IEEE Computational Intelligence Magazine - August 2021 - 58

It is difficult to forecast the future trend of a chaotic
time series such as a wind speed series because of
its irregularity. But it can be considered to represent a
type of random motion in a definite dynamical system.
This equation indicates that larger and smaller maxm
values
correspond to closer and more distant predictions, respectively.
E. Normalization
For a raw time series, the first task is normalization. Normalization
is a necessary and useful preprocessing step in the field of ANNs. By
normalizing the data, all features can be mapped to the same scale,
thereby reducing the computational cost and increasing the convergence
speed of optimization algorithms. In this study, the onedimensional
wind speed time series
" xi iN () ; 12 f= ,, ,
normalized using the min-max method, as follows:
()
Yt =
XXt
MAXx MINx
xMIN x
-
-
NXt
tt
tt
()
()
,
, is
(24)
where MA () and MI () represent the maximum and
minimum values of the input vector, respectively. Using Eq.
(24), both the training and test samples are normalized to the
range [0,1]. In addition to min-max normalization, other
methods, such as mean and variance normalization and simple
normalization, are also commonly used [54], [55].
IV. Experiments and Discussion
A. Experimental Setup
The wind speed data used for experimental
analysis in this study pertain to a wind farm
in Galicia and are available for free at http://
www.evwind.es. To comprehensively evaluate
the prediction performance of DNR, two sets of
wind speed data with different time intervals, specifically, ten
minutes and one day, were collected; these datasets are illustrated
in Figs. 3(a) and (b), respectively. The two datasets were
used to verify long-term and short-term predictions. Each
dataset contained 1,150 data points. The collected data were
divided into two subsets: training data and test data. The
training data were used to train the DNR parameters, and the
test data were utilized to evaluate the performance of the
trained model in terms of several indicators. The use of different
ratios of training data to test data can help determine the
dependence of an algorithm on the number of training data;
thus, three ratios were considered in our experiments: 1:1, 4:1
and 9:1. All experiments were conducted on a personal PC
with a 2.90 GHz Intel(R) Core i7 CPU and 16 GB of memory
using MATLAB R2018b.
B. Evaluation Indicators
To fairly evaluate the performance of each algorithm, several
evaluation methods were adopted in this study. The details of
these methods are given as follows.
Start
No
Estimate Whether
It Is Chaotic
Wind Speed Time Series
Yes
Divide Into the Training and
Testing Datasets
Calculate Time Delay and
Embedding Dimension
Conduct Phase Space
Reconstruction
Calculate Maximum
Lyapunov Exponent
End
FIGURE 2 Flowchart of DNR-based wind speed forecasting.
Implement the
Normalization Operator
Train DNR on the Training
Dataset
Evaluate DNR on the Test
Dataset
58 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
No Chaotic
http://www.evwind.es http://www.evwind.es
IEEE Computational Intelligence Magazine - August 2021

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