Hybrid deep learning approach for rock tunnel deformation prediction based on spatio-temporal patterns

Abstract

The ability to predict tunnel deformation holds great significance for ensuring the reliability, safety, and sustainability of tunnel structures. However, existing deformation prediction models often simplify or overlook the impact of spatial characteristics on deformation by treating it as a time series prediction issue. This study utilizes monitoring data from the Grand Canyon Tunnel and introduces an effective data-driven method for predicting tunnel deformation based on the spatio-temporal characteristics of the historical deformation of adjacent sections. The proposed model, a combination of graph attention network (GAT) and bidirectional long and short-term memory network (Bi-LSTM), is equipped with robust spatio-temporal predictive capabilities. Additionally, the study explores other possible spatial connections and the scalability of the model. The results indicate that the proposed model outperforms other deep learning models, achieving favorable root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) values of 0.34 mm, 0.23 mm, and 0.94, respectively. The graph structure based on intuitive spatial connections proves more suitable for meeting the challenges of predicting deformation. Integrating GAT-LSTM with transfer learning technology, remains stable performance when extended to other tunnels with limited data.

Keywords

GAT-LSTM / Deep learning / Transfer learning / Tunnel deformation

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was financially supported by the Sichuan Province Natural Science Foundation Innovative Research Group Project (Grant No. 2024NSFTD0013).

References

[1] Anitescu, C., Atroshchenko, E., Alajlan, N., & Rabczuk, T. (2019). Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua, 59(1), 345-359.

[2] Buczek, M., Long, N., Bui, X.-N., & Nguyen, H. (2018). Application of Knothe-Budryk theory and rigid body condition for assessment of subsidence. International Journal of Sustainable Development, 10(4), 595-603.

[3] Carranza-Torres, C., & Fairhurst, C. (2000). Application of the Convergence- Confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion. Tunnelling and Underground Space Technology, 15(2), 187-213.

[4] Chen, F., Xiong, H., Yin, Z.-Y., & Chen, X. S. (2023). Impermeable and mechanical stability of filter cake under different infiltration conditions via CFD-DEM. Acta Geotechnica, 18(8), 1-26.

[5] Chen, S.-Z., Feng, D.-C., Han, W. S., & Wu, G. (2021). Development of data-driven prediction model for CFRP-steel bond strength by implementing ensemble learning algorithms. Construction and Building Materials, 303(6), 124470.

[6] Chen, Y. G., Huang, J. T., Xu, H. B., Guo, J. C., & Su, L. Y. (2023). Road traffic flow prediction based on dynamic spatiotemporal graph attention network. Scientific Reports, 13, 14729.

[7] Cui, L., Zheng, J.-J., Zhang, R.-J., & Lai, H.-J. (2015). A numerical procedure for the fictitious support pressure in the application of the convergence-confinement method for circular tunnel design. International Journal of Rock Mechanics & Mining Sciences, 78, 336-349.

[8] Damine, Y., Bessous, N., Megherbi, A., & Sbaa, S. (2023). Early bearing fault detection using EEMD and three-sigma rule denoising method. Mechanika, 29(4), 302-308.

[9] Deng, P. H., Liu, Q. S., Liu, B., & Lu, H. F. (2023). Failure mechanism and deformation prediction of soft rock tunnels based on a combined finite-discrete element numerical method. Computers and Geotechnics, 161, 105622.

[10] Dhillon, A., Singh, A., & Bhalla, V. K. (2023). Biomarker identification and cancer survival prediction using random spatial local best cat swarm and bayesian optimized DNN. Applied Soft Computing, 146, 110649.

[11] Feng, T. G., Wang, C. R., Zhang, J., Wang, B., & Jin, Y.-F. (2022). An improved artificial bee colony-random forest (IABC-RF) model for predicting the tunnel deformation due to an adjacent foundation pit excavation. Underground Space, 7(4), 514-527.

[12] Fu, X. L., Wu, M. Z., Ponnarasu, S., & Zhang, L. M. (2023). A hybrid deep learning approach for dynamic attitude and position prediction in tunnel construction considering spatio-temporal patterns. Expert Systems with Applications, 212, 118721.

[13] Guo, Z. Z., Qiu, D. H., Yu, Y. H., Xue, Y. G., Liu, Q. S., Zhang, W. M., & Li, Z. Q. (2023). Analysis and prediction of nonuniform deformation in composite strata during tunnel excavation. Computers and Geotechnics, 157, 105338.

[14] He, Y. C., Chen, Q. N., Huang, X. C., & Chen, Z. H. (2023). Construction and application of lstm based prediction model for tunnel surrounding rock deformation. Sustainability, 15(8), 6877.

[15] Hu, Q. F., Cui, X. M., Liu, W. K., Feng, R. M., Ma, T. J., & Yuan, D. B. (2022). Knothe time function optimization model and its parameter calculation method and precision analysis. Minerals, 12(6), 745.

[16] Huang, Q., Yu, J. S., Wu, J., & Wang, B. (2020). Heterogeneous graph attention networks for early detection of rumors on twitter. In 2020 International Joint Conference on Neural Networks (IJCNN) (pp. 1-8). IEEE.

[17] Iasiello, C., Guerra Torralbo, J. C., & Torrero Fernández, C. (2021). Large deformations in deep tunnels excavated in weak rocks: study on y-basque high-speed railway tunnels in northern spain. Underground Space, 6(6), 636-649.

[18] Jia, Z. Y., Lin, Y. F., Wang, J., Ning, X. J., He, Y. L., Zhou, R. H., Zhou, Y. H., & Le Hman, L.-W. H. (2021). Multi-view spatial-temporal graph convolutional networks with domain generalization for sleep stage classification. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 29, 1977-1986.

[19] Jiang, Y. Z., Liu, H. Z., & Liu, J. Y. (2013). LS-SVM-Markov model for dam deformation prediction. Applied Mechanics and Materials, 423-426, 1144-1149.

[20] Khalili, M. A., Guerriero, L., Pouralizadeh, M., Calcaterra, D., & Di Martire, D. (2023a). Monitoring and prediction of landslide-related deformation based on the GCN-LSTM algorithm and SAR imagery. Natural Hazards, 119(1), 39-68.

[21] Khalili, M. A., Guerriero, L., Pouralizadeh, M., Calcaterra, D., & Di Martire, D. (2023b). Prediction of deformation caused by landslides based on graph convolution networks algorithm and DInSAR technique. In ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences ( vol. X-4-W1-2022, pp. 391-397). Copernicus GmbH.

[22] Kuang, P., Li, R. F., Huang, Y., Wu, J., Luo, X. C., & Zhou, F. (2022). Landslide displacement prediction via attentive graph neural network. Remote Sensing, 14(8), 1919.

[23] Li, C. (2014). Force and deformation of tunnel lining segments in soft soils. Journal of Hohai University, 42(1), 50-56.

[24] Li, J., Zhao, R.Y., Cao, S.L., & Ni, B.W. (2023). Monitoring and geological advance prediction for tunnel construction: A case study of shangzhuang tunnel. doi: 10.21203/rs.3.rs-3785715/v1 (preprint).

[25] Li, X., Xue, Y. G., Qiu, D. H., Ma, X. M., Qu, C., Zhou, B. H., & Kong, F. M. (2019). Application of data mining to lagging deformation prediction of the underwater shield tunnel. Marine Georesources & Geotechnology, 39(2), 1-13.

[26] Li, Y., Yu, D. Z., Liu, Z. K., Zhang, M. X., Gong, X. Y., & Zhao, L. (2023). Graph neural network for spatiotemporal data: methods and applications. arXiv: 2306.00012v1(preprint).

[27] Liu, M. B., Liao, S.-M., Zhu, M., Yang, J., & Men, Y. (2017). Effects of soft soil creep on the load and deformation of a tunnel lining. Modern Tunnelling Technology, 54(4), 107-114.

[28] Liu, S., Liu, T., Liu, B., & Dong, Z. (2011). Numerical simulation of creep deformation for large section tunnel in soil with visco-elastic-plastic FEM. Advanced Materials Research, 368-373, 2500-2503.

[29] Liu, X., Lu, J., Chen, X., Fong, Y. H. C., Ma, X. C., & Zhang, F. (2023). Attention based spatio-temporal graph convolutional network with focal loss for crash risk evaluation on urban road traffic network based on multi-source risks. Accident Analysis & Prevention, 192, 107262.

[30] Luo, H., Fang, Y., Wang, J. F., Wang, Y., Liao, H., Yu, T., & Yao, Z. G. (2023). Combined prediction of rockburst based on multiple factors and stacking ensemble algorithm. Underground Space, 13, 241-261.

[31] Man, C. K., Quddus, M., & Theofilatos, A. (2022a). Transfer learning for spatio-temporal transferability of real-time crash prediction models. Accident Analysis & Prevention, 165, 106511.

[32] Man, K., Liu, R. L., Liu, X. L., Song, Z. F., Liu, Z. X., Cao, Z. X., & Wu, L. W. (2022b). Water leakage and crack identification in tunnels based on transfer-learning and convolutional neural networks. Water, 14(9), 1462.

[33] Meng, Y. D., Qi, Y., Cai, Z. L., Tian, B., Yuan, C. W., Zhang, X. Y., & Zuo, Q. J. (2023). Dynamic forecast model for landslide displacement with step-like deformation by applying GRU with EMD and error correction. Bulletin of Engineering Geology and the Environment, 82(6), 211.

[34] Miao, J. B., LU, D. C., Lin, Q. T., Kong, F. C., & Du, X. L. (2021). Timedependent surrounding soil pressure and mechanical response of tunnel lining induced by surrounding soil viscosity. Science China Technological Sciences, 64(11), 2453-2468.

[35] Mitelman, A., & Urlainis, A. (2023). Investigation of transfer learning for tunnel support design. Mathematics, 11(7), 1623.

[36] Mu, B. G., Xie, X. K., Li, X., Li, J. C., Shao, C. M., & Zhao, J. (2021). Monitoring, modelling and prediction of segmental lining deformation and ground settlement of an EPB tunnel in different soils. Tunnelling and Underground Space Technology, 113, 103870.

[37] Mushtaq, E., Zameer, A., Umer, M., & Abbasi, A. A. (2022). A two-stage intrusion detection system with auto-encoder and LSTMS. Applied Soft Computing, 121, 108768.

[38] Oliveira Santos, V., Costa Rocha, P. A., Scott, J., Van Griensven Thé J., & Gharabaghi, B. (2023). Spatiotemporal analysis of bidimensional wind speed forecasting: development and thorough assessment of lstm and ensemble graph neural networks on the dutch database. Energy, 278, 127852.

[39] Pan, Y., Chen, L., Wang, J., Ma, H. S., Cai, S. L., Pu, S. K., Duan, J. L., Gao, L., & Li, E. B. (2021). Research on deformation prediction of tunnel surrounding rock using the model combining firefly algorithm and nonlinear auto-regressive dynamic neural network. Engineering with Computers, 37, 1443-1453.

[40] Riyadi, W., & Jasmir, J. (2023). Prediction performance of airport traffic using BiLSTM and CNN-Bi-LSTM models. JITK (Jurnal Ilmu Pengetahuan dan Teknologi Komputer), 9(1), 1-7.

[41] Samaniego, E., Anitescu, C., Goswami, S., Nguyen-Thanh, V., Guo, H. W., Hamdia, K., Zhuang, X. Y., & Rabczuk, T. (2020). 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, 362, 112790.

[42] Shi, S. S., Zhao, R. J., Li, S. C., Xie, X. K., Li, L. P., Zhou, Z. Q., & Liu, H. L. (2019). Intelligent prediction of surrounding rock deformation of shallow buried highway tunnel and its engineering application. Tunnelling and Underground Space Technology, 90, 1-11.

[43] Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., & Salakhutdinov, R. (2014). Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15, 1929-1958.

[44] Sun, Q. H., Ma, F. S., Guo, J., Zhao, H. J., Li, G., Liu, S. Q., & Duan, X. L. (2020). Excavation-induced deformation and damage evolution of deep tunnels based on a realistic stress path. Computers and Geotechnics, 129, 103843.

[45] Tamunopiriye, I.-N. & O.E, T. (2023). A random forest regressor model for forecasting air quality index from particulate matters. International Journal of Computer Science and Mobile Computing, 12(10), 57-70.

[46] Tao, Z. L., Wei, Y. W., Wang, X., He, X. N., Huang, X. L., & Chua, T.-S. (2020). MGAT: Multimodal graph attention network for recommendation. Information Processing & Management, 57(5), 102277.

[47] Tu, X.-H., Wang, Z.-L., Liang, Z.-M., & Li, Y.-C. (2005). Study on application of modified weibull model to settlement prediction of foundation. Rock and Soil Mechanics, 26(4), 621-623 (in Chinese).

[48] Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Liò P., & Bengio, Y. (2018). Graph attention networks. In International Conference on Learning Representations (ICLR) 2018. https://doi.org/10.48550/arXiv.1710.10903.

[49] Vlachopoulos, N., & Diederichs, M. (2009). Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnel. Rock Mechanics and Rock Engineering, 42, 131-146.

[50] Waikhom, L., Singh, Y., & Patgiri, R. (2023). PO-GNN: positionobservant inductive graph neural networks for position-based prediction. Information Processing & Management, 60(3), 103333.

[51] Wang, M. Z., & Cai, M. (2022). Numerical modeling of stand-up time of tunnels considering time-dependent deformation of jointed rock masses. Rock Mechanics and Rock Engineering, 55(7), 1-24.

[52] Wang, S. B., Shui, F. R., Stratford, T., Su, J., & Li, B. (2024a). Modelling nonlinear shear creep behaviour of a structural adhesive using deep neural networks (DNN). Construction and Building Materials, 414, 135083.

[53] Wang, S. Y., Liu, T. Y., Zheng, X. C., Yang, J. S., & Yang, F. (2024b). Dynamic collapse characteristics of the tunnel face induced by the shutdown of earth pressure balance shields (EPB): A 3D material point method study. Underground Space, 16, 164-182.

[54] Wang, X., He, X. N., Cao, Y. X., Liu, M., & Chua, T.-S. (2019). KGAT: Knowledge graph attention network for recommendation. In KDD 2019: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (pp. 950-958).

[55] Wei, J. C., Qi, J., Wu, Y., Lu, Y., & Wang, L. (2012). Prediction of the deformation of the surrounding rock around tunnels by GA-Bp network model. Applied Mechanics and Materials, 256-259, 1157-1160.

[56] Wu, X. D., Li, Y., Gong, M., Wu, H. J., & Wu, Y. F. (2023). Deformation and stress law of surrounding rock for a bifurcated tunnel with a superlarge section: A case study. Applied Sciences, 13(23), 12852.

[57] Wu, Z. Y., Pi, D. C., Chen, J. F., Xie, M., & Cao, J. J. (2020). Rumor detection based on propagation graph neural network with attention mechanism. Expert Systems with Applications, 158, 113595.

[58] Xiao, D.-H., Xie, Q.-M., & Yang, W.-D. (2018). Application of integrated forecasting model based on multiple variables in tunnel vault settlement. Journal of Highway and Transportation Research and Development (English Edition), 12(3), 46-52.

[59] Xu, G. T., Liu, P. Y., Zhu, Z. F., Liu, J., & Xu, F. Y. (2021). Attention-enhanced graph convolutional networks for aspect-based sentiment classification with multi-head attention. Applied Sciences, 11 (8), 3640.

[60] Xu, K. K., Hu, J. Q., Zhang, L. B., Chen, Y. Y., Xiao, S. R., & Shi, J. C. (2023). A risk factor tracing method for LNG receiving terminals based on GAT and a bidirectional LSTM network. Process Safety and Environmental Protection, 170, 694-708.

[61] Xu, W., Cheng, M., Xu, X. Y., Chen, C., & Liu, W. (2022). Deep learning method on deformation prediction for large-section tunnels. Symmetry, 14(10), 2019.

[62] Xue, Y. G., Ma, C. M., Yang, W. M., Ma, L., Qiu, D. H., Li, Z. Q., Li, X., & Zhou, B. H. (2020). Total deformation prediction of the typical loess tunnels. Bulletin of Engineering Geology and the Environment, 79 (4), 1-14.

[63] Xue, Y. G., Ma, X. M., Qiu, D. H., Yang, W. M., Li, X., Kong, F. M., Zhou, B. H., & Qu, C. Q. (2021). Analysis of the factors influencing the nonuniform deformation and a deformation prediction model of soft rock tunnels by data mining. Tunnelling and Underground Space Technology, 109, 103769.

[64] Yan, C., Ding, C. S., & Duan, G. H. (2022). PMMS: Predicting essential miRNAs based on multi-head self-attention mechanism and sequences. Frontiers in Medicine, 9, 1015278.

[65] Yang, H. R., Wang, J. L., Duan, R., & Yan, C. G. (2023). DCOM-GNN: A deep clustering optimization method for graph neural networks. Knowledge-Based Systems, 279, 110961.

[66] Yao, C. L., Chen, J., & Liu, L. P. (2014). Numerical simulation study on the delay of rockburst based on rock mass stress release rate. Applied Mechanics and Materials, 501-504, 20-26.

[67] Yu, B., Cai, R. P., Zhang, J., Fu, Y., & Xu, Z. S. (2023). A graph attention network under probabilistic linguistic environment based on bi-lstm applied to film classification. Information Sciences, 649, 119632.

[68] Yu, P., Zheng, J.-J., Cui, L., & Zhang, R.-J. (2018). Numerical analysis of ground displacement and pile response due to tunneling in soft soil considering the creep behavior In D. Zhang, X. Huang (eds) Proceedings of GeoShanghai 2018 International Conference: Tunnelling and Underground Construction(GSIC 2018), (pp. 121 - 130 ). Singapore: Springer.

[69] Zhang, L. G., Zeng, H. W., Ding, Y. L., Hu, H., Chen, L., Zhang, J. X., & Zhou, Y. (2023). Geo-environment-aware adversarial transfer learning method for landslide susceptibility evaluation of complex mountainous areas. Transactions in GIS, 27(5), 1418-1440.

[70] Zhang, L. L., Cheng, H., Yao, Z. S., & Wang, X. J. (2020). Application of the improved knothe time function model in the prediction of ground mining subsidence: A Case Study from Heze City, Shandong Province, China. Applied Sciences, 10(9), 3147.

[71] Zhang, W. G., Zhong, H. Y., Xiang, Y. Z., Wu, D. F., Zeng, Z. K., & Zhang, Y. M. (2022). Visualization and digitization of model tunnel deformation via transparent soil testing technique. Underground Space, 7(4), 564-576.

[72] Zhang, Z., & Jiao, X. H. (2023). A spatio-temporal grammar graph attention network with adaptive edge information for traffic flow prediction. Applied Intelligence, 53(12), 28787-28803.

[73] Zhang, Z. L., Zhang, T. T., Li, X. S., & Dias, D. (2024). Bayesian ensemble methods for predicting ground deformation due to tunnelling with sparse monitoring data. Underground Space, 16, 79-93.

[74] Zhao, H. X., Zhou, Z. L., & Zhang, P. Z. (2023a). Forecasting of the short-term electricity load based on WOA-BILSTM. International Journal of Pattern Recognition and Artificial Intelligence, 37(11), 2359018.

[75] Zhao, L. X., Li, Z. Y., Qu, L. L., Zhang, J. S., & Teng, B. (2023b). A hybrid VMD-LSTM/GRU model to predict non-stationary and irregular waves on the east coast of china. Ocean Engineering, 276, 114136.

[76] Zhou, H., Ren, D. C., Xia, H. X., Fan, M. Y., Yang, X., & Huang, H. (2021). AST-GNN: an attention-based spatio-temporal graph neural network for interaction-aware pedestrian trajectory prediction. Neurocomputing, 445, 298-308.