using the theory of statistics and machine learning when its identity is a special time series. The network analysis of the traffic flow time series, who uses the complex network of time series analysis method, is designed to inquire into the special law of traffic flow time series which uses its visualization characteristics. Through the network analysis of traffic data flow, the connotation of traffic data flow can be revealed, and the relationship between all data and some data can be further studied. Therefore, it is constructed by combination with the phase space reconstruction theory. The phase space trajectory may be squeezed and the structure of attractor may change. We need to use C-C method to estimate the time delay according to the characteristics of integral parameters, and use G-P algorithm to estimate the embedding dimension to avoid it. This study can effectively reveal the motion law of the system. After constructing the complex network of traffic flow time series with various traffic parameters, the degree distribution, clustering coefficient and modularization of the representative critical threshold corresponding network are statistically analysed. The analysis results show that the new networked structure of traffic flow time series proposed in this study has strong advantages, and its core is phase space reconstruction, which can well reflect the information space of traffic dynamic fluctuation. The time series networking method based on phase space reconstruction has become a new approach to inquire into the characteristics of traffic flow time series. The degree distribution of the actual multi-traffic parameter time series construction network satisfies the characteristics of a Gaussian distribution. Their average clustering coefficients have attenuation characteristics, and their modularization degree is obvious.

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

scholarly journals Combining Snow Depth From FY-3C and In Situ Data Over the Tibetan Plateau Using a Nonlinear Analysis Method

2021 ◽  
Vol 9 ◽  
Author(s):  
Aixia Feng ◽  
Feng Gao ◽  
Qiguang Wang ◽  
Aiqing Feng ◽  
Qiang Zhang ◽  
...  
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Tibetan Plateau ◽  
Satellite Data ◽  
Snow Depth ◽  
Hydrological Cycle ◽  
The Tibetan Plateau ◽  
Analysis Method

Snow cover over the Tibetan Plateau plays a vital role in the regional and global climate system because it affects not only the climate but also the hydrological cycle and ecosystem. However, high-quality snow data are hindered due to the sparsity of observation networks and complex terrain in the region. In this study, a nonlinear time series analysis method called phase space reconstruction was used to obtain the Tibetan Plateau snow depth by combining the FY-3C satellite data and in situ data for the period 2014–2017. This method features making a time delay reconstruction of a phase space to view the dynamics. Both of the grids and their nearby in situ snow depth time series were reconstructed with two appropriate parameters called time delay and embedding dimension. The values of the snow depth for grids were averaged over the in situ observations and retrieval of the satellite if their two parameters were the same. That implies that the two trajectories of the time series had the same evolution trend. Otherwise, the snow depth values for grids were averaged over the in situ observation. If there were no in situ sites within the grids, the retrieval of the satellite remained. The results show that the integrated Tibetan Plateau snow depth (ITPSD) had an average bias of –1.35 cm and 1.14 cm, standard deviation of the bias of 3.96 cm and 5.67 cm, and root mean square error of 4.18 cm and 5.79 cm compared with the in situ data and FY-3C satellite data, respectively. ITPSD expressed the issue that snow depth is usually overestimated in mountain regions by satellites. This is due to the introduction of more station observations using a dynamical statistical method to correct the biases in the satellite data.

A Methodology for the Modeling of Rail Vehicles From Time Series Measurements Using Time-Delay Neural Networks

2007 ◽  
Author(s):  
John Zolock ◽  
Robert Greif
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Dynamical Systems ◽  
Dynamic Systems ◽  
Phase Space Reconstruction ◽  
Series Data ◽  
Modeling Methodology ◽  
Forcing Function

The main goal of this research is to develop and demonstrate a general, efficient, mathematically and theoretically based methodology to model nonlinear forced vibrating mechanical systems from time series measurements. A system identification modeling methodology for forced dynamical systems is presented based on dynamic system theory and nonlinear time series analysis that employs phase space reconstruction (delay vector embedding) for modeling of dynamical systems from time series data using time-delay neural networks (TDNN). The first part of this work details the modeling methodology including background on dynamic systems, phase space reconstruction, and neural networks. In the second part of this work the methodology is evaluated based on its ability to model selected analytical lumped parameter forced vibrating dynamic systems including an example of a linear system predicting lumped mass displacement using a displacement forcing. function The work discusses the application to nonlinear systems, multi degree-of-freedom systems, and multi-input systems. The methodology is further evaluated on its ability to model an analytical passenger rail vehicle predicting vertical wheel/rail force using vertical rail profile as input. Studying the neural modeling methodology using an analytical systems shows the clearest observations from results which provide prospective users of this tool an understanding of the expectations and limitations of the modeling methodology.

A Methodology for the Modeling of Forced Dynamical Systems From Time Series Measurements Using Time-Delay Neural Networks

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
John Zolock ◽  
Robert Greif
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Dynamical Systems ◽  
Dynamic Systems ◽  
Phase Space Reconstruction ◽  
Series Data ◽  
Modeling Methodology ◽  
Forcing Function

The main goal of this research was to develop and present a general, efficient, mathematical, and theoretical based methodology to model nonlinear forced-vibrating mechanical systems from time series measurements. A system identification modeling methodology for forced dynamical systems is presented based on a dynamic system theory and a nonlinear time series analysis that employ phase space reconstruction (delay vector embedding) in modeling dynamical systems from time series data using time-delay neural networks. The first part of this work details the modeling methodology, including background on dynamic systems, phase space reconstruction, and neural networks. In the second part of this work, the methodology is evaluated based on its ability to model selected analytical lumped-parameter forced-vibrating dynamic systems, including an example of a linear system predicting lumped mass displacement subjected to a displacement forcing function. The work discusses the application to nonlinear systems, multiple degree of freedom systems, and multiple input systems. The methodology is further evaluated on its ability to model an analytical passenger rail car predicting vertical wheel∕rail force using a measured vertical rail profile as the input function. Studying the neural modeling methodology using analytical systems shows the clearest observations from results, providing prospective users of this tool an understanding of the expectations and limitations of the modeling methodology.

scholarly journals The Time Delay of Flow and Sediment in the Middle and Lower Yangtze River and Its Response to the Three Gorges Dam

2018 ◽  
Vol 19 (3) ◽  
pp. 625-638 ◽  
Author(s):  
Yangyang Li ◽  
Yingxin Zhu ◽  
Lei Chen ◽  
Zhenyao Shen
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Yangtze River ◽  
Sediment Concentration ◽  
Three Gorges Dam ◽  
Three Gorges ◽  
River Section ◽  
The Three Gorges ◽  
Lower Yangtze ◽  
The Three Gorges Dam

Abstract As the largest hydropower project in the world, the Three Gorges Dam (TGD) has drawn extensive concern in terms of its impact on downstream areas. In this study, an improved time delay estimation and wavelet analysis were used to investigate the influence of the TGD on the streamflow and sediment in the middle and lower Yangtze River, using time series of the daily discharge and sediment concentration data from three hydrological stations downstream of the dam. The results indicated that all of the time series at the three stations have prominent annual cycles, but the cycle of daily mean sediment concentration was nearly nonexistent after the impoundment of the TGD. Changes in discharge and sediment between the Yichang and the Hankou stations are larger than those between the Hankou and the Datong stations, which is mainly attributed to the streamflows of tributaries and Dongting Lake and the flood diversion area of Jingjiang. The transmission time of discharge for the whole Yichang–Datong river section is approximately 6 days. In addition, the attenuation of discharge from the Yichang station to the Datong station is 20%–30%. In contrast, the transmission of suspended sediment is slower than that of discharge, which takes 7–7.5 days to move from the Yichang station to the Datong station. The attenuation of sediment is approximately 30% in the Yichang–Datong river section and shows a clear increasing trend after 2006, mainly because a large amount of sediment was trapped by the TGD, and the dynamic balance of sediment was disturbed.

Sign in / Sign up

Export Citation Format

Share Document