## 4 Conclusions  
The stability of the underground roadways (headings, galleries, drifts, gate roads, and drives) is crucial for the smooth operation of a mine. When underground roadways are constructed in complex geological conditions and in a weak rock mass, installation of adequate support construction is necessary for the stability maintenance of the roadways in order to provide its functionality during exploitation time. Even then, mostly due to the influence of the dynamic loads from the rock mass, the deformations of the walls and arch of the underground roadways occur. These deformations are also represented in the support construction. Steel arch support is the most used support construction in the headings and gate roads in underground coal mines. As the deformations of the steel arch support cause the shrinking of the cross-section area of the underground roadways, it is important to monitor and forecast the deformations of the sections that can jeopardize the planned work cycle.  
In this paper, we presented a forecasting model based on the grey system theory, which observes the deformations of markers placed on a steel arch support. By measuring the coordinates of the marker in a defined period (25 days), data on the position of the marker are obtained, as well as the increment of the deformations along the \(x\)- and \(y\)-axis each day. Increments of the deformations along the \(x\)- and \(y\)-axis are observed as two univariate time series, which are later used for the forecasting of the future states of the markers, i.e., the steel arch support.  
The previous chapter detailed our model, which gave a MAPE of forecasting of 11.75% in the case when the error was analyzed from a time series point of view. With such an error, the model accuracy is described as good. As the nature of the described problem is such that the position of the marker, i.e., the future position of the underground construction, is of importance to mining engineers, we introduced the analysis of the error of the marker position to evaluate the effectiveness of the model. The MAPE of the forecasting model is 0.2143%, and in that term, the model accuracy is described as high. For the autoregressive model, the proposed window length of \(\rho\cong T/2-2\) showed high accuracy (92.34%) for the AR(10) model for fitted data of corresponding states, while it showed reasonable accuracy (57.14%) for the same model for the validity (forecasting) phase. One of the focuses of future research will be the definition of the optimal window length for an autoregressive  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & & & \\ \hline
**Phase** & **M1** & **M2** & **M3** & **M4** & **M5** & **M6** & **M7** \\ \hline Fitting & 0.064 & 0.023 & 0.003 & 0.677 & 0.007 & 0.010 & 0.010 \\ Forecasting & 0.081 & 0.021 & 0.013 & 1.314 & 0.027 & 0.031 & 0.013 \\ \hline \hline \end{tabular}
\end{table}
Table 30: Marker position error.  
model to achieve greater accuracy of the model in general. The development of a smart rolling model is also planned to make the model more user-friendly.  
This model can be used by mining engineers in underground coal mines for accurate forecasting of the future states of the steel arch support. Using this model, it is possible to plan the maintenance of underground roadways more efficiently, which further results in fewer stoppages in the process of coal production and lower operating costs of the mine.  
Conceptualization, L.C. and Z.G.; methodology, L.C.; software, L.C.; validation, S.L., R.T. and M.G.; formal analysis, Z.G.; data curation, L.C. and M.G.; writing--original draft preparation, L.C.; writing--review and editing, S.L. and R.T.; visualization, L.C. and Z.G.; supervision, Z.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.