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Comparación de los algoritmos random<= /span> forest y gradient boosting para una estimación global del índice de compresión

Comparison= of random forest and gradient boosting algorithms for global compression r= atio estimation

Comparação de algoritmos de floresta aleatória e de aumento= de gradiente para esti= mativa da taxa de compressão global

 = ;

RESUMEN

=
El asentamiento de las estructuras está determinado por la rigidez del sue= lo donde se construyen. El índice de compresión (Cc) cuantifica la compresibilidad del suelo y es un parámetro clave en el diseño de estructuras geotécnicas, por lo que desarrollar un modelo de Machine Learning para estimar el índice de compresión Cc podría ser una solución muy valiosa en el campo de la geotecnia que permitiría a los ingenieros obtener estimaciones rápidas y fiables sin = la necesidad de esperar los 15 días que generalmente tarda un ensayo de consolidación. Por lo tanto, la presente investigación tiene como objet= ivo estimar el índice de compresión, por lo que se recopiló y analizó una b= ase de datos de 230 puntos de datos obtenidas del Laboratorio Nº2 de Mecáni= ca de Suelos de la Facultad de Ingeniería Civil de la UNI. Se comparó dos modelos de Machine Learning basado en Random Forest (RF) y Gradient Boosti= n Machine (GBM) para estimar el Cc a partir d= e las variables de entradas las cuales son límite líquido, el índice de plasticidad, relación de vacíos inicial y el contenido de agua natural.= Los resultados indicaron que el modelo más adecuado para estimar el Cc fue el random forest que tuvo menores errores en la fase de ent= renamiento y prueba con respecto al GBM; para optimización de hiperparámetros se utilizó el método de grid search con validación cruzada.

=  

= Palabras claves: Machine Learning, Índice de compresión, Límite líquido, Índice de plasticidad, Contenido de agua natural y relación de vacíos inicial.

=  

RESUMO

=
O recalque das estruturas é determina= do pela rigidez do solo onde são construídas. A taxa de compressão (Cc) quantifica a compressibilidade do solo e é um parâmetro-chave no pro= jeto de estruturas geotécnicas, portanto, desenvolver um modelo de aprendizado de máquina para estimar a taxa de compressão Cc pode se= r uma solução muito valiosa no campo da geotecnia, que permitiria aos engenheiros obter est= imativas rápidas e confiáveis s= em a necessidade de esperar os 15 dias que um teste de = consolidação geralmente leva. Portanto, a presente pesquisa tem como objetivo estimar o índice de compressão, para o qual foi= coletado e analisado = um banco de dados de 230 pontos de dados obtidos no Laboratório de Mecânica dos Solos = 2 da Faculdade de Engenharia Civil da UNI. Dois modelos de aprendizado de máquina baseados em Random Forest (RF) e Gradient Boosting Machine (GBM) foram comparados para estimar= o Cc a partir das variáveis de entrada que são limite= de liquidez, índice de plasticidade, índice= de vazios inicial e teor= de água natural. Os resultados = indicaram que o modelo mais adeq= uado para estimar o Cc foi<= /span> o random forest, = que apresentou menores erros na<= /span> fase de treinamento e teste quando comparado ao GBM; Para otimização de hiperparâmetros, fo= i utilizado o método de busca em grade com validação cruzada.

=  

= Palavras<= /b>-chave: Aprendizado de máquina, índice de compressão, limite de liquidez, índice de plasticidade, teor de água natural = e índice de vazios inicial.=

Recibido 02 de Mayo 2025 | Arbitrado y aceptado 02 de Junio 2025 | Publicado el 16 de Julio 2025=

ABSTRACT=

=
The settlement of structures is determined by the stiffness of the soil on which they are built. The compression index (Cc) quantifies soil compressibility and i= s a key parameter in the design of geotechnical structures. Therefore, developing a Machine Learning model to estimate the compression index Cc could be a highly valuable solution in the field of geotechnics, allowi= ng engineers to obtain quick and reliable estimates without having to wait= the typical 15 days required for a consolidation test. Accordingly, the pre= sent study aims to estimate the compression index by compiling and analyzing= a dataset of 230 data points obtained from Soil Mechanics Laboratory No. = 2 of the Faculty of Civil Engineering at UNI (FIC-UNI). Two Machine Learning models—Random Forest (RF) and Gradient Boosting Machine (GBM)—were comp= ared to estimate Cc using input variables including liquid limit, plasticity index, initial void ratio, and natural water content. The results indic= ated that the Random Forest model was more suitable for estimating Cc, achie= ving lower error values in both training and testing phases compared to GBM. Hyperparameter optimization was performed using the grid search method = with cross-validation.

=  

= Keywords<= /b>: Artificial intelligence, XGBoost, Soil mechanical= properties, Roads

=  =

ARTÍCULO ORIGINAL

Jaime Yelsin Rosales Malpartida

jrosalesm@uni.pe

https://orcid.org/0000= -0003-4574-5172

Facultad de Ingeniería Civil

Universidad Nacional de Ingeniería, L= ima, Perú

César <= span class=3DSpellE>Loo Gil

cesarloo@biofab.com.pe

https://orcid.org/0000= -0001-8396-5972

Científico Investigador de Biofab Inc. y del Centro de Investigación y Producción Científica IDEOs, Lima - Perú<= o:p>

 

 

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1.     INTRODUCCIÓN

El índice de compresibilidad (Cc) que es obtenida del gráfic= o e vs Logσ’, y el coeficiente de consolidación (= cv) que es obtenida del gráfico δ vs √t, d= efinen primordialmente las propiedades de compresibilidad de los suelos de grano f= ino. (Craig 2004). El comportamiento de la compresibilidad y deformación bajo ca= rga de un suelo es muy usado en la ingeniería geotécnica para estimar el asentamiento y la deformación de estructuras del suelo, como cimientos y terraplenes (Das, 2021). Los suelos con un cc m= ás alto tiende a ser más compresibles y deformables bajo carga, mientras que l= os suelos con un cc más bajo son menos compresible= s y tienen una mayor capacidad para soportar la deformación cuando están cargad= os. Ambos valores cc y cv son determinados a partir de ensayos edométricos en= la primera representa la pendiente de la parte líneas de la curva de compresió= n en un gráfico antes mencionado y en la segunda la tasa de cambio del asentamie= nto con respecto al tiempo. Estos parámetros de estado se han utilizado para establecer correlaciones con diferentes propiedades de la ingeniería en los suelos. Además, la plasticidad está influenciada por el comportamiento electroquímico de minerales arcillosos (Carter y Bentley, 1991).=

2.     ANTECEDENTES

Hay diversos a= utores que proporcionaron ecuaciones lineales que relacionan = Cc con el límite líquido (LL) de suelos (como, Azzouz et al., Bowles, 1979; Park y Lee, 2011; Sridharan = y Nagaraj, 2000; Terzaghi et al., 1967; Tsuchida, 1991). Por otro lado, el índice de plasticidad (PI), también se relaciona c= on cc (por ejemplo, Sridharan y Nagaraj, 2000; Wroth and = Wood, 1978). Además, muchas correlaciones basado en una relación lineal con el contenido de agua natural (w) fueron propuestos (por ejemplo, Azzouz et al., 1976; Koppula, 1981; Rendon-Herrero, 1980).

Se analizó la relación con la relación de vacíos inicial e0 por Nish= ida (1956), Hough (1957) y Bowles (1979). Otros est= udios incluyeron más de una propiedad índice en la estimación de cc , como w y LL (Koppula, 1981) o e0 y LL (Al-Kha= faji y Andersland, 1992). Sin embargo, cuando estas correlaciones se probaron con nuevos datos, mostraron una dispersión significativa, con desviaciones que alcanzaron el 30% (Spagnoli y Shimobe, 2020), lo que nos hace pensar en una= falta de universalidad y validez aplicable. Sin embargo, son aplicables dentro de límites específicos y deben estar restringidos al tipo de suelo o ubicación donde fueron validados (Verbrugge y Schroeder, = 2018). Utilizando estas correlaciones en diferentes condiciones pueden conducir a resultados insatisfactorios (Onyejekwe et al., = 2016).

Para abordar l= os límites de los enfoques de regresión clásicos en ingeniería geotécnica, la aplicación de algoritmos de aprendizaje automático (ML) se han desarrollado ampliamente demostrando un rendimiento mejorado para predecir varias propiedades de ingeniería del suelo en comparación a los métodos estadístic= os tradicionales (por ejemplo, Dam Nguyen et al; <= span class=3DSpellE>Bardhan et al., 2023; 2022 Díaz y Tomás, 2021; Singh = et al, 2023). Sin embargo, es de suma importancia ser consciente de las limitacion= es e incertidumbres asociadas con enfoques de ML antes de aplicarlos a la geotec= nia de proyectos de ingeniería en el mundo real. Numerosos estudios (Baghbani et al., 2022; Zhang et al., 2023) han expues= to estas limitaciones, que son principalmente: a) la escasez de datos de alta calidad, b) la dificultad para interpretación de los modelos, y c) la falta= de generalización. Muy aparte también para la disponibilidad de datos, estos pueden llegar a ser muy costosos y a menudo incompletos o inciertos.

Esto puede lle= var a modelos de ML que no sean tan precisos o confiables como se desea. Otra limitación del ML es la interpretabilidad de los modelos. Los modelos de ML suelen ser complejos y no lineales, lo que dificulta comprender la relación entre los datos de entrada y predicciones de salida. Finalmente, debido a la heterogeneidad inherente y variabilidad espacial de los depósitos del suelo= , es difícil para los modelos empíricos capacitado en conjuntos de datos limitad= os para extrapolar de manera confiable más allá del ámbito geográfico represen= tado por esos datos. Por lo tanto, mientras ML muestra gran potencial para complementar los enfoques tradicionales en ingeniería geotécnica, es crucial abordar estas limitaciones antes de la implementación de cualquier modelo de ML.

Recientemente, numerosos estudios han empleado algoritmos de ML para predecir cc de algunos parámetros relacionados con esta propie= dad que se muestran prometedores resultados (por ejemplo,  Desai et al., 2009; Kalantary y Kordnaeij, 20= 12; Kurmar y Rani, 2011; Nesamatha y Arumairaj, 20= 15.

Por otro lado,= Alam et al. (2014) construyó una base de datos de 125 muestras de arcilla, donde incluyó w, LL, e0 y PI como variables de entrada y creó un modelo de red neuronal artificial (RNA) para predecir Cc. Kum= ar y Rani (2011) también utilizó una RNA para predecir cc considerando 41 muestras con las siguientes variab= les de entrada: contenido fino, LL, PI, densidad seca máxima y óptimo contenido de humedad. Por otra parte, Park y Lee (2011) desarrollaron una RNA utilizando= 947 pruebas de consolidación realizadas en muestras de suelo recolectadas de 67= zonas de construcción en la República de Corea, y consideraron variables de entra= da como w, LL, PI, e0, gravedad específica de partículas del suelo (Gs), y porcentaje en peso de arena, limo y arcilla. Benbouras= et al. (2019) desarrollaron un modelo RNA con 373 edómetros, muestras de pr= ueba para correlacionar cc con densidad húmeda, w, e= 0, contenido fino, LL, PI, y tipo de suelo.

Zhang et al. (= 2021) utilizaron un algoritmo de random forest utilizando una base de datos de 311 muestras con tres variables de entrada = (LL, PI, e0).

Cabe mencionar= que la relación de vacíos en LL es un parámetro que no suele estar disponible en las fases de diseño de proyectos geotécnicos, mientras que e0 se encuentra = con mayor frecuencia. Todos los estudios presentados confían en un conjunto de datos limitado o las muestras recolectadas tienen una naturaleza local, es decir que provengan de la misma zona o país. Por lo tanto, el objetivo principal de este trabajo es encontrar el mejor algoritmo entre Gradient Boosting machine= y Random Forest basado en un conjunto de datos con 230 muestras. El presente artículo aprovechó los estudios de conjunto, para desarrollar y validar un modelo de predicción para estimar el índice de compresión de suelos para 230 datos recopilados por muestras recogidos de diversos proyectos ejecutados en Perú en el Laboratorio de Mecánica de Suel= os de la Facultad de Ingeniería Civil de la Universidad Nacional de Ingeniería= .

3.     Metodología

a.     Base de datos experimental

La recopilació= n del conjunto de datos es el primer paso en la construcción de un modelo de Mach= ine Learning (ML). En el presente trabajo, la base de datos experimental de cc (230 muestras) son datos propios del autor correspondientes a las muestras generadas en el Laboratorio de Ingeniería Geotécnica de la Facultad de Ingeniería Civil en la Universidad Nacional de= Ingeniería. Se pudo apreciar que la base de datos tiene suelos desde baja plasticidad h= asta alta plasticidad. De hecho, LL oscila entre 20% y 88% e IP entre 3% y 54%. = Por otro lado, la base de datos incluía suelos con alta compresibilidad y suelos con baja compresibilidad según valores de  (que van desde 0.295 a 1.425= ). Este hecho también se corrobora al examinar los valores de Cc variando estos entre 0.009 y 0.438. Finalmente, los valores de w, también varían ampliamente, desde el 1.18% hasta 50.7%. Con base en todo lo anterio= r, la base de datos incluye una cantidad considerable de datos, haciéndolo adecuado para un estudio provisional. El conjunto de datos final se puede encontrar en tabla s1 (accesible en línea), que incluye detalles como referencias, tipos de suelo, mineralogía y origen cuando estén disponibles.=

La figura 1 mu= estra diagramas de caja para LL, IP, e0 , w y cc de la base de datos. Los gráficos se utilizan para visualizar la dispersión de los datos, que se dividió en cuartiles; esto se utiliza para detectar valores atípicos, simetría de datos, dispersión y asi= metría (Reagan y Kiemele, 2008). El cuadro en un diagr= ama de caja muestra el rango intercuartil (IQR), donde= la parte inferior y superior del cuadro representan los percentiles 25 y 75, respectivamente. La altura de la caja representa el rango intercuartil. Los valores atípicos se definen como puntos de datos que se extienden hasta 3xIQR (Reagan y Kiemele, 2008). Algunos puntos = en la Fig. 1 se identifican como valores atípicos, que corresponden principalment= e a valores elevados de las variables; este análisis revela el rango de variaci= ón y la elevada dispersión de las variables estudiadas, en clara relación con el carácter mundial de la base de datos compilada. Para una mejor interpretaci= ón de la Fig. 1, se pueden apreciar los datos incluidos en la Tabla I.

 

 

Fig. 1. Diagra= mas de caja de las variables consideradas.

Tabla I

Estadística descriptiva de los datos analizados

 

LL (%)

IP (%)

W (%)

e0

Cc

Muestra

230

230

230

230

230

Media

43.86

18.46

22.63

0.79

0.21

Desviación estándar

14.81

11.49

9.69

0.20

0.08

Mínimo

20

3

1.18

0.295

0.009

Percentil 25

32

9.53

15.8

0.65

0.163

Mediana

40

16

23.15

0.7855

0.2075

Percentil 75

52.75

26

27.9

0.91

0.249

Máximo

88

54

50.7

1.425

0.438

b.     Proceso de selección de modelo

Según el análi= sis de datos realizado en el anterior apartado, todos tienen la misma cantidad de datos (230). En este caso no se usó la técnica llamada imputación de datos = más que para el análisis de datos atípicos, la cual es una técnica ampliamente utilizada en algoritmos de ML para tratar con valores faltantes y ha sido utilizado en temas geotécnicos satisfactoriamente, por = ejemplo Aydin et al., 2023; Díaz et al., 2023.

Luego se reali= zó un análisis de detección de valores atípicos, utilizando el algoritmo SVM de u= na clase desarrollado por Scholkopf et al. (1999) y empleado con éxito en trabajos similares (por ejemplo Díaz et al., 2023). Este algoritmo es un método diseñado para identificar valores atípicos y anomalías dentro de un conjunto de datos, utilizando los principios de las máquinas de vectores de soporte tradicionales (SVM).=

Los valores at= ípicos son valores que se destacan significativamente del resto de los datos de un conjunto de datos. Pueden indicar una variabilidad extrema, errores de medi= ción o, en algunos casos, fenómenos únicos que merecen especial atención. Identificar estos valores atípicos es importante porque pueden distorsionar= los resultados estadísticos, como medias y varianzas, y afectar la validez de l= as conclusiones. Estos valores se identificaron con el diagrama de caja, que visualiza la distribución de un conjunto de datos. Los valores atípicos generalmente se representan como puntos aislados fuera de los “bigotes” del diagrama de caja. Los bigotes suelen extenderse hasta 1.5 veces el rango intercuartil (IQR) de los cuartiles ( Q1 y Q3).

El proceso de selección de algoritmo de Machine Learning se llevó a cabo utilizando la técnica de validación cruzada de k veces (con k=3D5). Los algoritmos fueron realizados con Random Forest Regressor (Ho, 1995) y Gradient Boos= ting Regressor (Friedman, 2001). <= /p>

Este proceso se realizó con las variables sin normalización. Pero cabe señalar que el mismo proceso de selección de algoritmos también se realizó la normalización de l= as variables mediante el método min-máx método, que escala cada variable individualmente entre cero y uno. Los resultados de es= te proceso de normalización de las variables, fueron exactamente lo mismo en a= mbos modelos con mejor desempeño.

c.      Desarrollo de modelos

Para garantiza= r una adecuada generalización de los algoritmos, es buena práctica evaluar su desempeño con datos desconocidos. Para este propósito, el conjunto de datos se dividió en= dos grupos (entrenamiento y prueba) con una partición 80% y 20% respectivamente= . luego ambos algoritmos con mejor desempeño fueron sometidos a un proceso de ajust= e de sus hiperparámetros para maximizar su desempeño= . Para ello se utilizó la optimización de Grid search con validación cruzada (Yang L. y Shami A, 2020), esta técnica evalúa todas las combina= ciones posibles de hiperparámetros en una cuadrícula predefinida y realizar múltiples rondas de validación para cada combinación= . Los resultados de esta optimización están en la tabla V, en términos RMSE, MAE,= MAPE y , con el resultado tanto en el conjunto de entrenamiento como en el d= e la prueba.

Tabla II.=

Matriz de correlación de las variables consideradas.

 

LL (%)

IP (%)

e0

W (%)

Cc

LL (%)

1.00

 

 

 

 

IP (%)

0.93

1.00

 

 

 

e0

0.41

0.29

1.00

 

 

W (%)

0.46

0.38

0.75

1.00

 

Cc

0.33

0.29

0.65

0.49

1.00

 

Fig. 2. Gráfic= os de dispersión e histogramas de distribución de las variables.

4.     ANÁLISIS DE RESULTADOS

a.     Estimación del índice de compresión (Cc ).

En las tablas III y IV se muestran los hiperparámetros de los algoritmos de Gradi= ent Boosting Machine y Random<= /span> Forest respectivamente optimizados con el método Grid<= /span> Search con validación cruzada considerando las variables de límite líquido, el índice de plasticidad, relación de vacíos inicial y el contenido de agua natural para estimar el Cc.

TABLA III

Hiperparámetros ajustados u optim= izados de Gradient Boosting Machine para estimar el índice de compresibilidad.

Parámetros

Descripción

Valor

Rango

leargning_rate

Para reducir el paso de gradiente

0.01

0.01-0.1

max_depth

Profundidad del árbol

3

 1 - 5

n_estimators

Construir el máximo número de árboles posible.

200

100-300

min_samples_split

número mínimo de muestras que se requieren para divi= dir un nodo en un árbol de decisión.

2

 2-10

min_samples_leaf

Número mínimo de muestras que un nodo hoja debe tener después de que se realice una división.

1

 1-4

subsample

Proporcion de muestras de entrenamiento que se utilizan para entrenar cada árbol.

0.8

0.8-1

TABLA IV

Hiperparámetros ajustados u optim= izados de Random forest pa= ra estimar el índice de compresibilidad.

Parámetros

Descripción

Valor

Rango

max_depth

Profundidad del árbol

3

 1 - 30

n_estimators

Construir el máximo número de árboles posible.

200

100 - 300

min_samples_split

número mínimo de muestras que se requieren para divi= dir un nodo en un árbol de decisión.

5

 2-10

min_samples_leaf

Número mínimo de muestras que un nodo hoja debe tener después de que se realice una división.

2

 1-4

Bootstrap

Proporcion de muestras de entrenamiento que se utilizan para entrenar cada árbol.

1

 1 - 0

De tabla V se determinan los valores de las métricas de desempeño (RM= SE, MAE, MAPE y ) para el Cc, mediante el algoritmo Gradie= nt Boosting Machine y Random<= /span> Forest para el escenario de entrenamiento (training) y escenario de prueba = (testing). Se pudo apreciar que en el escenario de entrenamiento y prueba el modelo Random<= b> Forest tuvo un =3D 0.74 y =3D 0.38 respectiv= amente, para el Gradient Boosting<= /span> Mahcine se pudo apreciar que en el escenario de entrenamiento y prueba se tuvo un =3D 0.67 y = =3D 0.33 respectiv= amente; y dado que los valores de RMSE, MAE y MAPE para el escenario de entrenamien= to y prueba son menores ligeramente para RF con respecto al GBM, por lo tanto, se concluye que es el mejor modelo para estimar el índice de compresión Cc para el presente estudio.

Tabla V.<= /o:p>

Resumen de las métricas de rendimiento.

Modelo

Conjunto

RMSE

MAE

MAPE

Random Forest

Training

0.039

0.030

31.811

0.74

Test

0.060

0.042

38.056

0.38

Gradient Boosting Machine

Training

0.046

0.036

35.725

0.67

Test

0.062

0.043

38.585

0.33

&= nbsp;

CONCLU= SIONES

REFERE= NCIAS

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Financiamiento de la investigación

Con recu= rsos propios.

&nb= sp;

Declaración de intereses

Declaro = no tener ningún conflicto de intereses, que puedan haber influido en los resultados obtenidos o las interpretaciones propuestas.

&nb= sp;

Declaración de consentimiento informa= do

El estud= io se realizó respetando el Código de ética y buenas prácticas editoriales de publicación.

&nb= sp;

Derechos de uso

Copyrigh= t© 2025 por Jaime Yelsin Rosales Malpartida, César Loo Gil

Este texto está protegido por la Licencia Creative <= span class=3DSpellE>Commons Atribución 4.0 Internacional.

&nb= sp;

Usted es= libre para compartir, copiar y redistribuir el material en cualquier medio o form= ato y adaptar el documento, remezclar, transformar y crear a partir del material para cualquier propósito, incluso comercialment= e, siempre que cumpla la condición de atribución: usted debe reconocer el créd= ito de una obra de manera adecuada, proporcionar un enlace a la licencia, e ind= icar si se han realizado cambios.  Puede hacerlo en cualquier forma razonable, pero no de forma tal que sugiera que tiene el apoyo del licenciante o lo recibe por el uso que hace.

 

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Estrate= gias didácticas y la comunicación, en los niños  y niñas de 5 años de la Villa Monte Castillo: Catacaos, Piura, Perú

&nbs= p;

Jaimin<= /span> Murillo Antón, Salomón Vásquez Villanueva 

Comparación de los algoritmos random forest y gradient boosting para una estimación global del índice de compresión

Jaime Yelsin Rosal= es Malpartida, César Loo Gil

=  

 

 PAGE   \* MERGEFORMAT 2

TecnoHu= manismo. Revis= ta Científica

Vol. 1,  No. 3,= Abril 2021

TecnoHumanismo= . Revista Científica<= o:p>

Vol. 5, No. 1, Febrero - Abril 2025

 

2<= /span>

 

 

Revista Científica TecnoHumanismo

https://tecnohumanismo.online

 Febrero - Abril 2025

Volumen 5 / No. 1
ISSN: 2710-2394

pp.

 

 147 - 162

 

 

TecnoHumanismo= . Revista Científica<= o:p>

Vol. 5, No. 1, Febrero - Abril 2025

2<= /span>

 

 

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