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Utilization of Support Vector Models and Gene Expression Programming for Soil Strength Modeling

  • Research Article-Civil Engineering
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Abstract

The subgrade strength of roads and highways is based on the California bearing ratio (CBR) value. In this investigation, attempts have been made to overcome the limited boundary condition approach by using advanced methods, support vector machine (SVM) and gene expression programming (GEP) for prediction of CBR value. A large and wide range of datasets of different types of soils have been utilized in the analysis. The grain size distribution, Atterberg’s limits and compaction characteristics of soils have been used as the input variables. Best models with different variables were developed by using GEP and the same were used for SVM analysis. The advantage of SVM over others is that it works on the principle of statistical risk minimization. A comparative study of SVM and GEP models indicates that the SVM has better predictability than GEP. Further, it was found that the five-input variable (including gravel content, sand content, plasticity index, maximum dry density and optimum moisture content) model is the best one to predict the CBR value. The detailed statistical analysis including Pearson coefficient correlation (R) and Error analysis have also been carried out. Based upon the statistical analysis, overfitting ratio of SVM was found to be 0.630 against the value of 1.02 in GEP analysis. Further, sensitivity analysis was carried out and it was found that the CBR value is highly dependent on gravel and sand contents. On the other hand, plastic limit plays an insignificant role in determining the CBR value of soils.

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Abbreviations

%E :

Percentage error (%)

ANFIS:

Adaptive network-based fuzzy inference system

ANN:

Artificial neural network

b :

Scalar threshold

BIS:

Bureau of Indian standards

C :

Cost or margin

CBR:

California bearing ratio

CBRExpt :

Experimental California bearing ratio

CBRPred :

Predicted California bearing ratio

CF:

Coarse fraction (G + S)

C u :

Coefficient of uniformity

d :

Degree of polynomial

e :

Loss

ERM:

Empirical risk minimization

ET:

Expression tree

F :

Functional set

FC:

Fine content

G :

Gravel percentage

GA:

Genetic algorithm

GEP:

Gene expression programming

GP:

Genetic programming

G S :

Specific gravity

h :

Head length or head size

I P :

Plasticity index

IS:

Insertion sequence

K :

Kernel functions

k :

Number of support vectors

MAE:

Mean absolute error

MAE:

Mean average error (%)

MS:

Mean of sum of squares

MSE:

Mean square error

N :

Number of data samples

n :

Number of variables

N c :

Number of chromosomes

N g :

Number of genes

OR:

Overfitting ratio

PEV:

Percentage of explained variability

r :

Constant function

R :

Pearson correlation coefficient

R 1 :

One dimensional vector space

R 2 :

Linear coefficient of determination

RBF:

Radial basis function

RIS:

Root insertion sequence

RMSE:

Root mean square error

R n1 :

n-dimensional vector space

S :

Sand percentage

SE:

Standard error

SRM:

Structural risk minimization

SVM:

Support vector machine

SVR:

Support vector regression

SVs:

Support vectors

t :

Tail length

VAF:

Variance ratio

\(W_{{{\text{c}}_{\text{opt}} }}\) :

Optimum water content

WEKA:

Waikato environment for knowledge analysis

W L :

Liquid limit

W LM :

Modified liquid limit

W P :

Plastic limit

W S :

Shrinkage limit

X :

Input variables in datasets

X avg :

Average value of input variable in datasets

X i :

Original value of the input variable

X max :

Maximum value of the input variable

X min :

Minimum value of the input variable

X n :

Normalized value of input variable

X SD :

Standard deviation of input variable

Y :

Output variables in datasets

\(\gamma_{{{\text{d}}_{{\rm max} } }}\) :

Maximum dry density

σ :

Standard deviation

ω :

Weight factor

ε :

Insensitive loss function

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Acknowledgements

The authors are very thankful to the City and Industrial Development Corporation of Maharashtra Limited (CIDCO), Mumbai (MH State), India to provide experimental data and their kind support to complete the research work.

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  1. Visvesvaraya National Institute of Technology, Nagpur, 440010, India

    Ashwini R. Tenpe & Anjan Patel

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Tenpe, A.R., Patel, A. Utilization of Support Vector Models and Gene Expression Programming for Soil Strength Modeling. Arab J Sci Eng 45, 4301–4319 (2020). https://doi.org/10.1007/s13369-020-04441-6

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