Dynamic prediction of moving trajectory in pipe jacking: GRU-based deep learning framework
Yi-Feng YANG1, Shao-Ming LIAO1, Meng-Bo LIU2()
1. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China 2. Key Laboratory of Road and Traffic Engineering of Ministry of Education, Tongji University, Shanghai 201804, China
The moving trajectory of the pipe-jacking machine (PJM), which primarily determines the end quality of jacked tunnels, must be controlled strictly during the entire jacking process. Developing prediction models to support drivers in performing rectifications in advance can effectively avoid considerable trajectory deviations from the designed jacking axis. Hence, a gated recurrent unit (GRU)-based deep learning framework is proposed herein to dynamically predict the moving trajectory of the PJM. In this framework, operational data are first extracted from a data acquisition system; subsequently, they are preprocessed and used to establish GRU-based multivariate multistep-ahead direct prediction models. To verify the performance of the proposed framework, a case study of a large pipe-jacking project in Shanghai and comparisons with other conventional models (i.e., long short-term memory (LSTM) network and recurrent neural network (RNN)) are conducted. In addition, the effects of the activation function and input time-step length on the prediction performance of the proposed framework are investigated and discussed. The results show that the proposed framework can dynamically and precisely predict the PJM moving trajectory during the pipe-jacking process, with a minimum mean absolute error and root mean squared error (RMSE) of 0.1904 and 0.5011 mm, respectively. The RMSE of the GRU-based models is lower than those of the LSTM- and RNN-based models by 21.46% and 46.40% at the maximum, respectively. The proposed framework is expected to provide an effective decision support for moving trajectory control and serve as a foundation for the application of deep learning in the automatic control of pipe jacking.
large cutter: 4675 mm (× 2), medium cutter: 2300 mm, 2100 mm, small cutter: 1700 mm (× 2)
motor power
large cutter: 37 kW × 8 = 296 kW (× 2), medium cutter: 45 kW (× 2), small cutter: 37 kW (× 2)
maximum torque of cutter
large cutter: 1700 kN·m (× 2), medium cutter: 140 kN·m (× 2), small cutter: 110 kN·m (× 2)
rotation speed of cutter
large cutter: 0−1.2 r/min, medium cutter: 0−2.5 r/min, small cutter: 0−2.5 r/min
stroke of rectifying oil cylinder
200 mm
maximum rectifying oil cylinder thrust
3000 kN × 12 = 36000 kN
maximum rectifying angle
up and down: 1.2°; left and right: 1.1°
screw conveyor power
90 kW (× 2)
screw conveyor rotating speed
1–14.5 r/min
screw conveyor dumping quantity
116 m3/h (× 2)
maximum jacking speed
40 mm/min
maximum thrust
2500 kN × 16 = 40000 kN
Tab.1
Fig.7
Fig.8
parameter
abbreviation
parameter type
mean
std
min
max
unit
total thrust
input
11321.25
1047.68
9142.1
14641.66
kN
advance rate of large cutter 1
input
29.97
5.03
17.92
41.5
mm/min
advance rate of large cutter 2
input
29.75
4.92
17.75
41.16
mm/min
rotation angle of large cutter 1
input
178.72
101.32
0
359
°
rotation angle of large cutter 2
input
179.06
103.68
0
359
°
jacking stroke of large cutter 1
input
1657.1
435.83
449.75
2408.88
mm
jacking stroke of large cutter 2
input
1641.46
435.55
870.63
2382.63
mm
torque of large cutter 1
input
321.70
19.51
258.28
408.99
kN·m
torque of large cutter 2
input
330.51
35.42
247.91
445.34
kN·m
torque of small cutter 1
input
19.09
2.12
10.79
25.51
kN·m
torque of small cutter 2
input
26.95
2.52
19.44
41.61
kN·m
torque of small cutter 3
input
12.63
0.76
10.01
15.42
kN·m
torque of small cutter 4
input
14.34
1.2
9.88
17.48
kN·m
rotation speed of large cutter 1
input
0.85
0.003
0.84
0.86
min−1
rotation speed of large cutter 2
input
0.85
0.004
0.84
0.86
min−1
rotation speed of small cutter 1
input
2.56
0.003
2.55
2.57
min−1
rotation speed of small cutter 2
input
2.56
0.005
2.52
2.6
min−1
rotation speed of small cutter 3
input
2.56
0
2.56
2.56
min−1
rotation speed of small cutter 4
input
2.56
0.0001
2.55
2.57
min−1
horizontal deviation of jacking machine head
JMH-HD
input and output
1.51
14.71
−34
38
mm
vertical deviation of jacking machine head
JMH-VD
input and output
–9.73
7.06
–27
16
mm
horizontal deviation of jacking machine tail
JMT-HD
input and output
–13.7
20.88
–52
32
mm
vertical deviation of jacking machine tail
JMT-VD
input and output
5.37
12.6
–17
37
mm
Tab.2
Fig.9
Fig.10
Fig.11
Fig.12
Fig.13
hyperparameter
tuning range
GRU layer units
16, 32, 64, 128, 256
learning rate
0.01, 0.001, 0.0001
Tab.3
model for prediction
GRU layer units
learning rate
batch size
optimizer
epochs
JMH-HD
32
0.001
32
Adam
300
JMH-VD
256
0.001
32
Adam
300
JMT-HD
64
0.001
32
Adam
300
JMT-VD
128
0.001
32
Adam
300
Tab.4
metrics
JMH-HD
JMH-VD
JMT-HD
JMT-VD
training
test
training
test
training
test
training
test
MAE
0.3442
0.6459
0.1302
0.1904
0.4151
0.3561
0.1609
0.5873
RMSE
1.5777
1.4748
0.4079
0.5011
1.5127
1.2468
0.4207
0.7476
Tab.5
Fig.14
Fig.15
model for predicting
LSTM
RNN
number of units
learning rate
number of units
learning rate
JMH-HD
256
0.001
32
0.001
JMH-VD
32
0.001
16
0.001
JMT-HD
32
0.001
16
0.001
JMT-VD
32
0.001
64
0.001
Tab.6
model
metrics
JMH-HD
JMH-VD
JMT-HD
JMT-VD
GRU
MAE
0.6459*
0.1904
0.3561
0.5873
RMSE
1.4748
0.5011
1.2468
0.7476
LSTM
MAE
0.8598
0.4614
0.4191
0.8015
RMSE
1.7740
0.6380
1.2603
0.9262
RNN
MAE
1.0636
0.6966
0.4833
1.1049
RMSE
2.2781
0.9349
1.3105
1.2556
Tab.7
Fig.16
Fig.17
length of input time steps
training
test
MAE
RMSE
MAE
RMSE
10
0.3568
1.5795
0.9814
1.7140
20
0.4002
1.5738
0.8795
1.6909
30
0.3785
1.5810
0.7787
1.5687
40
0.3586
1.5846
0.8432
1.6190
50
0.3491
1.5816
0.8216
1.5851
60
0.3442
1.5777
0.6459
1.4748
70
0.3371*
1.5725
0.7586
1.5174
80
0.3557
1.5799
0.8349
1.5333
90
0.3662
1.5811
0.6721
1.5073
Tab.8
1
J Wang, K Wang, T Zhang, S Wang. Key aspects of a DN4000 steel pipe jacking project in China: A case study of a water pipeline in the Shanghai Huangpu River. Tunnelling and Underground Space Technology, 2018, 72: 323–332 https://doi.org/10.1016/j.tust.2017.12.012
Z F Xue, W C Cheng, L Wang, G Song. Improvement of the shearing behaviour of loess using recycled straw fiber reinforcement. KSCE Journal of Civil Engineering, 2021, 25(9): 3319–3335 https://doi.org/10.1007/s12205-021-2263-3
4
W Hu, W C Cheng, S Wen, K Yuan. Revealing the enhancement and degradation mechanisms affecting the performance of carbonate precipitation in EICP process. Frontiers in Bioengineering and Biotechnology, 2021, 9: 750258 https://doi.org/10.3389/fbioe.2021.750258
5
W C Cheng, X D Bai, B B Sheil, G Li, F Wang. Identifying characteristics of pipejacking parameters to assess geological conditions using optimisation algorithm-based support vector machines. Tunnelling and Underground Space Technology, 2020, 106: 103592 https://doi.org/10.1016/j.tust.2020.103592
6
D J Ren, Y S Xu, J S Shen, A Zhou, A Arulrajah. Prediction of ground deformation during pipe-jacking considering multiple factors. Applied Sciences (Basel, Switzerland), 2018, 8(7): 1051 https://doi.org/10.3390/app8071051
7
R Kumar, P Samui, S Kumari, S S Roy. Determination of reliability index of cantilever retaining wall by RVM, MPMR and MARS. International Journal of Advanced Intelligence Paradigms, 2021, 18(3): 316–336 https://doi.org/10.1504/IJAIP.2021.113325
8
P Samui, D Kim, J Jagan, S S Roy. Determination of uplift capacity of suction caisson using gaussian process regression, minimax probability machine regression and extreme learning machine. Civil Engineering (Shiraz), 2019, 43(S1): 651–657 https://doi.org/10.1007/s40996-018-0155-7
9
Y F Yang, S M Liao, M B Liu, D P Wu, W Q Pan, H Li. A new construction method for metro stations in dense urban areas in Shanghai soft ground: Open-cut shafts combined with quasi-rectangular jacking boxes. Tunnelling and Underground Space Technology, 2022, 125: 104530 https://doi.org/10.1016/j.tust.2022.104530
10
C Zhou, H Xu, L Ding, L Wei, Y Zhou. Dynamic prediction for attitude and position in shield tunneling: A deep learning method. Automation in Construction, 2019, 105: 102840 https://doi.org/10.1016/j.autcon.2019.102840
11
M Sugimoto, A Sramoon. Theoretical model of shield behavior during excavation. I: Theory. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(2): 138–155 https://doi.org/10.1061/(ASCE)1090-0241(2002)128:2(138
12
P Zhang, S S Behbahani, B Ma, T Iseley, L Tan. A jacking force study of curved steel pipe roof in Gongbei tunnel: Calculation review and monitoring data analysis. Tunnelling and Underground Space Technology, 2018, 72: 305–322 https://doi.org/10.1016/j.tust.2017.12.016
13
X Ji, W Zhao, P Ni, M Barla, J Han, P Jia, Y Chen, C Zhang. A method to estimate the jacking force for pipe jacking in sandy soils. Tunnelling and Underground Space Technology, 2019, 90: 119–130 https://doi.org/10.1016/j.tust.2019.04.002
14
M Barla, M Camusso, S Aiassa. Analysis of jacking forces during microtunnelling in limestone. Tunnelling and Underground Space Technology, 2006, 21(6): 668–683 https://doi.org/10.1016/j.tust.2006.01.002
15
X Ji, P Ni, M Barla. Analysis of jacking forces during pipe jacking in granular materials using particle methods. Underground Space, 2019, 4(4): 277–288 https://doi.org/10.1016/j.undsp.2019.03.002
16
D Ong, C Choo. Back-analysis and finite element modeling of jacking forces in weathered rocks. Tunnelling and Underground Space Technology, 2016, 51: 1–10 https://doi.org/10.1016/j.tust.2015.10.014
17
R Rohner, A Hoch. Calculation of jacking force by new ATV A-161. Tunnelling and Underground Space Technology, 2010, 25(6): 731–735 https://doi.org/10.1016/j.tust.2009.11.005
18
K Wen, H Shimada, W Zeng, T Sasaoka, D Qian. Frictional analysis of pipe−slurry−soil interaction and jacking force prediction of rectangular pipe jacking. European Journal of Environmental and Civil Engineering, 2020, 24(6): 814–832 https://doi.org/10.1080/19648189.2018.1425156
19
W C Cheng, J C Ni, J S L Shen, H W Huang. Investigation into factors affecting jacking force: A case study. Proceedings of the Institution of Civil Engineers—Geotechnical Engineering, 2017, 170(4): 322–334 https://doi.org/10.1680/jgeen.16.00117
20
C Li, Z Zhong, X Liu, Y Tu, G He. Numerical simulation for an estimation of the jacking force of ultra-long-distance pipe jacking with frictional property testing at the rock mass–pipe interface. Tunnelling and Underground Space Technology, 2019, 89: 205–221 https://doi.org/10.1016/j.tust.2019.04.004
21
J Yen, K Shou. Numerical simulation for the estimation the jacking force of pipe jacking. Tunnelling and Underground Space Technology, 2015, 49: 218–229 https://doi.org/10.1016/j.tust.2015.04.018
22
D Chapman, Y Ichioka. Prediction of jacking forces for microtunnelling operations. Tunnelling and Underground Space Technology, 1999, 14: 31–41 https://doi.org/10.1016/S0886-7798(99)00019-X
23
B Sheil. Prediction of microtunnelling jacking forces using a probabilistic observational approach. Tunnelling and Underground Space Technology, 2021, 109: 103749 https://doi.org/10.1016/j.tust.2020.103749
24
S Yang, M Wang, J Du, Y Guo, Y Geng, T Li. Research of jacking force of densely arranged pipe jacks process in pipe-roof pre-construction method. Tunnelling and Underground Space Technology, 2020, 97: 103277 https://doi.org/10.1016/j.tust.2019.103277
25
K Shou, J Yen, M Liu. On the frictional property of lubricants and its impact on jacking force and soil–pipe interaction of pipe-jacking. Tunnelling and Underground Space Technology, 2010, 25(4): 469–477 https://doi.org/10.1016/j.tust.2010.02.009
26
C C Reilly, T L Orr. Physical modelling of the effect of lubricants in pipe jacking. Tunnelling and Underground Space Technology, 2017, 63: 44–53 https://doi.org/10.1016/j.tust.2016.11.005
27
Z He, J Chen. Experimental study on the complex contact frictional property of an ultralong distance large-section concrete pipe jacking and prediction of pipe string stuck. Advances in Materials Science and Engineering, 2019, 2019: 4353520 https://doi.org/10.1155/2019/4353520
28
Y Ye, L Peng, Y Zhou, W Yang, C Shi, Y Lin. Prediction of friction resistance for slurry pipe jacking. Applied Sciences, 2019, 10(1): 207 https://doi.org/10.3390/app10010207
29
W C Cheng, L Wang, Z F Xue, J C Ni, M M Rahman, A Arulrajah. Lubrication performance of pipejacking in soft alluvial deposits. Tunnelling and Underground Space Technology, 2019, 91: 102991 https://doi.org/10.1016/j.tust.2019.102991
30
Y Ye, L Peng, W Yang, Y Zou, C Cao. Calculation of friction force for slurry pipe jacking considering soil−slurry−pipe interaction. Advances in Civil Engineering, 2020, 2020: 1–10 https://doi.org/10.1155/2020/6594306
31
X D Bai, W C Cheng, G Li. A comparative study of different machine learning algorithms in predicting EPB shield behaviour: A case study at the Xi’an metro, China. Acta Geotechnica, 2021, 16(12): 4061–4080 https://doi.org/10.1007/s11440-021-01383-7
32
S S Lin, N Zhang, A Zhou, S L Shen. Time-series prediction of shield movement performance during tunneling based on hybrid model. Tunnelling and Underground Space Technology, 2022, 119: 104245 https://doi.org/10.1016/j.tust.2021.104245
33
T YanS L Shen A Zhou. Identification of geological characteristics from construction parameters during shield tunnelling. Acta Geotechnica, 2023, 18(1): 535−551
34
K Elbaz, T Yan, A Zhou, S L Shen. Deep learning analysis for energy consumption of shield tunneling machine drive system. Tunnelling and Underground Space Technology, 2022, 123: 104405 https://doi.org/10.1016/j.tust.2022.104405
35
P SamuiS S RoyV E Balas. Handbook of Neural Computation. San Diego: Academic Press, an imprint of Elsevier, 2017
36
D Kim. Handbook of Research on Predictive Modeling and Optimization Methods in Science and Engineering. Hershey: IGI Global, 2018
37
R Wang, D Li, E J Chen, Y Liu. Dynamic prediction of mechanized shield tunneling performance. Automation in Construction, 2021, 132: 103958 https://doi.org/10.1016/j.autcon.2021.103958
38
J Yang, Y Liu, S Yagiz, F Laouafa. An intelligent procedure for updating deformation prediction of braced excavation in clay using gated recurrent unit neural networks. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13(6): 1485–1499 https://doi.org/10.1016/j.jrmge.2021.07.011
39
N Zhang, A Zhou, Y Pan, S L Shen. Measurement and prediction of tunnelling-induced ground settlement in karst region by using expanding deep learning method. Measurement, 2021, 183: 109700 https://doi.org/10.1016/j.measurement.2021.109700
40
N Zhang, S L Shen, A Zhou. A new index for cutter life evaluation and ensemble model for prediction of cutterwear. Tunnelling and Underground Space Technology, 2023, 131: 104830 https://doi.org/10.1016/j.tust.2022.104830
41
Z Zhang, L Ma. Attitude Correction System and Cooperative Control of Tunnel Boring Machine. International Journal of Pattern Recognition and Artificial Intelligence, 2018, 32(11): 1859018 https://doi.org/10.1142/S0218001418590188
42
H Xie, X Duan, H Yang, Z Liu. Automatic trajectory tracking control of shield tunneling machine under complex stratum working condition. Tunnelling and Underground Space Technology, 2012, 32: 87–97 https://doi.org/10.1016/j.tust.2012.06.002
43
X Tang, K Deng, L Wang, X Chen. Research on natural frequency characteristics of thrust system for EPB machines. Automation in Construction, 2012, 22: 491–497 https://doi.org/10.1016/j.autcon.2011.11.008
44
Y Zhao, H Pan, H Wang, H Yu. Dynamics research on grouping characteristics of a shield tunneling machine’s thrust system. Automation in Construction, 2017, 76: 97–107 https://doi.org/10.1016/j.autcon.2016.12.004
45
S L Shen, K Elbaz, W M Shaban, A Zhou. Real-time prediction of shield moving trajectory during tunnelling. Acta Geotechnica, 2022, 17(4): 1533–1549 https://doi.org/10.1007/s11440-022-01461-4
46
M Längkvist, L Karlsson, A Loutfi. A review of unsupervised feature learning and deep learning for time-series modeling. Pattern Recognition Letters, 2014, 42: 11–24 https://doi.org/10.1016/j.patrec.2014.01.008
47
P RomeuF Zamora-Mart’ınezP Botella-RocamoraJ Pardo. Stacked denoising auto-encoders for short-term time series forecasting. In: Artificial Neural Networks: Methods and Applications in Bio-/Neuroinformatics. Cham: Springer, 2015
48
S Ben Taieb, G Bontempi, A F Atiya, A Sorjamaa. A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition. Expert Systems with Applications, 2012, 39(8): 7067–7083 https://doi.org/10.1016/j.eswa.2012.01.039
49
Q LiR Li K JiW Dai. Kalman filter and its application. In: 2015 8th International Conference on Intelligent Networks and Intelligent Systems (ICINIS). Tianjin: IEEE, 2015
50
R E Kalman. A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 1960, 82(1): 35–45 https://doi.org/10.1115/1.3662552
51
F Auger, M Hilairet, J M Guerrero, E Monmasson, T Orlowska-Kowalska, S Katsura. Industrial applications of the Kalman filter: A review. IEEE Transactions on Industrial Electronics, 2013, 60(12): 5458–5471 https://doi.org/10.1109/TIE.2012.2236994
52
S Särkkä. Bayesian Filtering and Smoothing. Cambridge: Cambridge University Press, 2013
53
N Zhang, N Zhang, Q Zheng, Y S Xu. Real-time prediction of shield moving trajectory during tunnelling using GRU deep neural network. Acta Geotechnica, 2022, 17(4): 1167–1182 https://doi.org/10.1007/s11440-021-01319-1
54
A Geron. Hands-on Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems. Sonoma: O’Reilly Media, 2019
K ChoB van MerrienboerC GulcehreD BahdanauF Bougares H SchwenkY Bengio. Learning phrase representations using RNN encoder–decoder for statistical machine translation. In: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). Doha: Association for Computational Linguistics, 2014
57
S M Liao, J H Liu, R L Wang, Z M Li. Shield tunneling and environment protection in Shanghai soft ground. Tunnelling and Underground Space Technology, 2009, 24(4): 454–465 https://doi.org/10.1016/j.tust.2008.12.005
58
H Xiao, Z Chen, R Cao, Y Cao, L Zhao, Y Zhao. Prediction of shield machine posture using the GRU algorithm with adaptive boosting: A case study of Chengdu Subway project. Transportation Geotechnics, 2022, 37: 100837 https://doi.org/10.1016/j.trgeo.2022.100837
59
G H Erharter, T Marcher. MSAC: Towards data driven system behavior classification for TBM tunneling. Tunnelling and Underground Space Technology, 2020, 103: 103466 https://doi.org/10.1016/j.tust.2020.103466
60
Q Zhang, Z Liu, J Tan. Prediction of geological conditions for a tunnel boring machine using big operational data. Automation in Construction, 2019, 100: 73–83 https://doi.org/10.1016/j.autcon.2018.12.022
61
P Zhang, H N Wu, R P Chen, T Dai, F Y Meng, H B Wang. A critical evaluation of machine learning and deep learning in shield-ground interaction prediction. Tunnelling and Underground Space Technology, 2020, 106: 103593 https://doi.org/10.1016/j.tust.2020.103593
62
P C Mahalanobis. On the generalized distance in statistics. Proceedings of the National Institute of Sciences (Calcutta), 1936, 2: 49–55
63
X Yin, Q Liu, X Huang, Y Pan. Perception model of surrounding rock geological conditions based on TBM operational big data and combined unsupervised-supervised learning. Tunnelling and Underground Space Technology, 2022, 120: 104285 https://doi.org/10.1016/j.tust.2021.104285
64
N WuB Green X BenS O’Banion. Deep transformer models for time series forecasting: The influenza prevalence case. 2020, arXiv:2001.08317
65
D P KingmaJ Ba. Adam: A Method for Stochastic Optimization. 2017, arXiv:1412.6980
66
J Li, P Li, D Guo, X Li, Z Chen. Advanced prediction of tunnel boring machine performance based on Big Data. Geoscience Frontiers, 2021, 12(1): 331–338 https://doi.org/10.1016/j.gsf.2020.02.011
67
R Kohavi. A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence. San Francisco: Morgan Kaufmann Publishers Inc., 1995
68
T T Wong. Performance evaluation of classification algorithms by k-fold and leave-one-out cross validation. Pattern Recognition, 2015, 48(9): 2839–2846 https://doi.org/10.1016/j.patcog.2015.03.009
69
S S Lin, S L Shen, N Zhang, A Zhou. Modelling the performance of EPB shield tunnelling using machine and deep learning algorithms. Geoscience Frontiers, 2021, 12(5): 101177 https://doi.org/10.1016/j.gsf.2021.101177
70
T Yan, S L Shen, A Zhou, X Chen. Prediction of geological characteristics from shield operational parameters by integrating grid search and K-fold cross validation into stacking classification algorithm. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(4): 1292–1303 https://doi.org/10.1016/j.jrmge.2022.03.002
71
S HayouA DoucetJ Rousseau. On the impact of the activation function on deep neural networks training. 2019, arXiv:1902.06853
72
S L Shen, N Zhang, A Zhou, Z Y Yin. Enhancement of neural networks with an alternative activation function tanhLU. Expert Systems with Applications, 2022, 199: 117181 https://doi.org/10.1016/j.eswa.2022.117181
73
M Liu, S Liao, Y Yang, Y Men, J He, Y Huang. Tunnel boring machine vibration-based deep learning for the ground identification of working faces. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13(6): 1340–1357 https://doi.org/10.1016/j.jrmge.2021.09.004
