Skip to main content

Advertisement

SpringerLink
Log in

Assessment of the uniaxial compressive strength of intact rocks: an extended comparison between machine and advanced machine learning models

  • Original Paper
  • Published:
Multiscale and Multidisciplinary Modeling, Experiments and Design Aims and scope Submit manuscript

Abstract

Rock strength is the most deterministic parameter for studying geological disasters in resource development and underground engineering construction. However, the experimental procedure for finding rock strength is arduous and lengthy. Therefore, this investigation introduces an optimal computational model for predicting the rock uniaxial compressive strength (UCS) by comparing eight machine learning approaches. For developing the predictive models, the selection of the most significant independent variables is essential. Hence, this investigation reveals the most suitable independent variable by developing three cases of input variables, i.e., (i) area, density, wave velocity, and Young's modulus; (ii) mass, density, wave velocity, and Young's modulus; and (iii) density, wave velocity, and Young's modulus. Sixteen performance metrics have analyzed machine learning models' prediction capabilities and reported that the Gaussian process regression (GPR) model has predicted rock UCS with a correlation coefficient (R) of 0.9788, root mean square error (RMSE) of 14.0804 MPa, performance index (PI) of 1.8821, variance accounted for (VAF) of 95.79, index of scatter (IOS) of 0.1167, and index of agreement (IOA) of 0.9063, close to the ideal values and higher than those of other computational models, in case 1. However, the impact of weak multicollinearity has been observed in the performance of the support vector machine model than GPR and ensemble tree models. The score analysis, error characteristics curve, and Anderson–Darling test confirm the robustness of assessing the rock UCS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

The database used in the research is mentioned in the manuscript.

Abbreviations

\(\bar{\omega}\) :

Mean of the computed value

a20:

A20-index

AAC:

Amplitude attenuation coefficient

ANFIS:

Adaptive neuro-fuzzy inference system

ANN:

Artificial neural networks

BF:

Bias factor

BPI:

Block punch index

BPNN:

Backpropagation neural network model

BTS:

Brazilian tensile strength

CatBoost:

CatBoost regressor

Chl:

Chlorite

CNN:

Convolutional neural network

COA_ANN:

Cuckoo optimization algorithm-based artificial neural network model

CP:

Confining pressure

D :

Density

d :

Diameter of the specimen

Db:

Bulk density

DD:

Dry density

DNN:

Deep neural network

DT:

Decision tree

D w :

Wet density

E:

Youngs' modulus

ELM:

Extreme learning machine

GA:

Genetic algorithm

GBR:

Gradient boosting regressor

GEP:

Gene expression programming

GMDH:

Group method data-handling model

GPR:

Gaussian process regression

GS:

Grain size

GWO_ELM:

Gray wolf algorithm-based extreme learning machine model

H :

Total number of data samples.

HLFR:

High- and low-frequency ratio

IOA:

Index of agreement

IOS:

Index of scatter

KELM_GWO:

Kernel extreme learning machine–gray wolf optimized model

kNN:

K-nearest neighbor

Kpr:

Alkali feldspar

L :

Length of the specimen

LGBM:

Light gradient boosting ensemble method

LMI:

Legate and McCabe's Index

LSTM:

Long short-term memory

M:

Mica

m20:

Ratio of lab test to the computed value varying from 0.8 to 1.2

MAE:

Mean absolute error

MAPE:

Mean absolute percentage error

MBE:

Mean bias error

MC:

Moisture content

MLP:

Multilayer perceptron neural network

MLR:

Multiple linear regression

n :

Porosity

N :

Schmidt hammer rebound number

NMBE:

Normalized mean bias error

NS:

Nash–Sutcliffe efficiency

P 50 :

Point load index

PI:

Performance index

Plg:

Plagioclase

PR:

Poisson ratio

PSO:

Particle swarm optimization algorithm

PSO_ANFIS:

Particle swarm optimized adaptive neuro-fuzzy inference system model

PSO_SVR:

Particle swarm algorithm-optimized support vector regression model

Q_SVR:

Quadratic support vector regression model

Qtz:

Coarse-grained crystals of quartz

R :

Correlation coefficient

R 2 :

Coefficient of determination

RF:

Random forest

RMSE:

Root mean square error

RSR:

Ratio of RMSE to the standard deviation of the observations

SANN:

Sequential artificial neural network model

SCS:

Static compressive strength

SDI:

Slake durability index

SFS_ANFIS:

Stochastic fractal search-optimized adaptive neuro-fuzzy inference system

SR:

Strain rate

SSA:

Sparrow search algorithm

SSA_RF:

Sparrow search algorithm-optimized random forest

SSA_XGBoost:

Sparrow search algorithm-optimized extreme gradient boosting model

SSH:

Shore hardness

SVR:

Support vector regressor

SVR_RBF:

Radial basis function-based support vector regression model

UME:

Macro uniaxial modulus of elasticity

UPR:

Macroscopic uniaxial Poisson's ratio

Uw:

Unit weight

Vp:

P-Wave velocity

Vs:

Shear wave

WI:

Willmott's index of agreement

WMAPE:

Weighted mean absolute percentage error

WOA_ELM:

Whale optimization algorithm-based extreme learning machine model

XGBoost:

Extreme gradient boosting model

α :

Lab test ith value

β :

Mean of the lab test values

k :

Number of inputs

\({\omega}\) :

Computed ith value

References

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

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

    Jitendra Khatti & Kamaldeep Singh Grover

Authors
  1. Jitendra Khatti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kamaldeep Singh Grover
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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

Corresponding author

Correspondence to Jitendra Khatti.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Tables 9, 10, 11, 12, 13 and 14.

Table 9 Performance details for case 1
Full size table
Table 10 Performance details for case 2
Full size table
Table 11 Performance details for case 3
Full size table
Table 12 Score analysis in case 1
Full size table
Table 13 Score analysis in case 2
Full size table
Table 14 Score analysis in case 3
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khatti, J., Grover, K.S. Assessment of the uniaxial compressive strength of intact rocks: an extended comparison between machine and advanced machine learning models. Multiscale and Multidiscip. Model. Exp. and Des. (2024). https://doi.org/10.1007/s41939-024-00408-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41939-024-00408-4

Keywords

Search

Navigation