# Displacement Patterns and Predictive Modeling of Slopes in the Bayan Obo Open-Pit Iron Mine
## 3 Results
### Slope Displacement Decomposition Results  
The parameters for VMD decomposition were optimized using PSO. The specific parameter settings are shown in Table 3, and the PSO optimization results are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Population Size**} & **Maximum** & \multirow{2}{*}{**Learning Factor**} & **Learning Factor** & **Inertia Weight** \\  & **Number of Iterations** & & & \\ \hline
10 & 100 & 1.5 & 1.5 & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter settings for PSO.  
Figure 9: Cumulative displacement curve.  
Using the optimized parameters, the total displacement was decomposed into trend component displacement (reflecting long-term trends influenced by geological conditions like lithology and structure) and periodic component displacement (driven by external factors such as rainfall).  
The decomposition effect of trend component displacement is shown in Figure 10. As seen in the figure, the trend component displacement curve is smoother than the original displacement curve, with high-frequency components removed. The original displacement curve exhibits several minor declines, while the trend component does not follow these declines, indicating that VMD successfully filtered out short-term disturbances and focused on long-term trends. The close alignment between the trend component and the original curve demonstrates a clear and rapidly increasing trend during this stage.  
The decomposition effects of periodic component displacement and rainfall data are shown in Figure 11. The periodic component displacement curve exhibits intense fluctuations with multiple peaks, representing high-frequency disturbance components. The current rainfall period shows multiple significant surges in rainfall, which align with the abrupt fluctuations in the displacement curve. The proximity of peaks between the two curves indicates that the current rainfall has a notable triggering effect, rapidly increasing the surface moisture content and pore water pressure, thereby inducing displacement disturbances. Rainfall fluctuations from the previous two days exhibit similarities to the displacement curve two days later, reflecting the lagged effect of rainfall.  
\begin{table}
\begin{tabular}{c c c} \hline
**Value of K** & **Alpha** & **Best Fitness Value** \\ \hline
2 & 150 & 0.014949 \\ \hline \end{tabular}
\end{table}
Table 4: PSO optimization results.  
Figure 10: Trend component displacement.  
The southern slope of the Bayan Obo Iron Mine features well-developed joint fractures and fault structures, along with water-sensitive minerals such as mica and montmorillonite. These minerals undergo disintegration and volume expansion upon water contact, confirming the significant impact of rainfall on landslide displacement. To visually quantify the correlation between rainfall and periodic component displacement, Grey Relational Degree analysis was employed. The specific workflow included using periodic component displacement, current rainfall, and prior two-day rainfall as input data; normalizing the data; calculating difference sequences and extremum values; and using these results to compute relational coefficients and GRD. A resolution coefficient \(\rho\)=0.5 was introduced to balance sensitivity and stability. The relationship between current rainfall, prior two-day rainfall, and periodic component displacement is illustrated in the figure, with GRD results listed in Table 5. The GRD values for current rainfall and prior two-day rainfall relative to periodic component displacement are 0.7008 and 0.5770, respectively, both exceeding 0.5, indicating strong correlations.