## 4 Application Examples
### Landslide Prediction Performance
Figures 14 and 15, once there is a step-change in the original data, since the GM(1, 1) model only predicts its own future displacement through the historical displacement data of sensing unit 1, it does not consider the influence of related factors on it thus the GM(1, 1) model cannot predict well, when the relevant displacement variables are added in the calculation, the situation will be much better, but due to the GM(1, N) model lacks consideration of the change rate of the relevant variables, compared with the prediction effect of our proposed model, there are still some defects. But this situation will change when displacement data prediction is performed for the fourth unit. Figure 16 is the displacement prediction of sensing unit 4, as we can see, when the displacement data to be predicted is linear, due to the influence of related variables in the GM(1, N) model, its fitting is fluctuating, and the prediction accuracy is not as good as that of the GM(1, 1) model. However, the new model we propose fully considers the fluctuation of relevant variables. When the current period is linear, its fluctuation is very small, so it will approximate the value of the previous moment. Therefore, no matter in a linear or nonlinear situation, the proposed models can fit the truth well. In the above Figures 14-16, we have additionally inserted the prediction data of the OGM(1, N) model and the BP neural network for comparison. In some cases, the accuracy of the proposed model is better than that of the BP neural network. The prediction errors of different methods in the three cases are shown in Table 3.  
Figure 14: The curve of prediction for sensing unit 1. (**a**) Graph of horizontal displacement prediction effect of sensing unit 1. (**b**) Graph of vertical displacement prediction effect of sensing unit 1. Figure 15: Curve of prediction for sensing unit 2. (**a**) Graph of horizontal displacement prediction effect of sensing unit 2. (**b**) Graph of vertical displacement prediction effect of sensing unit 2. The \(\left|\varepsilon_{\max}\right|\) in Table 3 above is the absolute value of residuals and the \(\overline{\Delta}\) has been defined in Equation (32). As shown in the table, the new model is closer to the actual values in most cases, so its average absolute percentage error is smaller than that of the other methods. In order to measure the effectiveness of different methods, we take Equation (33) as a measure. \[\eta=\frac{\overline{\Delta}-\overline{\Delta}_{b}}{\overline{\Delta}_{b}}\times 1 00\% \tag{33}\]  
where, the \(\overline{\Delta}_{b}\) is the MAPE as a reference standard and the \(\overline{\Delta}\) is the MAPE needed to measure performance. In case one, taking the \(\overline{\Delta}\) of GM(1, 1) as the benchmark \(\overline{\Delta}_{b}\), the prediction accuracy of other methods is improved by 77.32%, 93.58%, 63.62%, and 95.29% respectively. In case two, by using the same way, the results are 94.49%, 96.82%, 46.17%, and 98.32%. However, in the third case, the GM(1, N) has a poor prediction effect, and will take GM(1, N) as the benchmark \(\overline{\Delta}_{b}\). The enhancement effects of the remaining methods are 98.21%, 90.34%, 84.08%, and 98.82%. Figure 16: Curve of prediction for sensing unit 4. (**a**) Graph of horizontal displacement prediction effect of sensing unit 4. (**b**) Graph of vertical displacement prediction effect of sensing unit 4.