Fractal order evidences in wind speed time series

This paper describes some evidence of fractal order features in wind speed time series recorded at different observation stations both in USA and in Italy. Analysis were performed by using mono-fractal, multi-fractal and power spectra approaches. Results show that the average value of the box dimension for daily and hourly mean wind speed is D = 1.19 and D = 1.41 respectively, thus indicating that this kind of time series are fractal. The estimated average value of the Hurst exponent is H = 0.81 and H = 0.75 for daily and hourly time series respectively. From these Hurst exponents it is possible to infer the persistent behavior of wind speed. Furthermore, multi-fractal analysis shows that wind speed exhibits a bell-like shape spectrum with average width Δα = 0.47. Power spectra analysis has pointed out that wind speed time series behave as 1/f13 noise with average value of the β exponent of 0.46 and 1.37 for daily mean and hourly mean time series respectively. These latter results can be interpreted by saying that wind speed time series are Brown noise like.

[1]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[2]  Multifractal analysis of wind velocity data , 2014 .

[3]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[4]  Ying-Pin Chang,et al.  Fractal dimension of wind speed time series , 2012 .

[5]  Henrik Madsen,et al.  A review on the young history of the wind power short-term prediction , 2008 .

[6]  J. R. Wallis,et al.  Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence , 1969 .

[7]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 1994 .

[8]  Espen A. F. Ihlen,et al.  Introduction to Multifractal Detrended Fluctuation Analysis in Matlab , 2012, Front. Physio..

[9]  Nirupam Sarkar,et al.  An Efficient Differential Box-Counting Approach to Compute Fractal Dimension of Image , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[10]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[11]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[12]  Fahima Nekka,et al.  The modified box-counting method: Analysis of some characteristic parameters , 1998, Pattern Recognit..

[13]  R. Weron.  Estimating long range dependence: finite sample properties and confidence intervals , 2001, cond-mat/0103510.

[14]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Gregor Giebel,et al.  The State-Of-The-Art in Short-Term Prediction of Wind Power. A Literature Overview , 2003 .

[16]  D. Lathrop.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 2015 .

[17]  T. Higuchi.  Relationship between the fractal dimension and the power law index for a time series: a numerical investigation , 1990 .

[18]  Bellie Sivakumar,et al.  Chaos theory in geophysics: past, present and future , 2004 .