A novel ensemble learning approach for hourly global solar radiation forecasting

Abstract

Precise solar radiation forecasting can provide great benefits and solutions for smart grid distribution and electricity management. However, its non-stationary behavior and randomness render its estimation very difficult. In this respect, a new hybrid learning approach is proposed for multi-hour global solar radiation forecasting, relying on Convolutional Neural Network (CNN), Nonparametric Gaussian Process Regression (GPR), Least Support Vector Machine (LS-SVM), and Extreme Learning Machine (ELM) as essence predictors. Then compressive sensing technique is applied to perform a hybridization scheme of the model’s output. Hourly global solar radiation data from two sites in Algeria with different climate conditions are used to evaluate the full potential of the integrated model, with stationarity checks with an advanced clear sky model (MecClear model). Different comparative simulations show the superiority of the proposed pipeline in forecasting hourly global solar radiation data for multi-hour ahead compared to the stand-alone model. Experimental results show that the proposed hybridization methodology can effectively improve the prediction accuracy and outperforms benchmarking models during all the forecasting horizons.

Full text

ORIGINAL ARTICLE
A novel ensemble learning approach for hourly global solar radiation
forecasting
Mawloud Guermoui
1
•Said Benkaciali
1
•Kacem Gairaa
1
•Kada Bouchouicha
2
•Tayeb Boulmaiz
3
•
John W. Boland
4
Received: 19 February 2021 / Accepted: 17 August 2021
The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021
Abstract
Precise solar radiation forecasting can provide great benefits and solutions for smart grid distribution and electricity
management. However, its non-stationary behavior and randomness render its estimation very difficult. In this respect, a
new hybrid learning approach is proposed for multi-hour global solar radiation forecasting, relying on Convolutional
Neural Network (CNN), Nonparametric Gaussian Process Regression (GPR), Least Support Vector Machine (LS-SVM),
and Extreme Learning Machine (ELM) as essence predictors. Then compressive sensing technique is applied to perform a
hybridization scheme of the model’s output. Hourly global solar radiation data from two sites in Algeria with different
climate conditions are used to evaluate the full potential of the integrated model, with stationarity checks with an advanced
clear sky model (MecClear model). Different comparative simulations show the superiority of the proposed pipeline in
forecasting hourly global solar radiation data for multi-hour ahead compared to the stand-alone model. Experimental
results show that the proposed hybridization methodology can effectively improve the prediction accuracy and outperforms
benchmarking models during all the forecasting horizons.
Keywords Clear sky model Forecasting Machine learning Deep learning model Solar radiation energy 
Compressive sensing
Abbreviations
ANN Artificial neural network models
Bi-LSTM Bi-directional long short-term memory
CEEMDAN Complete ensemble empirical mode
decomposition with adaptive noise
CNN Convolutional neural network
ELM Extreme learning machine
ESN Echo state network
ESSS Exponential smoothing state space
FNN Feedforward neural network
GA Genetic algorithm
GANs Generative Adversarial Networks
GH Extra-terrestrial solar radiation
GOA Grasshopper optimization algorithm
GPR Gaussian process regression
CSI Clear sky index
LS-SVM Least support vector machine
MABE Mean absolute bias error
MARS Multivariate adaptive regression spline
MMFF Multi-model forecasting framework
MOS Model output statistics
NMAE Normalized mean absolute error
nRMSE Normalized root mean square error
nRMSE Normalized root mean square error
OMP Orthogonal matching pursuit
PACF Partial autocorrelation factor
r Correlation coefficient
RF Random forest
RLMD Robust local mean decomposition
RMSE Root mean square error
SCA Sine cosine algorithm
&Mawloud Guermoui
mawloud.guermoui@uraer.dz
1
Unite
´de Recherche Applique
´e en Energies Renouvelables,
URAER, Centre de De
´veloppement des Energies
Renouvelables, CDER, 47133 Ghardaı
¨a, Algeria
2
Unite
´de Recherche en Energies Renouvelables en Milieu
Saharien (URERMS), Centre de De
´veloppement des Energies
Renouvelables (CDER), 01000 Adrar, Algeria
3
Materials, Energy Systems Technology and Environment
Laboratory, Ghardaia University, Ghardaia, Algeria
4
Industrial AI Research Centre, UniSA STEM, University of
South Australia, Mawson Lakes 5095, Australia
123
Neural Computing and Applications
https://doi.org/10.1007/s00521-021-06421-9(0123456789().,-volV)(0123456789().,-volV)
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

St-OMP Stage-wise orthogonal matching pursuit
WPK Wavelet packet decomposition
WRF Numerical weather meso-scale model
Greek symbol
qLag value
rsSparse solution
rsResidual
1 Introduction
The implementation of photovoltaic with power grids
application is a very challenging task due to the non-sta-
tionary behavior of solar energy and its dependence on
climate and geographical location. It is important to
establish a precise forecasting model for solar radiation
components. In this respect, a broad range of models have
been created recently based on machine learning tech-
niques to handle these challenges. The machine learning
model can be extended to a wide variety of domains, and
its characteristic is that the model can define the nonlinear
relations among data sources [1]. This benefit encourages
the use of these models in computer vision, data mining,
filtering, and forecasting.
In the literature review of solar radiation components
assessments, artificial neural network models (ANN)
[5,30], support vector machine (SVM) [13,17,22],
Gaussian process regressions (GPR)[18,20], and random
forest (RF) [4] are often used models in this field due to
their high performance and small parameters tuning during
the modeling process.
Generally, speaking, these leading approaches con-
tribute differently to the forecasting process, so that the
merging of these models will improve the forecasting
efficiency over the stand-alone model. According to our
previous study [21], hybrid models can be divided into six
main categories: hybrid general-techniques; decomposi-
tion-technique; cluster-technique; evolutionary-technique;
decomposition-clustering-technique, and the residual-
technique. Recently, another class of hybrid models can be
added, which can be named the feature-based learning
ensemble approach, which is based on transforming the
weather input variables into new discriminative data. This
latter uses deep learning models such as CNN or auto-
encoder model to produce new input variables, and then the
resulting data are fed to the forecasting model [15,16].
Peng et al. [35] proposed a new hybrid model for solar
radiation prediction in the south of Dauphin Island, Ala-
bama (https://www.ndbc.noaa.gov/). The proposed
methodology is based mainly on the use of deep learning
model bidirectional long short-term memory (Bi-LSTM) as
essence regression model combined with complete
ensemble empirical mode decomposition with adaptive
noise (CEEMDAN) as a pre-processing method, and sine
cosine algorithm (SCA) for hyper-parameters tuning of Bi-
LSTM to build CEEMDAN- SCA-Bi-LSTM forecasting
model for hourly global solar radiation data. The fore-
casting results that the proposed approach performs better
than conventional Bi-LSTM, SCA-Bi-LSTM, and CEEM-
DAN- SCA- Bi-LSTM.
Castangia et al. [7] assessed the forecasting performance
of different models for short-term solar radiation fore-
casting combined with feature selection algorithms to
select the most relevant exogenous variables. In their work,
feature selection methods reduce the number of exogenous
variables from 15 inputs to eight inputs data. They found
that echo state network (ESN) provides the highest fore-
casting performance for the short term (15 min), and for
larger forecasting horizons they found that the LSTM
model provides high forecasting performance compared to
CNN-1D, random forest, echo state network (ESN), and
feedforward neural network (FNN). They showed also the
effect of exogenous variables against endogenous data in
improving the forecasting performance of global solar
radiation data.
Ngoc-Lan Huynh et al. [33] proposed a new integrated
model for global solar radiation forecasting based on the
use of robust local mean decomposition (RLMD) combined
with LSTM. The proposed RLMD-LSTM was evaluated on
five regions in Vietnam, for instantaneous scale. The pro-
posed methodology exhibits high performance compared to
multivariate adaptive regression spline (MARS), support
vector regression (SVR), persistence method, RLMD-
MARS, RLMD-SVR, and RLMS- Persistence.
Gao et al. [14] proposed a new soft computing model for
hourly global solar radiation in different regions in the
world. The proposed model is based on the use of
CEEMDAN for data pre-processing then the decomposed
hourly global solar radiation is fed to the CNN model for
features transformation, and the forecasting process is
performed employing the LSTM model. The proposed
CEEMDAN-CNN-LSTM model proves its forecasting
ability in different regions in the world compared to the
benchmarking model.
Meng et al. [31] proposed a new combined model for
precise solar power plants forecasting. The proposed model
uses wavelet transform for decomposing the global solar
radiation data into different sub-harmonics followed by a
feature selection scheme to select the most appropriate sub-
frequency signal, which is then fed into deep generative
adversarial networks (GANs). The proposed hybridization
methodology show high forecasting performance against
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

ARMA, ANN, CNN, GAN, SVR, and fuzzy method for
both studied regions.
Huang et al. [25] proposed a new hybrid model for one
hour-ahead forecasting of global solar radiation data. The
proposed model is based on four main steps: Firstly
wavelet packet decomposition (WPK) method is used for
decomposing the input data into four sub-frequency sig-
nals, and then each subset of decomposed data are fed into
an independent CNN-channel for features extraction.
Generated features from each CNN channel are used as
inputs for independent LSTM model, and then the outputs
of all LSTM model are used as input to MLP regression.
The forecasting results of the proposed model overall
studied regions show promising results and outperform
others, hybrid models.
Conventional models may not be able to find the desired
solution, which demonstrates the need for hybridization
methods. Currently, the use of the deep learning model is a
popular method for predicting solar energy resources [40].
The main advantage of deep learning techniques is that
they provide higher forecasting accuracy compared to
conventional models. However, they require a huge num-
ber of parameters to be adjusted and big historical data in
the training process.
It is difficult for standard prediction models to offer an
optimal solution to a complex forecasting model. Each
model has its advantages and disadvantages. Ensemble
learning models are effective and highly efficient methods
that combine the estimated results of some models to give
precise estimation instead of finding a single, robust
learner.
In this regard, the main contribution of this study is the
proposition of a new hybrid model to improve the fore-
casting of 12 h ahead for hourly global solar radiation by
integrated deep learning models and conventional learning
models in a competitive manner using a compressive
sensing approach [3]. This is given as follows:
•After data collection and processing, the historical data
are then normalized using the MecClear model (http://
www.soda-pro.com/).
•Suitable lags for endogenous/exogenous data are
determined employing partial autocorrelation and
cross-correlation function.
•Developing a new hybrid model by integrating the
grasshopper optimization algorithm (GOA) with LS-
SVM (GAO-LS-SVM) for solar radiation forecasting
[32].
•Then the resulting outcomes from individual models;
CNN-1D, GPR, GAO-LS-SVM, and ELM are merged
using a stage-wise compressed sensing algorithm to
build the final solar radiation forecasting.
The rest of the paper is organized as follows. In Sect. 2,
site location and data description are described. Next,
developed individual models and the hybridization
methodology are presented in detail. Afterward, the fore-
casting procedure is presented. Results and discussion are
presented in Sect. 3. Finally, Sect. 4summarizes the pre-
sented work and provides concluding remarks.
2 Materials and methods
This section presents the general principals of this work.
In the first subsection, we present a detailed explanation of
the studied region and the collection of the data. In the
second subsection, the developed models are presented and
the design of the proposed hybrid model for solar radiation
forecasting.
2.1 Case study and data description
The study area includes Algerian climate zones, and two
sites located at different climatic regions were selected for
models validation. The first one in Algiers which consti-
tutes the Mediterranean climate of Algeria, and the site is
located at 36.8 N latitude and 3.17 E longitude and an
elevation of 357 m. The second one is the Ghardaı
¨a region
which is characterized by an arid climatic zone with the
geographical coordinates of 32.3 N latitude and 3.8 E
longitude and an elevation of 450 m [34]. The geographical
coordinates of the studying sites are shown on the map of
Algeria (see Fig. 1).
The data used in this study were obtained from the
Renewable Energy Development Center (CDER) in
Algiers and the Renewable Energy Applied Research Unit
(URAER) in Ghardaı
¨a. The data refer to the global solar
irradiation (GHI), and the main meteorological parameters,
such as relative humidity, ambient temperature, air pres-
sure, wind direction, and wind speed, were collected using
different measurement stations in 5 Minutes and hourly
intervals, respectively, in CDER and URAER (Fig. 2). The
specific information about the solar radiation measurement
station and weather station can be found in Tables 1and 2.
The global solar radiation measurements are processed
through simple quality control procedures [2]. As shown in
Fig. 3, the distribution of 5-min and hourly solar irradiance
during a period of one year refers to the average of the
three (2013–2105) and four (2013–2016) years of mea-
surements, respectively, in CDER and URAER sites. As
can be seen, at the beginning of each day, the GHI value is
low, increases to reach the maximum values at noon, and
then gradually decreases to achieve zero values in the
afternoon, during the day it represents the low values which
are due to the presence of cloud in the sky, that depict a
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Fig. 1 Studied sites location
Fig. 2 Photograph of the measuring stations installed in aURAER
and bCDER sites (photograph by author)
Table 1 Characteristics of used
solar radiation instruments Station CDER-Algiers URAER- Ghardaı
¨a
Sensor Kipp & Zonen CMP21 CIMEL CE 180
Maximum operational irradiance 4000 W/m
2
–
Spectral range 270 to 3000 nm 300 to 2500 nm
Sensitivity 7 to 14 lV/W/m
2
120 ±20 lV/mW/cm
2
Directional response \10 W/m
2
–
Non-stability (change/year) \0.5% –
Temperature response \1% (-20 Cto?50 C) –
Response time \5s \30 s
Nonlinearity \0.2% \0.2%
Operating and storage temperature range -40 Cto?80 C–
Table 2 The weather station sensor reference
Parameter URAER- Ghardaı
¨a CDER-Algiers
Solar irradiance CIMEL CE 180 Kipp and Zonen CMP21
Wind velocity CIMEL–CE 155 N NRG #40C
Wind direction CIMEL–CE 157 N NRG #200P
Air temperature CIMEL–CE 185A Campbell Scientific CS215
Relative humidity CIMEL–CE 189–2
Air pressure CIMEL– A 711 Campbell CS100
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

more frequent phenomenon in the winter period for the
CDER site.
After the pre-processing and cleaning phase, the data are
then used for tuning the developed models. Before this, the
lag value must be determined by the mean of the partial
autocorrelation factor (PACF) [38]. The estimated lags will
be used as model input. For hyper-parameters tuning, each
model has its specific training method. Descriptive statis-
tics of measured parameters are provided in Table 3for the
training and testing subsets for both studied regions.
2.2 Machine learning models
In this section, we present a short description of the
developed models in this study.
2.2.1 Gaussian process regression (GPR)
Gaussian process regression models are nonparametric
approaches that can be applied to treat modeling and
classification problems. The application of GPR models for
solar radiation applications leads to high precision results
[18,20].
2.2.2 Grasshopper optimization least square support
vector machine (GAO-LS-SVM)
LS-SVM belongs to the kernel-based method derived from
the SVM model. LS-SVM proves its high performance in
the field of modeling and forecasting problems. In the
current work, the GAO algorithm is applied for hyper-pa-
rameter tuning of the LS-SVM model [13,17,22].
Fig. 3 Variation of solar radiation in aCDER and bURAER sites for an annual period
Table 3 Weather statistics used
for the locations under
investigation
Period Training data Testing data
Variable GHI P (hPa) T
avg
(C) RH (%) GHI P (hPa) T
avg
(C) RH (%)
Ghardaia site
Max 1 089.4 981.1 45.2 95.0 1081.4 988.5 46.6 100
Min 0.011 942.3 3.2 6.0 0.048 946.9 1.9 7.0
Mean 478.7 963.2 23.05 32.24 461.87 966.3 22.82 36.35
St. dev 320.86 5.3 9.11 16.18 314.45 5.8 9.48 17.46
Algiers site
Max 1006.08 995 34.49 94.74 1236 1001 37.32 93.3
Min 5 951 2.674 13.083 0.0101 951 1.35 2.1
Mean 346.42 975.74 16.88 67.26 382.26 976.17 17.61 61.62
St. dev 275.70 5.71 5.45 18.05 307.12 5.89 5.76 21
Overview statistics
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

2.2.3 Extreme learning machine (ELM)
ELM model, which is another kernel-based model,
according to the literature ELM network, produces high
generalization capability and shows fast learning speed
compared to other machine learning approaches [8].
2.2.4 Convolution neural network (CNN)
CNN model which belongs to the deep learning category is
an effective methodology for features extraction, and it
provides high performance in computer vision. Recently,
CNN-1D shows promising results for time series analysis
as feature learning or as a forecasting model. In this study,
we use the CNN-1D model as a forecasting model for solar
radiation data [14].
2.2.5 Convolution neural network-Gaussian process
regression CNN-GPR
The CNN-GPR model involves using CNN-1D that can
extract pertinent features from input data, and then the
resulting features from CNN-1D are used as new inputs for
the GPR model for hourly solar radiation forecasting [28].
2.3 Design hybrid forecasting approach
The main objective of this paper is to examine the possi-
bility of increasing the forecasting performance of hourly
global solar radiation for multi-horizon. Global solar
radiation data, as a meteorological parameter, has a random
process. Due to its non-stationary characteristic, forecast-
ing the dynamic behavior of solar radiation data with
acceptable accuracy is a very challenging task. In this
respect, a new integrated model was proposed for a multi-
hour-ahead forecasting of global solar radiation (see
Fig. 4). The proposed forecasting model is based on four
main steps:
(1) Different learning approach needs stationary variable
input/output; for this necessity, solar radiation data
are transformed using an advanced clear-sky model
(i.e., McClear) [27]. The measured solar radiation
(GHR) data are divided by the theoretical clear sky
model (CS) in the pre-processing stage:
CSI tðÞ¼GHR tðÞ
CS tðÞ ð1Þ
where CSI is the normalized clear sky index.
(2) Determination of the lag value (denoted q)is
determined for both endogenous and exogenous data
utilizing the partial autocorrelation function (PACF)
and Pearson and Spearman cross-correlation
coefficients between CSI and meteorological vari-
ables, respectively.
(3) Employing Different developed models are
employed in a cooperative manner (ELM, GPR,
GAO-LS-SVM, and CNN-1D) by fusing their out-
puts to construct the final forecasting signal.
(4) Fusing the outcomes from different stand-alone can
be accomplished competitively or cooperatively
fashion. For the competitive method, the best results
of the models for each input are selected; however, in
the cooperative method all learning models con-
tribute in a different manner to the final forecasting
output. Relative merits (contribution) for each model
must be known to build a robust ensemble learning
approach. Several possible ways are available in the
literature to estimate the contribution of each model
such as metaheuristic methods. In the current study,
the fusion strategy of different models is built based
on compressive sensing methodology (space coding/
representation) [6]. Our motivation behind the choice
of compressive sensing methodology as a hybridiza-
tion mechanism is due to its high performance in
sparse signal recovery.
2.4 Stage-wise compressed sensing for multi-
ensemble learning approach
Compressed sensing was introduced, by [6,11] firstly, for
signal recovery. It aims at representing a given signal/im-
age from empirical observation of linear projection. Con-
ventional methods deal with a signal presentation by a
fixed family of basic functions (Fourier series and Wavelet
Analysis). Practical reconstruction of a given signal using
sparse decomposition methodology leads to equivalent or
better performance compared to a conventional method.
The fundamental aspect of sparse decomposition is that
few weights of the dictionary atoms are nonzeros, while the
rest is equal to zeros. In this respect, a small set of atoms
are selected as essence atoms for the reconstruction. Let’s
consider our target V, and then the sparse decomposition
problem can be formed as [29]:
V¼D:afor D2Rnm
;nmð2Þ
Equation (1) can be solved by the following L
0
-min-
imisation problem:
min a0
kksubject to V ¼Dað3Þ
where D represents the dictionary with a small range of
features (atoms), V is the target vector that can be pre-
sented by sparse decomposition and arepresent the sparse
solution of Eq. (2). In the literature, various methods are
proposed for solving the optimization problem of Eq. (2).
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

In the current study, we briefly introduce Stage-wise
Orthogonal Matching Pursuit (St-OMP) [38], due to its
high performance compared to other greedy approaches
such as Orthogonal Matching Pursuit (OMP). Contrary to
the basic OMP method, St-OMP integrates many coeffi-
cients at each iteration, while OMP involves only one
coefficient. Additionally, St-OMP runs over a fixed number
of iterations, whereas OMP may take numerous iterations
[19].
The proposed fusion strategy is based mainly on build-
ing a learning dictionary from the learning phase. The
dictionary atoms represent the forecasting response of the
developed models. Our learning dictionary consists of four
atoms, which correspond to the output of ELM, CNN-1D,
GAO-LS-SVM, GPR, respectively. Then our learning
dictionary (DIC = { ELM
train
, CNN-1D
train
, GAO-LS-
SVM
train
, GPR
train
}) is used as sparse decomposition of the
target which is in our case the measured hourly global solar
radiation data ( GHR
train
) Eq. (3):
0 100 200 300 400 500 600 700 800 900 1000
0
200
400
600
800
1000
0 100 200 300 400 500 600 700 800 900 1000
0.2
0.4
0.6
0.8
1
-0.2
0
0.2
0.4
0.6
0.8
1
Sample Partial Autocorrelation
Sample Partial Autocorrelation Function
02468
10 12 14 16 18 20
Lag
0 100 200 300 400 500 600 700 800 900 1000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
ELM
LS-SVM
CNN-
GPR
Learning Diconary Training output
ELM GPR SVM CNN
Sparse
Coding
Sparse Soluon
Meteorological Station
Hourly Global Solar
Radiation data
Clear Sky Index
(MecClear) Lag Slection
Estimated Clear
Sky Index (Kc)
Fig. 4 Flowchart of the proposed method
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

min a0
kksubject to GHRtrain ¼DICtrain asð4Þ
We note here that the dictionary contains the forecasted
global solar radiation from each model DIC = { GHR
ELM
,
GHR
GAO-LS-SVM
,GHR
GPR
, GHR
CNN
}that is rebuilt from
the forecasted CSI.
The second step of the proposed fusion strategy is the
estimation of the sparse solution a, this is carried out
employing St-OMP as follows [19]:
•Consider an initial solution a
0
= 0, an initial residual
r
0
= V, a stage counter s set to 1 and an index sequence
denoted as T1,…,Ts which contains the locations of the
nonzeros in a
0
.
•Compute the inner product between the current residual
and the considered dictionary:
Cs¼DICt
train rs1ð5Þ
•Perform hard thresholding to find out the significant
nonzeros in Cs by searching for the locations corre-
sponding to the large coordinates Js:
js¼j:CsjðÞ[tsrs
fg ð6Þ
where rsrepresents a formal noise level and t
s
is a
threshold parameter taking values in the range
2ts3.
•Merge the selected coordinates with the previous
support.
Ts¼Ts1[jsð7Þ
•Project the vector GHRtrain on the columns of DICtrain
that correspond to the previously updated T
s
.This
yields a new approximation a
s
:
as
ðÞ
Ts¼DICt
trainTsDICtrain Ts

1DICt
trainTsGHRtrain ð8Þ
•Update the residual according to:
rs¼GHRtrain DICtrain:asð9Þ
•Check whether a stopping iterative condition (e.g.,
smax = 10) is met.
The obtained sparse solution asis then employed in the
test phase for the final forecast of the test target using
Eq. (9).
GHRtest ¼GHRtest ;asð10Þ
where GHRtest represents the test dictionary that contains
the estimated outputs from each model. We note here that
both learning and test dictionaries are applied once for each
time horizon.
2.5 Necessity of stationarity of time series
Covariance stationarity, also termed weak stationarity,
denotes that a time series, comprised of a sequence of
random variables, possesses a constant mean, and the
covariance between any two terms of the series only
depends on the time distance between them. If a time series
is non-stationary, its mean is undefined and its variance is
infinite. Thus, any estimate of mean and variance from a
finite sample will be biased. Additionally, spurious corre-
lations between the random variables will likely occur.
Apart from the drawbacks listed above, there are very
precise benefits from the stationary nature of a time series.
If the series xt;t2Z
fg
is weakly stationary, Wold’s
Decomposition Theorem states that it can be written as a
linear combination of an infinite number of white noise
random variables that are independent and identically
distributed.
xt¼X
1
j¼0
wjztjð11Þ
Here,
1. w0¼1;X
1
j¼1
w2
j\1
2. ztWN 0;r2
z

3. ztis the limit of linear combinations of xs;st:
This results in xtbeing able to be modeled as an
autoregressive moving average (ARMA) process.
3 Experimental methodology
The developed models in this study are adapted with a
maximum horizon of 12 h. The achieved results are de-
scribed in four subsections. Firstly, the obtained results
from the developed individual forecasting models with the
endogenous data for 12 horizons are presented in detail.
The second subsection deals with the use of exogenous
data for multi-hour-ahead forecasting using stand-alone
models. Then, the results of the proposed hybrid model are
presented and discussed for both endogenous, and exoge-
nous cases. In the last section, a comparison of all devel-
oped models in terms of forecasting metrics is presented
and discussed.
3.1 Verification metrics
In the current study, we use five common metrics to assess
the performance of studied models, which are root mean
square error (RMSE), normalized root mean square error
(nRMSE), mean absolute bias error (MABE), normalized
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

mean absolute error (NMAE) and correlation coefficient
(r), and they are expressed as [36]:
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
nXn
i¼1HH

2
rð12Þ
rRMSE ¼RMSE
Pn
i¼1Hð13Þ
MABE ¼1
nX
n
i¼1
HH


ð14Þ
NMAE ¼Pn
i¼1HH



Pn
i¼1Hð15Þ
r¼Pn
i¼1Hmean H

Hmean HðÞðÞ
Pn
i¼1Hmean H

2Hmean HðÞðÞ
2ð16Þ
where H represents the measured solar radiation data and H
the estimated solar radiation data.
Forecasting results of the proposed models was vali-
dated on two different solar radiation data from two
radiometric station.
3.2 Case of Ghardaia region
Before proceeding with the forecasting process, data
standardization is needed to avoid forecasting models to be
influenced by the different range, which is given as follow:
X¼Xmin XðÞ
max XðÞmin XðÞ ð17Þ
where Xrepresents the new-scaled data, minðXÞand
maxðXÞare the minima and maximum values of the his-
torical data.
After that, the lag selection is an important step before
the compute time series. To this end, the partial autocor-
relation function (PACF) is applied to select a suit-
able order of lags. The well-known PACF methodology is
based on the correlation of the fixed time series data CSI
(n) (clear sky index in our case) with its lagged values
CSI n sðÞto compute the order of time series data. For
Ghardaia regions, four time lags are suitable for forecasting
solar radiation data (CSI
t
, CSI
t-1,
CSI
t-2,
CSI
t-3
). In the case
of the Algiers location, three time lags are found as rele-
vant inputs.
For exogenous data in Ghardaia regions, we found that
two time lags for temperature and humidity and three time
lags for pressure and extra-terrestrial solar radiation are
suitable for forecasting hourly global solar radiation.
3.2.1 Forecasting-based endogenous variables
All developed models have been trained and tested with the
same strategy. Graphical representations and statistical
measures were used to evaluate the predictive ability of
each model.
The testing results of stand-alone and hybrid models in
terms of statistical metrics for Ghardaia region are listed in
Table 4.
From Table 4, we can observe that stand-alone models
revealed significant results and provide approximately
equal performance with a slight difference. As can be seen,
for horizons one, two, four, five, and six the GAO-LS-SVM
model provides the highest forecasting performance com-
pared to its counterpart models, and for horizons three,
eight, and eleven GPR models were selected as a robust
forecasting model. For time horizons seven, nine, and ten,
CNN-1D model provides better forecasting performance.
In general, in terms of statistical indicators, the ELM
forecasting model was found to be an excellent forecasting
model for the 12-h-ahead forecasting horizon.
Analyzing the case of developed hybrid models, where
the input data of the CNN-GPR model are the transformed
endogenous variables through the CNN model, then the
transformed input variables are fed into the GPR model for
the final forecast [28]. For the proposed hybrid model
(fusing the outcomes of stand-alone models), the inputs
variables are a matrix, where the column is the outputs of
the developed individual models and the output is the
desired CSI component. The final weights of our proposed
model are estimated by the mean of the sparse represen-
tation algorithm using St-OMP. As can be seen from
Table 4, the hybridization of CNN-GPR doesn’t improve
the forecasting performance during the entire forecasting
horizon. Another important remark that can be deduced
from Table 4is that the combination of the CNN-GPR
model outperforms the CNN model overall the studied
horizon. This can be justified by the use of CNN layers of
features transformation as input to the GPR model to out-
put the desired CSI, while in stand-alone CNN model the
CNN layers of features extraction are connected only to the
softmax layer for a final forecast.
Examining the achieved results by the proposed
methodology (see Table 4), we can observe that the pro-
posed hybridization mechanism can boost the performance
of the hourly global solar radiation forecasting in terms of
statistical metrics. The improvement of the proposed
hybrid models compared to the best stand-alone models
during all forecasting horizons is 0.3805 ±0.1039 (Wh/
m
2
) per hour in terms of RMSE, 0.1703 ±0.0379 (%) in
terms of nRMSE, and 0.5975 ±0.2272 (%) in terms of
NMAE. The improvement of the integrated models against
weak models during all the forecasting horizon is
1.6434 ±0.6575 (Wh/m
2
) per hour in terms of RMSE,
0.4546 ±0.142 (%) in terms of nRMSE, and
1.1838 ±0.4308(%) in terms of NMAE. The percent of
the improvement during the forecasting horizon in terms of
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Table 4 Performance comparison of the developed models with endogenous variables (case of Ghardaia region)
Forecasting horizon (hour) Model RMSE (Wh/m
2
) nRMSE MABE NMAE r(%)
1-Hour CNN-1D 51.8291 11.6859 26.2391 5.9161 98.3292
ELM 49.0523 11.0598 26.0597 5.8757 98.5082
GPR 49.1695 11.0862 25.6582 5.7851 98.4964
GAO-LS-SVM 49.0487 11.0590 25.7605 5.8082 98.5049
CNN-GPR 50.82 11.62 26.32 5.81 98.36
Proposed method 48.7826 10.9585 24.5072 5.5256 98.5180
2-hour CNN-1D 61.5512 13.8782 37.4287 8.4392 97.7300
ELM 59.7468 13.4714 33.3740 7.5250 97.7834
GPR 59.7680 13.4761 32.7265 7.3790 97.7747
GAO-LS-SVM 59.6744 13.4550 32.8001 7.3956 97.7836
CNN-GPR 60.41 13.76 34.41 7.86 97.95
Proposed method 59.3552 13.3224 31.0848 7.0093 97.7989
3-hour CNN-1D 66.2969 14.9485 37.3475 8.4211 97.2597
ELM 66.6071 15.0185 38.9752 8.7881 97.2578
GPR 65.2341 14.7089 36.7301 8.2819 97.3492
GAO-LS-SVM 65.2908 14.7217 36.8179 8.3016 97.3460
CNN-GPR 65.97 14.88 37.37 8.81 97.08
Proposed method 65.0301 14.5949 34.5063 7.7815 97.3512
4-hour CNN-1D 69.2735 15.6197 40.5473 9.1426 97.0260
ELM 69.7525 15.7277 41.3125 9.3151 96.9958
GPR 68.8594 15.5264 39.4710 8.8999 97.0484
GAO-LS-SVM 68.7472 15.5011 39.5505 8.9178 97.0610
CNN-GPR 69.22 15.46 40.05 9.46 96.98
Proposed method 68.4175 15.3499 36.6721 8.2705 97.0651
5-hour CNN-1D 70.9629 16.0004 39.9404 9.0056 96.8507
ELM 70.9029 16.0004 40.9404 9.00 96.8505
GPR 70.9214 15.9910 41.2472 9.3002 96.8780
GAO-LS-SVM 70.8262 15.9695 41.1220 9.2720 96.8854
CNN-GPR 70.3 15.98 40.55 9.00 96.86
Proposed method 70.3409 15.7911 37.9165 8.5516 96.8922
6-hour CNN-1D 72.5361 16.3543 43.2131 9.7430 96.7561
ELM 73.2796 16.5220 44.8256 10.1066 96.7138
GPR 72.1840 16.2750 42.1760 9.5092 96.7695
GAO-LS-SVM 72.0796 16.2514 42.0851 9.4887 96.7791
CNN-GPR 72.56 16.22 42.62 10.1 96.59
Proposed method 71.5395 16.0286 38.4930 8.6788 96.7909
7-hour CNN-1D 72.2889 16.2975 38.9863 8.7894 96.7223
ELM 73.7926 16.6365 45.2478 10.2011 96.6679
GPR 72.5850 16.3642 42.5502 9.5929 96.7342
GAO-LS-SVM 72.5590 16.3584 42.4797 9.5770 96.7350
CNN-GPR 72.53 16.35 38 8.75 96.76
Proposed method 72.0066 16.1305 38.8751 8.7649 96.7490
8-hour CNN-1D 73.5299 16.5762 44.9018 10.1224 96.6943
ELM 74.0173 16.6861 45.3573 10.2251 96.6453
GPR 72.7489 16.4001 42.6646 9.6181 96.7167
GAO-LS-SVM 72.8106 16.4140 42.6258 9.6094 96.7096
CNN-GPR 73.03 16.51 43.16 10.19 96. 64
Proposed method 72.2840 16.1925 39.0645 8.8077 96.7235
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

nRMSE and NMAE is considered valuable in the literature
of solar radiation forecasting [12]. The forecasting preci-
sion and stability of the proposed model are more accurate
against benchmarking models over the forecasting horizon
in terms of statistical indicators.
Graphical analysis of the forecasting error of all models
over the forecasting horizon is shown in Fig. 5. As can be
seen, the nRMSE starts to be important with the increase in
the forecasting horizon; the best performance was achieved
with our proposed model for all time steps in terms of
conventional metrics.
3.2.2 Forecasting-based exogenous variables
This section consists of adding other meteorological vari-
ables to the developed forecasting models (air temperature
(T), relative humidity (Rh), atmospheric pressure (Pr), and
GH
0
) and the choice of their time lags. Suitable lags of
different meteorological variables are defined by the mean
of the cross-correlation function between the clear sky
index and the available meteorological data. It was found
that lags = 3 is an appropriate lag of GH
0
and Pr. For
temperature and relative humidity, it was found that
lags = 2 is suitable for both variables. The forecasting
results of 12 h ahead for all developed models are listed in
Table 5; it’s clearly shown that the improvement of
exogenous data over endogenous data is limited but
important. We can also observe that by contrast to the case
of endogenous variables where the LS-SVM provides the
best forecasting performance for horizons one and two, in
the case of multivariate data ELM models achieve the best
forecasting performance for these horizons where the
nRMSE error is reduced by 0.24 and 0.115%, respectively.
For the rest of the horizons, different individual models
were selected to be suitable for each horizon step compared
to the endogenous data. Furthermore, the improvement in
terms of forecasting error for each model is important
compared to the first case.
The forecasting results related to the exogenous data of
the proposed models against individuals models are shown
Table 4 (continued)
Forecasting horizon (hour) Model RMSE (Wh/m
2
) nRMSE MABE NMAE r(%)
9-hour CNN-1D 72.9240 16.4386 41.8155 9.4261 96.6806
ELM 74.1533 16.7157 45.4298 10.2409 96.6307
GPR 73.0227 16.4609 42.8426 9.6576 96.6882
LS-SVM 73.2331 16.5083 42.9081 9.6724 96.6675
CNN-1D 73.21 16.36 41.86 9.55 96.61
Proposed method 72.5868 16.2613 39.2696 8.8540 96.6952
10-hour CNN-1D 73.2267 16.5059 42.8646 9.6620 96.6668
ELM 74.2074 16.7270 45.4717 10.2497 96.6244
GPR 73.2263 16.5058 42.9166 9.6738 96.6658
GAO-LS-SVM 73.2851 16.5191 42.9428 9.6797 96.6609
CNN-1D 73.38 16.45 43.2 10.22 96.48
Proposed method 72.7812 16.3055 39.3763 8.8782 966,770
11-hour CNN-1D 74.9518 16.8937 47.6831 10.7475 96.6321
ELM 74.1728 16.7181 45.4387 10.2416 96.6261
GPR 73.3345 16.5292 42.6669 9.6169 96.6486
GAO-LS-SVM 73.3678 16.5367 42.6811 9.6201 96.6468
CNN-1D 73.57 16.75 43.29 10.42 96.38
Proposed method 72.8743 16.3290 39.3803 8.8791 96.6675
12-hour CNN-1D 73.7555 16.6231 43.8796 9.8896 96.6293
ELM 73.5726 16.5819 42.9765 9.6861 96.6271
GPR 73.6284 16.5945 42.8604 9.6599 96.6188
GAO-LS-SVM 73.7070 16.6122 42.8528 9.6582 96.6122
CNN-1D 73.69 16.48 43.23 10.22 96.36
Proposed method 73.1410 16.3949 39.5526 8.9181 96.6405
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

in Fig. 6in terms of nRSME. During all forecasting hori-
zon, the proposed approach provides the lowest forecasting
error and shows stable performance compared to bench-
marking models. Another important remark can be
observed regarding the performance of the integrated
CNN-GPR model, in which we can see that the combina-
tion of CNN and GPR model doesn’t improve the fore-
casting accuracy of conventional models, and its
performance is less compared to the proposed hybridiza-
tion mechanism overall studied horizons. As can be seen,
all statistical parameters clearly show that the proposed
approach provides better forecasting results compared to
those of stand-alone models. During all forecasting hori-
zons, the combined model showed lower values of errors
metrics; the nRMSE varies in the range of [10.95–16.3],
and NMAE varies in the range [5.55–8.93]. During the
evaluation process, the improvement in the percent of the
proposed model against the best model for each forecasting
horizon is 0.2072 –0.066 (%) in terms of nRMSE, and an
improvement of 0.4873 –0.046% is achieved against the
weak models in terms of nRMSE.
3.3 Case of Algiers region
The second part of our experiment deals with the evalua-
tion and validation of all developed models on the Algiers
region which is characterized by high solar radiation
variability compared to the first case study (Ghardaia
region). Table 6lists the forecasting results of all devel-
oped models for 12 h ahead of forecasting of global solar
radiation. From the obtained results, it’s verified that our
proposed methodology outperforms stand-alone models
and the developed CNN-GPR model in terms of statistical
metrics for the entire forecasting horizon. Comparing the
achieved results of the Algiers site with the Ghardaia site,
we can observe that Ghardaia’s results are more accurate
compared to the Algiers site due to its low solar radiation
variability.
For benchmarking models, we observe that the devel-
oped GAO-LS-SVM provides high forecasting results for
the first seven hours ahead of the forecasting time horizon
and GPR model performs better in the eight and twelve
hours ahead. Deep CNN model achieves high forecasting
results in the 9-h-ahead forecasting time horizon, and for
the rest forecasting horizons, the combined CNN-GPR
model exhibits better performance compared to the
Fig. 5 Forecasting results using different models in terms of nRMSE
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Table 5 Performance comparison of all developed models with exogenous variables (case of Ghardaia region)
Forecasting horizon (hour) Model RMSE (Wh/m
2
) nRMSE MABE NMAE r(%)
1-Hour CNN-1D 50.1893 11.3162 27.4189 6.1821 98.4418
ELM 48.9439 11.0353 24.9063 5.6156 98.5040
GPR 49.1695 11.0862 25.6582 5.7851 98.4964
GAO-LS-SVM 50.6300 11.4155 26.1550 5.8972 98.3983
CNN-1D 50.02 11.12 25.6 6.03 98.05
Proposed method 48.6854 10.9463 24.6405 5.5557 98.5214
2-hour CNN-1D 59.8711 13.4994 33.4419 75.403 97.7755
ELM 59.1665 13.3405 31.7457 7.1578 97.8093
GPR 59.7680 13.4761 32.7265 7.3790 97.7747
GAO-LS-SVM 61.3862 13.8410 32.7190 7.3773 97.6347
CNN-1D 59.67 13.35 32.75 7.46 97.66
Proposed method 59.0836 13.2727 31.1509 7.0242 97.8161
3-hour CNN-1D 65.3102 14.7261 36.4652 8.2221 97.3358
ELM 66.1188 14.9084 37.4272 8.4390 97.2684
GPR 65.2341 14.7089 36.7301 8.2819 97.3492
GAO-LS-SVM 66.1596 14.9176 36.2341 8.1700 97.2469
CNN-1D 66.32 14.77 36.55 8.23 97.23
Proposed method 64.6587 14.5185 34.4988 7.7798 97.3799
4-hour CNN-1D 68.9486 15.5465 39.8322 8.9813 97.0370
ELM 69.6891 15.7134 40.8472 9.2102 96.9827
GPR 68.8594 15.5264 39.4710 8.8999 97.0484
GAO-LS-SVM 69.1601 15.5942 38.0754 8.5852 96.9883
CNN-1D 68.88 15.43 39.91 8.95 97.031
Proposed method 68.1351 15.2991 36.7069 8.2766 97.0845
5-hour CNN-1D 71.0279 16.0150 41.0222 9.2495 96.8490
ELM 71.8810 16.2074 43.2449 9.7506 96.8102
GPR 70.9214 15.9910 41.2472 9.3002 96.8780
GAO-LS-SVM 72.0606 16.2479 39.4700 8.8995 96.7253
CNN-1D 70.98 15.99 41 9.11 96.91
Proposed method 70.1520 15.7431 37.8814 8.5419 96.9092
6-hour CNN-1D 72.2565 16.2913 42.1010 9.4923 96.7417
ELM 72.6947 16.3901 43.8689 9.8909 96.7357
GPR 72.1840 16.2750 42.1760 9.5092 96.7695
GAO-LS-SVM 73.1038 16.4823 40.2924 9.0845 96.6283
CNN-1D 72.35 16.55 43.1 9.67 96.2
Proposed method 71.2796 15.9907 38.6074 8.7058 96.8090
7-hour CNN-1D 72.3888 16.3200 40.7216 9.1806 96.7101
ELM 73.2345 16.5106 44.4251 10.0156 96.6889
GPR 72.5850 16.3642 42.5502 95.929 96.7342
GAO-LS-SVM 73.4606 16.5616 40.9186 9.2250 9.6555
CNN-1D 72.13 16.36 40.71 9.2 96.69
Proposed method 71.7423 16.0923 38.9581 8.7849 96.7672
8-hour CNN-1D 72.7684 16.4045 41.4607 9.3467 96.6797
ELM 73.4383 16.5556 44.5895 10.0520 96.6690
GPR 72.7489 16.4001 42.6646 9.6181 9.6167
GAO-LS-SVM 73.9057 16.6609 41.5546 9.3679 96.5564
CNN-1D 72.51 16.3 41.2 9.985 96.68
Proposed method 72.0585 16.1578 39.1063 8.8184 96.7400
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

conventional models. An important remark can be deduced
from Table 6, where we can observe that CNN-1D provides
the lowest forecasting performance compared to their
counterpart models; this can be justified that deep learning
models need long historical data, especially in the case of
high variability global solar radiation in the learning phase
for precise hyper-parameters tuning.
The improvement of the proposed hybrid models com-
pared to the best of benchmarking models during all
forecasting horizons in terms of nRMSE equal to
2.41 ±0.76 (Wh/m
2
) per hour, which is considered very
important. The improvement of the proposed hybridization
methodology against weak benchmarking models during
the entire forecasting horizon is 3.07 ±0.5 (Wh/m
2
) per
hour in terms of nRMSE. The forecasting precision and
stability of the proposed model are more accurate against
stand-alone models over the forecasting horizon in terms of
statistical indicators.
Hyper-parameters settings for all studied models are
presented in Tables 7,8,9, and 10, for CNN-1D, GAO-LS-
SVM, GPR, and ELM, respectively. We note here that
some parameters are constants for all studied horizons, and
others are variables during the forecasting horizons and
their variation for each horizon is presented in a specific
range. We note that negative hyper-parameters of the GPR
model are presented in logarithms scale.
Forecasting results using our proposed fusing strategy
using test data from the Algiers site are displayed in fig-
ures and, for the third forecasting horizon Fig. 7. In this
case, we compare the best individual model in this horizon
which is GAO-LS-SVM with our proposed method. As can
be seen from Fig. 8, the deviation of the forecasted solar
radiation data obtained by the GAO-LS-SVM model from
the measured hourly global solar radiation data is important
and cannot follow the random nature of solar radiation.
Graphical results of the proposed forecasting model on the
same data are presented in Fig. 9. It observed that the
proposed methodology performs better than the GAO-LS-
SVM model, and the deviation between the measured and
the estimated global solar radiation data is improved. We
Table 5 (continued)
Forecasting horizon (hour) Model RMSE (Wh/m
2
) nRMSE MABE NMAE r(%)
9-hour CNN-1D 73.0688 16.4713 42.2780 9.5304 96.6605
ELM 73.5224 16.5735 44.6710 10.0698 96.6602
GPR 73.0227 16.4609 42.8426 9.6576 96.6882
GAO-LS-SVM 74.2292 16.7329 42.0357 94.757 96.5275
CNN-1D 73.02 16.62 42.3 9.68 96.65
Proposed method 72.3620 16.2255 39.3222 8.8671 96.7122
10-hour CNN-1D 73.2532 16.5119 43.0677 9.7078 96.6562
ELM 73.5617 16.5814 44.8197 10.1027 96.6604
GPR 73.2263 16.5058 42.9166 9.6738 96.6658
GAO-LS-SVM 74.4536 16.7825 42.1195 9.4941 96.5042
CNN-1D 73.1 16.42 42.9 9.5 96.75
Proposed method 72.5295 16.2639 39.4420 8.8942 96.6965
11-hour CNN-1D 73.6250 16.5947 45.0694 10.1584 96.6640
ELM 73.5494 16.5776 44.9322 10.1275 96.6661
GPR 73.3345 16.5292 42.6669 9.6169 96.6486
GAO-LS-SVM 74.4877 16.7891 41.7918 9.4196 96.4975
CNN-1D 72.56 16.55 44.95 10.02 96.71
Proposed method 72.5611 16.2747 39.4334 8.8923 96.6925
12-hour CNN-1D 73.1393 16.4842 42.4401 9.5652 96.6563
ELM 73.5768 16.5828 45.0148 10.1455 96.6660
GPR 73.6284 16.5945 42.8604 9.6599 96.6188
GAO-LS-SVM 74.5135 16.7940 41.8349 9.4288 96.4958
CNN-1D 73.1 16.38 42.34 9.5 96.56
Proposed method 72.7031 16.3066 39.6019 8.9304 96.6795
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

can also observe that the proposed model cannot follow the
maximum fluctuation of hourly global solar radiation this
can be justified by: (1) high variability of solar radiation of
Algiers regions,(2) need a long historical solar radiation
data, and (3) others sophisticated input data are needed
such as sunshine fraction, cloud cover…etc.
The dispersion between the measured and forecasted
data of the GAO-LS-SVM model is very important (See
Fig. 10), whereas the dispersion is low in the case of using
the proposed method. The more the dispersion is low, the
more the accuracy is high, which leads to small forecasting
errors.
3.4 Discussion
Another evaluation is conducted for further assessment of
the proposed model against the state-of-the-art models.
From Table 11, we can see that the hybridization mecha-
nism yields plausible scores with respect to several prior
contributions.
The advantage of the proposed model is related mainly
to its simplicity of implementation and its use of reduced
input data (accessible climatological data, and previous
global solar radiation).
The adopted models in this study show high perfor-
mance in handling the non-stationary behavior of solar
radiation data in a semiarid climate and Mediterranean
climate compared to the well-known stand-alone forecast-
ing models. Forecasting comparison of our proposed model
with previous works in the field of solar radiation fore-
casting is very complicated due to the diversity of data
duration, used input variables, and climate condition, and
most of the papers supply only the case of one-step-ahead
forecasting with a predefined time scale. Most of the papers
deal with solar radiation forecasting without any station-
arity check.
From Table 11, we can see that the hybridization
mechanism provides high forecasting scores concerning
several prior contributions.
Further improvement of the proposed model can be
done through other inputs such as satellite remote sensing
information; sunshine fraction also other techniques for
data analysis that can be used as wavelet decomposition or
empirical mode decomposition to enhance the forecasting
performance.
4 Conclusion
In this study, a new hybridization methodology for multi-
hour forecasting of global solar radiation was assessed.
Five developed models, GAO-LS-SVM, CNN-1D, ELM,
GPR, and CNN-GPR models, also have been tested over
two different regions in Algeria with different climate
Fig. 6 Forecasting results using different models in terms of nRMSE
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Table 6 Performance comparison of all developed models case endogenous variables (case Algiers regions)
Forecasting horizon (hour) Model RMSE (Wh/m
2
) nRMSE MABE NMAE r(%)
1-Hour CNN-1D 80.53 21.31 55.11 14.96 96.12
ELM 74.57 19.73 51.26 14.04 96.79
GPR 74.54 19.72 51.2 14.03 96.8
GAO-LS-SVM 73.77 19.52 49 13.34 96.79
CNN-GPR 76.79 20.32 52.07 14.23 96.54
Proposed method 71.2 18.67 41.6 11.01 96.84
2-hour CNN-1D 104.47 27.65 76.19 21.25 93.85
ELM 101.76 26.93 73.99 20.75 94.25
GPR 101.8 26.95 74.04 20.77 95.25
GAO-LS-SVM 101.05 26.75 71.76 19.98 94.12
CNN-GPR 104.25 27.6 75.69 21.31 94
Proposed method 95.59 24.86 60.39 15.99 94.28
3-hour CNN-1D 119.4 31.61 88.07 25.12 92.25
ELM 117.03 30.98 85.92 24.42 92.49
GPR 117.47 31.09 86.6 24.64 92.49
GAO-LS-SVM 116.9 30.94 84.85 24 92.32
CNN-GPR 119.74 31.7 88.35 25.25 92.28
Proposed method 109.25 28.23 71.16 18.84 92.53
4-hour CNN-1D 128.12 33.91 94.16 26.86 90.84
ELM 127.5 33.75 94.06 26.95 91.08
GPR 127.98 33.87 94.33 27 90.95
GAO-LS-SVM 127 33.62 92.83 26.43 90.86
CNN-GPR 129.34 34.24 95.64 27.51 90.91
Proposed method 118.78 30.62 78.17 20.69 91.17
5-hour CNN-1D 133.26 35.27 98.3 27.9 89.8
ELM 134.82 35.69 99.91 28.73 89.84
GPR 134.7 35.65 99.63 28.63 89.83
GAO-LS-SVM 133.79 35.41 98.04 28.04 89.7
CNN-GPR 135.24 35.79 100.15 28.82 89.76
Proposed method 118.78 31.92 78.17 20.7 91.18
6-hour CNN-1D 136.63 36.16 100.78 28.64 89.11
ELM 138.43 36.63 102.62 29.54 89.09
GPR 138.28 36.6 102.38 29.46 89.09
GAO-LS-SVM 137.75 36.46 101.41 29.09 88.89
CNN-GPR 138.5 36.35 102.74 298.58 89.08
Proposed method 129.54 33.52 86.02 22.76 89.22
7-hour CNN-1D 140.05 37.06 104.11 29.94 88.64
ELM 140.04 37.05 103.99 29.9 88.64
GPR 140.01 37.05 103.84 29.84 88.63
GAO-LS-SVM 139.85 37.009 103.04 29.56 88.48
CNN-GPR 140.06 37.06 104.09 29.94 88.64
Proposed method 132.19 34.26 88.21 23.34 88.71
8-hour CNN-1D 143.66 38.01 107.56 31.48 88.22
ELM 140.63 37.2 103.93 29.75 88.25
GPR 140.62 37.2 103.93 29.75 88.26
GAO-LS-SVM 141.0491 37.31 103.49 29.58 88
CNN-GPR 140.84 37.26 104.34 29.9 88.25
Proposed method 133.69 34.76 89.59 23.7 88.39
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

conditions. During the test phase, individual models pre-
sent the same forecasting results with a slight difference
between them for both studied regions over the forecasting
horizon. Each model performs better than other models in a
specified horizon. Fusing the outcomes from each model
through sparse representation methodology improves
Table 6 (continued)
Forecasting horizon (hour) Model RMSE (Wh/m
2
) nRMSE MABE NMAE r(%)
9-hour CNN-1D 138.93 36.75 101.18 28.3 88.05
ELM 140.73 37.23 103.75 29.59 88.07
GPR 140.72 37.24 103.45 29.49 88.09
GAO-LS-SVM 141.24 37.37 103.3 29.36 87.75
CNN-GPR 141.07 37.32 103.87 29.61 87.97
Proposed method 134.83 35.1 90.45 23.39 88.15
10-hour CNN-1D 141.38 37.4 104.14 29.74 87.89
ELM 140.54 37.18 103.08 29.26 87.94
GPR 140.52 37.18 103.11 29.28 87.95
GAO-LS-SVM 141.5 37.44 102.75 29.05 87.25
CNN-GPR 140.8 37.25 103.23 29.32 87.86
Proposed method 135.5 35.36 90.8 24.02 88
11-hour CNN-1D 139.48 36.9 101.79 28.63 87.94
ELM 140.25 37.11 102.73 29.11 87.87
GPR 140.22 37.1 103 29.21 87.97
GAO-LS-SVM 140.74 37.24 102.77 29.1 87.7
CNN-GPR 140.4 37.15 103.23 29.3 87.94
Proposed method 135.6 35.45 90.84 24.03 87.97
12-hour CNN-1D 144.63 38.27 109.08 32.06 87.99
ELM 140.31 37.16 103.54 29.42 88.03
GPR 140.3 37.12 103.55 29.43 88.03
GAO-LS-SVM 140.51 37.18 102.13 28.38 87.7
CNN-GPR 140.16 37.21 103.91 29.56 87.96
Proposed method 135.04 35.27 90.66 23.99 88.09
Table 7 Hyper-parameters settings for CNN-1D model
Model CNN-1D model
Regions Ghardaia site with endogenous variables Ghardaia exogenous variables Algiers exogenous variables
Optimizer Adam Adam Adam
Loss Mean square error Mean square error Mean square error
Learning rate 0.01 0.01 0.01
Epochs 300 400 500
Batch size 4 14 10
Convolution layer 5 Filters 7 Filters 7 Filters
Filter length 2 3 2
Sub-sampling layer 2 2 2
Activation function Sigmoid Sigmoid Sigmoid
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

significantly the forecasting results over the 12 h ahead.
The experimental hybridization mechanism of stand-alone
models boosts the forecasting scores with a considerable
improvement.
For all forecasting horizons for the two studied regions,
the proposed fusing strategy shows stable and high per-
formance in terms of statistical indicators, where the nor-
malized error is improved by 0.207–±0.066 (%) for the
Ghardaia region, and 2.41 ±0.76 (%) for the Algiers
region. Overall, the proposed forecasting model improves
multi-hours ahead forecasting of global solar radiation with
an acceptable rate compared with well-used machine
learning and deep learning forecasting models. As we
mentioned, further improvement of the proposed model can
be made through the combination of different deep learning
models and other inputs information from remote sensing
images and weather forecasts, which offers additional
information for the prediction process. The most important
finding of the proposed fusing strategy is its ability for
providing simple and clear input–output mapping
Table 8 Hyper-parameters settings for GAO-LS-SVM model
Model GAO-LS-SVM model
Regions Ghardaia site with endogenous variables Ghardaia exogenous
variables
Algiers
Exogenous variables
Loss Mean square error Mean square error Mean square error
Number of Initial populations of GAO algorithm 30 30 30
Max number of iterations 100 100 100
Kernel function RBF-Kernel RBF-Kernel RBF-Kernel
kernel width r[0.57–1] [0.4–1] [0.51–1.5]
Regularization constant C [5–80] [10–110] [7–60]
Table 9 Hyper-parameters settings for GPR model
Model GPR model
Regions Ghardaia site with
endogenous variables
Ghardaia exogenous variables Algiers exogenous variables
Loss Mean square error Mean square error Mean square error
Kernel function Mate
´rn covariance Function Mate
´rn covariance Function Mate
´rn covariance Function
Covariance characteristic (length-scale,
standard deviation)
Length = [.18: 2.2]
StdDev = [-0.58: 0.38]
Length = [-0.32: 1.8]
StdDev = [-0.35: 0.34]
Length = [-0.2: 2.088]
StdDev = [-0.41: 0.26]
Likelihood [-1.33: -0.1] [-0.9: -0.5] [-1.26: -0.7]
Table 10 Hyper-parameters settings for ELM model
Model GPR model
Regions Ghardaia site with Endogenous variables Ghardaia exogenous variables Algiers exogenous variables
Loss Mean square error Mean square error Mean square error
Kernel function RBF-Kernel RBF-Kernel RBF-Kernel
Number of layers 12 25 30
Kernel parameters [5:60] [0.5:60] [0.2:50]
Regularization [0.1:75] [0.15:75] [0.25:75]
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Fig. 7 Forecasting results using different models in terms of nRMSE
Fig. 8 Measured hourly global solar radiation against forecasted values using GAO-LS-SVM model 3-Hours ahead (Algiers data)
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Fig. 9 Measured hourly global solar radiation against forecasted values using the proposed method for 3-h ahead (Algiers data)
Fig. 10 Scatterplots of measured hourly global solar radiation against forecasted values using the proposed method and GAO-LS-SVM for 3 h
ahead (Algiers data)
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Table 11 Comparison of hourly ahead solar radiation forecast with some recently published techniques
Authors (year) Forecasting
method
Forecasting
horizon
Input variables Forecast
Variable
Data period Location Performance metrics
[9] WRF- MOS-
Kalman filter
Hourly
scale
Geographical and meteorological
data
Global solar
radiation
One year of 2011 South of Reunion
Island
rRMSE (%) = 35 nRMSE
(%) = [20.65–43.69].
R
2
(%) = [ 61.6–90.8]
[10] ESSS-ANN Hourly
scale
Global sola radiation Global solar
radiation
Satellites MTSAT 2
(Himawari-7)
(2010–2015
Singapore nRMSE (%) = [20.65–43.69].
R
2
(%) = [ 61.6–90.8].
nMBE (%) = [-0.54,0.97]
[23] Mycielski-
Markov
model
Hourly
scale
Sky cover Global solar
radiation
Four years of measurement
from Afyonkarahisar
region and two years
from Antalya region
Two different sites in
Turkey
RMSE (W/
m
2
) = [13.49–16.06] MABE
(%) = [10.75–13] RRMSE
(%) = [36.3–39.4] R
= [84.79–85.11
[41] STL- ETS,
closure
equation-
ETS, cloud
cover-ETS
Hourly
scale
cloud cover index Horizontal
Global
Radiation
TMY3 dataset U.S.A NRMSE (%) = [14.76–22.09]
[26] GA- ANNs Hourly
scale
13 meteorological data Global solar
radiation
01/01/2015—31/5/2015 Qatar in Doha rRMSE = [12–12.9]
[39] NWP-ARMA-
ANN
Hourly
scale
18 past input data Global solar
radiation
2002–2008 [8:00 to
4:00 AM]
Five different spaces
in Mediterranean
area
nRMSE = [16.3–19.9]
R
2
(%) = [95.04–96.19]
[38] ANN-ARMA Hourly
scale
Exogenous Meteorological
parameters
Global solar
radiation
01/01/ 1998 to 31/12/2007 Mediterranean area NRMSE (%) = [13.7–17.7]
[24] CAR-DS Hourly
scale
Previous Hourly Global Radiation
data
Global solar
radiation
1995 to 2000 Mildura Victoria
region, Australia
NRMSE (%) = 16.5
[37] ARMA-MLP
Persistence
Hourly
scale
Six sub-variables are constructed
from pressure time series
Global solar
radiation
1998 to 2011 Corsica, France nRMSE (%) = 36.59
[38] Combining
ANN and
ARMA
Hourly
scale
Global solar Radiation, nebulosity,
pressure, precipitation
Global solar
radiation
1998 to 2007 (10 years) Marseille, France nRMSE (%) = 13.7
[21] ABC-LS-SVM Hourly
scale
Different meteorological parameters Kt 2011 to 2016 Ghardaia, Algeria nRMSE (%) = [ 19.27–24.3]
[35] CEEMDAN-
SCA- Bi-
LSTM
Hourly
scale
14 input variables Three hour
ahead of
Global
solar
radiation
1 May 2011–18 Feb 2012 Alabama RMSE
h?1
(Wm
2
) = [41.68–68.42]
RMSE
h?2
(Wm
2
) = [55.6–91.32]
RMSE
h?3
(Wm
2
) = [58.5–103.55]
[7] Feature
selection
method
Hourly
scale
UV index, cloud cover, air
temperature, relative humidity,
K
C
(Up to
4h)
01/01/2010–31/12/2015 University Campus RMSE (%) = [29.81–55.19]
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

relationship, and the main limitation of the proposed
hybridization mechanism is that it fails to offer high fore-
casting precision for outlayers solar radiations data.
Acknowledgements We would like to acknowledge the German
federal bureau for supplying instrumentations used in this work, as
part of the enreMENA project.
Declarations
Conflict of interest No declaration of interest.
References
1. Ahmed R, Sreeram V, Mishra Y, Arif MD (2020) A review and
evaluation of the state-of-the-art in PV solar power forecasting:
techniques and optimization. Renew Sustain Energy Rev
124:109792. https://doi.org/10.1016/j.rser.2020.109792
2. Bailek N, Bouchouicha K, Al-mostafa Z, El-shimy M (2018) A
new empirical model for forecasting the diffuse solar radiation
over Sahara in the Algerian Big South. Renew Energy
117:530–537. https://doi.org/10.1016/j.renene.2017.10.081
3. Baraniuk RG (2007) Compressive sensing. IEEE Signal Process
Mag. https://doi.org/10.1109/MSP.2007.4286571
4. Benali L, Notton G, Fouilloy A, Voyant C, Dizene R (2019) Solar
radiation forecasting using artificial neural network and random
forest methods: application to normal beam, horizontal diffuse
and global components. Renew Energy 132:871–884. https://doi.
org/10.1016/j.renene.2018.08.044
5. Benghanem M, Mellit A, Alamri SN (2009) ANN-based mod-
elling and estimation of daily global solar radiation data: a case
study. Energy Convers Manag 50:1644–1655
6. Candes EJ, Wakin MB (2008) An introduction to compressive
sampling: a sensing/sampling paradigm that goes against the
common knowledge in data acquisition. IEEE Signal Process
Mag 25:21–30. https://doi.org/10.1109/MSP.2007.914731
7. Castangia M, Aliberti A, Bottaccioli L, Macii E, Patti E (2021) A
compound of feature selection techniques to improve solar radi-
ation forecasting. Expert Syst Appl. https://doi.org/10.1016/j.
eswa.2021.114979
8. Deo RC, S¸ ahin M, Adamowski JF, Mi J (2019) Universally
deployable extreme learning machines integrated with remotely
sensed MODIS satellite predictors over Australia to forecast
global solar radiation: a new approach. Renew Sustain Energy
Rev 104:235–261. https://doi.org/10.1016/j.rser.2019.01.009
9. Diagne M, David M, Boland J, Schmutz N, Lauret P (2014) Post-
processing of solar irradiance forecasts from WRF model at
Reunion Island. Sol Energy 105:99–108. https://doi.org/10.1016/
j.solener.2014.03.016
10. Dong Z, Yang D, Reindl T, Walsh WM (2015) A novel hybrid
approach based on self-organizing maps, support vector regres-
sion and particle swarm optimization to forecast solar irradiance.
Energy 82:570–577. https://doi.org/10.1016/j.energy.2015.01.066
11. Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory
52:1289–1306. https://doi.org/10.1109/TIT.2006.871582
12. Duchaud J-L, Voyant C, Fouilloy A, Notton G, Nivet M-L (2020)
Trade-Off between precision and resolution of a solar power
forecasting algorithm for micro-grid optimal control. Energies
13:3565. https://doi.org/10.3390/en13143565
13. Fan J, Wu L, Ma X, Zhou H, Zhang F (2020) Hybrid support
vector machines with heuristic algorithms for prediction of daily
diffuse solar radiation in air-polluted regions. Renew Energy
145:2034–2045. https://doi.org/10.1016/j.renene.2019.07.104
Table 11 (continued)
Authors (year) Forecasting
method
Forecasting
horizon
Input variables Forecast
Variable
Data period Location Performance metrics
combined
with LSTM
dew point, wind bearing, sunshine
duration and hour of the day
[33] RLMD-LSTM 30-min Previous GH Global solar
Radiation
01/07/2017- 01/05–2019 Vietnam nRMSE = [18–20]
[14] CEEMDAN-
CNN-LSTM
Hourly
scale
Previous GH Global solar
Radiation
05/05/2010–05/05/2016
2011–2016 2013–2018
2005–2010
Los Angeles (USA)
Denver (USA)
Hawaii’s big Island
Tamanrasset Algeria
nRMSE = 13.10
nRMSE = 20.69
nRMSE = 19.27
nRMSE = 15.87
[31] WTR-GANs Hourly
scale
Previous GH Global solar
Radiation
(up to 6 h)
One year (2019) Region 1 Region 2 RMSE (pu) = [
0.0473–0.0895] RMSE
(pu) = [ 0.0479–0.0946]
[25] WPK CNN-
LSTM-MLP
Hourly
scale
Previous 24 h of: solar irradiance
temperature, relative humidity,
and wind speed and their
combination
Global solar
Radiation
01/01/2012–31/12/2016
01/01/2009–31/12/2012
01/01/2014–31/12/2016
Denver Clark Folsom nRMSE = 23.917
nRMSE = 17.4132
nRMSE = 15.479
Proposed
methodology
Machine
learning
Hourly
scale
Kc,GH
0
Temperature, Relative
humidity, Atmospheric pressure
Kc 2013–2016 Ghardaia, Algeria nRMSE (%) = [10.94–16.3]
R
2
(%) = [96.68–98.52]
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

14. Gao B, Huang X, Shi J, Tai Y, Zhang J (2020) Hourly forecasting
of solar irradiance based on CEEMDAN and multi-strategy
CNN-LSTM neural networks. Renew Energy 162:1665–1683.
https://doi.org/10.1016/j.renene.2020.09.141
15. Gensler, A., Henze, J., Sick, B., Raabe, N., 2017. Deep Learning
for solar power forecasting - An approach using AutoEncoder and
LSTM Neural Networks, in: 2016 IEEE International Conference
on Systems, Man, and Cybernetics, SMC 2016 - Conference
Proceedings. Institute of Electrical and Electronics Engineers
Inc., pp. 2858–2865. https://doi.org/10.1109/SMC.2016.7844673
16. Ghimire S, Deo RC, Raj N, Mi J (2019) Deep solar radiation
forecasting with convolutional neural network and long short-
term memory network algorithms. Appl Energy 253:113541.
https://doi.org/10.1016/j.apenergy.2019.113541
17. Guermoui M, Gairaa K, Boland J, Arrif T (2021) A novel hybrid
model for solar radiation forecasting using support vector
machine and bee colony optimization algorithm: review and case
study. J Sol Energy Eng Trans ASME. https://doi.org/10.1115/1.
4047852
18. Guermoui M, Gairaa K, Rabehi A, Djafer D, Benkaciali S (2018)
Estimation of the daily global solar radiation based on the
Gaussian process regression methodology in the Saharan climate.
Eur Phys J Plus 133:1–17. https://doi.org/10.1140/epjp/i2018-
12029-7
19. Guermoui M, Melaab D, Mekhalfi ML (2016) Sparse coding joint
decision rule for ear print recognition. Opt Eng 55:093105.
https://doi.org/10.1117/1.oe.55.9.093105
20. Guermoui M, Melgani F, Danilo C (2018) Multi-step ahead
forecasting of daily global and direct solar radiation: a review and
case study of Ghardaia region. J Clean Prod 201:716–734. https://
doi.org/10.1016/j.jclepro.2018.08.006
21. Guermoui M, Melgani F, Gairaa K, Mekhalfi ML (2020) A
comprehensive review of hybrid models for solar radiation
forecasting. J Clean Prod. https://doi.org/10.1016/j.jclepro.2020.
120357
22. Guermoui M, Rabehi A, Gairaa K, Benkaciali S (2018) Support
vector regression methodology for estimating global solar radi-
ation in Algeria. Eur Phys J Plus 133:1–9. https://doi.org/10.
1140/epjp/i2018-11845-y
23. Hocaoglu FO, Serttas F (2017) A novel hybrid (Mycielski-Mar-
kov) model for hourly solar radiation forecasting. Renew Energy
108:635–643. https://doi.org/10.1016/j.renene.2016.08.058
24. Huang J, Korolkiewicz M, Agrawal M, Boland J (2013) Fore-
casting solar radiation on an hourly time scale using a Coupled
AutoRegressive and Dynamical System (CARDS) model. Sol
Energy 87:136–149. https://doi.org/10.1016/j.solener.2012.10.
012
25. Huang X, Li Q, Tai Y, Chen Z, Zhang J, Shi J, Gao B, Liu W
(2021) Hybrid deep neural model for hourly solar irradiance
forecasting. Renew Energy. https://doi.org/10.1016/j.renene.
2021.02.161
26. Jovanovic, R., Pomares, L.M., Mohieldeen, Y.E., Perez-As-
tudillo, D., Bachour, D., 2017. An evolutionary method for cre-
ating ensembles with adaptive size neural networks for predicting
hourly solar irradiance, in: Proceedings of the International Joint
Conference on Neural Networks. Institute of Electrical and
Electronics Engineers Inc., pp. 1962–1967. https://doi.org/10.
1109/IJCNN.2017.7966091
27. Lefe
`vre M, Oumbe A, Blanc P, Espinar B, Gschwind B, Qu Z,
Wald L, Homscheidt MS, Hoyer-Klick C, Arola A, Lefe
`vre M,
Oumbe A, Blanc P, Espinar B, Gschwind B, Qu Z, Wald L,
Schroedter-Homscheidt M, Hoyer-Klick C, Arola A, Benedetti A,
Kaiser JW, Morcrette J-J (2013) Atmospheric measurement
techniques. Eur Geosci Union 6:2403–2418. https://doi.org/10.
5194/amt-6-2403
28. Malek S, Melgani F, Bazi Y (2018) One-dimensional convolu-
tional neural networks for spectroscopic signal regression.
J Chemom. https://doi.org/10.1002/cem.2977
29. Mawloud G, Djamel M (2016) Weighted sparse representation
for human ear recognition based on local descriptor. J Electron
Imaging 25:013036. https://doi.org/10.1117/1.jei.25.1.013036
30. Mellit A, Pavan AM (2010) A 24-h forecast of solar irradiance
using artificial neural network: application for performance pre-
diction of a grid-connected PV plant at Trieste Italy. Sol Energy
84:807–821. https://doi.org/10.1016/j.solener.2010.02.006
31. Meng F, Zou Q, Zhang Z, Wang B, Ma H, Abdullah HM,
Almalaq A, Mohamed MA (2021) An intelligent hybrid wavelet-
adversarial deep model for accurate prediction of solar power
generation. Energy Rep. https://doi.org/10.1016/j.egyr.2021.04.
019
32. Mirjalili SZ, Mirjalili S, Saremi S, Faris H, Aljarah I (2018)
Grasshopper optimization algorithm for multi-objective opti-
mization problems. Appl Intell 48:805–820. https://doi.org/10.
1007/s10489-017-1019-8
33. Ngoc-Lan Huynh A, Deo RC, Ali M, Abdulla S, Raj N (2021)
Novel short-term solar radiation hybrid model: Long short-term
memory network integrated with robust local mean decomposi-
tion. Appl Energy. https://doi.org/10.1016/j.apenergy.2021.
117193
34. Peel MC, Finlayson BL, McMahon TA (2007) Updated world
map of the Ko
¨ppen-Geiger climate classification. Hydrol Earth
Syst Sci 11:1633–1644. https://doi.org/10.5194/hess-11-1633-
2007
35. Peng T, Zhang C, Zhou J, Nazir MS (2021) An integrated
framework of Bi-directional long-short term memory (BiLSTM)
based on sine cosine algorithm for hourly solar radiation fore-
casting. Energy 221:119887. https://doi.org/10.1016/j.energy.
2021.119887
36. Rabehi A, Guermoui M, Lalmi D (2020) Hybrid models for
global solar radiation prediction: a case study. Int J Ambient
Energy 41:31–40. https://doi.org/10.1080/01430750.2018.
1443498
37. Voyant C, Darras C, Muselli M, Paoli C, Nivet ML, Poggi P
(2014) Bayesian rules and stochastic models for high accuracy
prediction of solar radiation. Appl Energy 114:218–226. https://
doi.org/10.1016/j.apenergy.2013.09.051
38. Voyant C, Muselli M, Paoli C, Nivet ML (2013) Hybrid
methodology for hourly global radiation forecasting in Mediter-
ranean area. Renew Energy 53:1–11. https://doi.org/10.1016/j.
renene.2012.10.049
39. Voyant C, Muselli M, Paoli C, Nivet ML (2012) Numerical
weather prediction (NWP) and hybrid ARMA/ANN model to
predict global radiation. Energy 39:341–355. https://doi.org/10.
1016/j.energy.2012.01.006
40. Wang H, Lei Z, Zhang X, Zhou B, Peng J (2019) A review of
deep learning for renewable energy forecasting. Energy Convers
Manag. https://doi.org/10.1016/j.enconman.2019.111799
41. Yang D, Sharma V, Ye Z, Lim LI, Zhao L, Aryaputera AW
(2015) Forecasting of global horizontal irradiance by exponential
smoothing, using decompositions. Energy 81:111–119. https://
doi.org/10.1016/j.energy.2014.11.082
Publisher’s Note Springer Nature remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.
Neural Computing and Applications
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

1.
2.
3.
4.
5.
6.
Terms and Conditions
Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH (“Springer Nature”).
Springer Nature supports a reasonable amount of sharing of research papers by authors, subscribers and authorised users (“Users”), for small-
scale personal, non-commercial use provided that all copyright, trade and service marks and other proprietary notices are maintained. By
accessing, sharing, receiving or otherwise using the Springer Nature journal content you agree to these terms of use (“Terms”). For these
purposes, Springer Nature considers academic use (by researchers and students) to be non-commercial.
These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal
subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription
(to the extent of the conflict or ambiguity only). For Creative Commons-licensed articles, the terms of the Creative Commons license used will
apply.
We collect and use personal data to provide access to the Springer Nature journal content. We may also use these personal data internally within
ResearchGate and Springer Nature and as agreed share it, in an anonymised way, for purposes of tracking, analysis and reporting. We will not
otherwise disclose your personal data outside the ResearchGate or the Springer Nature group of companies unless we have your permission as
detailed in the Privacy Policy.
While Users may use the Springer Nature journal content for small scale, personal non-commercial use, it is important to note that Users may
not:
use such content for the purpose of providing other users with access on a regular or large scale basis or as a means to circumvent access
control;
use such content where to do so would be considered a criminal or statutory offence in any jurisdiction, or gives rise to civil liability, or is
otherwise unlawful;
falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association unless explicitly agreed to by Springer Nature in
writing;
use bots or other automated methods to access the content or redirect messages
override any security feature or exclusionary protocol; or
share the content in order to create substitute for Springer Nature products or services or a systematic database of Springer Nature journal
content.
In line with the restriction against commercial use, Springer Nature does not permit the creation of a product or service that creates revenue,
royalties, rent or income from our content or its inclusion as part of a paid for service or for other commercial gain. Springer Nature journal
content cannot be used for inter-library loans and librarians may not upload Springer Nature journal content on a large scale into their, or any
other, institutional repository.
These terms of use are reviewed regularly and may be amended at any time. Springer Nature is not obligated to publish any information or
content on this website and may remove it or features or functionality at our sole discretion, at any time with or without notice. Springer Nature
may revoke this licence to you at any time and remove access to any copies of the Springer Nature journal content which have been saved.
To the fullest extent permitted by law, Springer Nature makes no warranties, representations or guarantees to Users, either express or implied
with respect to the Springer nature journal content and all parties disclaim and waive any implied warranties or warranties imposed by law,
including merchantability or fitness for any particular purpose.
Please note that these rights do not automatically extend to content, data or other material published by Springer Nature that may be licensed
from third parties.
If you would like to use or distribute our Springer Nature journal content to a wider audience or on a regular basis or in any other manner not
expressly permitted by these Terms, please contact Springer Nature at
onlineservice@springernature.com