# Inversion Analysis Method for Tunnel and Underground Space Engineering: A Short Review
## 4 Inversion Analysis of Supporting Load
### Intelligent Inversion Analysis Method  
There have been few cases of using neural networks for load inversion analysis of support structures in tunnel construction. [PERSON] et al. [59] introduced a particle swarm optimization algorithm and finite element analysis method into the displacement inversion analysis process of supporting structure load. This provided technical support for the information design and intelligent construction of subway tunnel structures. [PERSON] et al. [60] proposed a TBM shield and surrounding-rock load inversion method based on Newton iteration and finite element theory. The external surface of the TBM shield is divided into regularly curved rectangular cells according to the circumferential or axial components of the column coordinates, and the four nodal load values of the rectangular cells are used as inversion parameters. To analyze the inversion efficiency and stability, the calculation is performed by assuming two cases, such as symmetric linear load and inhomogeneous load distributed on the external surface of the shield (shown in Figure 9). The results show that the inversion algorithm can realize the discrete fitting of the TBM shield surface under arbitrary surrounding rock loads, and the model has high robustness and good error immunity. He [61] proposed a random load inversion method based on probability density evolution theory. Compared with other intelligent optimization algorithms, this method starts from the randomness of monitoring information in practical engineering and usesrandom system theory to invert the distribution characteristics of loads in underground structures. [PERSON] et al. (2018) proposed a method to inverse the cohesion and internal friction angle of rock mass by grouting, bolt prestress and bolt arrangement based on mechanical analysis, machine learning, and reliability theory. Taking the deep-buried tunnel in loose rock mass as an example, the interaction between deep surrounding rock and support is studied, and its reliability is evaluated. In the field of tunnel and underground engineering, the load back analysis of supporting structure is a practical direction in the inverse theoretical research, and field measurement is the only way to study the stress data of supporting structure. High-precision detection and installation of more efficient measurement tools, such as advanced geological prediction systems (TSP), ground-penetrating radar and optical-fiber sensors, will provide more scientific and accurate observation data for load back calculation. The result of inverse calculation will have higher credibility, which is of great significance for the mechanical analysis of tunnel construction processes. [PERSON] et al. (2018) selected distributed optical fiber sensors to monitor the stress and deformation of damaged tunnel lining, and then proposed a more accurate back analysis method to calculate the deformation modes of tunnel arch structures, such as displacement, stress, and load. [PERSON] et al. (2018) relied on the optical-fiber sensor monitoring system of an optical time domain reflectometer to obtain real-time deformation parameters inside the tunnel. Through numerical experiments, the parameters obtained by orthogonal design and uniform design are calculated, and the mapping relationship between tunnel surrounding-rock parameters and monitoring displacement is established. Finally, the parameters are identified based on differential evolution algorithm. Combined with the Dalian Baiyunshan tunnel project, it is proved that this method has strong adaptability. The representative engineering cases of supporting structures load inversion are listed in Tables 3 and 4, respectively. It is not difficult to find from the above table that for the load inversion analysis, the method adopted by scholars is slightly different from the initial in situ stress inversion.