# Inversion Analysis Method for Tunnel and Underground Space Engineering: A Short Review
## 3 Inversion Analysis of Initial Ground Stress
### Intelligent Inversion Analysis Method  
At the beginning of the 21 st century, research on geo-stress inversion of rock masses entered its second stage. Researchers have combined neural networks and numerical analysis to perform initial ground stress inversion analysis [31]. However, for the initial in situ stress field inversion problem under complex geological conditions, the simplified model cannot obtain reasonable and accurate stress parameters due to objective factors such as discontinuity, non-uniformity, and non-elastic-plasticity of the rock mass itself. Therefore, approximating the in situ stress field under general conditions is difficult, and the solution process is very inefficient when considering multi-field coupling problems such as temperature and seepage field. Figure 5: Selection of computational domain coordinates. With the improvement of measurement technology, site construction workers can collect more in situ stress measurement data. The inversion analysis method combined with information theory and new optimization methods has gradually become the main direction of research. At the same time, intelligent algorithms such as machine learning are used to mine the measured data, increasing the generalization analysis ability of the inversion model. Figure 6 shows a technical roadmap of the intelligent inversion analysis method. In the process of initial geo-stress inversion analysis using intelligent algorithms, the neural network algorithm based on genetic algorithm optimization is one of the most commonly used methods. This algorithm originated from the simulation study of biological systems and drew on the mechanism of biological genetics, which can be more relevant to the mechanism of neural networks using human brain neurons to process information. Its application scope covers optimization problems that are difficult to solve in traditional inversion analysis. Many scholars also choose to use this method to solve the in situ stress distribution of dam bodies [32], underground powerhouses of hydropower stations, and deep-buried tunnels [33]. [PERSON] et al. [34] proposed a non-linear inversion method of in situ stress, which integrates ground abrasion simulation, elastoplastic calculation, and a neural network. The nonlinear relationship between the boundary conditions to be inverted and the stress can be described by such neural networks, as shown in Equation (3). This method considered the time series conditions of ancient structures and better simulated the strong  
Figure 6: Flow chart of intelligent inversion of initial in situ stress. erosion of rivers on the ground stress field in the current site area, so that the inversion results have higher credibility. \[\left. \begin{array}{l}NN\big{(}m,\ x_{1},\ \cdots,\ x_{p},\ n\big{)}:R^{m} \to R^{n}\\ D=NN\big{(}m,\ x_{1},\ \cdots,\ x_{p},\ n\big{)}(P)\\ P=(p_{1},\ p_{2},\ \cdots,\ p_{m});D=(d_{1},\ d_{2},\ \cdots,d_{n})\end{array} \right\} \tag{3}\]  
where \(P=(p_{1},p_{2},\ \cdots,p_{m})\) is the input variable of the neural network, expressed as the stress value at the measurement point, \(D=(d_{1},\ d_{2},\ldots,\ d_{n})\) is the output variable of the neural network, expressed as the displacement boundary condition of the constructed stress field, \(NN=(m,\ x_{1},\ x_{2},\ldots,\ x_{p},\ n)\) is the established multilayer neural network structure and m, n are the number of nodes in the input and output layers, respectively. Deep learning neural networks, such as the radial basis function (RBF) neural network and the generating adversarial network (GAN), are widely used in various tunnel and underground space projects. [PERSON] et al. [35] proposed a back analysis method of the earth's stress field considering the hydraulic fracturing environment by combining an artificial neural network with a genetic algorithm, based on the principle of the RBF neural network.