Performance of Statistical and Intelligent Methods in Estimating Rock Compressive Strength
Abstract
:1. Introduction
2. Methodology
2.1. Laboratory Tests
2.2. Random Forest Algorithm (RFA)
2.3. Gaussian Process Regression Based on Squared Exponential Kernel (GPR-SEK)
2.4. The SVM-RBF
2.5. K Nearest Neighbor Algorithm (KNNA)
2.6. ANFIS and FMP-ANN
2.7. Performance Evaluation of Results
3. Results and Discussion
3.1. Geomechanical Properties of Samples
3.2. Petrographic Features
3.3. Influence of Independent Variables on the UCS
3.4. Evaluation of Previous Emperical Relationships
3.5. Multiple Linear Regression (MPLR)
3.6. The Results of Modeling Using RFA and GPR-SEK Methods
3.7. The FMP-ANN Results
3.8. The KNNA Results
3.9. Results of SVM Method for Estimating UCS
3.10. Results of ANFIS Method for Estimating UCS
3.11. Evaluation of the Used Methods
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Equation | Reference | Lithology |
---|---|---|
UCS = 12.29PLI1.233 | Teymen and Mengüç [40] | Various Rocks |
UCS = −37.82 + (0.017PWV) | Salehin [41] | Sedimentary Rocks |
UCS = 0.043PWV − 136.8 | Aldeeky and Al Hattamleh [42] | Basalt Rocks |
UCS = 17.6PLI + 13.5 | Aliyu et al. [30] | Sedimentary Rocks |
UCS = 14.3PLI | Aladejare [8] | Sedimentary Rocks |
UCS = 9.95PWV(1.21) | Kahraman [43] | Sedimentary rocks |
Wen et al. [7] | Limestone | |
UCS = −5.10 + 110.79 | Edet [3] | Sandstone |
UCS = 0.025PWV − 8.619 | Azimian [29] | Limestone |
UCS = 6.6PWV1.6 | Uyanık et al. [44] | Sedimentary rocks |
UCS = 22.18PWV − 30.32 | Selcuk and Nar [31] | Various Rocks |
UCS = 0.041PWV − 15.40 | Abdi and Khanlari [4] | Sandstones |
UCS = 2.304(PWV)2.43 | Kılıç and Teyman [45] | Various Rocks |
UCS = 10 − 5D16.7 | Aladejare [8] | Sedimentary rocks |
Test | Standards and References | Descriptions |
---|---|---|
UCS | ISRM [47] | A constant loading rate of 0.7 MPa per second was applied to the samples. The amount of deformation was recorded using the corresponding gauge in the UCS test. |
Point load index (PLI) | ASTM D5731 [48] | This test was done on irregular and cylindrical samples. Then the PLI was calculated. |
Compressional wave velocity test | ASTM D2845 [49] | With a ½ MHz frequency |
Porosity (), density(D) and water absorption by weight (WW) | ISRM [47] | The total porosity () of specimens was measured using the method of saturation and immersion way. Density was computed from the ratio of mass to sample volume. |
Petrography | Folk [50], Dunham [51] | For classifying the samples using thin section images. |
Properties | Density (g/cm3) | PLI (MPa) | Water Absorption (%) | Porosity (%) | UCS (MPa) | Es (GPa) | PWV (km/s) | |
---|---|---|---|---|---|---|---|---|
Statistics | ||||||||
Average | 2.43 | 3.75 | 6.81 | 9.44 | 37.54 | 14.95 | 4.38 | |
Std. Dev. | 0.11 | 1.66 | 1.87 | 3.35 | 16.49 | 5.30 | 1.03 | |
Kurtosis | 0.13 | (0.58) | (0.50) | (0.41) | (0.58) | (0.51) | (0.38) | |
Skewness | (0.42) | 0.09 | 0.70 | 0.79 | (0.71) | (0.62) | (0.78) | |
Min. | 2.10 | 0.31 | 4.08 | 4.36 | 4.12 | 3.00 | 2.06 | |
Max. | 2.63 | 8.00 | 11.00 | 16.72 | 59.72 | 22.90 | 5.79 | |
Specimens | 65 | 65 | 65 | 65 | 65 | 65 | 65 |
Equation | R2 | RMSE (MPa) | MAPE% | VAF % | PI | DWS | ANOVA Results | Eq. No. |
---|---|---|---|---|---|---|---|---|
UCS = 5.03PWV − 1.735 + 2.667PLI | 0.88 | 1.10 | 1.08 | 87.85 | 0.66 | 1.93 | F-value = 79.37 p-value = 0.00 | (18) |
Term | Coefficients | T-Value | Significant Level (Sig.) | VIF (Variance Inflation Factor) |
---|---|---|---|---|
Constant | −32.1 | −1.34 | 0.187 | - |
PWV | 5.03 | 2.44 | 0.018 | 7.58 |
D | 21.4 | 1.82 | 0.074 | 3.02 |
WW | 0.281 | 0.35 | 0.728 | 3.81 |
−1.735 | −3.97 | 0.000 | 3.64 | |
PLI | 2.667 | 3.05 | 0.003 | 3.77 |
References | Neuron Numbers Calculated for This Study | Equations |
---|---|---|
Hecht-Nielsen [90] | 3 | ≤ |
Hush [91] | 3 | |
Ripley [92] | 3 | |
Paola [93] | 11 | |
Wang [94] | 1 | /3 |
Kaastra and Boyd [95] | 2 | |
Kanellopoulos and Wilkinson [96] | 1 |
Function | Description | Kernel Function Type |
---|---|---|
This kernel is widely used in image processing, where d is the degree of the polynomial. | Polynomial kernel (PK) | |
This kernel is used for general purposes. It is used when there is no prior knowledge about the data. In condition, parameter is used. | Radial basis function (RBF) | |
- | Linear kernel (LK) |
Kernel Function | Optimal Values of Parameters | Test Period | Train Period | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
t | d | c | RMSE | R2 | PI | MAPE | RMSE | R2 | PI | MAPE | |||
PK | 1.72 | 280.01 | 4 | - | 12.12 | 0.08 | 0.97 | 1.87 | 2.86 | 0.07 | 0.98 | 1.84 | 2.81 |
RBF | 0.02 | - | - | 1.10 | 27 | 0.06 | 0.99 | 1.90 | 2.82 | 0.06 | 0.99 | 1.90 | 2.80 |
LK | 0.45 | - | - | - | 0.90 | 0.09 | 0.96 | 1.83 | 2.84 | 0.09 | 0.97 | 1.81 |
FIS Generation Method | GENFIS4 |
---|---|
Influence radius | 0.60 |
Number of epochs | 500 |
Error goal | 0.00 |
Type | Sugeno |
Rules | 4 |
Number of membership functions (MFs) | 6 |
Input MF type | Gauss MF |
Output MF type | Linear |
APPROACHES | MAPE% | R2 | RMSE | VAF% | PI |
---|---|---|---|---|---|
RFA | 9.27 | 0.98 | 0.09 | 97.63 | 1.87 |
SVM-RBF | 2.83 | 0.99 | 0.06 | 98.96 | 1.92 |
ANFIS | 2.98 | 0.98 | 0.09 | 97.86 | 1.87 |
KNNA | 8.44 | 0.97 | 0.11 | 97.25 | 1.83 |
GPR-SEK | 6.63 | 0.98 | 0.09 | 97.45 | 1.86 |
FMP-ANN | 4.66 | 0.99 | 0.24 | 98.36 | 1.73 |
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Zhang, X.; Altalbawy, F.M.A.; Gasmalla, T.A.S.; Al-Khafaji, A.H.D.; Iraji, A.; Syah, R.B.Y.; Nehdi, M.L. Performance of Statistical and Intelligent Methods in Estimating Rock Compressive Strength. Sustainability 2023, 15, 5642. https://doi.org/10.3390/su15075642
Zhang X, Altalbawy FMA, Gasmalla TAS, Al-Khafaji AHD, Iraji A, Syah RBY, Nehdi ML. Performance of Statistical and Intelligent Methods in Estimating Rock Compressive Strength. Sustainability. 2023; 15(7):5642. https://doi.org/10.3390/su15075642
Chicago/Turabian StyleZhang, Xuesong, Farag M. A. Altalbawy, Tahani A. S. Gasmalla, Ali Hussein Demin Al-Khafaji, Amin Iraji, Rahmad B. Y. Syah, and Moncef L. Nehdi. 2023. "Performance of Statistical and Intelligent Methods in Estimating Rock Compressive Strength" Sustainability 15, no. 7: 5642. https://doi.org/10.3390/su15075642