Effects of Zeros in Phase Space Reconstruction for Small and Large Solar Radiation Data Points during Wet and Dry Seasonal Modeling and Prediction

The effect of zeros in the behaviour of nature system has been a major global concern which have been reported to bias the output of the analysis. This study examines the effect of zeros on small and large solar radiation data points in Nsukka from a nonlinear dynamic perspective. The solar radiation data used were collected from National Research for Space and Development Agency (NARSDA) and covers the period of two years (January 2012–December 2013). The influence of zeros on average mutual information method for delay time (𝜏), False nearest neighbour (FNN) for embedding dimension (𝑚), and phase space reconstruction is investigated by considering two different cases (one hour and five minutes interval for small and large data points on monthly basis respectively). The results reveal that the phase space trajectories of the raw and non-zero small data points for dry and wet seasons show evidence of an attractorin a well-defined region while raw and non-zero large data points have no attractor like shape but regular patterns and well-defined shapes are visible in dry and wet seasons. These imply low-dimensional and deterministic chaotic nature of the underlying dynamics of raw and non-zero data for small and large data points during wet and dry seasons. It is observed that there is little or no significant difference in the phase space reconstruction of raw and non-zero data for both small and large data points due to the low percentage of zeros in the time series data. Keywords: mutual information method, Phase space reconstruction, False nearest neighbour, chaotic nature.

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Wind Power Short-Term Prediction Method Based on Multivariable Mutual Information and Phase Space Reconstruction

Communications in Computer and Information Science - Intelligent Computing in Smart Grid and Electrical Vehicles ◽

10.1007/978-3-662-45286-8_1 ◽

2014 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Lu-Jie Liu ◽

Yang Fu ◽

Shi-Wei Ma

Keyword(s):

Phase Space ◽

Mutual Information ◽

Wind Power ◽

Prediction Method ◽

Phase Space Reconstruction ◽

Short Term ◽

Term Prediction ◽

Short Term Prediction

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

Anti-Corrosion Methods and Materials ◽

10.1108/acmm-11-2015-1613 ◽

2016 ◽

Vol 63 (3) ◽

pp. 214-225 ◽

Cited By ~ 5

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.

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On the 0/1 test for chaos in continuous systems

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.1515/bpasts-2016-0058 ◽

2016 ◽

Vol 64 (3) ◽

pp. 521-528 ◽

Cited By ~ 1

Author(s):

M. Melosik ◽

W. Marszalek

Keyword(s):

Phase Space ◽

Mutual Information ◽

Chaotic Systems ◽

Numerical Results ◽

Continuous Systems ◽

Information Method ◽

Memristive Circuits ◽

Frequency Properties

Abstract In this paper we discuss in detail the resonance and oversampling features of the 0/1 test for chaos in continuous systems and propose methods to avoid those undesired features. Our method is based on certain frequency properties of the 0/1 test. When reconstructing the phase space, our approach is compared with the first minimum of the mutual information method. Several numerical results for typical chaotic systems (including memristive circuits) are included.

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

Entropy ◽

10.3390/e23020221 ◽

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

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Motor Front Axle Temperature Forecasting Based on Phase Space Reconstruction and BP Neural Network

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.823.406 ◽

2013 ◽

Vol 823 ◽

pp. 406-410 ◽

Cited By ~ 1

Author(s):

Meng Tao Huang ◽

Xing Mei Gao

Keyword(s):

Neural Network ◽

Phase Space ◽

Bp Neural Network ◽

Phase Space Reconstruction ◽

Front Axle ◽

Temperature Series ◽

Nonlinear Characteristics ◽

Temperature Changes ◽

Temperature Forecasting ◽

Chaotic Nature

Predicting the temperatures of drive motors of important equipment can help to detect motor failure timely, avoiding the losses caused by the motor faults. Against the nonlinear characteristics of the equipment temperature changes, according to phase space reconstruction principle of chaos theory, the motor front axle temperature series were analyzed and the chaotic nature of the motor front axle temperature series is verified. In order to predict the trend of the motor axle temperature more accurately, the prediction based on BP neural network is conducted, and the embedding dimension of phase space reconstruction is chosen to be the number of input nodes. Simulation shows that this method has higher prediction accuracy and can be used to predict the motor axle temperature.

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