Detection of low-dimensional chaos in wind time series

Karakasidis, Theodoros E.; Charakopoulos, Avraam

doi:10.1016/j.chaos.2008.07.020

Cited by 27 publications

(8 citation statements)

References 20 publications

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“…Consequently, the pattern length D and the lag τ do not need to be selected following the methodologies usually employed in a conventional phase space reconstruction (the first zero of the autocorrelation function, the first minimum of the average mutual information, the false nearest-neighbor algorithm, etc.) [22].…”

Section: Ordinal Patternsmentioning

confidence: 99%

Unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics

et al. 2019

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In this paper, we introduce a model to describe the decay of the number of unobserved ordinal patterns as a function of the time series length in noisy chaotic dynamics. More precisely, we show that a stretched exponential model fits the decay of the number of unobserved ordinal patterns for both discrete and continuous chaotic systems contaminated with observational noise, independently of the noise level and the sampling time. Numerical simulations, obtained from the logistic map and the x coordinate of the Lorenz system, both operating in a totally chaotic dynamics were used as test beds. In addition, we contrast our results with those obtained from pure stochastic dynamics. The fitting parameters, namely, the stretching exponent and the characteristic decay rate, are used to distinguish whether the dynamical nature of the data sequence is stochastic or chaotic. Finally, the analysis of experimental records associated with the hyperchaotic pulsations of an optoelectronic oscillator allows us to illustrate the applicability of the proposed approach in a practical context.

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Section: Ordinal Patternsmentioning

confidence: 99%

Unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics

et al. 2019

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“…Analysis about the chaotic characteristics of wind speed in the process of wind power generation has been presented in a related article [26]. We record one of the wind speed data every 10 minutes, and 150 groups of wind speed data in Wulong city are used to simulate experiments in our study.…”

Section: Wind Speed Chaotic Series Forecasting Simulationmentioning

confidence: 99%

Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

Jia

Zhou

et al. 2013

Journal of Applied Mathematics

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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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“…Models, like wind tunnel simulations [6] or computational fluid dynamics methods [7] that are traditionally used to perform simulations, were quite limited in disclosing the dynamical complexity of wind field. Thus, to characterize the dynamics of wind speed series, robust methods have been employed, like distributional analysis [8], chaotic time series analysis [9], wavelets [10], fractal and multifractal analysis [11][12][13][14][15][16][17], multiscale entropy analysis [18], multiscale multifractal analysis [19]. Most of the studies on wind speed were based on hourly or daily averages; however, to detect inner characteristics of the wind dynamics, like turbulence phenomena [20], and to understand complex dynamical patterns at very low timescales, high-frequency wind records are necessary.…”

Section: Introductionmentioning

confidence: 99%

Wavelet Scale Variance Analysis of Wind Extremes in Mountainous Terrains

Telesca

Guignard

Helbig³

et al. 2019

Energies

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The 10-min average wind speed series recorded at 130 stations distributed rather homogeneously in the territory of Switzerland are investigated. Fixing a percentile-based threshold of the wind speed distribution, a wind extreme is defined as the duration of the sequence of consecutive wind values above the threshold. This definition allows to analyze the sequence of extremes as a temporal point process marked by their duration. Representing the sequence of wind extremes by the inter-extreme interval series, the wavelet variance, a useful tool to investigate the variance of a time series across scales, was applied in order to find a link between the wavelet scales and several topographic parameters. Our findings suggest that the mean duration of wind extremes and mean inter-extreme time are positively correlated and that such relationship depends on the threshold of the wind speed. Furthermore, the threshold of the wind speed distribution correlates best with a terrain parameter related to the Laplacian of terrain elevations; and, in particular, for wavelet scales less than 3, the terrain exposure may explain the formation of extreme wind speeds.

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Detection of low-dimensional chaos in wind time series

Cited by 27 publications

References 20 publications

Unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics

Unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics

Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

Wavelet Scale Variance Analysis of Wind Extremes in Mountainous Terrains

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