## 3 Results and Discussion
### Exploratory Data Analysis  
The exploratory analysis was carried out separately for each soot load zone (Zone 3 and Zone 4), with the primary objective of identifying relevant variable interactions for modeling the duration a vehicle remains in each zone. The process was iterative and guided by both domain expertise and data-driven criteria, which led to the progressive refinement of the dataset. Among the filtering steps, data points with extreme or implausible values were removed to improve the consistency and representativeness of the sample. For this purpose, the ydata-profiling library, previously introduced in the methodology, was used to generate a comprehensive statistical summary of the dataset. For instance, Figures 5 and 6 present the distribution of the variable \"Distance since last regeneration\" for Zones 3 and 4, respectively. In Zone 3, the distribution of distance since last regeneration exhibited a strong positive skew (skewness = 4.03), indicating a long right tail with the presence of extreme values. While the interquartile range (IQR) was 125.5 km and the 95 th percentile stood at approximately 563.6 km, the maximum recorded value reached 1644 km, more than  
Figure 4: Proposed methodological pipeline. three times the third quartile (Q3 = 325 km). The upper Tukey limit for this variable was calculated at 513.25 km, confirming the presence of outliers well beyond the expected range. Based on this analysis, a conservative upper threshold of 500 km was applied to remove these anomalous records and preserve only representative operational patterns. In Zone 4, a similar distributional shape was observed, with a skewness of 2.65. Although the values were less extreme than in Zone 3, the 95 th percentile still reached approximately 772 km, and the maximum value observed was 1275 km. The interquartile range was slightly higher (140 km), and the corresponding Tukey threshold was estimated at 533 km. Given this, a consistent cutoff of 500 km was also applied in this case to eliminate atypical observations that could distort model learning. This univariate filtering approach was systematically applied to other core features to identify and remove outliers, helping to define the normal operational range of each variable. Figure 5: Distance traveled since last regeneration summary—Zone 3. Figure 6: Distance traveled since last regeneration summary—Zone 4. Once the cleaning steps are completed, Figures 7 and 8 show the resulting correlation heatmaps for Zones 3 and 4, respectively, while Table 3 displays the codification used for presenting the variables. In the case of Zone 3, it is evident that the absolute variables, namely, distance traveled (Variable 1), time elapsed (Variable 4), and fuel consumed (Variable 3), exhibit the highest positive correlations with the target variable Delta_time [h] (Variable 10), with correlation coefficients of 0.61, 0.57, and 0.58, respectively. These variables, which reflect accumulated behavior since the last regeneration event, appear to offer slightly more predictive value than their delta-based counterparts (Variables 6-8), whose correlations with the target are somewhat lower. In line with these findings, the Fuel Intensity Index (Variable 5), which represents the ratio of fuel consumption over both distance and time, displays a negative correlation of \(-\)0.64 with the target, further supporting its relevance in capturing operational load patterns and its selection as a primary feature for modeling. However, it is also worth noting that the Fuel Intensity Index from the previous zone (Variable 13) shows a similarly strong correlation (\(-\)0.62), making it a promising secondary candidate or complementary input. While the current index is prioritized for initial model development, the previous-zone index remains a valuable candidate that may be tested in future iterations to assess its potential benefits. When turning to Zone 4, the correlation heatmap reveals a distinct pattern when compared to Zone 3.