Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
Abstract- This article presents a hybrid model that makes
use of ANFIS (adaptive neuro-diffuse inference system)
hybridized with Neural Networks (NN) and optimized
with algorithms that are based on natural behaviors, in
this case, ant colony (ACO). The model is designed to
predict primary resources in a particular region subject
to the planning and installation of distributed
photovoltaic (PV) generation. The solar primary resource
depends on the climatic conditions of the region to be
evaluated, and its high variability in short periods
presents a challenge in planning energy resources that use
variable sources in the long term. In this article, the
behavior of a hybrid ANFIS+NN+ACO model is
designed, developed, evaluated, and validated. The
methodology that is based on data analysis is detailed.
First, work is done on climatic databases, which give
guidelines for preprocessing and cleaning. Secondly, the
climatic variables that predict solar radiation are
established. The ANFIS membership functions are then
based on the data to capture nonlinearity and extract
relationships with predictors. Neural networks support
the membership function optimization process, and
finally, the optimizer refines and evaluates the response.
The response is evaluated using metrics that demonstrate
the robustness of the model when capturing and
processing data. The study contributes to making visible
tools and alternatives to determine energy potentials in
climatic regions subject to the future for distributed
generation.
Keywords- ANFIS, Fuzzy Systems, Neural Networks,
Optimization Algorithms, Solar Radiation Prediction
This manuscript was submitted on June 28, 2024, accepted on june 12,
2025 and published on June r 30, 2025. This work was supported by the
Cooperative University of Colombia, Pasto Colombia.
Obando Paredes. Edgar Dario, EnergIA research hotbed, Cooperative
University of Colombia, Pasto Colombia (e-mail:
Edgar.obandop@campusucc.edu.co).
Burbano Vallejo. Zarella Valentina Group, research hotbed, Cooperative
University of Colombia, Pasto Colombia (e-
mail:Zarella.burbano@campusucc.edu.co ).
Ramírez, Carlos Alonso is Group, research hotbed, Cooperative
University of Colombia, Pasto Colombia (e-mail:
carlos.ramirez@campusucc.edu.co ).
Revelo Tovar, Luis Carlos is Group, research hotbed, Cooperative
University of Colombia, Pasto Colombia (e-mail:
luis.revelot@campusucc.edu.co).
Resumen— Este artículo presenta un modelo híbrido
que utiliza ANFIS (sistema de inferencia neurodifusa
adaptativa) hibridado con redes neuronales (NN) y
optimizado con algoritmos basados en comportamientos
naturales, en este caso, colonias de hormigas (ACO). El
modelo está diseñado para predecir los recursos
primarios en una región específica, sujeta a la
planificación e instalación de generación fotovoltaica (FV)
distribuida. El recurso solar primario depende de las
condiciones climáticas de la región a evaluar, y su alta
variabilidad en períodos cortos representa un desafío en
la planificación de recursos energéticos que utilizan
fuentes variables a largo plazo. En este artículo, se diseña,
desarrolla, evalúa y valida el comportamiento de un
modelo híbrido ANFIS+NN+ACO. Se detalla la
metodología basada en el análisis de datos. En primer
lugar, se trabaja con bases de datos climáticas, que
proporcionan pautas para el preprocesamiento y la
limpieza. En segundo lugar, se establecen las variables
climáticas que predicen la radiación solar. Las funciones
de pertenencia de ANFIS se basan en los datos para
capturar la no linealidad y extraer relaciones con los
predictores. Las redes neuronales respaldan el proceso de
optimización de la función de pertenencia y, finalmente,
el optimizador refina y evalúa la respuesta. Esta se evalúa
mediante métricas que demuestran la robustez del
modelo al capturar y procesar datos. El estudio
contribuye a visibilizar herramientas y alternativas para
determinar el potencial energético en regiones climáticas
sujetas al futuro de la generación distribuida.
Palabras clave—ANFIS, Sistemas Difusos, Redes
Neuronales, Algoritmos de Optimización, Predicción de la
Radiación Solar
I. INTRODUCTION.
A
ccurate solar radiation prediction is critical for
managing and optimizing solar energy systems
and is essential for sustainable development and
reducing carbon emissions [1]. Solar radiation, which
depends on various meteorological factors such as
atmospheric pressure, clarity index, wind speed, and
precipitation, is crucial in planning solar photovoltaic (PV)
energy production [2].
Implementation of ANFIS +NN and nature-inspired
optimization Algorithms for Solar Radiation Prediction.
Implementación de ANFIS + NN y Algoritmos inspirados en la naturaleza para predicción de
radiación solar.
E. D. Obando-Paredes ; Z. V. Burbano Vallejo ; C. A. Ramírez ; L. C. Revelo Tovar
DOI: https://doi.org/10.22517/23447214.25682
Scientific and technological research paper
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
Traditional forecasting methods, such as deterministic and
statistical models, have shown limitations in handling the
complexity and nonlinearity of weather data [3]. Climate
nonlinearity, lack of complex data, and variable prediction
horizons make traditional models increasingly challenging.
In this context, artificial intelligence (AI) systems have
emerged as powerful tools to improve the accuracy of solar
radiation predictions [4]. Neural networks (NN), support
vector machines (SVM), and Fuzzy Logic perform better
when considering traditional techniques. However, new
trends in research propose hybridization between AI
algorithms and nature-inspired optimizers to address the issue
of prediction with better results [5], [6].
Among the methods used, the Adaptive Neuro-Fuzzy
Inference System (ANFIS) is a technique that integrates the
advantages of artificial neural networks (ANNs) and fuzzy
logic systems to model complex and nonlinear problems.
ANFIS has been successfully used in various prediction and
control applications due to its ability to learn from data and
handle uncertainty [7], [8], [9]. However, the effectiveness of
ANFIS is highly dependent on the proper selection of its input
parameters and characteristics. Nature-inspired optimization
algorithms, such as Ant Colony Optimization Algorithms
(ACOs), offer a robust approach to finding optimal solutions
in complex search spaces. ACO has been widely used in
optimization problems because it can efficiently explore the
search space and adapt to different scenarios. [10], [11]
In this study, we propose a hybrid approach that combines
ANFIS with ACO for solar radiation prediction. This
approach seeks to optimize the parameters and input
characteristics of ANFIS using ACO to improve the accuracy
of predictions. The meteorological data used in this study
includes variables such as atmospheric pressure, clarity
index, wind speed, and precipitation. Given the country's
climatic variability, the model is applied to a city in
Colombia. Section 2 shows a review of the literature and
works related to the application of hybrid models for primary
resource prediction. Section 3 presents the methodology for
developing the model. Section 4 shows the application and
results of the model and, finally, the conclusions. With this
work, we aim to overcome the limitations of traditional
methods and offer a more accurate and efficient tool for
predicting solar radiation.
II. LITERATURE REVIEW
Optimization algorithms are widely used in primary
resource quantification, prediction, and the energy industry
[12]. The concepts of fuzzy logic and neural networks are
combined in the adaptive neuro-fuzzy inference system
(ANFIS), an artificial intelligence system [13]. Complex
systems that behave nonlinearly and uncertainly may be
modeled using ANFIS. Fuzzification, inference engines, and
defuzzification are the three essential components of any
fuzzy system [14]. The human expert in fuzzy systems
obtains fuzzy rules. Fuzzy systems were enhanced with
artificial neural networks to use learning algorithms to gather
the knowledge of human experts. The neuro-fuzzy system is
the name of this link (ANN to fuzzy system) [5].
Much research has been done to evaluate the ANFIS model
concerning solar radiation. The work focused on applying the
ANFIS model to identify the essential factors that may scatter
solar energy. To analyze the impact of such predictions, as
stated in Kerman City, the research relied on 10 essential
factors. According to the study's results, the length of sunlight
is crucial since it impacts how solar radiation diffuses. The
mix of sunlight, horizontal global solar radiation, and
extraterrestrial solar radiation are crucial factors. The subjects
of similar research were the relevance of horizontal sun
radiation and the location of interest in affecting thermal or
photovoltaic systems. The research aimed to maximize the
essential ANFIS model inputs, such as air temperature,
month, day, relative humidity, longitude, latitude, and wind
speed. The results provide evidence for the influence of
global horizontal irradiance on solar radiation and the growth
of such systems. Discuss the current state of research on
diffuse irradiance and evaluate three reliable machine
learning models using almost eight years of hourly
observations from Almeria, Spain. The authors suggest that
future machine learning models can benefit from advanced
optimization techniques, such as evolutionary algorithms and
nature-inspired optimization, which can fine-tune the models'
parameters and improve their performance on a given dataset.
The study compares different types of machine learning
models and finds that hybrid models show promise in
predicting diffuse fractions. The authors recommend further
exploration of hybrid and ensemble models to address gaps
in current research.[5], [14], [15], [16]
In work, hybrid models and a standalone adaptive neuro-
fuzzy inference system have been created to estimate monthly
global solar radiation from various meteorological indicators,
such as sunlight duration and air temperature. The findings
demonstrated that the hybrid models created had the most
dependable and precise estimating capabilities and are
thought to be the most effective way of forecasting global
solar radiation for diverse purposes [17].
According to this, the SVM approach was used to apply the
strategy for attaining the clearness index using the
performance metrics for the ANFSI model. It was clear that
the ANFSI model and the photovoltaic systems performed
better because of the alien solar radiation. Considering this, it
is reasonable to use this to estimate solar system radiation [7].
The study [5] discussed the model's importance in correctly
forecasting solar diffuse fraction. Following a discussion of
the status of diffuse irradiance research, three reliable
machine learning (ML) models are tested against a large
dataset (spanning over eight years) of hourly observations
from Almeria, Spain. The ANFIS model, the multilayer
perceptron (MLP), and the hybrid multilayer perceptron grey
wolf optimizer (MLP-GWO) were all used in the research.
The results showed that the ANFIS model performed better
when calculating solar diffuse percentage and was effective.
The ANFIS [18], the adaptive system, and the standard
solar radiation prediction model were contrasted. The goal
was to comprehend the adaptive system's relevance as a
precise and accurate model for calculating and forecasting
solar radiation. This worked well since it demonstrated the
value of the ANFIS model in increasing solar radiation
efficiency.
Some more advanced empirical models can be used to
forecast solar radiation. However, this work aims to evaluate
the efficiency and dependability of the ANFIS model. It was
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
simpler to connect the meteorological parameters with the
present change in duration values for the sunlight and
temperature using data from the Hunan province in China,
situated in a subtropical monsoon climatic zone. Intriguingly,
a model's alteration might affect how accurately a prediction
is made; other researchers utilizing the ANFIS model are
interested in implementing this [19].
The work uses air temperature to forecast solar radiation.
Consistency in air temperature was crucial for solar energy
gathering in the North Dakota experiment. The ANFIS model
was crucial in establishing the ideal air temperature for
optimizing solar energy harvesting worldwide, even though
they could have chosen any number of models to analyze the
performance accuracy of solar energy harvesting. The results
showed that applying the ANFIS model increased the
prediction accuracy when using the temperature alone to
estimate solar radiation. As a result, it demonstrated its
advantages and the necessity of applying it to North Dakota
and other places with comparable climatic and
meteorological characteristics. A novel intelligence model by
fusing the Adaptive Neuro-Fuzzy Inference System (ANFIS)
with two metaheuristic optimization algorithms, Salp Swarm
Algorithm and Grasshopper Optimization Algorithm, to
predict the global solar radiation at various locations in North
Dakota, USA. The findings suggest the potential of boosting
prediction accuracy by integrating ANFIS with metaheuristic
optimization methods [20]. The work conducted a study to
predict monthly solar radiation for semi-arid, dry, and wet
regions. To estimate solar radiation, they utilized several
models, including the multilayer perceptron, radial basis
function neural network, and adaptive neuro-fuzzy interface
system (ANFIS). The Grasshopper algorithm was utilized to
improve the performance of the ANFIS, RBFNN, and MLP
models. Three Iranian stations, namely Rasht (with a humid
climate), Yazd (with a semi-arid climate), and Tehran (with a
slightly arid environment), were used as case studies. The
results revealed that relative humidity, wind speed, rainfall,
and temperature were these locations' most influential input
variables. The study's primary contribution is the
development of innovative hybrid ANFIS models for
forecasting monthly solar radiation in various locations [21].
To estimate the daily global solar radiation in Iraq using
several metrological properties, the work developed multiple
linear regression (MLR) and numerous other AI models,
including ANFIS. According to the findings, the results
provided by ANFIS are more accurate than those from other
prediction models [22].
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
TABLE I.
REPRESENTATIVE WORKS IN THE USE OF OPTIMIZATION ALGORITHMS INSPIRED BY NATURE+ANFIS.
References
Case study
Input parameters
Output
parameter
AI model
Data scale
Research remark
Other if you find appropriately
Performance metrics
[23]
Kerman
Iran
Daily diffuse solar
radiation on a horizontal
surface, global solar
radiation on a horizontal
surface, sun shine
duration, minimum air
temperature, maximum
air temperature, average
air temperature, relative
humidity, and water vapor
pressure, as well as the
calculated values of daily
maximum possible
sunshine duration, solar
declination angle and
extraterrestrial solar
radiation on a horizontal
surface.
Horizontal
diffuse
solar
radiation
ANFIS
Daily
The literature does not research
the selection of the most crucial
variables for predicting diffuse
solar radiation well. This study
(ANFIS) selects the essential
elements impacting horizontal
diffuse solar radiation using the
adaptive neuro-fuzzy inference
method.
The findings indicated that
considering the most relevant
combinations of two or three
ideal inputs offers a
compromise between ease of
use and high accuracy.
MAPE, MABE,
RMSE and R,
[24]
Iran
Global solar radiation in
terms of month, day,
average air temperature,
maximum air
temperature, minimum air
temperature, air pressure,
relative humidity, wind
speed, top-of-atmosphere
insolation, latitude and
longitude
predict the
daily
global
solar
radiation
(GMDH)
type neural
network
(MLFFNN)
ANFIS
Daily
The findings showed that the
GMDH model beats the other
produced models even though
all studied models can
accurately estimate the global
horizontal irradiance.
This research has been done to
evaluate and compare the
accuracy of six artificial
intelligence systems since it is
crucial to comprehend the
availability of solar Energy and
the lack of monitoring stations
in particular regions.
RMSE, MSE, R2,
[25]
Malaysia
Global solar radiation,
including s sunshine
duration S (h), and air
temperature
Monthly
Global
Solar
Radiation
ANFIS
Monthly
The importance of this study
stems from the need for more
precise measurements of solar
radiation that may be employed
in various applications across a
range of sectors, in addition to
the measured meteorological
parameters that are now
accessible.
The results show how
effectively ANFIS predicts the
level of solar radiation globally
and how well it may be used
with other soft computing
methods.
Clearness index
[26]
Yucatan
Peninsula,
Mexico
measured meteorological
variables: minimum and
predicting
daily
horizontal
-
Daily
The evaluation shows that the
SVM technique performs better
than the other techniques. This
suggests that the SVM
According to the study's
findings, using SVM improves
the precision of forecasting
global solar radiation in tropical
RMSE, MAE, and
R2
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
maximum air
temperatures, rainfall, and
global solar radiation
global
solar
radiation
technique may offer a
promising alternative to the
conventional methods for
predicting solar radiation.
warm and humid regions such
as Mexico's Yucatán,
particularly when rainfall is
factored into the equation.
[27]
Almeria,
Spain
Global Irradiance,
Beam Irradiance,
Sunshine Duration Index,
(Global/Extraterrestrial-
Clearance Index),
(Diuse/Extraterrestrial)
Solar
(Global/D
iuse-Diuse
Fraction)
(DF)
ANFIS,
MLP,
Hourly
The results demonstrated that
the MLP-GWO model
performed better in the training
and testing processes, followed
by the ANFIS model.
Subsequent investigations ought
to employ more advanced
hybrid machine-learning
techniques. Through
hybridization, machine learning
models have become more
effective and precise. As a
result, upcoming models could
significantly benefit from
tailored evolutionary algorithms
and nature-inspired
optimization methods to
enhance their parameters and
scrutinize their algorithmic
influence on the quality control
of a particular dataset.
MAE, ME, and
RMSE
[28]
10
different
cities
worldwide
Latitude, longitude,
minimum and maximum
temperatures (°C),
relative humidity (%),
wind speed (m/s), surface
pressure (kPa), amount of
air pollutants (O3, NO2,
PM2.5, PM10), dew frost
point, wet bulb
temperature (°C) and
mean solar radiation
(MJ/m2 /day) on a
horizontal surface
Mean
monthly
global
solar
radiation
ANN and
ANFIS
Daily
Based on the number of
statistical indices specified in
this study, the offered model is
roughly more formidable in
accuracy and credibility than
other models created by other
researchers.
It may also be expensive or
impossible to objectively
measure global solar radiation
in certain locations since it
requires specific equipment.
The authors consequently
recommend replacing the
empirical approach with
artificial intelligence to
anticipate mean monthly global
solar radiation while accounting
for input factors in light of the
modeling results, particularly
the ANFIS method.
RSME= 5.90E−05 ,
R2 = 0.999, ASM =
5.50E−04, EBM =
0.425
[29]
China
Daily sunshine duration
(S), relative humidity
(RH), precipitation (Pre),
air pressure (AP), daily
mean/maximum/minimu
m temperature
(DT/Tmax/Tmin)
Daily
global
solar
irradiance
(Hg)
ANFIS,
E-IBCM,
IYHM
Daily
The findings show that the
enhanced empirical models (E-
IBCM and IYHM) are more
accurate than the original
models and that the ANFIS
model is more accurate in
predicting Hg than the E-IBCM
and IYHM models.
The ANFIS model offers the
highest accuracy in calculating
daily global solar irradiance in
China compared to the other E-
IBCM and IYHM models. Our
future work will enhance the
ANFIS model with additional
methodologies and combine
more diverse input factors to
increase modeling accuracy.
RMSE and MAE
[30]
North
Dakota,
USA
maximum, mean, and
minimum air temperature
Solar
radiation
ANFIS
Daily
The most intriguing finding is
that almost every prior SR
prediction model was created
It can be claimed that the
performance of the hybridized
ANFIS-muSG model proved
RMSE. At Baker,
Beach, Cando,
Crary, and Fingal
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
using a variety of parameters.
However, the model suggested
in this research was built using
temperature, and it performed
well with an R2 in the range of
0.769 to 0.802.
the muSG algorithm's
usefulness for enhancing
ANFIS parameters when just
one predictor (in this instance,
air temperature) is used. This
demonstrates the possibility of
the proposed method being
extensively used for accurate
SR prediction.
stations,
respectively, the
ANFIS-muSG
demonstrated a
prediction boost
compared to the
conventional
ANFIS model by
42.2%, 32.6, 54.8%,
25.7%, and 49.0%
in terms of RMSE.
[31]
Three
stations in
Iran,
namely
Rasht
(humid
climate),
Yazd
(semi-
arid) and
Tehran
(slightly
arid),
relative humidity, wind
speed, rainfall, and
temperature
monthly
solar
radiation
ANFIS,
RBFNN,
MLP
Monthly
The primary contribution of the
research is the development of
novel hybrid ANFIS models for
monthly solar radiation
forecasting in various regions.
Future researchers may
simultaneously choose the best
input combinations and seek the
optimal model parameter values
using multi-objective
optimization methods.
Furthermore, prediction models,
climatic scenarios, and climate
models may be used to forecast
solar estimates for the future.
Utilizing solar Energy for
electricity generation in the
future may assist decision-
makers.
mean absolute error
(MAE), RMSE,
NSE, P BIAS
[32]
Iranian
city of
Tabass
by day of the year (day)
as the only input
Estimatin
g the
horizontal
global
solar
radiation
an
intelligent
optimizati
on scheme
based
upon the
adaptive
neuro-
fuzzy
inference
system
(ANFIS)
Daily
The survey's findings strongly
supported using ANFIS to
calculate daily worldwide
horizontal sun radiation using
just n
day.
There are two benefits to basing
global solar radiation
predictions on the day of the
year. First, there is no reliance
on any input component, such
as weather information.
Additionally, no pre-calculation
analysis is required.
Bias error (BE)
ranges from –3 to 3
MJ/m2, mean
absolute percentage
error (MAPE) =
3.9569%, mean
absolute bias error
(MABE) = 0.6911
MJ/m2, root mean
square error =
0.8917 MJ/m2
(RMSE), and
correlation
coefficient (R) =
0.9908.
[33]
Iraq
daily meteorological data
of maximum temperature,
minimum temperature,
mean temperature,
relative humidity, and
wind speed
Daily
Global
Solar
Radiation
Artificial
Neural
Network,
adaptive
neuro-
fuzzy
inference
Daily
The study's findings confirmed
that the ensemble techniques
may improve the performance
of single models in the training,
validation, and testing processes
by up to 19.19%, 7.59%, and
16.81%, respectively.
It might be proposed that
additional AI-based models,
like SVM, must be used in
future research and that their
outputs be incorporated in
ensemble modeling in light of
the study's findings,
Determination
coefficient (DC or
Nash–Sutcliffe
efficiency criterion)
and root mean
square error
(RMSE)
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
systems,
Meza–
Varas,
Hargreave
s–Samani,
and Chen,
multi-
linear
regression
(MLR)
model
demonstrating that more diverse
inputs for ensemble modeling
can result in better overall
outcomes.
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
A. SURVEY ASSESSMENT
According to research by and, the adaptive neuro-fuzzy
inference system (ANFIS) model is crucial for accurately
forecasting solar radiation. There has always been interest
in employing renewable energy to solve the issues of
resource depletion and the need for renewable energies
[34]. The ANFIS model demonstrates that solar radiation
may be forecasted accurately utilizing a variety of factors
and suggested performance criteria, including the
correlation coefficient, root mean square error, mean
absolute percentage error and mean absolute bias error.
These are all crucial in evaluating the accuracy of solar
radiation and the steps to minimize any inaccuracies that
could occur [20]
The results are compared with earlier research
conducted in several places throughout the globe to offer a
fair evaluation of the chosen ANFIS-muSG model in solar
radiation prediction. In this respect, a fair evaluation is
carried out to confirm the efficacy of the chosen model in
forecasting solar radiation. Notably, in contrast to other
research in the literature, the suggested ANFIS-muSG
model study attained the desired accuracy. The most
intriguing finding is that almost every prior model for
predicting solar radiation was built using a variety of
inputs. However, the model suggested that the research
was building temperature and performed well with an
R[20]
2
between 0.769 and 0.802.
One of the most effective modeling methods for AI
models is the Adaptive Neuro-Fuzzy Inference System
(ANFIS), which combines ANN and FL methodologies.
According to many studies, ANFIS is more accurate in
estimating solar radiation.[3]
For instance, a station in Kuala Terengganu, Malaysia,
employed a conventional and hybrid ANFIS model to
forecast monthly global solar radiation using several
metrological characteristics, such as maximum and lowest
air temperature, rainfall, clearness index, and sunlight
duration. This model integrated ANFIS with genetic
algorithms, particle swarm optimization, and differential
evolution methods. Results indicate that the hybrid
ANFIS-PSA model predicts solar radiation better than the
other models. According to the findings, the results
provided by ANFIS are more accurate than those from
other prediction models.[17]
Due to its capacity to capture the uncertainty associated
with time series data, a comparison of several AI models
for solar radiation prediction found that ANFIS is best for
solar radiation modeling. However, tuning ANFIS
hyperparameters, such as optimizing membership function
parameters, is the main issue with this approach. As a
result, in earlier research, the classic ANFIS model was
hybridized with other optimization techniques to enhance
its performance. Although the performance of the current
hybrid ANFIS model is promising, it is still necessary to
improve the prediction capabilities, given the significance
of the precision required in solar radiation measurement.
In addition, one of the main drawbacks of current solar
radiation prediction models is the need for various input
variables that are not always accessible in certain places
owing to a lack of monitoring infrastructure.[35]
III. METHODOLOGY OF THE MODEL.
A. DATA TO USE IN THE MODEL.
Various databases and variables are used in resource
quantification-prediction in solar primary resource
models. According to [36], databases should have
features such as:
• Geographical location
• Prediction Horizon
• Co-dependent variables of solar radiation.
• Geographical mesh.
Detailed meteorological data was used to develop and
validate the hybrid ANFIS model optimized with ACO,
covering multiple variables that directly influence solar
radiation. This dataset includes daily atmospheric pressure
measurements, clarity index, wind speed, and precipitation
collected from reliable weather stations in strategically
selected locations.
Atmospheric pressure is a crucial variable that affects air
density and, consequently, the amount of solar radiation
that passes through the atmosphere. Variations in
atmospheric pressure can influence the scattering and
absorption of solar radiation. The clarity index is a
dimensionless measure representing the fraction of diffuse
global solar radiation. This index is critical for
understanding the ratio of direct to diffuse radiation, which
is essential for modeling the availability of solar Energy
under different atmospheric conditions. Wind speed,
measured in meters per second (m/s), can affect the
scattering of clouds and aerosols in the atmosphere,
altering the amount of solar radiation that reaches the
Earth's surface. In addition, strong wind conditions are
often associated with weather systems that can reduce
direct solar radiation. Precipitation, measured in
millimeters (mm), indicates the presence of clouds and
storm systems that block solar radiation. Periods of high
precipitation generally correspond to conditions of low
solar radiation due to dense cloud cover.[37]
The data used in this study were obtained from weather
stations such as those provided by NASA POWER DAVE
V2.0.5 weather services. According to technical
documentation, each station provides highly accurate data
updated and maintained to rigorous quality standards.
Before using the data in the model, a preprocessing process
was carried out to ensure its quality and consistency. This
process included the elimination of outliers, identifying
and eliminating values significantly outside the normal
ranges, and using statistical techniques such as percentile
analysis and standard deviation. Missing data were
imputed using advanced methods such as interpolation,
minimizing bias and loss of information. All variables
were normalized to a standard scale to ensure that machine
learning algorithms can effectively handle differences in
variable scales. The typology to develop the model is
shown below [38].
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B. TYPOLOGY TO BE USED IN THE HYBRID
MODEL
The model typology used in this study combines an
Adaptive Neuro-Fuzzy Inference System (ANFIS) with
Neural Networks (NN) and an Ant Colony Algorithm
(ACO) [19], [39]. This combination is chosen due to
ANFIS's ability to model complex nonlinear systems, NN's
effectiveness in finding optimal solutions in large and
complex search spaces, and ACO's robustness in parameter
optimization.
ANFIS is a hybrid model that integrates the advantages
of neural networks and fuzzy logic systems. Its structure is
based on a network of five layers, each of which plays a
crucial role in the inference process [39]
1. Input Layer: Receives inputs from the system (in this
case, weather variables such as pressure, clarity index,
wind speed, and precipitation).
2. Fuzzification Layer: Transform inputs into fuzzy
values using membership features.
3. Rules Layer: Applies the fuzzy rules that represent
the expert knowledge of the system.
4. Normalization Layer: Normalizes the fuzzy values
resulting from the rules.
5. Output Layer: Generates the system's output using a
set of inference functions.
ANFIS is trained using a supervised learning process
that adjusts the parameters of membership functions and
fuzzy rules using optimization algorithms. This allows it to
capture the nonlinear relationships between input and
output variables [7].
The neural network (NN) is a computational model
inspired by the workings of the human brain. This
algorithm can learn complex patterns from data by
optimizing their weights and biases through
backpropagation processes [40], [41]. The NN optimizes
the parameters of the ANFIS model and selects the most
relevant features from the dataset. The NN process
includes the following steps:
1. Initialization: It starts with a defined neural network
structure and establishes random initial weights.
2. Forward propagation: The input data is propagated
through the network, calculating activations at each layer
until it reaches the output.
3. Error calculation: The error between the output
predicted by the network and the actual values is calculated
using a loss function, such as mean square error (MSE).
4. Backpropagation: The error propagates backward
through the network, adjusting weights and biases to
minimize the error.
5. Optimization: The iterative process continues until a
stopping criterion is reached, such as a maximum number
of iterations or a convergence in error reduction.
The Ant Colony Algorithm (ACO) is an optimization
algorithm inspired by the behavior of ants in foraging. This
algorithm is characterized by its ability to find optimal
graph paths using pheromones, which are chemical
substances that ants deposit to mark effective routes. ACO
is used to optimize the parameters of the ANFIS model and
select the most relevant features from the dataset [42]. The
implementation of the ANFIS+NN+ACO hybrid model
follows the following steps:
1. Data Preprocessing: Weather data is preprocessed to
remove outliers, impute missing data, and normalize
variables.
2. Initial ANFIS Training: An initial ANFIS model is
trained using the full features of the dataset.
3. Optimization with NN: NN is used to adjust ANFIS
parameters and select the most relevant features, iteratively
improving the model's accuracy.
4. Optimization with ACO: ACO is used to fine-tune
the parameters of the NN-optimized model and select the
most relevant features, iteratively further improving the
model's accuracy.
5. Model Evaluation: The optimized model is evaluated
using a validation set to measure its performance in terms
of mean square error (MSE) and other relevant metrics
[39].
This typology combines the learning and adaptability of
ANFIS with the robustness of NN and ACO in parameter
optimization, providing a powerful and efficient approach
to solar radiation prediction. The integration of these
techniques makes it possible to capture the inherent
complexity of weather data and significantly improve the
accuracy of predictions. Below is the application in a
particular region and the model results.
IV. APPLICATION AND RESULTS OF THE
MODEL
A. DATA USED IN THE MODEL.
The data used in this study contains meteorological data
relevant to the prediction of solar radiation from 1-01-2020
to 20-07-2024. The city chosen is Pasto, located in
southwestern Colombia (Latitude 1°12'52.48"N
·Longitude 77°16'41.22" W). This dataset includes six key
variables, as shown in Table 2
.
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
TABLE II. PHYSICAL VARIABLES USED IN THE DATABASE- SOURCES: AUTHORS.
Variable Name
Physical Variable
Units
Min Value
Max Value
Variable Type
PS
Atmospheric pressure
kPa
0.0016
101.40
WS10M
Wind speed at 10 meters
M/s
0.00
12.20
T2M
Temperature at 2 meters
°C
-16.60
41.60
QV2M
Humidity at 2 meters
g/kg
0.0027
24.20
RIGHT CORR
Corrected precipitation
mm/hour
0.00
63.70
Predictor
CLRSKY_SFC_SW_DWN
Surface radiation
Wh/m^2
0.00
1268.57
Target Variable
The preliminary analysis of the predictors shows that the
data are in good condition. The distributions of the
variables indicate variability and diversity in the
meteorological conditions captured. As shown in Figure 1,
the variables do not have anomalous data and high
variability is not shown in a few periods, which influences
the quality of the model results. The climate predictors that
act as input to the model
Fig 1. Predictors used in the ANFIS+NN+ACO model. Source: Authors
Figure 2 shows solar radiation in Pasto, the primary
resource in the region, which shows high variability. The
region's high variability suggests the presence of
cloudiness patterns over time and fluctuations in the clarity
of the sky, an essential variable in solar PV power
generation planning. In addition, seasonal patterns must be
captured and predicted by the model.
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
Fig 2. Solar radiation of the particular region in the period. Source: Authors.
B. APPLICATION OF THE MODEL
Figure 3 shows the model's design. The preprocessing
and data cleansing stages are responsible for looking for
anomalous data or null values that the dataset may have to
have continuous inputs to the model. Subsequently, the
dataset is normalized to have the predictor variables in the
same range. Finally, the dataset is mixed so that the model
can capture nonlinearity without redundancy.
Fig 3. ANFIS+NN+ACO Predictor Model Schema. Own source.
The prediction stage consists of the ANFIS predictor
first. In its initial training stage, Gaussian membership
functions are defined to model the input variables. The
inputs are then transformed into fuzzy values using the
built-in Fuzzification engine. Then, by applying rules
based on fuzzy logic, relationships are established between
the input and output variables. Finally, the output of this
predictor is the initial training with parameter adjustment
of memory functions and fuzzy rules employing a
supervised learning algorithm. From a mathematical point
of view, ANFIS takes each input variable.

=

defines the fuzzy membership functions,
where being Gaussian, we have as in Equation (1):
(
)
=

2
(1)
Where
(
)
, is the degree of membership of the
function of membership, is the center of the function, and
is the standard deviation.
For each Fuzzy rule









, 
=
+
+
…
+
The weight of the ruler is calculated as shown in
Equation 2:
=

(
)
(2)
Finally, the output of the ANFIS model, defuzzification,
is calculated as shown in Equation 3:
=


(3)
Where
, is the number of rules.
The neural network and ACO stages optimize the
response of the ANFIS model. With forward typology and
hidden layer, the neural network compares the predicted
output of ANFIS with the actual values, employing a loss
function that adjusts the weights and biases of the network
to minimize error. The process is repeated until a stopping
criterion is reached, which is the convergence in reducing
error for this study. Layers of neurons represent the
optimization neural network. For a layered network, the
output of the layer is shown in Equation 4:
=
(

)
+
(4)
Where
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214 1
=
Network Input
W These are the weights and biases of the layer
is the activation function, in this case, sigmoid
The training process adjusts weights and biases to
minimize the loss function
, as indicated by Equation 5:
(
)
=
1

(
)
(5)
The ants in ACO build a solution by moving through the
graph and choosing paths based on the probability
determined by the number of pheromones and the local
heuristic. The pheromones are updated according to the
quality of the solutions found by the ants, reinforcing the
paths that lead to better solutions. The integration of ACOs
for feature selection optimizes the model's parameters, and
finally, in the results stage, the performance against
standardized metrics is evaluated.
It starts with a population of ants and establishes an
initial level of pheromones in the paths of the graph. Each
solution is built by moving across the graph and choosing
probability-based paths, as shown in Equation 6, which are
determined by the number of pheromones and the local
heuristic.


.

=





(6)
where are parameters that control the influence of
pheromone and heuristics, respectively
,
The pheromones are updated according to the quality of
the solutions found by the ants, reinforcing the pathways
that lead to better solutions, as shown in Equation 7:

=
(
1
)

+


(7)
Where is the rate of pheromone evaporation, and is the
amount of pheromone deposited by the ant.

The results are then described, and the model is
validated.
C. RESULTS AND VALIDATION OF THE
MODEL
Figure 4 shows the results of the primary resource
prediction. The ANFIS +NN+ACO model performs well.
The membership functions implemented in the model, of
Gaussian type, can consolidate a solid base of prediction
based on fuzzification processes. In addition, the linguistic
rules used cover all the spectra found in the cleaning and
characterization part of the dataset. The configuration of
64 input layer neural networks and 48 hidden layer neural
networks can take resource variations and predictors. By
implementing optimization functions represented in
Nested and Loss ACOs, the model can capture and respond
to the nonlinearity of climate resources.
Fig 4. Measured solar radiation vs. predicted solar radiation. Source: Authors
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214
13
Figure 5 shows the evolution of the data during the model's
training and validation stages over 200 epochs. The portion of
data used to train-validate the model has a ratio of 70-30. The
curves in the graph decrease rapidly at first and then stabilize,
suggesting that the model is learning effectively and shows no
signs of significant overfitting. The generalization of the model
represented by the loss of validation, which is slightly more
significant than the training loss, suggests that the model is
robust.
Fig 5. Learning curve of the ANFIS +NN+ACO model.
Source: Authors.
Regarding the metrics analysis, shown in Table 3, the MSE
(Mean Square Error) indicates that the mean square error
between the predicted and actual values is low, suggesting
strengths in the model's performance. The RMSE (Root Mean
Square Error) makes interpreting the error in the units more
accessible. The MAE (Mean Absolute Error) shows that, on
average, the model's predictions are 3.07 units away from the
actual solar radiation values, which is a relatively low error.
Finally, the correlation coefficient indicates that the model
explains approximately 91% of the variability of solar radiation
data. The metric results are pretty explicit in determining that
the model has strengths and can capture the high nonlinearity
of the region's data.
/
TABLE III. MODEL PERFORMANCE EVALUATION
METRICS. FUETNE AUTORES.
Metric
Value
MSE
12.818108
RMSE
3.5023
R
2
0.912214
V. FUTURE RESEARCH.
Future researchers may simultaneously choose the best input
combinations and seek the optimal model parameter values
using multi-objective optimization methods. Furthermore,
prediction models, climatic scenarios, and climate models may
be used to forecast solar estimates for the future. Utilizing solar
Energy for electricity generation in the future may assist
decision-makers.
To estimate global sun radiation at various places in North
Dakota, USA, Tao et al. (2021) suggested a unique intelligence
model by fusing two metaheuristic optimization algorithms
with the Adaptive Neuro-Fuzzy Inference System (ANFIS).
The study's findings showed that by properly optimizing
ANFIS parameters, solar radiation forecast capacity may be
increased. The models used in this work can only estimate solar
radiation from readily accessible temperatures (maximum,
mean, and lowest) in any place. Such less resource-intensive
models are crucial for underdeveloped nations with limited
access to meteorological information besides rainfall and
temperature. The ANFIS-muSG model created in the Tao et al.
(2021) research may thus be used for energy harvesting and
monitoring in various geographical areas. However, future
research may assess how well the model performs when
additional meteorological factors include wind speed, cloud
cover, sunlight, humidity, and rainfall (Tao et al., 2021).
Additionally, data from satellite remote sensing may be used
as an input to enhance model performance in solar radiation
forecasting. Using an ensemble strategy, the performance of the
hybridized ANFIS-muSG model might be significantly
enhanced. In addition, additional cutting-edge optimization
methods like quantum-behaved PSO and the Firefly Algorithm
may be used to choose input predictors that have been proven
successful in model input selection. Empirical mode
composition and wavelet transform could also be additional
data analysis methods.
VI. CONCLUSIONS
This work presented the design and development of an
ANFIS+NN+ACO model. The latter is representative of nature
and is an inspiration in data-driven model optimizers. The
model is robust in predicting primary solar resources in a
particular region. ANFIS settings can be managed so that
different strategies are considered in membership functions that
can provide greater modeling capacity for nonlinear data.
Parameter optimization using ACO is a process of trial and
error to determine the best combination(s) for the totalized
model. Finally, hybridizing ANFIS with other models, such as
neural networks (NN), can leverage the strengths of both
approaches, where ANFIS handles uncertainty and fuzzy logic,
and NN captures the complex nonlinear relationships, thus
achieving greater accuracy in predictions. However, several
limitations must be acknowledged. First, the model relies on the
availability and quality of meteorological data, which may be
limited in some regions. Second, although the model was
trained and tested using data from a specific geographic area
(Pasto, Colombia), its generalization capability to other climatic
zones remains to be validated. Third, the computational cost of
hybrid models that include metaheuristic optimization can be
relatively high, especially for large datasets or longer prediction
horizons. Finally, the current model does not incorporate
satellite-based inputs or multi-objective optimization, which
could further enhance its accuracy and adaptability.
Despite these limitations, the hybrid ANFIS+NN+ACO
model provides a strong framework for evaluating solar energy
potential and supporting the planning of distributed generation
Scientia et Technica Año XXVIII, Vol. 29, No. 01, enero-marzo de 2024. Universidad Tecnológica de Pereira.
14
systems. Future work should address these constraints by
incorporating diverse geographic datasets, reducing
computational load, and integrating additional optimization
strategies to improve generalizability and scalability.
Models of this nature are essential inputs to quantify the solar
potentials of regions subject to distributed generation
installation with variable primary resources.
ACKNOWLEDGMENT
The authors thank the project Development of a multi-agent
transactional model of non-conventional Energy for the
department of Nariño, Pasto BPIN 2021000100499.
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Scientia et Technica Año XXVIII, Vol. 29, No. 01, enero-marzo de 2024. Universidad Tecnológica de Pereira.
16
Burbano-Vallejo Zarella, Sixth
semester Software Engineering student
at the Universidad Cooperativa Campus
Pasto. I belong to the ESLINGA
Semillero EnergIA research group. I
have completed a diploma in coding and
programming at the Universidad
Pontificia Javeriana.
Ramirez, Carlos Alonso, Master in
Environmental Engineering from the
Mariana University of Pasto. Specialist in
Finance from the University of Valle Cali.
Industrial Engineer from the National
University of Colombia, Manizales.
Research Professor from the Cooperative
University of Colombia - UCC Pasto.
Research topics: Alternative energies and
industrial production systems.
Revelo Tovar, Luis Carlos, Systems
engineer with emphasis on software from
the Antonio Nariño University, with
specialization in marketing management
from the Jorge Tadeo Lozano University
and systems auditing from the Antonio
Nariño University, master's degree in free
software from the Autonomous University
of Bucaramanga. With experience in
software development, software project
management, computer networks and software architecture in
public and private entities.