# Back Analysis of Geotechnical Engineering Based on Data-Driven Model and Grey Wolf Optimization
## 6 Conclusions  
This study developed a novel back analysis framework to identify the geomaterial property by combining a numerical model, ROM, and GWO. The ROM was utilized to establish the surrogate model for capturing deformation during excavation in geotechnical engineering. The numerical method was adopted to construct snapshots for the ROM based on the design of the experiment. The geomaterial properties were identified based on the monitored displacement data by the developed framework. Meanwhile, GWO was selected as an optimal technology for back analysis due to its global optimization performance. The developed back analysis framework was illustrated successfully by a numerical example and Goupitan experimental tunnel. The geomaterial properties identified by this study were compared with the ROM prediction. The predicted displacement of the surrounding rock mass was also close to the actual monitored displacement. The results showed that the developed back analysis framework provides a convenient, practical, and accurate way to understand the geomaterial properties based on the monitored response during construction.  
1. The ROM model was utilized to construct a low-order surrogate model for capturing the response-induced excavation in geotechnical engineering and replacing the numerical model in the back analysis. It is critical to practical engineering due to the difficulties in obtaining the analytical solution for geotechnical engineering;
2. Back analysis is a scientific and practical tool widely used in geotechnical engineering. The numerical model and optimal technology are the two critical components of back analysis. The developed back analysis framework takes full advantage of the merits of ROM and GWO and provides a feasible way for determining the property of the surrounding rock mass in geotechnical engineering;
3. ROM is an excellent physics-based data-driven surrogate model that can capture the mechanism of surrounding rock mass. GWO is an efficient metaheuristic method developed recently and is suitable for solving the black-box problem. However, ROM depends on the numerical fidelity model, and the parameters of the GWO algorithm influence the optimal performance. In a future study, the authors will further improve the developed framework by absorbing and combining the advantages and merits of various methods.  
Conceptualization, L.Z. and H.Z.; methodology, L.Z. and H.Z.; software, L.Z. and H.Z.; validation, X.L. and X.Z.; formal analysis, L.Z. and H.Z.; investigation, L.Z. and H.Z.; data curation, L.Z. and H.Z.; writing--original draft preparation, L.Z. and H.Z.; writing--review and  
Figure 15: Convergence process of the developed framework.  
editing, X.L. and X.Z.; visualization, H.Z. All authors have read and agreed to the published version of the manuscript.  
This study is sponsored in part by the Shandong Provincial Natural Science Foundation, China under grant ZR2022 ME198, to which the authors are very grateful.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.