# Inversion Analysis Method for Tunnel and Underground Space Engineering: A Short Review
## 3 Inversion Analysis of Initial Ground Stress
### Intelligent Inversion Analysis Method
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Inversion Analysis Method** & **Project Cases** & **Brief Description of Analysis Results** \\ \hline \multirow{4}{*}{Atlas method [23]} & 1580 hoist cavern of Muding copper deposits & Only elastic stress and displacement can be inferred, but for some underground engineering with special section shapes and complex geological conditions, the applicability is poor \\ \hline \multirow{2}{*}{Finite element method [27]} & \multirow{2}{*}{Ertan hydropower station} & Some deviation in the stress of the part affected by lithology change or local structure \\ \hline \multirow{2}{*}{Displacement back analysis [38]} & \multirow{2}{*}{Urumqi Wudong Coal Mine} & The actual vertical stress value is smaller than the inverse calculation result, while the minimum principal horizontal stress value is similar to the inverse calculation result \\ \hline \multirow{2}{*}{Multiple regression analysis [39]} & \multirow{2}{*}{Daxiangling Tunnel, Ya’an City, Sichuan Province} & The regression analysis results are basically consistent with the measured results, and the relative error is controlled within 10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The statistical results of the simulation cases for initial geo-stress inversion analysis in traditional inversion analysis. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Inversion Analysis Method** & **Project Cases** & **Brief Description of Analysis Results** \\ \hline \multirow{4}{*}{Artificial neural networks (ANNs) and genetic algorithms (GAs) [35]} & \multirow{2}{*}{Hydropower projects at Huizhou Pumped Storage Power Station} & The relative errors between the theoretical and network calculated values of maximum and minimum horizontal soil stress are only 1.01\% and 0.24\%, respectively. \\ \hline \multirow{2}{*}{GMDH neural network algorithms [36]} & \multirow{2}{*}{Xingshan iron mine} & The average inversion accuracy reached 84\%, and the inversion error of stress components is less than 10\% for most of the measuring points \\ \hline \multirow{2}{*}{BP neural network [40]} & \multirow{2}{*}{Sichuan-Tibet Railway Tunnel} & Compared with the multiple regression analysis method, the average relative error of the inversion results of maximum horizontal principal stress and vertical stress is reduced by 26.44\% and 77.27\%, respectively. \\ \hline \multirow{2}{*}{Segmentation feature capsule Network based on convolution Neural Network Enhancement [41]} & \multirow{2}{*}{China coal mine underground stress database} & Mean square error is as low as 0.06\%, which is lower than 0.62\% of deep neural network prediction algorithms and 0.98\% of traditional machine learning algorithms \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The statistical results of the simulation cases for initial geo-stress inversion analysis in intelligent inversion analysis. and cannot reflect the stress field under complex conditions. Additionally, the inversion analysis method based on elastic mechanics theory does not consider the plastic state of rock mass in tunnel and underground engineering construction under deep complex geological conditions. Therefore, it is a matter of urgency to develop new deep rock mechanics theories and methods that consider non-linear factors such as construction [42; 43] and the inversion method of in situ stress variation under the influence of major geological conditions such as faults and geological structures [44]. With the help of stress inversion, it is possible to predict and diagnose the diseases of supporting structures [45]. In future research, the method of in situ stress monitoring and inversion optimization algorithm can be combined to reduce measurement errors and further improve the theory of multi-scale geostress inversion under complex geological conditions. It is also necessary to explore the inversion analysis method of initial geostress under high geostress conditions and high-altitude cold areas, and other special environments.