## 4 Application Examples
### Landslide Prediction Performance
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & **Unit 1** & **Unit 2** & **Unit 3** \\ \hline \multirow{4}{*}{GM(1, 1)} & Horizontal displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 56.7208 mm & 63.1630 mm & 0.8081 mm \\  & \(\overline{\Delta}\) & 7.01\% & 10.72\% & 0.55\% \\ \cline{2-5}  & Vertical displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 131.1281 mm & 131.3932 mm & 5.1944 mm \\  & \(\overline{\Delta}\) & 9.74\% & 9.29\% & 0.30\% \\ \hline \multirow{4}{*}{GM(1, N)} & Horizontal displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 23.9556 mm & 6.2681 mm & 35.0282 mm \\  & \(\overline{\Delta}\) & 1.59\% & 0.59\% & 30.66\% \\ \cline{2-5}  & Vertical displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 0.5571 mm & 0.5766 mm & 8.4680 mm \\  & \(\overline{\Delta}\) & 0.03\% & 0.03\% & 0.67\% \\ \hline \multirow{4}{*}{OGM(1, N)} & Horizontal displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 9.7855 mm & 3.3216 mm & 2.9627 mm \\  & \(\overline{\Delta}\) & 0.45\% & 0.34\% & 2.96\% \\ \cline{2-5}  & Vertical displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 1.6290 mm & 1.6596 mm & 3.6594 mm \\  & \(\overline{\Delta}\) & 0.11\% & 0.11\% & 0.41\% \\ \hline \multirow{4}{*}{BP neural network} & Horizontal displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 26.2313 mm & 46.8203 mm & 3.9909 mm \\  & \(\overline{\Delta}\) & 2.55\% & 5.77\% & 4.88\% \\ \cline{2-5}  & Vertical displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 22.2676 mm & 5.9030 mm & 4.2476 mm \\  & \(\overline{\Delta}\) & 0.94\% & 0.30\% & 0.34\% \\ \hline \multirow{4}{*}{FOBGM(1, N)} & Horizontal displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 22.8125 mm & 7.6742 mm & 0.4377 mm \\  & \(\overline{\Delta}\) & 0.33\% & 0.18\% & 0.36\% \\ \cline{1-1} \cline{2-5}  & Vertical displacement prediction & \(\left|\varepsilon_{\max}\right|\) & 0.3073 mm & 0.3110 mm & 4.7260 mm \\ \cline{1-1} \cline{2-5}  & \(\overline{\Delta}\) & 0.01\% & 0.01\% & 0.35\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of prediction errors between different methods for different units. After predicting the displacement, it is necessary to discriminate the state of the landslide. We judge the stability of the landslide at each moment by using all the data obtained in the experiment. By observing Figure 11, it can be known that sensing units 5 to 10 are below the sliding surface, and their weights are extremely small and negligible compared to units 1 to 4. Therefore, the change of the orientation vector angle of sensing units 1 to 4 during the whole experiment is shown in Figure 17. Those sensing unit which has large displacement in the whole experiment process will have a large change in the orientation vector angle than others. According to Equation (31), the final landslide sensitivity coefficient is calculated by weighted summation. Due to the complexity of weight calculation, we assign the same weight coefficient to these four sensing units. The stability diagram calculated by units 1 to 4 is shown in Figure 18.  
Since different landslide deformations have different displacement thresholds, it is difficult to have a unified standard, but setting the alarm threshold from the angle of direction angle will have better versatility. Figure 18 shows the curve of the risk of landslide occurrence during the whole experiment obtained by the orientation vector angle method of landslide hazard calculation. As a comparison, the result of the TOPSIS-Entropy weight theory is also plotted, which has a broad versatility in the current landslide stage division. The horizontal and vertical positions of sensing unit 1 are drawn in the picture to show the relationship between hazard and displacement. The danger  
Figure 17: The curve of orientation vector angle. Figure 18: The curve of danger rate of landslide. level rises sharply when the sensor starts to undergo a large displacement.