## 4 Experiments and Analysis  
### Experimental Data Processing  
The traffic flow dataset (PeMS) used in this study originates from a comprehensive data collection initiative by the California Department of Transportation (Caltrans) across the state's freeway system, supplemented by contributions from other state transportation agencies and partners. The dataset spans 48 months from 2016 to 2018 and concentrates on roadway occupancy along San Francisco's freeway. Aggregating and organizing this data enabled researchers to offer a unified, comprehensive analytical framework for assessing the freeway system's operational performance. The framework builds on a thorough analysis of the freeway network's current state, facilitating the development of effective operational strategies and identifying and examining critical bottleneck zones for potential improvements, thereby offering robust data support for traffic management decisions. Collecting and analyzing this dataset is crucial in optimizing traffic flow management and enhancing road usage efficiency. This study's data were meticulously segmented into training, validation, and testing sets, with allocations of 70%, 10%, and 20%, respectively. This allocation aims to ensure the model training's effectiveness and generalizability while affording ample data to validate and test the model's performance, striving for high accuracy and reliability. Details of the dataset are provided in Table 1.  
This study employs an innovative seasonal characterization approach to explore seasonal trends within the PeMS Traffic dataset. As depicted in Figure 6, the data were first segmented by season, and then average values were calculated for each season. Comparative analysis reveals that the dataset exhibits more pronounced trend fluctuations during summer and winter, as opposed to spring and fall. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Time** & **Acquisition Frequency** & **Total Number** & \multicolumn{3}{c}{**Splitting Strategy**} \\ \cline{4-6}  & & **Training** & **Validation** & **Test** \\ \hline PeMS & 1 July 2016–2 July 2018 & 60 min & 17,544 &
\begin{tabular}{c} 0–12 \\ 281 \\ \end{tabular} & 12,281–14,035 & 14,035–17,544 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of PeMS data details. Figure 6: Segmentation illustrating the seasonal characteristics of the PeMS Traffic dataset. Integrating the computation of autocorrelation coefficients (ACF) and partial autocorrelation coefficients (PACF) within the Variational Mode Decomposition (VMD) framework enhances the analysis further. This addition aimed to facilitate an in-depth assessment of the temporal properties of each subsequence derived from VMD. Calculating the ACF and PACF values for each subseries enabled the accurate determination of seasonal trends within each; higher values of ACF and PACF indicate stronger correlations with the season. This analysis not only deepened the understanding of seasonal variations within the dataset but also, by melding VMD with time-series characterization, propelled the identification of seasonal trends. Applying this approach yields a more precise and systematic framework for the seasonal characterization of the PeMS Traffic dataset, thus enriching the comprehension of traffic flow trends. Assuming that the time series is {\(x_{t}\)}, the autocovariance function (ACVF) of lag order \(k\) is as follows in Equation (11):  
\[ \begin{split} c_{k}&=\frac{1}{n}\sum_{t=1}^{n-k}(x _{t}-\overline{x})(x_{t+k}-\overline{x})\\ c_{0}&=\frac{1}{n}\sum_{t=1}^{n}(x_{t}-\overline{x} )^{2}\end{split}