Influence of Sub-Daily Variation on Multi-Fractal Detrended Fluctuation Analysis of Wind Speed Time Series
January
Influence of Sub-Daily Variation on Multi- Fractal Detrended Fluctuation Analysis of Wind Speed Time Series
Xianxun Wang 0 1
Yadong Mei 0 1
Weinan Li 0 1
Yanjun Kong 0 1
Xiangyu Cong 0 1
0 1 State Key Laboratory of Water Resource and Hydropower Engineering Science, Wuhan University , Wuhan, Hubei , China , 2 Hubei Collaborative Innovation Center for Water Resources Security , Wuhan, Hubei , China , 3 POWERCHINA Kunming Engineering Corporation Limited , Kunming, Yunnan , China
1 Editor: Wei-Xing Zhou, East China University of Science and Technology , CHINA
Using multi-fractal detrended fluctuation analysis (MF-DFA), the scaling features of wind speed time series (WSTS) could be explored. In this paper, we discuss the influence of subdaily variation, which is a natural feature of wind, in MF-DFA of WSTS. First, the choice of the lower bound of the segment length, a significant parameter of MF-DFA, was studied. The results of expanding the lower bound into sub-daily scope shows that an abrupt declination and discrepancy of scaling exponents is caused by the inability to keep the whole diel process of wind in one single segment. Additionally, the specific value, which is effected by the sub-daily feature of local meteo-climatic, might be different. Second, the intra-day temporal order of wind was shuffled to determine the impact of diel variation on scaling exponents of MF-DFA. The results illustrate that disregarding diel variation leads to errors in scaling. We propose that during the MF-DFA of WSTS, the segment length should be longer than 1 day and the diel variation of wind should be maintained to avoid abnormal phenomena and discrepancy in scaling exponents.
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OPEN ACCESS
Data Availability Statement: All relevant data are
within the paper and its Supporting Information files.
Funding: This study was supported by the Major
Program of National Natural Science Foundation of
China, grant number: 51239004, (URLs: http://npd.
nsfc.gov.cn/fundingProjectSearchAction.action),
Recipient: Yadong Mei; and the Program of National
Natural Science Foundation of China, grant number:
51479140 (URLs: http://npd.nsfc.gov.cn/
fundingProjectSearchAction.action), Recipient:
Yadong Mei. The funder provided support in
experiment field and tools. The POWERCHINA
Kunming Engineering Corporation Limited provided
Introduction
A renewable resource and potential energy source, wind power needs to be further explored in
an effort to meet the increasing requirement for electricity and avoid depleting fossil resources,
which are aggravating environmental pollution [
1–2
]. Wind is one kind of natural signal, and
it is important to discover the regular patterns of wind. It has been found that there are
longrange power-law correlations in wind speed time series (WSTS) [3]. These long-range power
correlations could be used in wind feature research and the prediction of wind [
4
].
The auto-correlation function and power spectrum are traditional methods for capturing
long-range power correlation. The spectrum E(f) follows a power law of the form E(f) ~ f-α in
log-log scale. Due to sensitivities to non-stationary effects, traditional methods are limited [
3
].
Recently, the detrended fluctuation analysis (DFA) [
5
] method has been widely applied for
support in data collection. The funder and the
commercial company did not have any additional role
in the study design, data analysis, decision to publish,
or preparation of the manuscript. The specific roles of
the authors are articulated in the ‘author contributions’
section.
Competing Interests: The authors have declared
that no competing interests exist. This commercial
affiliation, POWERCHINA Kunming Engineering
Corporation Limited, does not alter the authors'
adherence to PLOS ONE policies on sharing data
and materials.
scaling analysis of non-stationary data. However, DFA is inadequate for addressing processes
governed by more than one scaling exponent. Based on DFA, multi-fractal detrended
fluctuation analysis (MF-DFA) [
6
] has been introduced and successfully applied in many fields [
3–4,
7–20
]. Many research studies have indicated that WSTS is multi-fractal and used MF-DFA to
scale analysis of WSTS [
3–4, 6–10
].
In discussions of the effects of trends on scaling exponents in the literature, it was found
that a crossover (i.e., inconsistency of scaling exponent) usually arises from a change in the
correlation properties of the signal at different temporal or spatial scales or trends in the data [
13
].
As a natural signal, wind has features of diel variation and seasonal alternation. Some
researchers have found inconsistencies in scaling exponents of WSTS from several days to seasonal
time scales. The scaling exponent of WSTS is influenced by meteorology, climate, and weather
patterns and displays different values in various ranges of segment length (s) [
10–12
]. Ref. [
10
]
reveals that when s was larger than seasonal length, the scaling exponen (...truncated)