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Real-time prediction of shield moving trajectory during tunnelling

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Abstract

This paper presents a novel deep learning model for real-time prediction of shield moving trajectory during tunnelling. The proposed model incorporates a wavelet transform (WT) into Adam-optimised long short-term memory (LSTM) (WT-Adam-LSTM). The WT is employed to remove the irrelevant noise of data in the time and frequency domains, which allows the sequence pattern to be detected easily. The Adam algorithm is used to increase the reliability and optimise the gradient training process of the LSTM neural network for a given time series. The developed model considers the shield performance database, complex geological conditions, soil geometry, and operational parameters. A case study of a tunnel section under Bao'an International Airport was employed to verify the performance of the proposed model. A comparison with other models, i.e. recurrent neural network, LSTM, and support vector regression, was also made. The results show that WT-Adam-LSTM provides an effective solution and can achieve better results compared with other models.

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Acknowledgements

The research work was funded by “The Pearl River Talent Recruitment Program” in 2019 (Grant No. 2019CX01G338) and Guangdong Province and the Research Funding of Shantou University for New Faculty Member (Grant No. NTF19024-2019).

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Authors and Affiliations

  1. MOE Key Laboratory of Intelligence Manufacturing Technology, Department of Civil and Environmental Engineering, College of Engineering, Shantou University, Shantou, 515063, Guangdong, China

    Shui-Long Shen, Khalid Elbaz & Wafaa Mohamed Shaban

  2. Civil and Infrastructure Discipline, School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne, VIC, 3001, Australia

    Annan Zhou

  3. Department of Civil Engineering, Higher Future Institute of Engineering and Technology, El Mansoura, Egypt

    Khalid Elbaz

  4. Department of Civil Engineering, Misr Higher Institute of Engineering and Technology, El Mansoura, Egypt

    Wafaa Mohamed Shaban

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  1. Shui-Long Shen
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  2. Khalid Elbaz
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  4. Annan Zhou
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Correspondence to Shui-Long Shen.

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Appendix

Appendix

The interpolation equations and their explanations are illustrated below [25]:

Having measured n data values,\(z\left( {x_{1} } \right)\), \(z\left( {x_{2} } \right)\), …, \(z\left( {x_{n} } \right)\) at \(x_{1}\), \(x_{2}\), …, \(x_{n}\) locations, the basic principles of kriging approach can be formulated by estimating the \(z^{*} \left( {x_{0} } \right)\) at the unknown location of x0 with the following equation:

$$z^{ * } (x_{0} ) = \sum\limits_{i = 1}^{n} {\lambda_{i} z(x_{i} } )$$
(16)

where \(z^{*} \left( {x_{0} } \right)\) is the estimated value for the unmeasured point x0; \(z\left( {x_{i} } \right)\) refers to the measured value of variable z at point xi; λ is the interpolation weight coefficient; n is the total number of values required for the interpolation.

The minimum variance of error (σk) is required to achieve the optimal estimation, where

$$\sigma_{k} = {\text{var}} \left[ {z(x_{o} ) - z^{ * } (x_{i} )} \right] = E\left\{ {\left[ {z(x_{0} ) - \sum\limits_{i = 1}^{n} {\lambda_{i} z(x_{i} )} } \right]^{2} } \right\}$$
(17)

For the unbiased prediction, the resulting constraint should be specified, where

$$\sum\limits_{i = 1}^{n} {\lambda_{i} } = 1$$
(18)

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Shen, SL., Elbaz, K., Shaban, W.M. et al. Real-time prediction of shield moving trajectory during tunnelling. Acta Geotech. 17, 1533–1549 (2022). https://doi.org/10.1007/s11440-022-01461-4

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