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Citation: Cao, R.; Tian, H.; Li, D.;
Feng, M.; Fan, H. Short-Term
Photovoltaic Power Generation
Prediction Model Based on Improved
Data Decomposition and Time
Convolution Network. Energies 2024,
17, 33. https://doi.org/10.3390/
en17010033
Received: 13 November 2023
Revised: 16 December 2023
Accepted: 17 December 2023
Published: 20 December 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Article
Short-Term Photovoltaic Power Generation Prediction Model
Based on Improved Data Decomposition and Time
Convolution Network
Ranran Cao 1,2, He Tian 1,2 ,*, Dahua Li 1 ,2 ,*, Mingwen Feng 1,2 and Huaicong Fan 1,2
1Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,
School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China;
ran3401517075@stud.tjut.edu.cn (R.C.)
2National Demonstration Center for Experimental Mechanical and Electrical Engineering Education (Tianjin
University of Technology), Tianjin 300384, China
*Correspondence: tianhe@tjut.edu.cn (H.T.); lidah@tjut.edu.cn (D.L.)
Abstract: In response to the volatility of photovoltaic power generation, this paper proposes a
short-term photovoltaic power generation prediction model (HWOA-MVMD-TPA-TCN) based on
a Hybrid Whale Optimization Algorithm (HWOA), multivariate variational mode decomposition
(MVMD), temporal pattern attention mechanism (TPA), and temporal convolutional network (TCN).
In order to improve the accuracy of photovoltaic power generation forecasting, HWOA-MVMD
is used for data decomposition, the Minimum Mode Overlap Component (MMOC) is used as the
objective function, the photovoltaic power generation sequence is decomposed into finite Intrinsic
Mode Functions (IMFs) according to the optimal solution, and the training set is formed with
key meteorological variable data such as total radiation (unit: W/m
2
), ambient temperature, and
humidity. Then, the TPA-TCN model is used to train the sub-sequences, the final predicted values are
obtained after superimposing the reconstruction of the prediction results, and finally the prediction
error of the photovoltaic power generation data is studied. The proposed method is applied to
real photovoltaic power generation data from a commercial center in Tianjin and is compared with
HWOA-MVMD-BiLSTM, GWO-MVMD-TPA-TCN, and TPA-TCN prediction models. The simulation
results demonstrate that the MAE value of the forecast method proposed in this paper is 1.95 MW
and the RMSE value is 2.55 MW, which can be reduced by up to 33.74% and 38.85%, respectively.
The HWOA-MVMD-TPA-TCN-based short-term photovoltaic power generation prediction model
presented in this paper achieves higher prediction accuracy and superior performance, serving as a
valuable reference for related research.
Keywords: photovoltaic power generation forecast; hybrid whale algorithm; multivariate variational
mode decomposition; time convolutional network; time pattern attention mechanism
1. Introduction
With the rapid development of photovoltaic power generation, the impact of large-
scale photovoltaic grid connections on the power system is becoming more and more
obvious, and accurate short-term photovoltaic power generation prediction can effectively
alleviate the pressure caused by photovoltaic grid connections on the power system, which
is of great significance to ensure the stable operation of the power grid and the reasonable
allocation of resources [
1
,
2
]. Therefore, obtaining reliable data for the power generation
forecast of photovoltaic power plants has also become an important issue [3].
In recent years, research in photovoltaic power generation forecasting has predomi-
nantly focused on artificial intelligence technologies, utilizing machine learning and neural
networks to capture the randomness of photovoltaic power generation sequences [
4
].
Table 1shows the current research status.
Energies 2024,17, 33. https://doi.org/10.3390/en17010033 https://www.mdpi.com/journal/energies
Energies 2024,17, 33 2 of 18
Table 1. Research status.
File
Number Main Content Areas of Shortcoming
Establish a single
predictive model
[5]
Using ant element data packets to probe the network
environment, selecting information transmission links,
constructing roaming paths, and enhancing predictive
accuracy through iterative computations to search for
optimal solutions.
Ignored the problem of poor
population diversity and the
tendency for the initialization
to fall into local optima.
[6]
Optimizing the photovoltaic power output prediction
algorithm based on the Whale Optimization Algorithm
for Support Vector Machines. Optimizing time delay and
embedding dimensions in the kernel function to improve
generalization ability and convergence speed, resulting in
better adaptability.
[7]
Optimizing the photovoltaic power prediction algorithm
using the Grey Wolf Algorithm to optimize the weights of
Long Short-Term Memory (LSTM) neural networks.
Predicting power based on optimal weights, overcoming
the drawbacks of backpropagation, and improving
prediction accuracy.
[8–12]
Establishing optimization models using the Honey Badger
Algorithm, Sparrow Algorithm, and PSO (Particle Swarm
Optimization) Algorithm for predicting the power
generation of photovoltaic power stations. Enhancing
prediction accuracy.
[13,14]
Taking into account the impact of solar irradiance on
photovoltaic power generation. Integrating variational
quantum circuits with Long Short-Term Memory (LSTM)
neural networks, forming a Quantum LSTM neural
network applied in predictive research. Accelerating the
prediction algorithm through an FPGA hardware
platform to reduce computational complexity.
Required a large amount of
historical data support.
Combined
forecasting
method [4]
[15–20]
Pointing out the random fluctuations due to
meteorological factors in ultra-short-term photovoltaic
power generation forecasting.
Low prediction accuracy and
did not comprehensively
consider all
meteorological factors.
[21]
Utilizing the Artificial Bee Colony Optimization Support
Vector Machine (ABC-SVM) classification model,
combined with the Particle Swarm Optimization Random
Forest (PSO-RF) model, for classification training based on
meteorological data.
Suitable for small sample
analysis, but the time
complexity increased with the
growth of the sample size.
[22]
Adopting the Complex Empirical Mode Decomposition
with Adaptive Noise (CEEMDAN) method to decompose
the photovoltaic power sequence, reducing the impact of
non-stationary features on the prediction.
There were challenges related
to mode mixing and difficulty
in determining the stopping
conditions.
[23–26]
Establishing a combined forecasting model to enhance the
accuracy and stability of ultra-short-term load forecasting.
For nonlinear time series, it
did not perform well in
capturing nonlinearity.
While there are many forecasting methods as mentioned above, they often struggle
to effectively capture nonlinearity in time series data that exhibit dynamic and complex
behaviors with multiple variables. Many data points within these sequences may not be
adequately represented, which can directly impact the final prediction results, potentially
leading to forecast errors exceeding acceptable limits. Therefore, this paper proposes a
short-term photovoltaic power generation prediction model based on the HWOA-MVMD-
TPA-TCN. This approach utilizes HWOA-MVMD to decompose the photovoltaic power
Energies 2024,17, 33 3 of 18
generation sequence comprehensively, reducing the sequence complexity while deeply
mining data features. The obtained subsequences and key meteorological factors are used
as inputs for iterative training in the TPA-TCN. The prediction results for each subsequence
are then aggregated and reconstructed to obtain the final forecast value. When compared
to HWOA-MVMD-BiLSTM, GWO-MVMD-TPA-TCN, and TPA-TCN models, the proposed
forecasting model demonstrates a higher level of prediction accuracy. This approach not
only provides valuable insights for energy forecasting but also has the potential to be
applied in a broader context of energy prediction.
The overall organization of this article is as follows: The first chapter is an introduction.
The second chapter introduces data decomposition, using a multivariational mode to
decompose photovoltaic power generation data and using the improved Hybrid Whale
Algorithm to optimize the hyperparameters of multivariational modal decomposition. The
third chapter presents iterative training using the results and key meteorological factors
obtained in the second chapter as the input of the TPA-TCN. The fourth chapter presents
the prediction process of the short-term photovoltaic power generation prediction model
based on the HWOA-MVMD-TPA-TCN, and the fifth chapter presents the analysis of
an example.
2. Optimization of Multivariate Variational Modal Decomposition
2.1. Common Data Decomposition Methods
From the current research status, data decomposition methods generally fall into
several categories, as shown in Table 2. These methods were used in many aspects, such as
wind power prediction [
27
], bearing fault diagnosis [
28
], and the low-frequency oscillation
mode identification of power systems [
29
]. These methods often exhibit certain issues
during the data decomposition process.
Table 2. Classification and existing problems of data decomposition methods.
Data Decomposition Method Problems
Wavelet decomposition
Wavelet transform is limited by the need for the
manual determination of wavelet bases and the
Heisenberg uncertainty principle, which ultimately
affects the accuracy of the prediction results.
Empirical mode decomposition (EMD)
There are problems such as modal aliasing,
endpoint effects, and difficulty in determining the
stopping conditions.
Variational mode decomposition (VMD)
VMD requires predefined modal numbers.
Inaccurate modal numbers can lead to insufficient
or excessive modal decomposition, and if the
signal is long, the bandwidths may overlap.
Multivariate variational modal
decomposition (MVMD)
The influencing parameters in its decomposition
process are related to the number of intrinsic
modes and the quadratic penalty factor, and these
parameters must be preset.
According to Table 2, there are currently two main issues with data decomposition
methods: (1) In signal decomposition, the selection of primary parameters is often based on
past empirical experience, which limits the results of the decomposition. (2) Problems exist
such as modal aliasing, endpoint effects, and difficulty in determining stopping conditions.
To address these issues, this paper employs an improved Hybrid Whale Optimization
Algorithm. It defines the modal overlap component as the fitness function, and when this
indicator reaches its minimum value, the independence and correlation between different
modal components are maximized. This helps avoid modal aliasing. At this point, the
corresponding optimal combination of intrinsic mode numbers and penalty factors is
achieved, preventing under-decomposition or over-decomposition phenomena.
Energies 2024,17, 33 4 of 18
2.2. Hybrid Whale Optimization Algorithm
The Whale Optimization Algorithm (WOA) has the advantages of simple operation
and few setting parameters and has been widely used in the optimization of target problems.
And the introduction of the WOA in the prediction model can effectively search the solution
space and find the global optimal solution or the approximate optimal solution. However,
the traditional WOA is prone to fall into local optima, and the global search capability and
local development capability are unbalanced [
30
]. Therefore, this article improves on the
traditional WOA.
2.2.1. Tent Mapping
The Whale Optimization Algorithm (WOA), like most swarm intelligence optimization
algorithms, initially starts with a random distribution of individuals, which can lead
to population clustering and poor diversity. The population may struggle to achieve a
uniform distribution throughout the search space. To enhance the performance of the
Whale Optimization Algorithm, Tent Mapping is applied in the optimization process of the
WOA [30]. The Tent Mapping formula is as follows:
If 0 <xj<0.5:
xj+1=δ×xj(1)
If 0.5 ≤xj≤1:
xj+1=δ1−xj(2)
Assuming a population size of
N
, we obtain a population
χ=χj,j=1, 2, · · · N
,
where
δ=(0, 2]
is the chaos parameter, and the larger the value of this parameter, the
better the chaotic effect.
xj
is the position of each whale in the search space. Therefore,
when
δ=
2, the population’s exploration capability and the algorithm’s solving speed are
expected to be superior to other mapping methods.
2.2.2. Elite Reverse Learning Strategy
First, by employing a group selection strategy, after generating reverse solutions
from elite individuals, the
s
individuals with lower fitness values are selected as the next
generation’s whale individuals [31].
In a D-dimensional space, if there is a feasible solution
X=(x1,x2,· · · ,xn)
, then its
reverse solution
X=(x1,x2,· · · ,xn)
, which is an elite individual in the population, corre-
sponds to the extremum point
Xe
i,j
in the whale population itself.
Xe
i,jXe
i,1,Xe
i,1,· · · ,Xe
i,n
(i=1, 2, · · · ,s;j=1, 2, · · · ,n)
is set as its reverse solution
Xe
i,jXe
i,1,Xe
i,1,· · · ,Xe
i,n
, which
can be defined as
Xe
i,jXe
i,1,Xe
i,1,· · · ,Xe
i,n
, where
γ
is a random number between 0 and 1,
and αjand βjare dynamic boundaries.
The elite reverse learning strategy can effectively enhance the diversity of the popula-
tion and, when there are many selectable solution variables, using fitness-based sorting
significantly improves the search efficiency of the algorithm. Additionally, for each gener-
ation of the whale population, the use of the elite reverse learning strategy can generate
reverse solutions that are not near extremum points. This can help the algorithm escape
local optima, strengthen its global optimization capabilities, and enhance algorithm stability.
Lastly, incorporating dynamic boundaries can preserve the algorithm’s search experience,
aiding convergence, and improving both local exploitation and global exploration capabili-
ties. This speeds up the algorithm’s convergence rate.
2.2.3. Nonlinear Adaptive Weight Strategy
Taking into consideration the impact of the target prey, which is the optimal location,
on the whale population during the hunting process in the original WOA (Whale Optimiza-
tion Algorithm), a weight is introduced before the optimal location. This weight represents
Energies 2024,17, 33 5 of 18
the degree to which the current whale individual inherits the previous generation’s optimal
location [32]. The whale position updating formula is as follows:
XT=1
i=ω·XT
b−A×D1,p<0.5 (3)
XT=1
i=ω·XT
b−D2·eZM ·cos(2πM),p≥0.5 (4)
The weight
ω
, which controls the variation in the whale individual positions, is
adjusted by using the following calculation formula:
ω=ω1+(ω1−ω2)2
π·arccosT
TMAX (5)
where
ω1
is the initial weight value,
ω2
is the final weight value,
T
represents the current
iteration count, and TMA X represents the maximum iteration count.
The Hybrid Whale Optimization Algorithm (HWOA) is built upon the foundation of
the WOA but incorporates the use of Tent chaotic mapping to initialize positions within
the search space. It employs MMOC (Multi-Modal Optimization Competition) as the
objective function and introduces both elite reverse learning and nonlinear adaptive weight
strategies. This not only accelerates the algorithm’s convergence speed but also enhances its
capability to track global minimum modes. By using the Hybrid Whale Algorithm to search
and update the positions of the whales, it aims to find the optimal solution, ultimately
improving the global search capability and the computational accuracy of the algorithm.
2.3. HWOA-MVMD Algorithm
MVMD is a typical data decomposition algorithm, which has good generalization
ability when dealing with sample data decomposition problems. In practice, the selection
of eigenmode numbers
k
and penalty parameters
α
is often subjective, which will directly
affect the generalization ability and decomposition accuracy of the algorithm, and the core
idea of the algorithm is to construct a variational problem for solving the modality [
33
], so
the Hybrid Whale Optimization Algorithm is used to optimize these two parameters to
achieve the optimal decomposition effect.
The improved multivariate variational modal decomposition applies the HWOA to
the parameter optimization of MVMD, allowing the algorithm to set parameters based
on the characteristics of the signal itself and achieve the best decomposition effect. The
flowchart of the proposed HWOA-MVMD algorithm is shown in Figure 1, and the detailed
implementation steps are as follows:
(1) Set the whale population size, maximum number of iterations, optimization parameter
optimization space, and initialization population position;
(2)
Take the minimum modal overlap component as the fitness function, calculate the
fitness value according to the position of the population, and save the current opti-
mal value;
(3)
Search for the optimal individual update search area, and update the position of the
whale’s next iteration according to the fitness value level;
(4)
Determine whether the termination conditions are met: if it is met, jump out of the
loop to execute step (5); otherwise, re-execute steps (2)–(3);
(5)
Save the result of the final global optimal solution [
k0
,
α0
]; HWOA-MVMD will
decompose the original data according to the parameter optimal solution to obtain
different modal components.
Energies 2024,17, 33 6 of 18
Energies2023,16,xFORPEERREVIEW6of19
(1) Setthewhalepopulationsize,maximumnumberofiterations,optimizationparam-
eteroptimizationspace,andinitializationpopulationposition;
(2) Tak e theminimummodaloverlapcomponentasthefitnessfunction,calculatethe
fitnessvalueaccordingtothepositionofthepopulation,andsavethecurrentoptimal
value;
(3) Searchfortheoptimalindividualupdatesearcharea,andupdatethepositionofthe
whale’snextiterationaccordingtothefitnessvaluelevel;
(4) Determinewhethertheterminationconditionsaremet:ifitismet,jumpoutofthe
looptoexecutestep(5);otherwise,re-executesteps(2)–(3);
(5) Savetheresultofthefinalglobaloptimalsolution[0
k,0
];HWOA-MVMDwillde-
composetheoriginaldataaccordingtotheparameteroptimalsolutiontoobtaindif-
ferentmodalcomponents.
start
initialization parameters
set the optimi zation space fo r and
MVMD decomposes data
k
calculate the MOC value of the
applicability function
update MMOC
update
whale
location
obtaining the optimal parameter combination
end
MOC<MMOC
Tt
1tt
Y
Y
N
N
Figure1.FlowchartofHWOA-MVMDalgorithm.
3.TPA-TCNPredictionModel
3.1.AnalysisofPhotovoltaicPowerGenerationCharacteristics
Solarenergyhastheadvantagesofbeingrenewable,pollution-free,andlow-cost.
Therearesignificantdifferencesinclimatetypesacrossregions,whichhasasignificant
impactonthecharacteristicsofphotovoltaicpowergeneration.Variousfactorshaveled
totheuncontrollabilityofnaturalsolarenergy,andphotovoltaicpowergenerationhas
significantrandomnessandvolatility.Inordertoimprovetheaccuracyofphotovoltaic
powergenerationprediction,accordingtothecorrelationanalysisbetweeneachinfluenc-
ingfactorandphotovoltaicpowergeneration[34],themaininfluencingfactorsconsidered
inthispaperincludetotalradiation(unit:W/m2),directradiation,scaeredradiation,am-
bienttemperature,windspeed,humidity,andatmosphericpressure.
3.2.TimeConvolutionalNetwork
Timeconvolutionalnetworksareeffectivemodelsforpredictingtimeseries.Itscore
structureisshowninFigure2,whereitgraduallyincreasesthereceptivefielddirectly
throughaseriesofdilatedconvolutions,allowingtheoutputtocontainrichinformation.
Incausaldilatedconvolutions,capturingtheoverallcharacteristicsoflong-timese-
quencescanbeachievedbyadjustingparameterssuchastheconvolutionalkernel,con-
volutionallayers,anddilationfactor‘d’,therebyfurtherdeepeningtheimpactofthese-
quenceonthedeepnetwork.Inthecausaldilationnetwork,thepartconnectedbythearc
Figure 1. Flow chart of HWOA-MVMD algorithm.
3. TPA-TCN Prediction Model
3.1. Analysis of Photovoltaic Power Generation Characteristics
Solar energy has the advantages of being renewable, pollution-free, and low-cost.
There are significant differences in climate types across regions, which has a significant
impact on the characteristics of photovoltaic power generation. Various factors have led
to the uncontrollability of natural solar energy, and photovoltaic power generation has
significant randomness and volatility. In order to improve the accuracy of photovoltaic
power generation prediction, according to the correlation analysis between each influencing
factor and photovoltaic power generation [
34
], the main influencing factors considered
in this paper include total radiation (unit: W/m
2
), direct radiation, scattered radiation,
ambient temperature, wind speed, humidity, and atmospheric pressure.
3.2. Time Convolutional Network
Time convolutional networks are effective models for predicting time series. Its core
structure is shown in Figure 2, where it gradually increases the receptive field directly
through a series of dilated convolutions, allowing the output to contain rich information.
In causal dilated convolutions, capturing the overall characteristics of long-time sequences
can be achieved by adjusting parameters such as the convolutional kernel, convolutional
layers, and dilation factor ‘d’, thereby further deepening the impact of the sequence on the
deep network. In the causal dilation network, the part connected by the arc is the residual
module, which can solve the problem of information loss that may occur when the number
of TCN layers deepens.
The amount of electricity generated in time
t∈{1, 2, 3, · · · k}
is recorded as
xt
,
x(t)=
[x1,x2,x3,· · · xt].
For an input one-dimensional sequence
x0(t)
, the specific output expression for feature
extraction through the TCN is
F(s)=(x∗f)(s)=
k−1
∑
i=0
f(i)∗xs−d×i(6)
where
d
is the expansion coefficient,
∗
is a convolution operation for extracting feature
information,
f
:
{0, · · · ,k−1}
is the convolutional kernel, and
k
is the size of the convolu-
tional kernel.
Energies 2024,17, 33 7 of 18
By combining the multivariate feature
x1(t),x2(t),xk(t)
with the subcomponent
sequence
x0(t)
to form a multivariate time series
x(t)
and extracting features from the
multidimensional time series, the following can be concluded:
hn
t=Fhn
t−1,xt(7)
where n={1, 2, · · · m}and mis the dimension of the multivariate time series dataset.
Energies2023,16,xFORPEERREVIEW7of19
istheresidualmodule,whichcansolvetheproblemofinformationlossthatmayoccur
whenthenumberofTCNlayersdeepens.
d=1
d=2
d=3
input sequenceoutput sequence
output sequenceoutput sequence
tx
th
causal expansion convolution TCN residual module
input
layer
causal convolutional expansion Layer
normalize weights
active layer
random deactivation layer
causal convolutional expansion layer
normalize weights
active layer
Dropout layer
output
layer
convolutional layer
11
Figure2.Causalexpansionnetwork.
Theamountofelectricitygeneratedintime
kt ,3,2,1 isrecordedast
x,
t
xxxxtx ,,, 321
Foraninputone-dimensionalsequence
tx0,thespecificoutputexpressionforfea-
tureextractionthroughtheTCNis
ids
k
i
xifsfxsF
1
0
(6)
wheredistheexpansioncoefficient,isaconvolutionoperationforextractingfeature
information,
1,,0: kf istheconvolutionalkernel,andkisthesizeofthecon-
volutionalkernel.
Bycombiningthemultivariatefeature
txtxtx k
,, 21 withthesubcomponentse-
quence
tx0 toformamultivariatetimeseries
tx andextractingfeaturesfromthe
multidimensionaltimeseries,thefollowingcanbeconcluded:
t
n
t
n
txhFh ,
1
(7)
where
mn ,2,1and𝑚isthedimensionofthemultivariatetimeseriesdataset.
3.3.Tem pora lConvolutionalNetworkModelBasedonTimePaernAention
Intheactualpredictionofphotovoltaicpowergeneration,theimportantdatanot
onlyincludethehistoricaltotalradiantintensityofthesunbutalsoincludethetempera-
ture,humidity,atmosphericpressure,andothermultivariatevariables.Eachvariablehas
adifferentimpactonphotovoltaicpowergeneration,andthedegreeofinfluencevariesas
well.Therefore,inordertoimprovetheaccuracyofphotovoltaicpowergenerationpre-
dictionandsolvethecomplex,dynamic,andinterdependentrelationshipbetweenvaria-
bles,inthisstudy,multivariatevariablesandtimeseriesarecombinedtoformamulti-
variatetimeseries,andthetimepaernaention(TPA)isintroducedintotheTCNmodel
[35],whichcancapturetheimpactofeachvariableonthepredictionsequenceinthepre-
dictionmodelandeffectivelyimprovethepredictionaccuracy.Figure3showstheTPA-
TCNpredictionmodel.
Figure 2. Causal expansion network.
3.3. Temporal Convolutional Network Model Based on Time Pattern Attention
In the actual prediction of photovoltaic power generation, the important data not only
include the historical total radiant intensity of the sun but also include the temperature,
humidity, atmospheric pressure, and other multivariate variables. Each variable has a
different impact on photovoltaic power generation, and the degree of influence varies
as well. Therefore, in order to improve the accuracy of photovoltaic power generation
prediction and solve the complex, dynamic, and interdependent relationship between
variables, in this study, multivariate variables and time series are combined to form a
multivariate time series, and the time pattern attention (TPA) is introduced into the TCN
model [
35
], which can capture the impact of each variable on the prediction sequence in
the prediction model and effectively improve the prediction accuracy. Figure 3shows the
TPA-TCN prediction model.
Energies2023,16,xFORPEERREVIEW8of19
Multivariate
time series
TCN
network
TPA
mechanism
×
×
×
×
＋
C
H
1,1
t
h
t
h
t
v
1t
y
1
h
2
h
1t
h
C
H
2,1
C
k
H
,1
C
H1,2
C
H
2,2
C
k
H
,2
C
m
H
1,
C
m
H
2,
C
km
H
,
Figure3.TPA-TCNpredictionmodel.
(1) TCNlayer
TheoutputoftheTCNlayeristhehiddenstateofeachtimestep,andthehidden
informationm
tRh attimetisoutput.ItcanberepresentedbyEquation(7).
(2) Timemodecapturelayer
UsingtheTCN’sconvolutionalkernelontherowvectoroffeaturematrix
121 ,,
t
HHHH forfeatureextraction,theoutputis
lj
w
l
li
C
ji CHH ,
1
1,,
(8)
whereC
ji
H.istheconvolutionoutputvalueofthei-throwvectorandthej-thconvolu-
tionkernel,Crepresentsallconvolutionalkernels,andlisthelengthofthetimese-
ries.
(3) TimeModeAentionLayer
Letfbetheevaluationcorrelationfunction,andselecttheactivationfunctionout-
putbytheweightofthesigmoidfunction;then,
t
T
C
it
C
ihWHhHf
,(9)
Then,theweighti
is
t
C
ii hHfsigmoid ,
(10)
Calculatet
vbyweightingC
H
:
t
i
i
C
tt Hv
1
(11)
Integratet
handt
v,withweightcoefficientmatrixW,toobtain
tvtht vWhWh
(12)
th hW
1t
y(13)
Figure 3. TPA-TCN prediction model.
(1)
TCN layer
The output of the TCN layer is the hidden state of each time step, and the hidden
information ht∈Rmat time tis output. It can be represented by Equation (7).
Energies 2024,17, 33 8 of 18
(2)
Time mode capture layer
Using the TCN’s convolutional kernel on the row vector of feature matrix
H=
{H1,H2,· · · Ht−1}for feature extraction, the output is
HC
i,j=
w
∑
l=1
Hi,l−1·Cj,l(8)
where
HC
i.j
is the convolution output value of the i-th row vector and the j-th convolution
kernel, Crepresents all convolutional kernels, and lis the length of the time series.
(3)
Time Mode Attention Layer
Let
f
be the evaluation correlation function, and select the activation function output
by the weight of the sigmoid function; then,
fHC
i,ht=HC
iTWαht(9)
Then, the weight αiis
αi=sigmoidfHC
i,ht (10)
Calculate vtby weighting HC:
vt=
t
∑
i=1
HC
tαi(11)
Integrate htand vt, with weight coefficient matrix W, to obtain
h′
t=Whht+Wvvt(12)
yt+1=Wh′h′
t(13)
4. Short-Term Photovoltaic Power Generation Prediction Model Based
on HWOA-MVMD-TPA-TCN
4.1. Prediction Model Process
Based on the modelling process mentioned above, the prediction process of the short-
term photovoltaic power generation prediction model based on the HWOA-MVMD-TPA-
TCN can be obtained, as shown in Figure 4. The specific prediction steps of the combined
model are as follows:
(1)
Utilize the HWOA to optimize the modal number
k
and penalty factor
α
in MVMD,
with the MMOC as the objective function, to obtain and save the optimal solution.
(2)
According to the optimal solution in (1), the original photovoltaic power generation
sequence is decomposed using the HWOA-optimized MAMD to obtain
k
different
IMF components and a residual component r1.
(3) Each component of the original data after decomposition,
k
different IMF components,
and the key influencing factor variable data are combined into a training set and input
into the TPA-TCN model to obtain kdifferent IMF′components.
(4)
The superposition and reconstruction of the predicted values of
k
different
IMF′
compo-
nents are performed to obtain the final predicted value of photovoltaic power
generation
.
(5)
The predicted photovoltaic power generation value is compared with the actual
photovoltaic power generation data, and the error is analyzed.
Energies 2024,17, 33 9 of 18
Energies2023,16,xFORPEERREVIEW9of19
4.Short-TermPhotovoltaicPowerGenerationPredictionModelBasedon
HWOA-MVMD-TPA-TCN
4.1.PredictionModelProcess
Basedonthemodellingprocessmentionedabove,thepredictionprocessoftheshort-
termphotovoltaicpowergenerationpredictionmodelbasedontheHWOA-MVMD-TPA-
TCNcanbeobtained,asshowninFigure4.Thespecificpredictionstepsofthecombined
modelareasfollows:
(1) UtilizetheHWOAtooptimizethemodalnumberk andpenaltyfactor
in
MVMD,withtheMMOCastheobjectivefunction,toobtainandsavetheoptimal
solution.
(2) Accordingtotheoptimalsolutionin(1),theoriginalphotovoltaicpowergeneration
sequenceisdecomposedusingtheHWOA-optimizedMAMDtoobtainkdifferent
IMFcomponentsandaresidualcomponent1
r.
(3) Eachcomponentoftheoriginaldataafterdecomposition,kdifferentIMFcompo-
nents,andthekeyinfluencingfactorvariabledataarecombinedintoatrainingset
andinputintotheTPA-TCNmodeltoobtainkdifferent
F
I
Mcomponents.
(4) Thesuperpositionandreconstructionofthepredictedvaluesofkdifferent
F
I
M
componentsareperformedtoobtainthefinalpredictedvalueofphotovoltaicpower
generation.
(5) Thepredictedphotovoltaicpowergenerationvalueiscomparedwiththeactualpho-
tovoltaicpowergenerationdata,andtheerrorisanalyzed.
photovoltaic power generation data
MVMD decomposition for HWOA optimization
overlay reconstruction
1
IMF
2
IMF
n
IMF
1
r
TPA-TCN
predicted value of photovoltaic power generation
1
IMF
2
IMF
n
IMF
keyva riables
Figure4.Specificpredictionprinciplediagramofthecombinationpredictionmodel.
4.2.DataPreprocessing
4.2.1.Normalization
First,allthehistoricaldatainthispaperarenormalized,thatis,alldataaremapped
to[–1,1]:
minmax
min
xx
xx
x
(14)
wheremin
xandmax
xaretheminimumandmaximumvaluesoftheinputdata,respec-
tively.
Figure 4. Specific prediction principle diagram of the combination prediction model.
4.2. Data Preprocessing
4.2.1. Normalization
First, all the historical data in this paper are normalized, that is, all data are mapped to
[–1, 1]:
x=x−xmin
xmax −xmin
(14)
where
xmin
and
xmax
are the minimum and maximum values of the input data, respectively.
4.2.2. Selection of Evaluation Indicators for Prediction Error
To ensure that the accuracy of the overall model can be effectively evaluated, two
evaluation indicators are selected to evaluate the prediction model of the time series,
namely, the mean absolute error (MAE) and root-mean-square error (RMSE) [
22
]. The error
calculation formulas are
MAE =1
n
n
∑
i=1Yi−e
Yi(15)
RMSE =s1
n
n
∑
i=1Yi−e
Yi2(16)
where
n
represents the total predicted amount, while
Yi
and
e
Yi
represent the true and
predicted photovoltaic power generation values of the input data, respectively.
It can be seen from the above that MAE and RMSE are inversely proportional to the
final evaluation effect, and the smaller the number of MAE and RMSE, the smaller the gap
between it and the actual data, and the better the evaluation effect.
4.2.3. Preprocessing of the Photovoltaic Power Generation Sequence
To improve the final prediction accuracy of photovoltaic power generation and weaken
the influence of nonstationary features on the prediction, an improved MVMD algorithm is
used to decompose and preprocess the photovoltaic power generation sequence obtained
from data feature extraction. During the process of optimizing the parameters of MVMD
using the HWOA, when the algorithm performs the 38th iteration, the fitness value is the
smallest, that is, the minimum modal overlap component is 2.111, as shown in Figure 5.
At this time, the optimal solution is obtained by the modal
k
number and penalty factor
α
,
where
k
is 5 and
α
is 3249. Therefore, the original data of photovoltaic power generation
will be decomposed into five subsequences, and the IMF components obtained from the
decomposition are shown in Figure 6.
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Energies2023,16,xFORPEERREVIEW10of19
4.2.2.SelectionofEvaluationIndicatorsforPredictionError
Toensurethattheaccuracyoftheoverallmodelcanbeeffectivelyevaluated,two
evaluationindicatorsareselectedtoevaluatethepredictionmodelofthetimeseries,
namely,themeanabsoluteerror(MAE)androot-mean-squareerror(RMSE)[22].Theer-
rorcalculationformulasare
n
i
ii
YY
n
MAE
1
~
1(15)
n
i
ii
YY
n
RMSE
1
2
~
1
(16)
where
n
representsthetotalpredictedamount,whilei
Y
and
i
Y
~
representthetrue
andpredictedphotovoltaicpowergenerationvaluesoftheinputdata,respectively.
ItcanbeseenfromtheabovethatMAEandRMSEareinverselyproportionaltothe
finalevaluationeffect,andthesmallerthenumberofMAEandRMSE,thesmallerthegap
betweenitandtheactualdata,andthebeertheevaluationeffect.
4.2.3.PreprocessingofthePhotovoltaicPowerGenerationSequence
Toimprovethefinalpredictionaccuracyofphotovoltaicpowergenerationand
weakentheinfluenceofnonstationaryfeaturesontheprediction,animprovedMVMD
algorithmisusedtodecomposeandpreprocessthephotovoltaicpowergenerationse-
quenceobtainedfromdatafeatureextraction.Duringtheprocessofoptimizingthepa-
rametersofMVMDusingtheHWOA,whenthealgorithmperformsthe38thiteration,the
fitnessvalueisthesmallest,thatis,theminimummodaloverlapcomponentis2.111,as
showninFigure5.Atthistime,theoptimalsolutionisobtainedbythemodal
k
number
andpenaltyfactor
,where
k
is5and
is3249.Therefore,theoriginaldataofpho-
tovoltaicpowergenerationwillbedecomposedintofivesubsequences,andtheIMFcom-
ponentsobtainedfromthedecompositionareshowninFigure6.
Figure5.Convergenceiterationdiagram.
Figure 5. Convergence iteration diagram.
Energies2023,16,xFORPEERREVIEW11of19
Figure6.DecomposedIMFcomponents.
5.ExampleAnalysis
Weselect,asanexample,theactualphotovoltaicpowergenerationdataofabusiness
centerinTianjinthatislocatedateastlongitude
2117
andnorthlatitude
3139
from
23Juneto2Augus t2021.TianjinislocatedinnorthernChina,andthecloudcoverduring
thesummermonths(JunetoJuly)istypicallyinfluencedbyseasonalweatherpaerns.
TheclimateinTianjinisgenerallyhotwithhighhumidity,leadingtofrequentcloudfor-
mation,especiallyintheafternoonandevening.Duringthisseason,varioustypesof
cloudsmayappear,includingcumuluscloudsandstratocumulusclouds.Afternooncon-
vectiveheatingoftenresultsintheformationofcumulonimbusclouds,leadingtopossible
increasedrainfallandthunderstormactivitywithdensecloudcover.Thecloudcover
throughoutthedaycanvarysignificantly.Forinstance,themorningmayberelatively
clear,butastemperaturesriseintheafternoon,cloudcovermayincrease.Foramorepre-
cisedescription,localmeteorologicaldata,includingcloudcoverrecords,sunshinehours,
andprecipitation,canbereferenced.Amongthem,meteorologicaldataincludetotalra-
diation(unit:W/m
2
),directradiation,scaeredradiation,ambienttemperature,humidity,
windspeed,andatmosphericpressurecharacteristics;thesamplingintervalbetween
everytwogroupsofdatais1h;andthenumberofdatasamplesobtainedforeachfeature
is432.Thefirst90%ofthedataareusedasthetrainingset,andthelast10%ofthedata
areusedasthetestset[27].
5.1.ParameterSeingsforthePredictionModels
Afterdecomposingandnormalizingtheoriginalsequence,fordifferentrecon-
structedcomponents,thedatabatchsizebisadjustedbasedontheirdifferentcharacter-
istics.Repeatedexperimentsareconductedonhyperparameterssuchasthesize,learning
ratelr,randominactivationratiodropout,andresidualblockexpansioncoefficientd,as
showninTabl e 3.Theseingsofothertrainingparameters(suchastheconvolutionkernel
Figure 6. Decomposed IMF components.
5. Example Analysis
We select, as an example, the actual photovoltaic power generation data of a business
center in Tianjin that is located at east longitude 117
◦
2
′
and north latitude 39
◦
13
′
from
23 June to 2 August 2021. Tianjin is located in northern China, and the cloud cover during
the summer months (June to July) is typically influenced by seasonal weather patterns. The
climate in Tianjin is generally hot with high humidity, leading to frequent cloud formation,
Energies 2024,17, 33 11 of 18
especially in the afternoon and evening. During this season, various types of clouds may
appear, including cumulus clouds and stratocumulus clouds. Afternoon convective heating
often results in the formation of cumulonimbus clouds, leading to possible increased rainfall
and thunderstorm activity with dense cloud cover. The cloud cover throughout the day can
vary significantly. For instance, the morning may be relatively clear, but as temperatures
rise in the afternoon, cloud cover may increase. For a more precise description, local
meteorological data, including cloud cover records, sunshine hours, and precipitation, can
be referenced. Among them, meteorological data include total radiation (unit: W/m
2
),
direct radiation, scattered radiation, ambient temperature, humidity, wind speed, and
atmospheric pressure characteristics; the sampling interval between every two groups of
data is 1 h; and the number of data samples obtained for each feature is 432. The first 90%
of the data are used as the training set, and the last 10% of the data are used as the test
set [27].
5.1. Parameter Settings for the Prediction Models
After decomposing and normalizing the original sequence, for different reconstructed
components, the data batch size b is adjusted based on their different characteristics.
Repeated experiments are conducted on hyperparameters such as the size, learning rate lr,
random inactivation ratio dropout, and residual block expansion coefficient d, as shown
in Table 3. The settings of other training parameters (such as the convolution kernel size
k_size, optimizer, activation function, and training epoch) are shown in Table 4. The TPA-
TCN model is built using the Python language, and a deep learning network model is
constructed using the TensorFlow framework and Keras. The GridSearchCV method in
the sklearn library is called to perform a grid search on the hyperparameters and find the
optimal parameter settings.
Table 3. Training parameter setting 1.
Weight b_Size Ir Dropout d
IMF1
IMF232, 64, 128 0.001 0.01 3, 4, 5, 6, 7
IMF3
IMF4
IMF5
r1
32, 64, 128 0.001 0.00001 3, 4, 5, 6, 7
Table 4. Training parameter setting 2.
Training Parameter Value
k_size 3
Optimizer Adam
Activation Sigmoid
Epochs 80
Through repeated experiments, it was found that a higher dilation factor can yield
better predictive results for high-frequency reconstruction components. Consistent with the
analysis in the previous section, a higher dilation factor allows for a larger convolutional
receptive field, thus more accurately capturing the overall sequence characteristics of high-
frequency components while ignoring local trends. In other words, a larger dilation factor
‘d’ is more suitable for predicting high-frequency components.
5.2. Photovoltaic Power Generation Prediction Based on TAP-TCN
The IMF components obtained through HWOA-MVMD, along with the seven key
influencing factors, serve as inputs to the TPA-TCN model. In order to more comprehen-
sively uncover the patterns of photovoltaic power generation and effectively enhance the
Energies 2024,17, 33 12 of 18
prediction accuracy, predictions were separately conducted for five sub-sequences. The
predictive results for each component are shown in Figure 7.
Energies2023,16,xFORPEERREVIEW13of19
Figure7.Predictionresultsofeachcomponent.
5.3.ComparativeAnalysisofPredictionMethods
TovalidatetheeffectivenessoftheHWOA-MVMDdatadecompositionmethod,this
papercomparestheproposedmethodwithHWOA-MVMD-BiLSTM(MethodOne).Ad-
ditionally,todemonstratetheeffectivenessoftheHWOA,theproposedmethodissimu-
latedincomparisonwiththeGWO-MVMD-TPA-TCN(MethodTwo)andTPA-TCN
(MethodThree).Toincreasethepersuasivenessofthepredictioneffect,thephotovoltaic
powergenerationforfiveconsecutivedaysfrom29Julyto2August ispredicted.Theline
chartandbarchartareusedtodisplaytheforecastresultsmoreintuitively,andthepre-
dictionresultsofeachmethodareshowninFigure8,ofwhichFigure8a,bshowthecor-
respondingphotovoltaicpowergenerationpredictionresultsofeachmethodon29July;
Figure8c,dshowthepredictionresultsofeachmethodwhenthephotovoltaicpowergen-
erationischangedfromalargefluctuationseries(30July)toamorestableseries(31July);
andFigure8e,fshowthepredictionresultsofeachmethodwhentherearetwosuccessive
largefluctuationsequencesofphotovoltaicpowergeneration.Thedetailedpredictioner-
rorresultsforeachmethodandtheaverageerrorresultsoverthepastfivedaysareshown
inTable 5.
Figure 7. Prediction results of each component.
Through the prediction results of each component in Figure 7, it can be seen that the
five subseries are basically consistent with their corresponding prediction results, which
proves that the photovoltaic power generation prediction performance based on the TAP-
TCN is better.
5.3. Comparative Analysis of Prediction Methods
To validate the effectiveness of the HWOA-MVMD data decomposition method,
this paper compares the proposed method with HWOA-MVMD-BiLSTM (Method One).
Additionally, to demonstrate the effectiveness of the HWOA, the proposed method is
simulated in comparison with the GWO-MVMD-TPA-TCN (Method Two) and TPA-TCN
(Method Three). To increase the persuasiveness of the prediction effect, the photovoltaic
power generation for five consecutive days from 29 July to 2 August is predicted. The
line chart and bar chart are used to display the forecast results more intuitively, and the
prediction results of each method are shown in Figure 8, of which Figure 8a,b show the
corresponding photovoltaic power generation prediction results of each method on 29 July;
Figure 8c,d show the prediction results of each method when the photovoltaic power
generation is changed from a large fluctuation series (30 July) to a more stable series
(31 July); and Figure 8e,f show the prediction results of each method when there are two
successive large fluctuation sequences of photovoltaic power generation. The detailed
prediction error results for each method and the average error results over the past five
days are shown in Table 5.
Energies 2024,17, 33 13 of 18
Table 5. Prediction errors of various methods.
Time Standard/MW Proposed Method HWOA-MVMD-
BiLSTM (Method 1)
GWO-MVMD-TPA-
TCN (Method 2)
TPA-TCN
(Method 3)
29 July MAE 2.07 3.14 4.12 5.31
RMSE 2.20 4.21 5.83 6.83
30 July MAE 2.74 4.75 6.01 11.22
RMSE 3.58 6.76 7.18 10.58
31 July MAE 1.07 1.69 3.68 5.03
RMSE 1.31 2.09 4.53 7.12
1 August MAE 2.46 3.32 5.08 6.38
RMSE 3.07 4.50 6.18 7.62
2 August MAE 1.93 2.58 4.13 5.51
RMSE 2.59 3.56 5.67 6.79
average error MAE 1.95 3.10 4.60 6.69
RMSE 2.55 4.17 5.88 7.79
Energies2023,16,xFORPEERREVIEW14of19
(a)
(b)
0
10
20
30
40
50
60
70
80
90
100
110
120
photovoltaic power generation/kwh
time/h
actual value
actual value The method proposed in this article
HWOA-MVMD-BiLSTM(Method 1)
GWO-MVMD-TPA-TCN(Method 2)
TPA-TCN(Method 3)
Figure 8. Cont.
Energies 2024,17, 33 14 of 18
Energies2023,16,xFORPEERREVIEW15of19
(c)
(d)
0
20
40
60
80
100
120
140
160
180
200
220
photovoltaicpowergeneration/kwh
time /h
actual value
actual value The method proposed in this article
HWOA-MVMD-BiLSTM(Method 1)
GWO-MVMD-TPA-TCN(Method 2)
TPA-TCN(Method 3)
Figure 8. Cont.
Energies 2024,17, 33 15 of 18
Energies2023,16,xFORPEERREVIEW16of19
(e)
(f)
Figure8.Predictionresultcurvesofvariousmodelsfrom29Julyto2Augu st. (a)Curveofpre-
dictedresultsbyvariousmethodson29July;(b)curveofpredictedresultsbyvariousmethodson
29July;(c)curveofpredictedresultsbyvariousmethodsfrom30to31July;(d)curveofpredicted
resultsbyvariousmethodsfrom30to31July;(e)predictionresultcurvesofvariousmethodsfrom
1to2Augus t;(f)predictionresultcurvesofvariousmethodsfrom1to2August .
AnalyzingthepredictiveresultsinFigure8,itcanbeobservedthatMethodOne,
MethodTwo,andMethodThreetosomeextentcapturetheoveralltrendofpowergener-
ation.However,thefiingoftheirpredictioncurvestotheactualcurveispoor,withsig-
nificantlocaldeviations.Notably,MethodThreeexhibitsthepoorestpredictiveperfor-
mance,indicatingthatdatadecompositioncanenhanceforecastingaccuracy.Incontrast,
theproposedmethodshowsahighdegreeofalignmentwiththeactualvalues,minimal
volatility,andahighdegreeofcurvesimilarity.ThissuggeststhattheHWOA-MVMD-
TPA-TCNmodeloutperformstheothersintermsofperformance.
ThepredictiveresultsofMethodOne,MethodTwo,andMethodThreeallexhibit
noticeablelocaldeviations.Incontrast,theresultsofthemethodproposedinthispaper
0
20
40
60
80
100
120
140
160
180
200
photovoltaic power generation/kwh
time/h
actual value
actual value The method proposed in this article
HWOA-MVMD-BiLSTM(Method 1)
GWO-MVMD-TPA-TCN(Method 2)
TPA-TCN(Method 3)
Figure 8. Prediction result curves of various models from 29 July to 2 August. (a) Curve of predicted
results by various methods on 29 July; (b) curve of predicted results by various methods on 29 July;
(c) curve of predicted results by various methods from 30 to 31 July; (d) curve of predicted results
by various methods from 30 to 31 July; (e) prediction result curves of various methods from 1 to 2
August; (f) prediction result curves of various methods from 1 to 2 August.
Analyzing the predictive results in Figure 8, it can be observed that Method One,
Method Two, and Method Three to some extent capture the overall trend of power gen-
eration. However, the fitting of their prediction curves to the actual curve is poor, with
significant local deviations. Notably, Method Three exhibits the poorest predictive perfor-
mance, indicating that data decomposition can enhance forecasting accuracy. In contrast,
the proposed method shows a high degree of alignment with the actual values, minimal
volatility, and a high degree of curve similarity. This suggests that the HWOA-MVMD-
TPA-TCN model outperforms the others in terms of performance.
The predictive results of Method One, Method Two, and Method Three all exhibit
noticeable local deviations. In contrast, the results of the method proposed in this paper
Energies 2024,17, 33 16 of 18
show only brief, slight fluctuations while still effectively capturing the trend in photovoltaic
power generation. This indicates superior forecasting performance.
Based on Figure 8and Table 5, Method One and Method Two proposed in this paper
decompose the data first, while Method Three does not decompose the data, and the
prediction error of Method Three is the largest, indicating that decomposition of the original
data is conducive to power generation prediction. In addition, compared with Methods
Two and Three, the method proposed in this paper shows that after HWOA-MVMD, the
change trend of short-term photovoltaic power generation can be better predicted as a
whole, and the prediction error is significantly reduced, among which the average MAE
value is 1.95 MW and the RMSE value is 2.55 MW, which can be reduced by 33.74% and
38.85%, respectively. In addition, under the condition that the actual data of photovoltaic
power generation fluctuate greatly (29 July~2 August), the prediction error of the method in
this paper remains basically stable, which verifies the effectiveness of the method proposed
in this paper.
6. Conclusions
This article proposes a short-term photovoltaic power generation prediction model
based on the HWOA-MVMD-TPA-TCN model, which improves the prediction accuracy
for photovoltaic power generation and draws the following conclusions:
(1)
Using the actual data example analysis of a business center in Tianjin, the HWOA-
MVMD-TPA-TCN model effectively reduces the prediction error of photovoltaic
power generation, in which the MAE value is 1.95 MW and the RMSE value is
2.55 MW, which can be reduced by up to 33.74% and 38.85%, respectively. The
effectiveness of the forecasting model proposed in this paper is proved, and the model
has certain reference value in the field of time series forecasting.
(2)
The IMF components resulting from the decomposition of photovoltaic power gen-
eration possess distinct characteristic changes. Exploring more efficient prediction
methods for these components requires further research. Additionally, analyzing
error components and improving prediction accuracy through error correction should
be considered. Future research can focus on these aspects to advance photovoltaic
power generation prediction.
Author Contributions: Conceptualization, R.C., H.T. and D.L.; methodology, R.C.; software, R.C.;
validation, R.C.; formal analysis, R.C.; investigation, R.C.; resources, M.F.; data curation, H.F.;
writing—original draft preparation, R.C.; writing—review and editing, R.C., H.T. and D.L.; visualiza-
tion, R.C.; supervision, H.T. and D.L.; project administration, R.C., H.T. and D.L. All authors have
read and agreed to the published version of the manuscript.
Funding: This research was funded by State Grid Tianjin Electric Power Company Science and Tech-
nology Project, grant number KJ21-1-21; Tianjin Postgraduate Scientific Research Innovation Project,
grant number 2022SKYZ070; and Tianjin University of Technology 2022 school-level postgraduate
scientific research innovation practice project, grant number YJ2209.
Data Availability Statement: The data involve project confidentiality and cannot be disclosed.
Conflicts of Interest: The corresponding author represents all authors and declares that there are no
conflict of interest.
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