## 5 Theoretical Case Study, Results, and Discussion
### Result and Discussion  
Based on the TBM operating parameters and geological parameters of the rock, a machine learning algorithm was applied to predict TBM performance in advance and help visualize the project progress status. The most important TBM parameters during tunnel excavation are advance speed (mm/min), rotational speed (rpm), advance pressure (bar), cutterhead torque (MNm), total advance force (kN), penetration (mm/rot), the pressure of crown-support-cylinder left and right (bar), and path of crown-roof-support-cylinder (mm), which are recorded at a specific interval during the excavation process of the tunnel. All this information is recorded to systematically understand the behavior of the TBM. Also, it includes the geological data, TBM's geographic location, daily progress, and remaining tunnel excavation length. The daily progress of the TBM over a month is shown in Figure 13.  
A digital twin-based framework for TBM performance prediction, visualization, and monitoring was designed with machine learning. Based on TBM design and operational information, TBM manufacture was carried out in a virtual environment. It is a virtual TBM product that replicates a real TBM and its behavior in a virtual environment to help the manufacturer quickly understand TBM design and decision-making for project scheduling. For that purpose, a digital twin and a machine learning-based six-step process were adopted to visualize and monitor TBM performance on virtual platforms. The operating parameters were then transferred to the virtual model to visualize the operating condition. The operating parameters of the TBM and the geological factors of the ground were selected carefully to prepare the dataset in a suitable format for the desired machine learning algorithm. A machine leaning algorithm was developed to feed the virtual model with different RPM values and the revolution of the machine was demonstrated in a virtual gaming environment. Figure 14 shows the TBM virtual model rotating at the given RPMs. Real-time monitoring was carried out to visualize and understand TBM performance and progress in virtual environments close to the real case. Feedback based on TBM performance was sent back to the database to update the data. The TBM's historical and current operating parameters were collected for visualization, performance prediction, and progress comparison. This provides an opportunity for the end user to understand and monitor the state of the TBM and real-time information about the system, subsystem, and key components by forming a closed loop of a physical TBM, virtual TBM model, digital twin data platform, and the virtual environment to visualize each change in the state of the TBM. Figure 13: TBM daily progress (in meters). TBMs have many advantages, they still encounter many problems due to complex geological conditions. AI-based algorithms such as SVR can test the feasibility and applicability of a TBM before project commencement. Using the SVR model, TBM penetration rate predictions can be made to an adequate level, which helps control cost, as the interaction between machine and rock mass can be accommodated. The efficiency of the SVR model is estimated by comparing the measured and predicted values. The SVR model shows an accurate PR prediction compared to the measured ones. The predictive performance indices RMSE, R\({}^{2}\), and VAF are computed to evaluate the efficacy of the model. The performance indices RMSE, R\({}^{2}\), and VAF are predicted quite accurately, as shown in Figure 15(a1,a2) and Table 3. The findings of the SVR predictions show high conformity between predicted and actual SVR values of TBM PR. Similar results were reported in [2] using a limited dataset. Recently, authors of [18] presented promising results by using rock strength properties as input parameters. PR prediction using the ANN model was carried out using L-BFGS as a solver function.