Vibration monitoring of converter transformer onload tap-changer using phase space reconstruction and poincare section

2017 ◽  
Author(s):  
Yiming Zheng ◽  
Wenlin He ◽  
Fenghua Wang ◽  
Shushi Li
Keyword(s):  
Phase Space ◽  
Phase Space Reconstruction ◽  
Vibration Monitoring ◽  
Poincaré Section ◽  
Poincare Section ◽  
Tap Changer

scholarly journals Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

2017 ◽  
Vol 34 ◽  
Author(s):  
Ali Taani ◽  
Juan C. Vallejo
Keyword(s):  
Phase Space ◽  
Invariant Tori ◽  
Dynamical Behavior ◽  
Dark Halo ◽  
Short Axis ◽  
Poincaré Section ◽  
Invariant Curves ◽  
Poincare Section ◽  
Dynamical Behaviors ◽  
Stable Periodic

AbstractWe describe the dynamical behavior of isolated old ( ⩾ 1Gyr) objects-like Neutron Stars (NSs). These objects are evolved under smooth, time-independent, gravitational potentials, axisymmetric and with a triaxial dark halo. We analysed the geometry of the dynamics and applied the Poincaré section for comparing the influence of different birth velocities. The inspection of the maximal asymptotic Lyapunov (λ) exponent shows that dynamical behaviors of the selected orbits are nearly the same as the regular orbits with 2-DOF, both in axisymmetric and triaxial when (ϕ, qz)= (0,0). Conversely, a few chaotic trajectories are found with a rotated triaxial halo when (ϕ, qz)= (90, 1.5). The tube orbits preserve direction of their circulation around either the long or short axis as appeared in the triaxial potential, even when every initial condition leads to different orientations. The Poincaré section shows that there are 2-D invariant tori and invariant curves (islands) around stable periodic orbits that bound to the surface of 3-D tori. The regularity of several prototypical orbits offer the means to identify the phase-space regions with localized motions and to determine their environment in different models, because they can occupy significant parts of phase-space depending on the potential. This is of particular importance in Galactic Dynamics.

FRACTALS AND CLOSURES OF LINEAR DYNAMICAL SYSTEMS EXCITED STOCHASTICALLY BY TEMPORAL INPUTS

2001 ◽  
Vol 11 (03) ◽  
pp. 755-779 ◽  
Author(s):  
RYOICHI WADA ◽  
KAZUTOSHI GOHARA
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Vector Fields ◽  
Invariant Set ◽  
Poincaré Section ◽  
Poincare Section ◽  
Linear Dynamical Systems ◽  
Cylindrical Phase ◽  
Iterated Functions ◽  
Cylindrical Phase Space

Fractals and closures of two-dimensional linear dynamical systems excited by temporal inputs are investigated. The continuous dynamics defined by the set of vector fields in the cylindrical phase space is reduced to the discrete dynamics defined by the set of iterated functions on the Poincaré section. When all iterated functions are contractions, it has already been shown theoretically that a trajectory in the cylindrical phase space converges into an attractive invariant set with a fractal-like structure. Calculating analytically the Lipschitz constants of iterated functions, we show that, under some conditions, noncontractions often appear. However, we numerically show that, even for noncontractions, an attractive invariant set with a fractal-like structure exists. By introducing the interpolating system, we can also show that the set of trajectories in the cylindrical phase space is enclosed by the tube structure whose initial set is the closure of the fractal set on the Poincaré section.

Analysis of High-Dimensional Phase Space via Poincaré Section for Patient-Specific Seizure Detection

2016 ◽  
Vol 24 (3) ◽  
pp. 386-398 ◽  
Author(s):  
Morteza Zabihi ◽  
Serkan Kiranyaz ◽  
Ali Bahrami Rad ◽  
Aggelos K. Katsaggelos ◽  
Moncef Gabbouj ◽  
...  
Keyword(s):  
Phase Space ◽  
Seizure Detection ◽  
Patient Specific ◽  
High Dimensional ◽  
Poincaré Section ◽  
Poincare Section ◽  
Dimensional Phase Space

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.

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