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Prediction of soaked CBR of fine-grained soils using soft computing techniques

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Abstract

The present research determines the effect of training data sets, correlation, and multicollinearity on the performance and overfitting of gene expression programming (GEP) and relevance vector machine (RVM) models in predicting the soaked CBR of fine-grained soil. For this purpose, one hundred and 82 training data sets have been compiled and subdivided into 50%, 60%, 70%, 80%, 90%, and 100%. In addition, 15 testing, 36 validation, and 12 laboratory-tested data sets have been compiled for trained models. The linear, polynomial, gaussian, and Laplacian kernels have been used to develop each GA and PSO optimized relevance vector machine (RVM) model, which have been trained by 50–100% training data sets. Thus, SRVM (single kernel-based) and HRVM (dual kernel-based) models have been developed and trained. The performance of models has been measured by RMSE, MAE, and R performance indicators. Based on the performance comparison, Model 21 (R = 0.9874) & Model 39 (R = 0.9748) of SRVM, and Model 51 (R = 0.9606) and Model 57 (R = 0.9701) of HRVM have been identified as better performing RVM models. However, GEP model 62 has performed (R = 0.8847) less than RVM models. The test performance comparison shows that model 21 has outperformed models 39, 51, 57, and 62 in predicting the soaked CBR of fine-grained soil. In addition, model 21 (performance = 0.8631) has predicted soaked CBR for the validation data set better than published models. Finally, the present research concludes that model 21 (GA optimized Laplacian kernel-based SRVM model) is a robust model that can predict the soaked CBR of fine-grained soil with the least prediction error and high performance.

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Data availability

All data, models, and code generated or used during the study appear in the submitted article. The laboratory-test database can be provided on the request.

Abbreviations

AI:

Artificial intelligence

ANN:

Artificial neural networks

C:

Clay content

CBR:

California bearing ratio

CC :

Coefficient of curvature

CL:

Confidence level

CL:

Inorganic clays of low plasticity

CS:

Coarse sand

C U :

Coefficient of uniformity

D 10 :

Particle size at 10% fine

D 30 :

Particle size at 30% fine

D 50 :

Particle size at 50% fine

D 60 :

Particle size at 60% fine

DCP:

Dynamic cone penetration

DUW:

Dry unit weight of soil

FC:

Fine content

FD:

Frequency distribution

FS:

Fine sand

FSI:

Free swell index

G:

Gravel content

GA:

Genetic algorithm

GEP:

Gene expression programming

GMDH-NN:

Group method of data handling neural network

HRVM:

Hybrid/two kernel-based relevance vector machine

IS:

Indian Standards

LL:

Liquid limit

M:

Silt content

MAE:

Mean absolute error

MDD:

Maximum dry density

MLR:

Multiple linear regression

NUW:

Natural unit weight of soil

OC:

Organic content

OMC:

Optimum moisture content

OWC:

Optimum water content

PI:

Plasticity index

PL:

Plastic limit

PSO:

Particle swarm optimization

R :

Correlation coefficient

R 2 :

Coefficient of determination

RMSE:

Root mean square error

RVM:

Relevance vector machine

S :

Sand content

SPSS:

Statistical package for the social sciences

SPT-N:

Standard penetration test number

SRVM:

Single kernel-based relevance vector machine

St. Dev:

Standard deviation

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  1. Department of Civil Engineering, Rajasthan Technical University, Kota, Rajasthan, 324010, India

    Jitendra Khatti & Kamaldeep Singh Grover

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  1. Jitendra Khatti
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JK: main author, conceptualization, literature review, manuscript preparation, application of AI models, methodological development, statistical analysis, detailing, and overall analysis; KSG: conceptualization, manuscript finalization, detailed review and editing.

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Correspondence to Jitendra Khatti.

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Khatti, J., Grover, K.S. Prediction of soaked CBR of fine-grained soils using soft computing techniques. Multiscale and Multidiscip. Model. Exp. and Des. 6, 97–121 (2023). https://doi.org/10.1007/s41939-022-00131-y

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