Innovative Data-Driven Machine Learning Approaches for Predicting Sandstone True Triaxial Strength
Abstract
:1. Introduction
2. Methodologies
2.1. Multilayer Perceptron (MLP)
2.2. Harris Hawks Optimization (HHO)
- (1)
- Soft besiege (see Figure 2a):
- (2)
- Hard besiege (see Figure 2b):
- (3)
- Soft besiege with progressive rapid dives (see Figure 2c):
- (4)
- Hard besiege with progressive rapid dives (see Figure 2d):
3. Strength Criteria
3.1. Principal Stress Space
3.2. DP Criterion
3.3. HB Criterion
3.4. MGC Criterion
3.5. ML Criterion
3.6. MWC Criterion
4. Data Description
5. Model Building and Training
6. Performance Comparison
6.1. Comparisons Using the Collection Dataset
6.2. Comparison on the Meridian Plane
6.3. Comparison on the Deviatoric Plane
6.4. Comparison on 3D Failure Envelope
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Number | Number of Data | (MPa) | (MPa) | (MPa) | References | |||
---|---|---|---|---|---|---|---|---|
Min | Max | Min | Max | Min | Max | |||
1 | 29 | 92.1 | 492.1 | 10 | 413 | 10 | 100 | [38] |
2 | 17 | 87.48 | 302.8 | 0 | 62.5 | 0 | 37.5 | [39] |
3 | 23 | 25.91 | 172 | 0 | 60 | 0 | 20 | [40] |
4 | 24 | 34.62 | 128.68 | 0 | 24 | 0 | 10 | [41] |
5 | 44 | 74.22 | 279 | 0 | 171 | 0 | 50 | [42] |
6 | 20 | 75.4 | 194 | 0 | 118.3 | 0 | 15 | [42] |
7 | 14 | 48.5 | 159.1 | 0 | 24 | 0 | 6.6 | [43] |
8 | 14 | 49.4 | 165.9 | 0 | 24 | 0 | 6.6 | [43] |
9 | 14 | 46.4 | 147.6 | 0 | 24 | 0 | 6.6 | [43] |
10 | 31 | 60 | 465 | 0 | 436 | 0 | 50 | [44] |
11 | 27 | 184.17 | 378.68 | 0 | 160 | 0 | 10 | [45] |
12 | 20 | 23.69 | 192.97 | 0 | 55.2 | 0 | 55.2 | [46] |
13 | 78 | 56.1 | 648 | 0 | 620.7 | 0 | 150 | [47] |
14 | 62 | 29.7 | 370.2 | 0 | 346.3 | 0 | 150 | [47] |
Name | Equation |
---|---|
sigmoid | |
softplus | |
swish | |
tanh |
Sandstone Number | DP | HB | MGC | ML | MWC | |||
---|---|---|---|---|---|---|---|---|
(MPa) | ||||||||
1 | 0.17 | 33.87 | 21 | 3.9 | 21.3 | 13.71 | 2.84 | 7.6 |
2 | 0.33 | 25.04 | 21 | 5.87 | 17.38 | 45.7 | 4.77 | 1.37 |
3 | 0.32 | 13.73 | 21 | 8.96 | 12.16 | 54.21 | 0.64 | 0.73 |
4 | 0.37 | 7.25 | 21 | 7.13 | 10.29 | 60.11 | 6.19 | 1255.77 |
5 | 0.21 | 28.3 | 13.86 | 3.62 | 19.29 | 17.18 | 3.09 | 0.14 |
6 | 0.16 | 38.4 | 18.68 | 4.19 | 20 | 18.93 | 3.89 | 0.26 |
7 | 0.46 | 1.78 | 21 | 12.04 | 6.67 | 184.7 | 9.29 | 0.63 |
8 | 0.45 | 6.27 | 21 | 14.07 | 8.31 | 169.15 | 10.65 | 4.91 |
9 | 0.43 | 4.58 | 21 | 10.56 | 7.86 | 138.2 | 8.28 | 0.89 |
10 | 0.23 | 31.92 | 21 | 6.02 | 17.54 | 37 | 4.41 | 2.23 |
11 | 0.18 | 92.66 | 21 | 6.56 | 33.79 | 31.26 | 6.21 | 0.66 |
12 | 0.24 | 9.72 | 15.01 | 3.49 | 13.54 | 16.12 | 0.43 | 0.97 |
13 | 0.17 | 53.62 | 21 | 3.8 | 29.63 | 11.44 | 1.04 | 1.87 |
14 | 0.1 | 43.29 | 13 | 2.43 | 26.56 | 1.68 | 0.73 | 3.6 |
Model | Training | Test | ||||||
---|---|---|---|---|---|---|---|---|
R2 | MAE | RMSE | MAPE | R2 | MAE | RMSE | MAPE | |
HHO-MLP | 0.9700 | 25.4266 | 32.7273 | 0.1435 | 0.9615 | 28.5801 | 36.9180 | 0.1587 |
DP | 0.9564 | 28.6053 | 39.9217 | 0.1681 | 0.9444 | 31.3053 | 44.2664 | 0.2138 |
HB | 0.9594 | 39.2814 | 51.345 | 0.1819 | 0.9562 | 42.8719 | 54.2242 | 0.2011 |
MGC | 0.9618 | 32.105 | 46.4841 | 0.1382 | 0.9514 | 32.6736 | 50.8198 | 0.14 |
ML | 0.9124 | 54.2102 | 71.7347 | 0.2601 | 0.9119 | 53.1789 | 71.7476 | 0.237 |
MWC | 0.6453 | 80.4979 | 148.0962 | 0.4868 | 0.6543 | 83.0136 | 149.1945 | 0.4666 |
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Zhang, R.; Zhou, J.; Wang, Z. Innovative Data-Driven Machine Learning Approaches for Predicting Sandstone True Triaxial Strength. Appl. Sci. 2024, 14, 7855. https://doi.org/10.3390/app14177855
Zhang R, Zhou J, Wang Z. Innovative Data-Driven Machine Learning Approaches for Predicting Sandstone True Triaxial Strength. Applied Sciences. 2024; 14(17):7855. https://doi.org/10.3390/app14177855
Chicago/Turabian StyleZhang, Rui, Jian Zhou, and Zhenyu Wang. 2024. "Innovative Data-Driven Machine Learning Approaches for Predicting Sandstone True Triaxial Strength" Applied Sciences 14, no. 17: 7855. https://doi.org/10.3390/app14177855
APA StyleZhang, R., Zhou, J., & Wang, Z. (2024). Innovative Data-Driven Machine Learning Approaches for Predicting Sandstone True Triaxial Strength. Applied Sciences, 14(17), 7855. https://doi.org/10.3390/app14177855