SOLUTION OF GENERALIZED DENSITY EVOLUTION EQUATION VIA A PHASE SPACE RECONSTRUCTION METHOD

2015 ◽  
Author(s):  
Zhong-Ming Jiang ◽  
Jie Li
Keyword(s):  
Phase Space ◽  
Evolution Equation ◽  
Phase Space Reconstruction ◽  
Reconstruction Method ◽  
Density Evolution

ROTATING SYNCHRONIZATION IN THREE-DIMENSIONAL CHAOTIC SYSTEMS

2012 ◽  
Vol 26 (20) ◽  
pp. 1250120 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Phase Space ◽  
Chaotic Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Phase Space Reconstruction ◽  
Projective Synchronization ◽  
Reconstruction Method ◽  
Self Similarity ◽  
Application Fields ◽  
Three Dimensional Space

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other.

Identification of drivers’ driving habits and shift schedule correction for vehicles with automatic transmission

2021 ◽  
pp. 095440702110343
Author(s):  
Guang Xia ◽  
Hualei Zhang ◽  
Xiwen Tang ◽  
Shilong Wu ◽  
Linfeng Zhao ◽  
...  
Keyword(s):  
Phase Space ◽  
Control Strategy ◽  
Automatic Transmission ◽  
Resource Conservation ◽  
Phase Space Reconstruction ◽  
Evaluation Index ◽  
Reconstruction Method ◽  
Kolmogorov Entropy ◽  
Gear Shift ◽  
Control Signals

Resource conservation has become a hot topic, and driving habits also have a significant impact on a car’s fuel consumption. In view of the different needs of drivers with different driving habits for automatic transmission and shift characteristics, a vehicle automatic transmission, and shift correction control strategy based on driving habit recognition is proposed. Based on the analysis of drivers’ driving behavior, the phase space reconstruction method is first used to reconstruct the time series of driving control signals, and the driving habit identification and gear shift correction control are conducted based on the correlation dimension and Kolmogorov entropy evaluation index. Simulation and real car test show that the identification method based on phase space reconstruction method and driving habits evaluation index can accurately identify drivers’ driving habits. The gear shift correction control strategy based on driving habit recognition fully meets the different requirements of different drivers for the gearshift performance of vehicles and improves the intelligence degree of automatic transmission of vehicles.

Structural Damage Detection of the Simple Beam Based on Responses Phase Space

2012 ◽  
Vol 605-607 ◽  
pp. 989-995 ◽  
Author(s):  
Cheng Cheng ◽  
Zhen Hua Nie ◽  
Hong Wei Ma
Keyword(s):  
Phase Space ◽  
Dynamic Response ◽  
Damage Detection ◽  
Structural Damage ◽  
Phase Plane ◽  
Damage Index ◽  
Phase Space Reconstruction ◽  
Dynamic Responses ◽  
Reconstruction Method ◽  
Structural Damage Detection

In this paper, the technology of attractor phase space in chaotic theory is introduced and applied in the structural damage detection. Firstly the phase plane is constructed with the displacement and acceleration responses. Using the changes of phase plane topology of intact and damaged responses, a new damage index is extracted, and the structural damage existence and severity are identified successfully. Since some of the state variables can not be measured, a method of phase space reconstruction is proposed using single dynamic response. The dynamic responses are directly displayed into phase space, realizing transforming the signals from time domain to space domain. Then using the reconstructed phase space, the damage is diagnosed. The results indicate that the phase space reconstruction method has good robustness to noise, and higher sensitivity compared with traditional modal-based methods. The phase space reconstruction method can calculate the value of the damage index using single dynamic response, so that a single sensor can monitor structural damage existence and severity.

Research on the Phase Space Reconstruction Method of Chaotic Time Series

2010 ◽  
Vol 26-28 ◽  
pp. 236-240
Author(s):  
Yun Fei Ma ◽  
Pei Feng Niu ◽  
Xiao Fei Ma
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Chaotic Dynamics ◽  
Original System ◽  
Chaotic Signal ◽  
Phase Space Reconstruction ◽  
Reconstruction Method ◽  
Numerical Verification ◽  
Signal Recognition

The puzzle over the recognition of the quality of the Chaotic Dynamics based on single variable time series brings forward the new method of phase space reconstruction—identify the embedding dimension with the FNN after delay time is fixed through the method of autocorrelation function. By means of the numerical verification of a few typical examples of chaotic dynamic system, the result shows that this method can be able to efficiently reconstruct the phase space of the original system out of the time series and relatively completely reduce the dynamic characteristics of the original system and thus the validity of the method is testified on chaotic signal recognition.

scholarly journals Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tai-fu Li ◽  
Wei Jia ◽  
Wei Zhou ◽  
Ji-ke Ge ◽  
Yu-cheng Liu ◽  
...  
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Phase Space ◽  
Adaptive Evolution ◽  
Kalman Filtering ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Reconstruction Method ◽  
Extended Kalman Filtering ◽  
Subspace Approximation

The chaotic time series can be expanded to the multidimensional space by phase space reconstruction, in order to reconstruct the dynamic characteristics of the original system. It is difficult to obtain complete phase space for chaotic time series, as a result of the inconsistency of phase space reconstruction. This paper presents an idea of subspace approximation. The chaotic time series prediction based on the phase space reconstruction can be considered as the subspace approximation problem in different neighborhood at different time. The common static neural network approximation is suitable for a trained neighborhood, but it cannot ensure its generalization performance in other untrained neighborhood. The subspace approximation of neural network based on the nonlinear extended Kalman filtering (EKF) is a dynamic evolution approximation from one neighborhood to another. Therefore, in view of incomplete phase space, due to the chaos phase space reconstruction, we put forward subspace adaptive evolution approximation method based on nonlinear Kalman filtering. This method is verified by multiple sets of wind speed prediction experiments in Wulong city, and the results demonstrate that it possesses higher chaotic prediction accuracy.

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