Ensemble unit and AI techniques for prediction of rock strain
Pradeep T1, Pijush SAMUI1, Navid KARDANI2(), Panagiotis G ASTERIS3
1. Civil Engineering Department, National Institute of Technology, Patna 800005, India 2. Civil and Infrastructure Discipline, School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne, Victoria, Australia 3. Computational Mechanics Laboratory, School of Pedagogical and Technological Education, Heraklion, GR 14121, Greece
The behavior of rock masses is influenced by a variety of forces, with measurement of stress and strain playing the most critical roles in assessing deformation. The laboratory test for determining strain at each location within rock samples is expensive and difficult but rock strain data are important for predicting failure of rock material. Many researchers employ AI technology in order to solve these difficulties. AI algorithms such as gradient boosting machine (GBM), support vector regression (SVR), random forest (RF), and group method of data handling (GMDH) are used to efficiently estimate the strain at every point within a rock sample. Additionally, the ensemble unit (EnU) may be utilized to evaluate rock strain. In this study, 3000 experimental data are used for the purpose of prediction. The obtained strain values are then evaluated using various statistical parameters and compared to each other using EnU. Ranking analysis, stress-strain curve, Young’s modulus, Poisson’s ratio, actual vs. predicted curve, error matrix and the Akaike’s information criterion (AIC) values are used for comparing models. The GBM model achieved 98.16% and 99.98% prediction accuracy (in terms of values of R2) in the longitudinal and lateral dimensions, respectively, during the testing phase. The GBM model, based on the experimental data, has the potential to be a new option for engineers to use when assessing rock strain.
. [J]. Frontiers of Structural and Civil Engineering, 2022, 16(7): 858-870.
Pradeep T, Pijush SAMUI, Navid KARDANI, Panagiotis G ASTERIS. Ensemble unit and AI techniques for prediction of rock strain. Front. Struct. Civ. Eng., 2022, 16(7): 858-870.
i. No. of trees (train) = 100,200,…,1000ii. Max. tree leaves = 3,5,7,9,11,13,15iii. Max. tree depth = 4,5,6iv. learning rate = 0.001,0.005,0.01,0.05,0.1v. Min. No. of data in a leaf = 5,10,15,20
SVR
i. Penalty of the error = 1000 (max.)ii. Sigma = 1 (max.)
RF
i. No. of trees = 1000 (max.)ii. No. of input (best split) = 3iii. Min. No. of samples (internal node) = 20iv. Min. No. of samples (leaf node) = 15
GMDH
i. N-layer = 4ii. α = 0.6iii. Max-Neurons = 20
Tab.1
Fig.2
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
Fig.9
parameter
model
GBM
SVR
RF
GMDH
EnU
train
test
train
test
train
test
train
test
train
test
R2
value
0.9931
0.9816
0.8915
0.9052
0.9391
0.9347
0.8784
0.8951
0.9503
0.9484
rank
1
1
4
4
3
3
5
5
2
2
WMAPE
value
0.0391
0.0483
0.1065
0.1004
0.1734
0.1672
0.1316
0.1226
0.0928
0.0889
rank
1
1
3
3
5
5
4
4
2
2
RMSE
value
0.0125
0.0194
0.0501
0.0443
0.0544
0.0522
0.0521
0.0464
0.0371
0.0348
rank
1
1
3
3
5
5
4
4
2
2
VAF
value
99.3044
98.1576
88.8898
90.4512
86.4918
86.6854
87.8359
89.4863
93.8477
94.0761
rank
1
1
3
3
5
5
4
4
2
2
PI
value
1.9737
1.9437
1.7301
1.7651
1.7496
1.7492
1.7045
1.7433
1.8516
1.8542
rank
1
1
4
3
3
4
5
5
2
2
RSR
value
0.0831
0.1334
0.3348
0.3046
0.3670
0.3585
0.3476
0.3187
0.2474
0.2391
rank
1
1
3
3
5
5
4
4
2
2
MAPE
value
8.6163
9.4273
15.0512
17.0682
53.0258
50.0705
22.5055
21.8960
29.5867
31.2156
rank
1
1
2
2
5
5
3
3
4
4
WI
value
0.9982
0.9955
0.9678
0.9743
0.9526
0.9558
0.9666
0.9730
0.9822
0.9838
rank
1
1
3
3
5
5
4
4
2
2
MAE
value
0.0083
0.0101
0.0226
0.0210
0.0359
0.0349
0.0280
0.0256
0.0197
0.0186
rank
1
1
3
3
5
5
4
4
2
2
MBE
value
2.8E–05
3.5E–04
–6.2E–03
–3.6E–03
–-1.8E–03
1.1E–03
–5.1E–04
1.5E–03
–1.6E–03
–1.5E–04
rank
1
2
5
5
4
3
2
4
3
1
most likely rank
1
3
5
4
2
Tab.2
parameter
model
GBM
SVR
RF
GMDH
EnU
train
test
train
test
train
test
train
test
train
test
R2
value
0.9998
0.9884
0.9965
0.9860
0.9804
0.9693
0.9920
0.9819
0.9974
0.9869
rank
1
1
3
3
5
5
4
4
2
2
WMAPE
value
0.0067
0.0114
0.0321
0.0345
0.1298
0.1332
0.0390
0.0406
0.0368
0.0397
rank
1
1
2
3
5
2
4
5
3
4
RMSE
value
0.0038
0.0287
0.0167
0.0319
0.0755
0.0778
0.0241
0.0359
0.0218
0.0335
rank
1
1
2
2
5
5
4
4
3
3
VAF
value
99.9802
98.8321
99.6486
98.5662
92.1973
91.3857
99.2047
98.1734
99.3504
98.4038
rank
1
1
2
2
5
5
4
4
3
3
PI
value
1.9958
1.9480
1.9763
1.9397
1.8268
1.8052
1.9600
1.9277
1.9691
1.9373
rank
1
1
2
2
5
5
4
4
3
3
RSR
value
0.0139
0.1081
0.0614
0.1201
0.2769
0.2933
0.0884
0.1352
0.0801
0.1263
rank
1
1
2
2
5
5
4
4
3
3
MAPE
value
4.6528
6.8070
29.7569
46.4693
63.0917
71.4464
13.4474
19.0890
32.8977
35.2632
rank
1
1
3
4
5
5
2
2
4
3
WI
value
1.0000
0.9971
0.9991
0.9964
0.9749
0.9717
0.9980
0.9954
0.9983
0.9958
rank
1
1
2
2
5
5
4
4
3
3
MAE
value
0.0030
0.0051
0.0146
0.0155
0.0590
0.0599
0.0177
0.0183
0.0167
0.0178
rank
1
1
2
2
5
5
4
4
3
3
MBE
value
2E–05
1E–03
–5E–03
–3E–03
–6E–04
2E–04
–7E–05
1E–03
–1E–03
–5E–06
rank
1
3
5
5
3
2
2
4
4
1
most likely rank
1
2
5
4
3
Tab.3
Fig.10
Fig.11
Fig.12
models
train (x)
test (x)
train (y)
test (y)
GBM
–18415.1
–7089.486
–23364.93
–6386.733
SVR
–12564.4
–5603.029
–17173.15
–6196.313
RF
–12159.1
–5309.413
–10848.1
–4589.758
GMDH
–12406
–5521.362
–15642.85
–5984.094
EnU
–13833.6
–6038.649
–16058.97
–6107.009
Tab.4
Fig.13
1
T Bruning, M Karakus, G D Nguyen, D Goodchild. An experimental and theoretical stress−strain−damage correlation procedure for constitutive modelling of granite. International Journal of Rock Mechanics and Mining Sciences, 2019, 116 : 1– 12 https://doi.org/10.1016/j.ijrmms.2019.03.003
2
P Yu, P Z Pan, G Feng, Z Wu, S Zhao. Physico-mechanical properties of granite after cyclic thermal shock. Journal of Rock Mechanics and Geotechnical Engineering, 2020, 12( 4): 693– 706 https://doi.org/10.1016/j.jrmge.2020.03.001
3
G Zhang, F Gao, Z Wang, S Yue, S Deng. Quantifying the progressive fracture damage of granite rocks by stress–strain, acoustic emission, and active ultrasonic methods. Journal of Materials in Civil Engineering, 2021, 33( 12): 04021353 https://doi.org/10.1061/(ASCE)MT.1943-5533.0003962
4
K Zhao, X Yu, Y Zhou, Q Wang, J Wang, J Hao. Energy evolution of brittle granite under different loading rates. International Journal of Rock Mechanics and Mining Sciences, 2020, 132 : 104392 https://doi.org/10.1016/j.ijrmms.2020.104392
5
K Duan, Y Ji, W Wu, C Y Kwok. Unloading-induced failure of brittle rock and implications for excavation-induced strain burst. Tunnelling and Underground Space Technology, 2019, 84 : 495– 506 https://doi.org/10.1016/j.tust.2018.11.012
6
S Goswami, C Anitescu, S Chakraborty, T Rabczuk. Transfer learning enhanced physics informed neural network for phase-field modeling of fracture. Theoretical and Applied Fracture Mechanics, 2020, 106 : 102447 https://doi.org/10.1016/j.tafmec.2019.102447
7
E Samaniego, C Anitescu, S Goswami, V M Nguyen-Thanh, H Guo, K Hamdia, X Zhuang, T Rabczuk. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering, 2020, 362 : 112790 https://doi.org/10.1016/j.cma.2019.112790
8
V M Nguyen-Thanh, C Anitescu, N Alajlan, T Rabczuk, X Zhuang. Parametric deep energy approach for elasticity accounting for strain gradient effects. Computer Methods in Applied Mechanics and Engineering, 2021, 386 : 114096 https://doi.org/10.1016/j.cma.2021.114096
9
X Zhuang, H Guo, N Alajlan, H Zhu, T Rabczuk. Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning. European Journal of Mechanics. A, Solids, 2021, 87 : 104225 https://doi.org/10.1016/j.euromechsol.2021.104225
10
C Anitescu, E Atroshchenko, N Alajlan, T Rabczuk. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua, 2019, 59( 1): 345– 359 https://doi.org/10.32604/cmc.2019.06641
11
H Guo, X Zhuang, T Rabczuk. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59( 2): 433– 456 https://doi.org/10.32604/cmc.2019.06660
12
A Bardhan, N Kardani, A GuhaRay, A Burman, P Samui, Y Zhang. Hybrid ensemble soft computing approach for predicting penetration rate of tunnel boring machine in a rock environment. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13( 6): 1398– 1412 https://doi.org/10.1016/j.jrmge.2021.06.015
13
P G Asteris, A Mamou, M Hajihassani, M Hasanipanah, M Koopialipoor, T T Le, N Kardani, D J Armaghani. Soft computing based closed form equations correlating L and N-type Schmidt hammer rebound numbers of rocks. Transportation Geotechnics, 2021, 29 : 100588 https://doi.org/10.1016/j.trgeo.2021.100588
14
N Kardani A Bardhan B Roy P Samui M Nazem D J Armaghani A Zhou. A novel improved Harris Hawks optimization algorithm coupled with ELM for predicting permeability of tight carbonates. Engineering with Computers, 2021
15
N Kardani, A Zhou, S L Shen, M Nazem. Estimating unconfined compressive strength of unsaturated cemented soils using alternative evolutionary approaches. Transportation Geotechnics, 2021, 29 : 100591 https://doi.org/10.1016/j.trgeo.2021.100591
16
N Kardani, A Bardhan, P Samui, M Nazem, P G Asteris, A Zhou. Predicting the thermal conductivity of soils using integrated approach of ANN and PSO with adaptive and time-varying acceleration coefficients. International Journal of Thermal Sciences, 2022, 173 : 107427 https://doi.org/10.1016/j.ijthermalsci.2021.107427
17
N Kardani, A Bardhan, S Gupta, P Samui, M Nazem, Y Zhang, A Zhou. Predicting permeability of tight carbonates using a hybrid machine learning approach of modified equilibrium optimizer and extreme learning machine. Acta Geotechnica, 2022, 17 : 1239– 1255 https://doi.org/10.1007/s11440-021-01257-y
18
M R Kaloop, A Bardhan, N Kardani, P Samui, J W Hu, A Ramzy. Novel application of adaptive swarm intelligence techniques coupled with adaptive network-based fuzzy inference system in predicting photovoltaic power. Renewable & Sustainable Energy Reviews, 2021, 148 : 111315 https://doi.org/10.1016/j.rser.2021.111315
19
M Laghaei A Baghbanan H Hashemolhosseini M Dehghanipoodeh. Numerical determination of deformability and strength of 3D fractured rock mass. International Journal of Rock Mechanics and Mining Sciences, 2018, 110: 246– 256
20
C S Gundewar. Government of India Ministry of Mines INDIAN BUREAU OF MINES Controller General Indian Bureau of Mines Application of Rock Mechanics in Surface and Underground Mining. New Delhi: Indian Bureau of Mines, 2014
21
W G Zhang, H R Li, C Z Wu, Y Q Li, Z Q Liu, H L Liu. Soft computing approach for prediction of surface settlement induced by earth pressure balance shield tunneling. Underground Space, 2021, 6( 4): 353– 363 https://doi.org/10.1016/j.undsp.2019.12.003
22
J Zhou, Y Qiu, D J Armaghani, W Zhang, C Li, S Zhu, R Tarinejad. Predicting TBM penetration rate in hard rock condition: A comparative study among six XGB-based metaheuristic techniques. Geoscience Frontiers, 2021, 12( 3): 101091 https://doi.org/10.1016/j.gsf.2020.09.020
23
T Pradeep, A Bardhan, P Samui. Prediction of rock strain using soft computing framework. Innovative Infrastructure Solutions, 2021, 7( 1): 37 https://doi.org/10.1007/s41062-021-00631-9
24
N Kardani, P Samui, D Kim, A Zhou. Smart phase behavior modeling of asphaltene precipitation using advanced computational frameworks: ENN, GMDH, and MPMR. Petroleum Science and Technology, 2021, 39( 19−20): 804– 825 https://doi.org/10.1080/10916466.2021.1974882
25
T Pradeep, A Bardhan, A Burman, P Samui. Rock strain prediction using deep neural network and hybrid models of ANFIS and Meta-Heuristic optimization algorithms. Infrastructure, 2021, 6( 9): 129
26
N Li, H Nguyen, J Rostami, W Zhang, X N Bui, B Pradhan. Predicting rock displacement in underground mines using improved machine learning-based models. Measurement, 2022, 188 : 110552 https://doi.org/10.1016/j.measurement.2021.110552
27
A I Lawal, S Kwon. Application of artificial intelligence to rock mechanics: An overview. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13( 1): 248– 266 https://doi.org/10.1016/j.jrmge.2020.05.010
28
L Breiman. Random forests. Machine Learning, 2001, 45( 1): 5– 32
G Louppe. Understanding Random Forests from Theory to Practice. University of Liège, 2014
31
M Gong, Y Bai, J Qin, J Wang, P Yang, S Wang. Gradient boosting machine for predicting return temperature of district heating system: A case study for residential buildings in Tianjin. Journal of Building Engineering, 2020, 27 : 100950 https://doi.org/10.1016/j.jobe.2019.100950
32
A V Konstantinov, L V Utkin. Interpretable machine learning with an ensemble of gradient boosting machines. Knowledge-Based Systems, 2021, 222 : 106993 https://doi.org/10.1016/j.knosys.2021.106993
33
J Zhou, E Li, S Yang, M Wang, X Shi, S Yao, H S Mitri. Slope stability prediction for circular mode failure using gradient boosting machine approach based on an updated database of case histories. Safety Science, 2019, 118 : 505– 518 https://doi.org/10.1016/j.ssci.2019.05.046
G F Fan, M Yu, S Q Dong, Y H Yeh, W C Hong. Forecasting short-term electricity load using hybrid support vector regression with grey catastrophe and random forest modeling. Utilities Policy, 2021, 73 : 101294 https://doi.org/10.1016/j.jup.2021.101294
37
R Roohi, H Emdad, K Jafarpur. Toward a realistic reconstruction and determination of blood flow pattern in complex vascular network: 3D, non-Newtonian, multi-branch simulation based on CFD and GMDH algorithm. International Communications in Heat and Mass Transfer, 2021, 122 : 105185 https://doi.org/10.1016/j.icheatmasstransfer.2021.105185
38
I Ebtehaj, H Bonakdari, A H Zaji, H Azimi, F Khoshbin. GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs. Engineering Science and Technology, an International Journal, 2015, 18( 4): 746– 757 https://doi.org/10.1016/j.jestch.2015.04.012
39
B W Isah H Mohamad N R Ahmad I S H Harahap M A M Al-Bared. Uniaxial compression test of rocks: Review of strain measuring instruments. In: IOP Conference Series: Earth and Environmental Science, Volume 476, 2nd International Conference on Civil & Environmental Engineering. Langkawi, 2019.
40
J H Friedman. Greedy function approximation: A gradient boosting machine. Annals of statistics, 2001, 29( 5): 1189– 1232
41
Y Chen, W Zheng, W Li, Y Huang. Large group activity security risk assessment and risk early warning based on random forest algorithm. Pattern Recognition Letters, 2021, 144 : 1– 5 https://doi.org/10.1016/j.patrec.2021.01.008
42
Z Jin, J Shang, Q Zhu, C Ling, W Xie, B Qiang. RFRSF: Employee turnover prediction based on random forests and survival analysis. In: International Conference on Web Information Systems Engineering. Cham: Springer, 2020, 503– 515 https://doi.org/10.1007/978-3-030-62008-0_35
43
C N Ko, C M Lee. Short-term load forecasting using SVR (support vector regression)-based radial basis function neural network with dual extended Kalman filter. Energy, 2013, 49 : 413– 422 https://doi.org/10.1016/j.energy.2012.11.015
44
M Koopialipoor, S S Nikouei, A Marto, A Fahimifar, D Jahed Armaghani, E T Mohamad. Predicting tunnel boring machine performance through a new model based on the group method of data handling. Bulletin of Engineering Geology and the Environment, 2019, 78( 5): 3799– 3813 https://doi.org/10.1007/s10064-018-1349-8
45
V Nourani, Z Abdollahi, E Sharghi. Sensitivity analysis and ensemble artificial intelligence-based model for short-term prediction of NO2 concentration. International Journal of Environmental Science and Technology, 2021, 18( 9): 2703– 2722 https://doi.org/10.1007/s13762-020-03002-6
46
F S Wong. Slope reliability and response surface method. Journal of geotechnical Engineering, 1985, 111( 1): 32– 53
47
S Srinivasulu, A Jain. A comparative analysis of training methods for artificial neural network rainfall-runoff models. Applied Soft Computing, 2006, 6( 3): 295– 306 https://doi.org/10.1016/j.asoc.2005.02.002
T Chai, R R Draxler. Root mean square error (RMSE) or mean absolute error (MAE)?—Arguments against avoiding RMSE in the literature. Geoscientific Model Development, 2014, 7( 3): 1247– 1250 https://doi.org/10.5194/gmd-7-1247-2014
50
M C Villeneuve M J Heap A R L Kushnir T Qin P Baud G Zhou T Xu. Estimating in situ rock mass strength and elastic modulus of granite from the Soultz-sous-Forêts geothermal reservoir (France) . Geothermal Energy, 2018, 6: 1– 29
51
N Domede, T Parent, A Sellier. Mechanical behaviour of granite: A compilation, analysis and correlation of data from around the world. European Journal of Environmental and Civil Engineering, 2019, 23( 2): 193– 211 https://doi.org/10.1080/19648189.2016.1275984
52
T Pradeep, A GuhaRay, A Bardhan, P Samui, S Kumar, D J Armaghani. Reliability and prediction of embedment depth of sheet pile walls using hybrid ANN with optimization techniques. Arabian Journal for Science and Engineering, 2022, 1– 19 https://doi.org/10.1007/s13369-022-06607-w
53
A Guven, Ö Kişi. Estimation of suspended sediment yield in natural rivers using machine-coded linear genetic programming. Water Resources Management, 2011, 25( 2): 691– 704 https://doi.org/10.1007/s11269-010-9721-x
54
M K Ayoubloo, H M Azamathulla, E Jabbari, M Zanganeh. Predictive model-based for the critical submergence of horizontal intakes in open channel flows with different clearance bottoms using CART, ANN and linear regression approaches. Expert Systems with Applications, 2011, 38( 8): 10114– 10123 https://doi.org/10.1016/j.eswa.2011.02.073
