## 4 Conclusions  
A damage detection study for underground metro shield tunnels was presented in this paper. A numerical model of a metro shield tunnel was utilized, and data obtained from the model through a moving load analysis were used as inputs for the existing deep auto-encoders (DAE) and convolutional neural networks (CNN). Varying levels of damage and noise were considered in the analyses and the utilized deep learning model accurately identified the damage.  
* First, an FEM model of the underground metro shield tunnel structure was built based on previous experimental studies. The dynamic analyses on the numerical model were conducted under a moving load with different severity levels of damage at different locations and elements. To simulate the real-world tunnel scenarios, a different percentage of white noise was added to the calculated responses of the tunnel model to simulate polluted data measurements;
* Second, a DAE-based framework was used for damage identification, which can support deep neural networks in accurately investigating structural damage via damage feature extraction from input vibration raw signals (without any processing). In addition, root means square (RMS) was used to locate the damage at the different elements and locations in the model. The results were compared under the different schemes: white noise, varying levels of damage, and an intact state. The proposed deep auto encoder algorithm is trained and executed using MATLAB;
* To check the feasibility of the proposed approach on a small dataset such as a beam, a finite element model of the simply supported beam was built with ABAQUS software, and numerical simulations were conducted under an impact load. To evaluate the efficiency of the proposed DAE approach, two deep learning-based methods (LSTM and SVM) were also compared with the same input vibration data of the beam. The results of evaluating the beam and comparing it to the other two methods showed that the proposed DAE framework is also feasible for a small structure;
* A numerical investigation of the underground metro shield tunnel structure validated the accuracy and efficacy of the proposed deep autoencoder (DAE)-based framework execution regarding damage detection, damage size evaluation, and damage localization.  
Conceptualization, N.A. and M.A.; methodology, N.A.; software, N.A.; validation, N.A., M.A. and Z.H.; formal analysis, N.A.; investigation, N.A.; resources, T.U.; writing--original draft preparation, M.A. and Z.H.; writing--review and editing, R.S., T.U. and X.H.; supervision, T.U.; project administration, T.U. All authors have read and agreed to the published version of the manuscript.  
This paper was supported by the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (Grant No. 2019 QZKK0902), and National Natural Science Foundation of China (Grant No. 42077275). It was also supported by Youth Innovation Promotion Association of the Chinese Academy of Sciences (2018405).  
We declare that we do not have human participants, human data, or human tissue.  
All data available as per request to corresponding author.  
The authors declare that there is no conflict of interest regarding the publication of this paper.