## 2 Methods
### The Proposed Hybrid Early Warning Method
#### 2.1.1 Conventional Early Warning  
Since landslide failure must occur after a large deformation, the entire landslide process can be divided into three zones based on cumulative displacement, with the \(S_{ia}\) and \(S_{ka}\) division separating them. As shown in Figure 1, when the cumulative displacement is less than \(S_{ia}\), the landslide will not slide. Therefore, it is considered safe in this zone regardless of the deformation velocity or acceleration. When the displacement is between \(S_{ia}\) and \(S_{ka}\), the landslide has a certain displacement, but not a large amount, so the landslide deserves initial attention. This zone can be divided into three sections according to velocity and acceleration. As shown in Table 1, when the velocity is less than \(v_{21}\), the landslide is considered to be safe at present. When the velocity is between \(v_{21}\) and \(v_{22}\), a blue warning is considered. When the velocity is greater than \(v_{22}\), a yellow warning is considered. This zone has no orange warning or red warning, as the cumulative displacement is smaller than \(S_{ka}\). When the cumulative displacement is greater than \(S_{ka}\), the landslide has relatively large deformation, and the failure may occur in any subsequent acceleration process, which needs key attention. This zone can be divided into five sections according to the velocity and acceleration, which are safe, blue warning, yellow warning, orange warning, and red warning. Because the acceleration process of landslides is the most dangerous, each section can be further divided according to the acceleration. If the acceleration is positive, the current warning level is maintained, and if the acceleration is negative, the level is lowered. Listing all the possible situations, we get the conventional early warning-level judgment method (see Table 1). Since the automated monitoring data has large volume, periodic fluctuations, outliers, and unequal intervals of acquisition time, using the traditional differential method to calculate the velocity and acceleration will inevitably produce large errors. In order to solve this problem, this research proposes using the monitoring data acquired in a certain \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cumulative Deformation \(S\)** & **Velocity \(v\)** & **Acceleration** & **Warning Level** \\ \hline \(S\)\(<\)\(S_{a}\) & / & / & Safe \\ \hline \multirow{5}{*}{\(S_{u}\)\(<\)\(S\)\(<\)\(S_{ka}\)} & \(v\)\(<\)\(v_{21}\) & / & Safe \\ \cline{2-4}  & \(v\)\(<\)\(v_{22}\) & / & Safe \\ \cline{2-4}  & \(v\)\(=\)\(v_{22}\) & \(\underline{\text{positive}}\) & Blue Warning \\ \cline{2-4}  & \(v\)\(\geq\)\(v_{22}\) & \(\underline{\text{positive}}\) & Yellow Warning \\ \cline{2-4}  & \(v\)\(\leq\)\(v_{31}\) & / & Safe \\ \cline{2-4}  & \(v\)\(=\)\(v_{32}\) & \(\underline{\text{positive}}\) & Blue Warning \\ \cline{2-4}  & \(v\)\(=\)\(v_{33}\) & \(\underline{\text{positive}}\) & Yellow Warning \\ \cline{2-4}  & \(v\)\(=\)\(v_{34}\) & \(\underline{\text{negative}}\) & Blue Warning \\ \cline{2-4}  & \(v\)\(\geq\)\(v_{34}\) & \(\underline{\text{positive}}\) & Red Warning \\ \cline{2-4}  & \(v\)\(\geq\)\(v_{34}\) & \(\underline{\text{negative}}\) & Orange Warning \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Early warning levels obtained by the conventional early warning method. period, called a time window, to calculate the velocity and acceleration by regression. For the data within a time window before the present, the 3\(\sigma\) criterion is first used to roughly eliminate outliers, then the least-squares method is used for linear regression and quadratic polynomial regression, and finally the speed and acceleration are calculated according to the regression coefficients. Assume the monitoring data series with unequal intervals as follows:  
\[S=\left\{(t_{0},S_{0}),\ \ \ (t_{1},S_{1}),\ \ \cdots,\ \ (t_{N},S_{N})\right\} \tag{1}\]  
where \(t_{i}\) is the collection time of the \(i-\)th datapoint, and \(S_{i}\) is the cumulative deformation of the \(i-\)th datapoint.