## 3 Results
### Damage Localization of Different Cases  
The results of numerical simulations were discussed, and the damage localization was presented using an RMS deviation. The changes in the damage index of different damage cases were also discussed. Usually, the damage index is imperative for the condition assessment of the structures, which is based on the real part of the acceleration sensors as a sign of condition variations through perceiving the changes and quantifying the damage statistically. A mean function is a useful tool for arranging and analyzing large datasets. The RMS is a powerful statistical measure for figuring out the number of changes when the changes are both positive and negative. The damage index of the underground metro tunnel structure was calculated and evaluated under motion using acceleration response raw data (without any processing). The raw vibration data acquired from the numerical simulation of a tunnel model using 300 elements with different percentages of damage severity were used for the localization of damage in the structure. The RMS deviation was used for the localization of each damage condition. Each damaged case was given a separate damage index, which shows the damage index of each damaged and undamaged case. In order to simulate the real tunnel environment, 6% white noise and 12% of white noise were added to the input signals, respectively. The damage identification results under the condition of adding two types of white noise are shown in Figures 11 and 12, respectively. As shown in Figure 11, even though the damage severity is 4%, the maximum damage index value can be accurately observed at the damage indicator when 6% white noise is added. Besides, the damage index increased from 1.40 to 4.68 as the damage severity risen from 4% to 10%. Damage cases, 1, 2, and 3 have one damage on element 100, and cases 6, 7, 8, and 9 have damage on three elements of different severities. Similarly, when 12% white noise is added, 4% damage can also be accurately identified, and the damage index increased from 1.48 to 5.28 as the damage degree increased from 4% to 10%. Figure 10: Confusion matrix results efficiency. Figure 11: _Cont._  
The results of damage identification in two cases demonstrate that the proposed method is feasible to identify structural damage with 6% white noise and 12% white noise, respectively. At the same time, when different types of noise pollution were added, the structural damage index value changed slightly. This shows that the method is reliable and can be used to find, locate, and classify damage in underground tunnel structures. It should be noted from the damage identification results that the higher damage degree on the damage indicator clearly demonstrates the change in the value of damage with damage severity. It can be seen from the observation that the damage identification values at elements 100 and 200 are significantly higher than the element 180 damage index values. As shown in Figure 13a, the higher damage indicator value corresponds to the damage severity. The damage case has a higher damage index of 10% damage severity. Furthermore, there is no damage in cases 1 and 2 when the damage rigorousness is 10%, as shown in Figure 13a. It is noted that in case 4, element 100 has damage; however, elements 180 and 200 have no damage. Similarly, damage case 9 has maximum damage on all elements. As shown in Figure 13b, element 200 has no damage in the first six damage cases, and element 180 has no damage in the first three cases. Similarly, element 100 has maximum damage in all cases. All the above simulations, analyses of the results, and discussions show that the proposed deep auto encoder (DAE)-based framework execution for damage recognition, damage size assessment, and damage localization is accurate and possible for underground metro tunnel structures.