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https://doi.org/10.37815/rte.v37nE1.1356
<=
span
lang=3DES>Artículos originales
&nb=
sp;
Fragmentación =
de Roca por Voladura
en Minería a Cielo Abierto: Predicción con IA
Rock Fragmentation by Blasting in Open-Pit Mining:
an AI Predictive Model<=
/span>
Steven Toapanta-Delgado1 https://orcid.org/0009-0001-0015-5008 , Byron
Guerrero-Rodriguez1 <=
/span>
https://orcid.org/0000-0002-6288-4=
804 , Christian Mejia-Escobar 1 https://orcid.org/0000-0001-=
6715-191X
Enviado: <=
/o:p>
2025/06/29 <=
/o:p>
Aceptado:
2025/08/24
Publicado: <=
/o:p>
2025/10/15
1 Universidad
Central del Ecuador , Quito, Ecuador sftoapanta@uce.edu.ec , bvguerreror@uce.edu.ec , cimejia@uce.edu.ec
Esta o=
bra
está bajo una licencia internacional Creative
Commons Atribución-NoComercial 4.0
&nb=
sp;
Resumen La fragmentación de rocas por voladura es
fundamental en el sector minero. Este proceso busca optimizar el tamaño de la roca para su posterior extracción, transporte y procesamiento. Predecir esta
fragmentación se vuelve una tarea crucial para mejorar la eficiencia
operativa; sin embargo, la aplicación de fórmulas simplificadas carece de precisión y adaptabilida=
d a las variaciones litológica=
s.
Este estudio propone el uso de inteligencia artificial (IA) para la
estimación precisa del diámetro promedio de rocas ígne=
as,
sedimentarias y metamórficas. A partir de un conjunto de 97 datos de
fragmentación y voladuras reales a nivel mundial, se evaluaron los
algoritmos de Random Forest (RF), Support Vector Regressor (SVR) y Kernel R=
idge
Regression (KRR), junto con la ecuación de Kuz-Ram, ampliamente
utilizada en la industria. Los resultados indican que los modelos de IA sup=
eran
notablemente la ecuación convencional.
RF ofrece la mayor precisión con valores de MSE de 0.0017 y R2 de 95.38 %. En
contraste, SVR alcanza valores=
de 0.0064 y 83.13 %, mientras que KRR obtiene
0.016 y 69.60
%. El adecuado desempeño de estos algoritmos ha
motivado el desarrollo de una aplicación que facilita a los usuarios=
la
visualización de mallas de perforación, establecer dimensiones
concretas y comparar las proyecciones del tama&ntild=
e;o medio
de las rocas. Esta herramienta facilita la toma de decisiones informadas, mejorando los
procesos de minería, fomentando resultados más confiables y
sostenibles en distintos contextos operativos.
<=
/o:p>
&nb=
sp;
Palabras clave: fragmentación, minería, perforación, voladura, estimación, machin=
e learning,
inteligencia=
artificial.
&nb=
sp;
Abstract Rock fragmentation by blasting is fundamental in the =
mining
sector. This process seeks to optimize rock size for subsequent extraction,
transport, and processing. Predicting this fragmentation becomes a crucial =
task
for improving operational efficiency; however, the application of simplified
formulas lacks precision and adaptability to lithological variations. This
study proposes the use of artificial intelligence (AI) for the accurate
estimation of the average diameter of igneous, sedimentary, and metamorphic
rocks. Based on a set of 97 real fragmentation and blasting data from around
the world, the Random Forest (RF), Support Vector Regressor (SVR), and Kernel Ridge Regression (KRR) algorithms were evaluated, along with
the Kuz-Ram equation, widely used in the industry. The results indicate tha=
t AI models significantly outperform =
the
conventional equation. RF offers the highest accuracy with MSE of 0.0017 an=
d R2
of 95.38%. In contrast, SVR achieves values of 0.0064 and 83.13%, while KRR=
achieves
0.016 and 69.60%.
The adequate performance of these algorithms has led to the
development of an application that allows users
to view drilling
grids, set specific
dimensions, and compare projections of average rock size. This tool facilitates informed
decision-making, improving mining processes and promoting more reliable and
sustainable results in different operational contexts.
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Keywords: Fragme=
ntation, mining, drilling, blasting,
estimation, machine learning,
artificial
intelligence.
&nb=
sp;
Introducción La fragmentación de la roca=
es un
pilar fundamental en la viabilidad económica y la eficiencia operati=
va
de cualquier proyecto minero (Xie et al., 2021; Zamora-Paredes et al., 2020=
). La voladura, como etapa inicial
de conminución,<=
span
style=3D'letter-spacing:1.35pt'> impacta
directamente los costos
y la productividad de operaciones subsiguientes como carga, transpor=
te,
trituración y molienda (Yakovlev et al., 2024). Una fragmentaci&oacu=
te;n
óptima es crucial (Aryafar et al., 2020), pero la presencia de rocas
sobredimensionadas aumenta costos por voladuras secundarias y genera impact=
os
ambientales como polvo y vibraciones (Su & Ma, 2022) (Guerrero-Rodrigue=
z et
al., 2024). De hecho, más del 70 % de la energía explosiva se
desperdicia en efectos adversos, en lugar de contribuir a una fragmentación efectiva. Tradicionalmente, la predicción se ha basado en modelos emp&iacu=
te;ricos como Rosin-Rammler o Kuz-Ram (Vu & Bao, 2021); no obstante, estos métodos son limitados por su dependencia de trabajo manual,
sesgos de datos y la incapacidad
de capturar las complejas<=
span
style=3D'letter-spacing:-.15pt'> relaciones no lineales y propiedades de la masa rocosa (Ohadi
et al., 2020).
&nb=
sp;
Para superar estas limitaciones, la
inteligencia artificial (IA) se presenta como una alternativa prometedora en la ingeniería minera (Saadou=
n et al., 2024).
Los modelos de IA, con su capacidad de autoaprendizaje y reconocimiento de patrones no lineales, permiten predicciones
más precisas
y la optimización de los diseños de voladura (Leng et al., 2020). El presente estudio
propone el desarrollo de un modelo
predictivo aplicando técnicas de IA para la fragmentación de roca en vol=
aduras
a cielo abierto. Para optimizar los parámetros de voladura y lograr =
una
rotura de roca más efectiva, se evalúan tres algoritmos de
aprendizaje automático (Random Forest, Support Vector Machine y Kern=
el
Ridge Regression) con el fin de reducir costos y minimizar impactos
ambientales (Zhao et al., 2024).
La contribución<=
span
style=3D'letter-spacing:-.65pt'> concreta
de este trabajo
es
&nb=
sp;
una herramienta de software predictiva confiable y precisa con una interfaz gráfica =
de usuario que permitir&a=
acute; ajustar proactivamente la voladura, mejorando la eficiencia operativa, la productividad y
la recuperación<=
span
style=3D'letter-spacing:-.05pt'> del mineral, mientras
se mitigan los daños económicos y ecoló=
gicos (Górriz et al., 2023).
&nb=
sp;
Metodología Trabajo previo
El análisis comparativo de once investigaciones sobre fragment=
ación una amplia
variedad de metodologías utilizadas y variables seleccionadas, las
cuales se ven afectadas por los objetivos particulares y el contexto
geográfico y operativo de cada uno de los trabajos. La fuente de los datos
difiere en gran medida: hay investigaciones que se centran
en una única &=
aacute;rea,
mientras que otras incluyen varias regiones y naciones, como Chile, Turquía, Perú, Finland=
ia,
Cuba y Zambia, o incluso
abarcan escalas a nivel global,
lo que influye en la cantidad y el tipo de información analizad=
a.
Respecto a las metodologías, la Figura 1 destaca la aplicació=
n de
técnicas de IA y modelos empíricos.
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Figura 1 Frecuencia =
de los modelos empleados en las investigaciones analizadas <=
/o:p>
La red neuronal
artificial (ANN) utilizada
en tres investigaciones =
(Amoako et al., 2022; de Castro, 2021; Rosales-Huama=
ni et
al., 2020) y el modelo Kuz-Ram aplicado en cuatro (Bunga et al., 2020; Castro, 2021; Mwango, 2019; Rojas Linares,
2018) son los más frecuentes, lo que indica su versati=
lidad
y establecimiento. Métodos alternativos comprenden la máquina=
de
vectores de relevancia (RVM), la regresión de procesos Gaussianos (G=
PR),
la regresión de probabilidad minimax (MPMR), la regresión
múltiple y la matriz de decisión, cada uno con sus respectivos
fundamentos teóricos. No obstante, ellos están limitados por =
la
adaptabilidad al tipo de roca y la presentación de los resultados, ya
que no facilitan una mejor visualización para el usuario final.
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Propuesta A diferencia
de los trabajos anteriores, este estudio busca cuantificar la
fragmentación durante voladuras considerando diferentes tipos de rocas. Incorpora nueve categorías de litologías,
que incluyen ígneas, metamórficas y sedimentarias, con=
el
fin de analizar el comportamiento de =
los materiales geológicos. Además, se seleccionaron los tres algoritmos de IA con la mayor
&nb=
sp;
precisión reportada en la literatura, que son evaluados y comparados,<=
span
style=3D'letter-spacing:-.75pt'> tanto
entre ellos como con
un
método convencional ampliamente utilizado. Posteriormente, se desarrolla una aplicación de
software para optimizar
la calidad del producto, implementando un sistema de retroalimentación
constante. En esencia,
la metodología sigue
los pasos del aprendizaje automático (ML) clá=
;sico,
agrupados en dos grandes etapas: datos y modelo, tal como se ilustra en la
Figura 2.
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p;
Figura 2 Flujograma de la metodología empleada par=
a el
proyecto
La primera etapa se dedica al conj=
unto
de datos, donde se recopilan y analizan datos de caracterización geotécnica, registros históricos y mediciones de fragmentaci=
ón para obtener
métricas como el tamaño
crítico P(50), para identificar inconsistencias por variaciones
geológicas o errores. La segunda etapa corresponde a los
métodos de procesamiento de estos datos. Aquí se utilizan modelos
matemáticos y algoritmos de IA para correlacionar variables como dureza del
material y parámetros de diseño, para predecir resultados y
mejorar la planificación. Este enfoque reduce incertidumbre, optimiza
eficiencia energética y económica y se adapta a diversos contextos mineros, priorizando
sostenibilidad. La integración de datos experimentales, simul=
aciones
y registros históricos asegura robustez, ajustando factores como
separación de barrenos =
o cantidad
de explosivo para maximizar recursos
y minimizar costos.
A continuación, =
se
explican con más detalle los datos y modelos utilizados.
&nb=
sp;
Datos Los datos
se recopilaron a partir de una investigación detallada
realizada por Hudaverdi
et al. (2006), que abarca un total de 97 registros de
diversas partes del mundo, asegurando así una adecuada repres=
entatividad. Cada registro incluye
ocho factores principales que afectan la fragmentación y el rendimiento en las voladuras (Tabla 1): espaciamiento/burden (S/B),
altura de banco/burden (H/B), burden/diámetro de barreno (B/D=
),
stemming/burden (T/B), factor de pólvora (PF), tamaño de bloq=
ue
in situ (XB), módulo de elasticidad (E) y tamaño medio de
fragmentación (P50) como variable dependiente.
&nb=
sp;
Tabla 1 Variables =
del conjunto
de datos y sus indicadores estadísticos más importantes
=
VARIABLES
DEFINICIÓN
CLASIFICACIÓN
=
TIPO
=
MÍNIMO
=
MÁXIMO
=
MEDIA
DE=
SVIACIÓN =
EST&Aacu=
te;NDAR
S/B
Relación de parámetro central (Espaciamiento
/Burden)
Cuantitativa continua=
Independiente
1
1.75
1.201778
0.110134
H/B
Relación de geometría de la malla
(Altura de banco/
Burden)
Cuantitativa continua=
Independiente
1.33
6.82
3.458889
1.638696
B/D
Relación de eficiencia vertical o de profundidad de=
hoyo
(Burden/ Diámet=
ro de agujero)
Cuantitativa continua=
Independiente
17.98
39.47
27.216333
4.798088
T/B
Relación de confinamiento de la energía (Taco
estéril/ Burden)
Cuantitativa continua=
Independiente
0.5
4.67
1.267556
0.691722
PF (kg/m3)
Factor de pólvora
Cuantitativa continua
Independiente
0.22
1.26
0.536556
0.239227
XB (m)
Tamaño de bloque
estimado
Cuantitativa continua
Independiente
0.02
2.35
1.178667
0.479209
E (GPa)
Módulo de elasticidad o de Young de roca intacta
Cuantitativa continua=
Independiente
9.57
60
30.585333
17.75583
P50 (m)
Ta=
maño medio de roca fragmentada
Cuantitativa continua
Dependiente
0.12
0.96
0.315667
0.185576
Aunque
el número de registros es limitado, ya que su contenido es único, especializado y de difí=
cil acceso,
este conjunto de datos es particularmente relevante para el estudio.
Mediante el uso de unidades del Sistema Internacional, se crearon
relaciones sólidas para modelos de predicción que son
útiles en situaciones geotécnicas y mineras. El anális=
is
estadístico expone las conexiones entre las variables, enfatizando la
desviación estándar. Un valor elevado en el módulo de
elasticidad (E =3D 17. 755830 GPa) indica una alta variabilidad, lo que inf=
luye
en la capacidad para realizar
predicciones. En contraste, el reducido valor del factor de pólvora (PF
=3D 0. 239227 kg/m&su=
p3;) sugiere
una uniformidad que propicia resultados consistentes.
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p;
Métodos =
Kuz-Ram Es un modelo empírico muy
utilizado en la minería, anticipa cómo se fragmentan las rocas
después de las explosiones, mejorando las operaciones en la planta al
calcular cómo se distribuirán los tamaños de los
fragmentos (Hekmat et al., 2019). Se fundamenta en criterios tales como el factor
geológico (volab=
ilidad), diseño de voladura (burden,
espaciamiento, altura d=
el banco)
y propiedades del material explosivo (cantidad, tip=
o, densidad) (López =
et al., 2003).
El tamaño promedio del fragmento (P50) se determina utilizando la Ec=
. 1
(Kuznetsov, 1973). Para optimiz=
ar la granulometría, se modifican el burden y el espaciamiento, lo que incrementa la productividad. La
validación confronta las predicciones con el análisis de
imágenes (Split Desktop, =
WipFrag), lo que permite realizar ajustes para incrementar la precisió=
n (Das et =
al.,
&nb=
sp;
2023). A=
pesar
de que Kuz-Ram es sencillo
de aplicar y valioso para los diseños iniciales, pue=
de
sobreestimar el tamaño de los fragmentos en algunas rocas, dependien=
do
de la calidad de los datos y del factor de la roca (Lawal, 2021). Los modelos ajustados y los elementos de corrección
optimizan su calibración y alineación con los resultad=
os
experimentales.
<=
/o:p>
&nb=
sp;
Random Forest Es<=
/span> un algoritmo de aprendizaje <=
/span>automático; se caracteriza <=
/span>por su eficacia en la predicción de la fragmentaci=
ón de rocas en los procesos
de voladuras mineras,
lo que permite optimi=
zar los procesos y aumentar la eficiencia (Shafl,
2024). Comienza recolectando información de campo, como características
geomecánicas (resistencia uniaxial y módulo de elasticidad),
parámetros relacionados <=
span
style=3D'letter-spacing:-.3pt'> con la voladura (distancia entre agujeros/carga y factor de carga) y datos empíricos
(promedio del tamaño de los fragmentos) (Hu et al., 2023). Se
entrena un conjunto de árboles de decisión utilizando
subconjuntos aleatorios de datos, aplicando la técnica de bootstrapping y la selección
aleatoria de variables, con el fin de disminuir las correlaciones y mejorar=
la
robustez (Raj et al., 2024). Se establece el hiperparámetro de
número de estimadores (número de árboles) para preveni=
r el
sobreajuste (Zhao et al., 2024). Validado
con indicadores como el error cuadrático medio y el coeficiente de
determinación, el modelo Random Forest presenta una mayor
precisión en comparación con otros modelos. Además, identifica variables=
clave
a través de análisis de sensibilidad y optimiza diseño=
s de
voladura, logrando las distribuciones granulométricas deseadas
y aumentando la productividad en minería (Y. L. Zhang
et al., 2024).
&nb=
sp;
Support Vector Regressor El algoritmo SVR se distingue por su exactitud en la predicción de la fragmentación de rocas
durante las voladuras, superando a los modelos empíricos convencionales (=
Rabbani et al.,
2024). Comienza con la recopilación de datos, que debe incluir
los parámetros de voladura, las propiedades geomecánicas y
métricas tales como P50 o P80 (Hasanipanah et al., 2018). Estos
conjuntos de datos, que están separados en grupos de entrenamiento y de prueba,
se obtuvieron a partir de
explosiones reales (Li et al., 2021). El modelo SVR es entrenado para estim=
ar
el tamaño de los fragmentos, adecuando el hiperparámetro de regularización C (Miao et al., 2021). Su
rendimiento se valora mediante indicadores tales como el Error
Cuadrático Medio.
&nbs=
p;
Kernel Ridge Regre=
ssion La regresión KRR es una
técnica de aprendizaje automático utilizada para modelar
relaciones no lineales en la predicción de la fragmentación de rocas durante
voladuras mineras,
destacándose por su alta precisión (Wu et al., 2024). Emplea funciones de kernel para trasladar
datos a espacios dimensionales más altos y aplica regularizaci&oacut=
e;n
ridge para prevenir el sobreajuste, lo que mejora la solidez de las
predicciones (Lin, 2023). El procedimiento inicia con la recopilaci&oa=
cute;n de datos a partir de investigaciones de campo o simulaciones, separándolos en grupos de
entrenamiento y de prueba (R. Zhang et al., 2023). Se entrena el modelo KRR
optimizando el hiperparámetro de coeficiente de kernel. Métod=
os
como KRR autoadaptativo mejoran el rendimiento, medido con métricas estándar, garantizando así pronósticos precisos y consistentes (Yin et al., 2020).<=
/span>
&nb=
sp;
Resultados y Discusión Análisis estadístico <=
/b>
La Figura 3 representa el diagrama de pairplot, que muestra conexiones relevantes entre=
las variables
del estudio, dispuestas de acuerdo con su tipo y fuerza. En las correlaciones positivas,
se detectaron desde débiles a moderadas (0.31 a 0.48), destac=
ando
XB-P50 y E-P50 (ambas 0.48), las cuales evidenciaron tendencias claramente =
en
aumento y un agrupamiento notable de los puntos. Por otra parte, T/B-P50 (0=
.42)
y H/B-T/B (0.39) mostraron una concentración inferior. Respecto a las
correlaciones pequeñas (0.15 a 0.20), como S/B-H/B (0.16) y XB-E (0.=
20),
se observó una considerable dispersión. Dado que los coeficie=
ntes
de correlación van de mo=
derados a bajos, no existe una multicolinealidad significativa entre las variables. Por ello, se jus=
tifica
su uso en un modelo predictivo, donde se definen claramente los roles de
variable independiente y dependiente.
&nbs=
p;
Figura 3 Pairplot <=
/span>de los datos de entrada y salida
Los=
histogramas en diagonal del pairplot apoyaron este análisis, exhibiendo distribuciones asimétricas (S/B con se=
sgo
hacia la derecha), uniformes (H/B entre 2.5 y 5) y simétricas (XB
centrado en valores promedios). En situaciones de correlaciones negativas,
estas fluctuaron entre bajas (-0.22 a -0.45) y moderadamente altas (-0.60),
destacándose PF-B/D (-0.60) como la más robusta,
con una clara tendencia a la baja,
seguida por PF-P50
(-0.45) y PF-XB (-0.41).
Las relaciones débiles n=
egativas (B/D-T/B:
-0.10; T/B-PF: -0.03) exhibieron patrones
que se
&nb=
sp;
asemejan a la aleatoriedad; además, los histograma=
s destacaron características relevantes en la
distribución: B/D se concentra entre 20 y 40, T/B presenta un sesgo
hacia la izquierda y P50 tiene una distribución ajustada alreded=
or de un valor medio. Al exhibir patrones
que no siguen una l&ia=
cute;nea recta,
estos diagramas confirman la ausencia de una correlación lineal, lo cual justifica
plenamente la implementación de un modelo de IA para capturar la complejidad inherente de estas relaciones.<=
/span>
=
;
El gráfico de caja y bigotes (Figura
4) ilustra la distribución logarítmica de las variables S/B, H/B, B/D, T/B, PF, XB=
, E y
P50. En el caso de S/B, B/D y P50, existe una importante concentración, con cajas compactas; S/B presenta una mediana cercana a 10¹ y un rango limitado
(10⁰-10¹). En comparación, H/B, T/B, PF, XB y E
exhiben una dispersión más amplia. H/B presenta un 50 % centr=
al
extenso, con una mediana de 10¹, en tanto que T/B y XB exhiben amplios
rangos intercuartílico=
s y medianas próximas a 10⁰. Los valores atípicos de S/B, T/B y PF
(círculos) muestran
desviaciones importantes, lo que refleja la variabilidad presente en los datos.
&nbs=
p;
Figura 4 Diagrama de caja y bigotes
de las variables del<=
span
style=3D'letter-spacing:-.05pt'> estudio
Aunque los diagramas de caja resal=
tan la
variabilidad y la presencia de valores=
atípicos que sugieren comportamientos inusuales, est=
os son escasos y, por lo tanto, no afectan
significativamente al modelo,
obviando la necesidad
de un análisis especial. Esta variabilidad,
particularmente en P50 y el factor de pólvora, subraya la diversidad de reacciones de cada unidad
litológica a la explosión, lo que resalta
la importancia de desarrollar modelos
adaptativos para optimiz=
ar los
procesos mineros.
&nbs=
p;
Entrenamiento de los algoritmos de IA El entrenamiento de los tres model=
os de
IA revela las variaciones en su
habilidad para hacer predicciones (Figura 5). El modelo SVR (línea r=
oja)
muestra una gran consistencia, con valores de objetivo alrededor de 0.26 y sin cambios
significativos. Por otra parte, KRR (verde)
muestra valores cercanos
a cero, con un ligero
incremento al inicio,
permaneciendo casi cons=
tante, lo que indica
una reacción mínima. Por otro lado,
RF (azul) exhibe
una conducta más activa, con cambios destacados
y picos que sobrepasan el 0.60, logrando una mejor comprensión
de las variaciones del objetivo. En relación con los tiempos =
de
procesamiento, el modelo RF requiere 0.152 segundos para el entrenamiento y
0.254 segundos para la predicción. KRR es más eficiente, con un tiempo de entrenamiento de 0.296 segundos
y un tiempo de =
predicción
&nb=
sp;
de 0.154 segundos.
SVR, aunque se asemeja a=
KRR en su proceso de entrenamiento, requiere
0.506 segundos para realizar la predicción. RF=
se
caracteriza por su capacidad de adaptación, mientras que KRR y SVR proporcionan mayor estabilida=
d, aunque
son menos receptivos a las variacion=
es en
los datos.
&nbs=
p;
Figura 5 Comparación
del rendimiento de los modelos
de IA empleados
Por=
otra parte, en la Figura 6, el modelo KRR presenta un comportamient=
o más inestable y=
es muy
sensible a la cantidad de datos que se le suministran. Se pueden observar p=
icos
de error en los valores intermedios, particularmente cerca de las 20 muestras, donde el MSE excede
0.09. A<=
span
style=3D'letter-spacing:-.25pt'> pesar de que su desempeño pr=
esenta
una ligera mejora más adelante, nunca consigue igualar la precisión del SVR ni del RF, lo que sugiere modificaciones en su regularización o en
las funciones kernel que emplea.
Respecto al modelo
RF, muestra una trayectoria más variable, particularmente entre las 20 y 55 muestras, lo que podría indicar una inclinación al sobreajuste=
en
conjuntos pequeños o medianamente grandes. No obstante, a partir de =
las
60 muestras, el error se reduce considerablemente y se mantiene
alrededor de 0.025, convirtiéndose en uno de los más destacados en esa
sección del gráfico.
&nbs=
p;
Figura 6 Curvas
de aprendizaje de cada uno de los modelos empleados
En la Figura 7, el gráfico =
de la
izquierda (a) ilustra el MSE durante el entrenamiento. Se observa
que el modelo RF sobresale, alcanzando el<=
span
style=3D'letter-spacing:-.35pt'> menor
error con un valor de 0.0017638.
Por otro lado, el modelo KRR presentó el MSE más elevado, aproxim=
adamente 0.0116156, lo que sugiere que no se adaptó con la misma eficacia=
a
los datos de entrenamiento. El modelo =
SVR se encontró en una posición intermedia, con un MSE aproximado de 0.0064449. El gráfico
de la derecha (b) muestra
un conjunto de resultados que se alinean
con la métrica mencionada
anteriormente. El modelo
RF obtuvo el R2 más alto (95.38 %), lo que indica que este modelo
es capaz de explicar
una gran parte de la variación en los datos de entrenamiento. En contraste, el modelo
KRR presentó el valor de R2 más bajo, cercano a 69.60 %, que señala menor habilidad =
para
captar la varianza. Una vez más, el modelo SVR se situó en el
medio, obteniendo un R2 de 83.13 %.
=
;
Figura 7 Métricas de evaluación para el análisis de los algoritmos empleados <=
/o:p>
Evaluación La Figura 8 muestra la conexi&oacu=
te;n y
las discrepancias entre un grupo de valores reales y aquellos que se obtienen de la
ecuación Kuz-Ram, a lo largo de un índice de datos. Los valor=
es
reales, indicados con puntos grises, exhiben una disposición
predominantemente horizontal. En contraste, los valores estimados por la ec=
uación,
representados como puntos azules, normalmente siguen el mismo rumbo que los
valores reales en la mayor parte de los puntos de datos, permaneciendo cerca
del eje. No obstante, existe una marcada diferencia en algunos segmentos, particularmente entre los índices 30 y 40, donde la ecuación sugiere
valores que son considerablemente más eleva=
dos que los reales,
alcanzando máximo=
s que exceden los 2500 e incluso sobrepasando los 3500. Esta discrepancia pone de relieve la limitación del modelo
predictivo para entender
la dinámica =
esencial en esos puntos concretos, aunque, en la mayoría del conjunto de datos, la ecuación parece ajustarse con notable precisión a los valores
observados.
&nbs=
p;
La Figura 9 presenta una
comparación del desempeño de los tres algoritmos de aprendiza=
je
automático en la predicción de valores frente a los valores
reales. Se observa que los tres métodos de IA son capaces, en gran parte, de coincidir con los valores
reales, lo que indica que han logrado identificar algunas pautas en los dat=
os
fundamentales. No obstante, se pueden notar variaciones en su capacidad de
predicción; en ciertos segmentos del índice de datos, el mode=
lo
RF puede coincidir más estrechamente con los valores reales que los
otros, mientras que, en otros, se aprecia una desviación más
evidente. A medida que el índice de datos avanza, hay variaciones en=
la
precisión, con cambios que muestran las particularidades y habilidad=
es
específicas de cada algoritmo para generalizar a partir de los datos
utilizados en su entrenamiento.
&nb=
sp;
Figura 8 Comparativa=
entre los valores predichos por la ecuación Kuz-Ram y los valores reales
Figura 9 Comparativa entre los valores predichos por los modelos
IA y los valores reales
En la valoración de los modelos
de IA, la capacidad de adaptación y la eficiencia en el uso de computadoras son aspectos fundamentales que muestran una narrativa compleja
acerca del desempe&ntild=
e;o de RF, SVR y KRR. El modelo RF, similar
a un camaleón =
digital, muestra
una destacada habilidad para seguir el comportamiento de la variable
objetivo, variando de forma significativa y, en numerosas ocasiones, aproximándose con una notable precisión a los valores reales del proceso de fragmentación. Esta capacidad de predicción, demostrada por su mínimo MSE durante el proceso
de entrenamiento y un R2 que se aproxima a la perfección (cercano a 0.98), lo establece como un estándar en la
comprensión de la complejidad de los datos, alcanzando un porcentaje=
de
efectividad en el ajuste del 95 % o superior.
&nbs=
p;
No obstante, esta habilidad para
predecir implica un precio. Al
examinar las métricas temporales, el modelo RF es el más lent=
o en
la etapa de predicción, exhibiendo tiempos de ejecución
consistentemente más elevados que sus equivalentes SVR y KRR (supera=
ndo
10−2 segundos en la mayoría de los tamaños de entrenamiento=
), además de mostrar un mayor tiempo de ajuste en ciertos interval=
os. La
característica fundamental del RF, que analiza un conjunto de
árboles para efectuar cada predicción, conlleva una mayor nec=
esidad
de capacidad de procesamiento. En
situaciones donde la respuesta inmediata es esencial, esto podría
comprometer su funcionalidad práctica. =
Por lo tanto, RF hace que la predicción sea más comprensible al mostrar
la realidad: su debilidad se encuentra en el tiempo
que requiere para ofrecer sus pronósticos, un aspecto que no se puede ignorar =
en el
ámbito de una aplicación práctica en minería.
&nb=
sp;
Aplicación El buen desempeño de nuestr=
os
modelos de IA ha sido transform=
ado en
una solución tangible: una aplicación de software desarrollad=
a en
Python y Visual Studio Code. Esta herramienta práctica para predecir=
la
fragmentación de rocas ofrece una interfaz que logra, a travé=
s de
un botón, conectar los modelos entrenados, previamente guardados y
codificados en un archivo binario (.pkl), permitiendo que, al presionar el
botón, el sistema decodifique este archivo, reconstruyendo el modelo=
en
memoria para procesar los datos de entrada del usuario y realizar el c&aacu=
te;lculo
eficiente del tamaño medio de fragmentación de la roca. La Fi=
gura
10 muestra la interfaz del usuario,
que se estructura en tres vistas diferentes, cada una enfocada
en un aspecto esencial
del estudio de parámetros en voladura y la valoración de modelos de IA. Su diseño está conc=
ebido para promover la interacción con las personas,
con el propósito de hacer más comprensible la complejidad de los datos y los algoritmos, proporcionando una visi&oacu=
te;n
de la mente que subyace a la fragmentación de la roca.
=
;
En la primera pantalla (a), denomi=
nada
"Parámetros de Análisis", observamos un panel de
control bastante accesible que facilita enormemente la introducción =
de
datos para el usuario. Se tiene la posibilidad de cargar documentos que
contienen información específica sobre perforación y voladura.
Existen opciones como "Modo de Entrada", que aparenta señalar si la informaci&o=
acute;n es histórica o si corresponde a un diseño reciente, y "Opción", que sugiere una elección de diversos
escenarios de análisis, siendo “Opción 1”, la
relación de "Parámetros de Entrada" comprende variables esen=
ciales tales
como "S/B" (Relación Espaciamiento/Burden), "H/B" (Relación Alt=
ura
de banco/Burden) , “B/D” (Relación Burden/Diámetr=
o de
agujero), "PF" (Facto=
r de pólvora), "XB" (Tamaño d=
e bloque)
y "E" (Módulo de elasticidad)<=
span
style=3D'letter-spacing:-.1pt'> y “Opción
2” considerando las variables "B (m)" (Burden), "D
(m)" (Diámetro de agujero), "S (m)" (Espaciamiento),
"H" (Altura del banco), "T" (Taco inerte), "PF&quo=
t;
(Factor de pólvora), "XB" (Tamaño de bloque) y "E" (Módulo de elasticidad=
). Esta parte se presenta como la introducción de la interfaz,=
el
espacio donde el operador puede utilizar su comprensión del terreno =
y de
la voladura en el sistema. Asimismo, en la esquina superior derecha, se
encuentra una sección titulada “Parámetros de Entrada
Utilizados”, que proporciona conceptos breves sobre cada variable,
actuando como un glosario en el mismo lugar. Esto facilita la
comprensión de la terminología
técnica, permiti=
endo al usuario interactuar con mayor seguridad en el vocabulario del franqueo
de roca. Los "Parámetros de Patrones" y "Radios de Influencia Conceptual" ofrecen
un contexto adicional, definiendo las configuraciones habituales y las consecuencias espaciales de la voladura, lo cual r=
efleja
la realidad física de la mina.
&nbs=
p;
La segunda sección (b),
denominada "Visualizaciones", nos invita a descubrir el interesan=
te
ámbito de la comprensión espacial de los patrones de
perforación. En este lugar, podemos observar dos diagramas esquemáticos: uno que representa un "Patr&oa=
cute;n Rectangular (S vs B)" y otro que representa un "Patrón
Triangular (S vs B)". Estos gráficos, con radios de n metros, no solo ilustran
la disposición geométrica de la malla
de perforación,<=
span
style=3D'letter-spacing:-.35pt'> sino que también nos facilitan la
comprensión de la "Influencia en Malla Rectangular" e
"Influencia en Malla Triangular" mediante representaciones de la
fragmentación conceptual. Esta parte es un claro ejemplo de có=
;mo
la interfaz funciona como un traductor visual: transforma cifras y concepto=
s en
imágenes que un ingeniero puede entender y con las que puede interac=
tuar
en su mente. La habilidad de ob=
servar
el impacto de la malla es fundamental, ya que permite al usuario entender
rápidamente cómo la organización de los barrenos influ=
ye
en la distribución de la energía
explosiva y, por lo tanto, en la fragmentación. En este punto, la abstracción matemática se convierte en algo concreto.
&nb=
sp;
Figura 10 Interfaz <=
/span>gráfica de la aplicación y ejemplo de cálculo del tamaño medio de fragmentación
Finalmente, la tercera
vista (c), "Predicciones", representa el punto más importante del p=
roceso de análisis, en el que los modelos
de IA presentan sus conclusiones. A continuaci&o=
acute;n, se muestra un gráf=
ico de barras titulado
"Comparación de Métricas de Modelos (R2 y MSE)",<=
span
style=3D'letter-spacing:-.45pt'> que resume el rendimiento de los modelos SVR, KRR y RF. En esta plataforma, los datos estadísticos
se presentan de manera visualmente atractiva: el modelo RF se destaca
como el mejor en R2 , alcanz=
ando aproximadamente 0.98, y exhibe un MSE notablemente bajo, lo que sugiere un ajuste
&nb=
sp;
casi
ideal a los datos de entrenamiento. SVR presenta un R2 de aproximadamente 0.8, mientras
que KRR se encuentra ligeramente rezagado. Este<=
span
style=3D'letter-spacing:-.05pt'> panel
funciona como la decisión del jurado
algorítmico, permitiendo al usuario reconocer de manera rápida
qué modelo ha demostrado ser <=
/span>el más efectivo para<=
span
style=3D'letter-spacing:-.05pt'> predecir
la fragmentación=
. Más adelante, la parte
titulada "Resultad=
os
Detallados" proporciona un análisis más exhaustivo de las
predicciones, exhibiendo "Valor Predicho" de P50,
"Desviación Estimada" y "Confianza", lo que
proporciona una dimensión adicional de interpretación y permi=
te
al usuario comprender el pronóstico.
&n=
bsp;
Conclusiones Este estudio ha demostrado la implementación de los algoritmos Forest (RF), Sup=
port
Vector Regressor (SVR) y Kernel Ridge Regressor (KRR) para la predicci&oacu=
te;n
de la fragmentación óptima de la roca en minería, lo q=
ue
mejora considerablemente la eficiencia operativa. Los resultados=
indican
que RF superó =
a los demás en términos de precisión, logrando un error cuadr&aa=
cute;tico medio
bajo que ronda
el 0.13 % y un valor R²
cercano a los valores objetivo del conjunto de datos.
=
;
El mejor desempeño de los m=
odelos
de IA y su habilidad para capt=
urar
las complejas interrelaciones entre los parámetros de perforación y voladura (espaciamiento, burden, diámetro
de agujero, altura de banco y taco de estéril), de la roca
(módulo de elasticidad) y el tamaño medio de los fragmentos
(P50), demuestran que son una alternativa más conveniente que el
método de estimación convencional.
&nbs=
p;
Los bajos valores
de MSE obtenidos por los modelos de IA confirman que los factores geotécnicos y opera=
tivos
son predictores válidos para la fragmentación de las rocas. E=
ste hallazgo
es relevante, ya que demuestra la capacidad de los modelos para manejar la variabilidad
inherente a la composición litológica. Además, =
la
matriz de correlación muestra conexiones significativas, como la relación inversa entre el factor de pólvora y la relación carga/diámetro, =
el módulo de elasticidad o el tamaño promedio de fragmentación (P50), indicando que un mayor uso
de pólvora tiende a reducir estos valores.
&nbs=
p;
Se resalta la importancia de conta=
r con
una aplicación que convierta resultados complicados de modelos
de IA en información comprensible. Mostrar gráficos de fragmentación
y previsiones, permite a los usuarios trabajar con datos, simular
situaciones de voladura y modificar parámetros geotécnicos,
asistiendo a estudiantes y profesionales sin necesitar conocimientos profun=
dos
en decisiones cotidianas en minería.
&nbs=
p;
Si bien los modelos presentados han
demostrado su eficacia, su rendimiento podría optimizarse al aumenta=
r la
calidad y la cantidad de los datos de entrenamiento. Aunque la recolección de datos asociados con el uso de explosivos es un desafío por la escasa accesibilidad
y la alta sensibilidad, se sugieren indicadores clave de desempeño (KPI) del proceso de voladura,
el precio del material
(USD/Ton) y los gastos que conlleva extraerlo. Además, el resultado P50 se puede complementar con sus homólogos =
P20 y
P80, permitiendo trazar una curva granulométrica aproximada.
&nbs=
p;
Fin=
almente, los estudios futuros pueden identificar y caracterizar =
otros factores influyentes para la fragmentación (ej.=
RMR,
Q de Barton) ligados al tipo de roca, lo cual es esencial para mejorar los diseños de voladuras, minimizar la incertidumbre=
y garantizar resultados fiables en las
operaciones mineras.
&nb=
sp;
Reconocimientos y Declaraciones Los=
autores declaran que, en la elaboraci&oa=
cute;n de este artíc=
ulo, se han utilizado las siguientes =
herramientas
de inteligencia artificial: Research Rabbit (versión 2025), Consensus
(versión 2025) y Elicit
(versión 2025).<=
span
style=3D'letter-spacing:-.45pt'> Consensus y Elicit se usaron para encontrar respuestas y resumir artículos científicos, ayudando en la recopilación de información bibliográfica. Research Rabbit
se usó para encontrar documentos relacionados y construir map=
as
de citaciones, optimizando la revisión de literatura.
=
;
Los autores declaran
la contribución y participación equitativa de roles de autoría para esta publicación.=
&nb=
sp;
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letter-spacing:-.1pt'>of <=
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letter-spacing:-.1pt'>blasting <=
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letter-spacing:-.1pt'>mean <=
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Raj, A. K., <=
span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>Choudhary, B. <=
span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>S., & <=
span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>Deressa, G. <=
span
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03%;
letter-spacing:-.1pt'>W. (2024). <=
span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>Prediction of <=
span
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03%;
letter-spacing:-.1pt'>Rock Fragmentation <=
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lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>for Surface <=
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span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
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letter-spacing:-.1pt'>learning <=
span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>approach <=
span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>to <=
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lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>predicting <=
span
lang=3DES style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:1=
03%;
letter-spacing:-.1pt'>the <=
span
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9
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