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.

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.

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.

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

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.

Damage in Composite Materials: Experiment Vs a Computational Chaotic Model

1992 ◽  
Vol 278 ◽  
Author(s):  
Franco Meloni ◽  
Alberto Varone ◽  
Francesco Ginesu
Keyword(s):  
Composite Materials ◽  
Simple Model ◽  
Critical Points ◽  
Dynamic Load ◽  
Theoretical Study ◽  
Real System ◽  
Time Diagram ◽  
Structural Behaviour ◽  
Chaotic Model ◽  
Non Linear Mechanics

AbstractWe present the results of a combined experimental and theoretical study performed using non-linear mechanics schemes to investigate the structural behaviour of a composite macroscopic material. A simple model is considered to define the order of the complexity of the real system represented by a graphite peek polymer under static and dynamic load In particular a relationship has been found between the critical points in the energy-time diagram and in the bifurcation plot.

scholarly journals Hybrid prediction method of ECG signals based on VMD, PSR, and RBF neural network

2020 ◽  
Author(s):  
Fuying Huang ◽  
Tuanfa Qin ◽  
Limei Wang ◽  
Haibin Wan
Keyword(s):  
Neural Network ◽  
Phase Space ◽  
Delay Time ◽  
Prediction Accuracy ◽  
Rbf Neural Network ◽  
Prediction Method ◽  
Prediction Methods ◽  
Embedding Dimension ◽  
Ecg Signals ◽  
Ecg Data

Abstract Background: It is significant for doctors and body area networks (BANs) to predict ECG signals accurately. At present, the prediction accuracy of many existing ECG prediction methods is generally low. In order to improve the prediction accuracy of ECG signals in BANs, a hybrid prediction method of ECG signals is proposed in this paper. Methods: The proposed prediction method combines variational mode decomposition (VMD), phase space reconstruction (PSR), and a radial basis function (RBF) neural network. First, the embedding dimension and delay time of PSR are calculated according to the trained set of ECG data. Second, the ECG data are decomposed into several intrinsic mode functions (IMFs). Third, the phase space of each IMF is reconstructed according to the embedding dimension and the delay time. Fourth, an RBF neural network is established and each IMF is predicted by the network. Finally, the prediction results of all IMFs are added to realize the final prediction result. Results: To evaluate the prediction performance of the proposed method, simulation experiments are carried out on ECG data from the MIT-BIH Arrhythmia Database. The experimental results show that the prediction index RMSE (root mean square error) of the proposed method is only 10-3 magnitude and that of some traditional prediction methods is 10-2 magnitude.Conclusions: Compared with some traditional prediction methods, the proposed method improves the prediction accuracy of ECG signals obviously.

A multiple-parameter approach for short-term traffic flow prediction

2021 ◽  
pp. 2150245
Author(s):  
Xiaoquan Wang ◽  
Wenjun Li ◽  
Chaoying Yin ◽  
Shaoyu Zeng ◽  
Peng Liu
Keyword(s):  
Phase Space ◽  
Support Vector Regression ◽  
Traffic Flow ◽  
Conditional Entropy ◽  
Entropy Method ◽  
Support Vector ◽  
Embedding Dimension ◽  
Short Term ◽  
Traffic Flow Prediction ◽  
Flow Prediction

This study proposes a short-term traffic flow prediction approach based on multiple traffic flow basic parameters, in which the chaos theory and support vector regression are utilized. First, a high-dimensional variable space can be obtained according to the traffic flow fundamental function. Then, a maximum conditional entropy method is proposed to determine the embedding dimension. And multiple time series are reconstructed based on the phase space reconstruction theory using the time delay obtained by mutual information method and the embedding dimension captured by the maximum conditional entropy method. Finally, the reconstructed phase space is used as the input and the support vector regression optimized by the genetic algorithm is utilized to predict the traffic flow. Numerical experiments are performed and the results show that the approach proposed has strong fitting capability and better prediction accuracy.

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.

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