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

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

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.

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,

This manuscript was submitted on August 14, 2024. Accepted on May

06, 2025. And published on June 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 ).

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

INTRODUCTION.

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].

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].

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).

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

100

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

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.

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101

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

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

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]

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102

TABLE I.

REPRESENTATIVE WORKS IN THE USE OF OPTIMIZATION ALGORITHMS INSPIRED BY NATURE+ANFIS.

References

Case study

Input parameters

Output

parameter

AI model

Optimization

algorithm

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

ANFIS-PSO

ANFIS-GA

ANFIS-ACO

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

ANFIS- PSO,

ANFIS-GA

and 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

ANFIS, SVM,

and ANN

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

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103

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,

MLP-GWO

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]

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

GA-ANN

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

ANFIS-SSA,

ANFIS-GOA

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

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(ANFIS-

muSG)

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

GOA, PSO,

SSA

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

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)

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105

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.

106

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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]

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.

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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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]

Input Layer: Receives inputs from the system (in this

case, weather variables such as pressure, clarity index,

wind speed, and precipitation).

Fuzzification Layer: Transform inputs into fuzzy

values using membership features.

Rules Layer: Applies the fuzzy rules that represent

the expert knowledge of the system.

Normalization Layer: Normalizes the fuzzy values

resulting from the rules.

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:

Initialization: It starts with a defined neural network

structure and establishes random initial weights.

Forward propagation: The input data is propagated

through the network, calculating activations at each layer

until it reaches the output.

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).

Backpropagation: The error propagates backward

through the network, adjusting weights and biases to

minimize the error.

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:

Data Preprocessing: Weather data is preprocessed to

remove outliers, impute missing data, and normalize

variables.

Initial ANFIS Training: An initial ANFIS model is

trained using the full features of the dataset.

Optimization with NN: NN is used to adjust ANFIS

parameters and select the most relevant features, iteratively

improving the model's accuracy.

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.

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

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

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TABLE II. PHYSICAL VARIABLES USED IN THE DATABASE- SOURCES: AUTHORS.

Variable Name

Physical Variable

Units

Min Value

Max Value

Variable Type

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

Predictor

QV2M

Humidity at 2 meters

g/kg

0.0027

24.20

RIGHT CORR

Corrected precipitation

mm/hour

0.00

63.70

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.

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)

𝑗

Fig 2. Solar radiation of the particular region in the period. Source: Authors.

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

𝑛

𝑤

𝑗

𝖦

𝜇𝐴

𝑗

(

𝑥

𝑖

)

𝑖=1

(2)

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

Finally, the output of the ANFIS model, defuzzification,

is calculated as shown in Equation 3:

the input and output variables. Finally, the output of this

∑

𝑚 𝑤

𝑗

𝑦

𝑗

𝑦 =

𝑗=1

(3)

predictor is the initial training with parameter adjustment

𝑚

𝑗=1

𝑤

𝑗

of memory functions and fuzzy rules employing a

supervised learning algorithm. From a mathematical point

of view, ANFIS takes each input variable. 𝑥

𝑖

(𝑖 =

1,2,3, … , 𝑛) defines the fuzzy membership functions,

where being Gaussian, we have as in Equation (1):

𝜇𝐴

(

𝑥

)

= 𝑒𝑥𝑝 (−

(𝑥

𝑖

−𝑐

𝑗

)

(1)

Where 𝑚, 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

𝑗 𝑖

2𝜎

to minimize error. The process is repeated until a stopping

Where 𝜇𝐴

𝑗

(

𝑥

𝑖

)

, is the degree of membership of the

function of membership, is the center of the function, and

is the standard deviation.𝑥

𝑖

𝐴

𝑗

𝑐

𝑗

𝜎

𝑗

For each Fuzzy rule 𝑅

𝑗

𝑅

𝑗

: 𝑖𝑓 𝑥

𝑖𝑠 𝐴

1𝑗

𝑎𝑛𝑑 𝑥

𝑖𝑠 𝐴

2𝑗

𝑎𝑛𝑑 … 𝑎𝑛𝑑 𝑥

𝑛

𝑖𝑠 𝐴

𝑛𝑗

, 𝑡ℎ𝑒𝑛 𝑦

𝑗

= 𝑎

𝑗

𝑥

+ 𝑏

𝑗

𝑥

+ ⋯ + 𝑧

𝑗

𝑥

𝑛

The weight of the ruler is calculated as shown in

Equation 2:

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:

𝑎

𝑙

= 𝑓

(

𝑊

𝑙

𝑎

𝑙−1

)

+ 𝑏

𝑙

(4)

Where

∑

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𝑖𝑗

𝑎

= 𝑋 Network Input

W These are the weights and biases of the layer 𝑏

𝑙

𝑓 is the activation function, in this case, sigmoid

The training process adjusts weights and biases to

minimize the loss function 𝐽, as indicated by Equation 5:

where are parameters that control the influence of

pheromone and heuristics, respectively 𝛼, 𝛽

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:

𝜏

𝑖𝑗

(

1 − 𝜌

)

𝜏

𝑖𝑗

∑

𝑎𝑛𝑡

𝑘

Δ𝜏

𝑘

(7)

𝐽

(

𝜃

)

= (

)

∑

𝑚

(

ℎ

(

𝑥

𝑖

)

− 𝑦

𝑖

)

(5)

𝑚

𝑖=1

𝜃

Where is the rate of pheromone evaporation, and is the

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. 𝜏

𝑖𝑗

𝜂

𝑖𝑗

𝛼

𝛽

amount of pheromone deposited by the ant.𝜌Δ𝜏

𝑘

𝑖𝑗

The results are then described, and the model is

validated.

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

𝑃

𝑖𝑗

𝜏

𝑖𝑗

𝜂

𝑖𝑗

∑

𝛼

𝛽

(6)

implementing optimization functions represented in

𝑘 𝑐𝑎𝑙𝑙𝑜𝑤𝑒𝑑

𝜏

𝑖𝑗

𝜂

𝑖𝑗

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

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111

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.𝑊ℎ/𝑚

𝑅

TABLE III. MODEL PERFORMANCE EVALUATION

METRICS. FUETNE AUTORES.

Metric

Value

MSE

12.818108

RMSE

3.5023

0.912214

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.

112

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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Fraunhofer ISE.

Edgar Dario Obando is a Physical Engineer from the

Universidad del Cauca and holds a Master’s degree in

Electrical Engineering from the Universidad Nacional de

Colombia. He currently works as a professor at the

Universidad Cooperativa de Colombia, where he has

been recognized for his outstanding teaching

performance. His research interests include energy

systems, machine learning, Big Data, and solar radiation

prediction, with several scientific publications focused on

metaheuristic techniques, photovoltaic systems, and

artificial intelligence applications in energy resources.

ORCID: https://orcid.org/0000-0002-2515-7640.

Scientia et Technica Año XXVIII, Vol. 29, No. 01, enero-marzo de 2024. Universidad Tecnológica de Pereira.

114

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. ORCID:

https://orcid.org/0009-0000-6559-9980

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. ORCID: https://orcid.org/0000-

0002-3559-6225

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. ORCID: https://orcid.org/0009-

0001-0990-9603