# Real-Time Prediction of Operating Parameter of TBM during Tunneling
###### Abstract  
With the increasing use of the tunnel boring machine (TBM), attempts have been made to predict TBM operating parameters. Prediction of operating parameters is still an important step in the adaptability of the TBM for the future. In this study, we employ a walk forward (WF) prediction method based on ARIMAX, which can consider time-varying features and geological conditions. This method is applied to two different TBM projects to evaluate its performance, and is then compared with WF based on ordinary least squares (OLS). The simulation results show that the ARIMAX predictor outperforms the OLS predictor in both projects. For practical applications, an additional analysis is carried out according to the real-time prediction distance. The results show that time series-based ARIMAX provides meaningful results in 8 rings (11 m) or less of real-time prediction distance. The WF based on ARIMAX can provide reasonable TBM operating conditions with time-varying data and can be utilized in decision-making to improve excavation performance.  
real-time prediction; operating parameter; TBM; ARIMAX; walk forward +
Footnote †: journal: Applied  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Real-Time Prediction of Operating Parameter of TBM during Tunneling. _Appl. Sci._**2021**, _11_, 2967. [[https://doi.org/10.3390/app11072967](https://doi.org/10.3390/app11072967)]([https://doi.org/10.3390/app11072967](https://doi.org/10.3390/app11072967))  
rock conditions. A study applying random forest (RF) was also conducted based on heterogeneous in situ data [12].  
The aforementioned works based on experimental, numerical, and empirical methods provide insights into the prediction of thrust, but these methods have limitations in terms of field applicability because they provide thrust values in the form of a range. In addition, operating parameters such as thrust are dependent on time-varying and non-stationary features. For example, since non-time series methods such as GEP and RF only use the current inputs without the aid of previous input information, they are not suitable for thrust prediction in real time.  
Recently, a time series-based method has been utilized for real-time prediction of thrust [13]. Since this method considers both current inputs and previous input information, it is suitable for application to non-stationary time series parameters, such as TBM thrust. However, the inputs of the existing model include only operating parameters and not geological conditions, which are known to be the main parameters related to TBM thrust. For example, higher thrust is generally suitable for hard rock and non-discontinuity rock conditions. The importance of geological conditions has been shown in several literature works [5; 14; 15].  
In this study, we simulate walk forward (WF) based on ARIMAX in consideration of both geological parameters and TBM thrust. Two actual projects with different construction conditions are employed to obtain the data used for constructing empirical models, respectively. For comparative analysis, the proposed method is compared with non-time series WF based on ordinary least squares (OLS). Additionally, the thrust prediction is examined according to the real-time prediction distance to validate the field applicability.