The rapid proliferation of battery electric vehicles (BEVs), championed for their environmental benefits, has introduced new dynamics into urban traffic safety ecosystems. While offering advantages in emissions and noise reduction, the unique operational characteristics of battery electric vehicles, particularly at low speeds, necessitate a focused examination of their interaction with vulnerable road users (VRUs) such as pedestrians and cyclists. Statistics consistently show a significant portion of traffic fatalities and injuries involve VRUs. Therefore, understanding the precise spatio-temporal patterns of collisions between battery electric vehicles and VRUs is paramount for developing targeted safety interventions. This study proposes a novel methodology for identifying spatio-temporal hotspot segments of such collisions. By integrating a weighted network kernel density estimation with advanced clustering algorithms that incorporate temporal dimensions, we aim to move beyond traditional spatial analysis and provide a more granular, actionable understanding of when and where these critical interactions most frequently and severely occur.
1. Introduction and Background
The global shift towards sustainable transportation has positioned the battery electric vehicle at the forefront of personal mobility. Their growing market penetration is a positive trend for environmental goals. However, this transition coincides with persistent safety challenges concerning VRUs in urban and suburban environments. Traditional internal combustion engine vehicles provide audible cues that alert pedestrians and cyclists to their presence and movement. The quieter operation of a battery electric vehicle, especially at speeds below approximately 30 km/h, can reduce these auditory cues, potentially affecting the situational awareness of VRUs. This sensory discrepancy may contribute to unique collision patterns. Furthermore, the driving dynamics, instant torque, and regenerative braking of a battery electric vehicle can influence driver behavior. Consequently, analyzing collision data through the specific lens of battery electric vehicle involvement is not merely a subset of general traffic safety research but a necessary specialization to address emerging risks.
Conventional methods for identifying accident-prone locations, often termed “black spots,” have primarily focused on spatial aggregation using techniques like kernel density estimation (KDE). While effective for highlighting geographical concentrations, these methods often treat time as a separate, discrete variable (e.g., morning peak, night) or ignore its continuous influence altogether. This is a significant limitation, as traffic flow, pedestrian activity, and environmental conditions like lighting change continuously throughout the day and across seasons. A true hotspot is defined not just by a cluster of points on a map, but by a cluster within a specific spatio-temporal context. A location may be high-risk only during school dismissal hours or on weekend nights. Identifying these nuanced patterns requires models that process spatial coordinates and time as interconnected dimensions. This research addresses this gap by developing a framework that weights collision events based on their severity and contextual factors, models their spatial tendency using an improved density estimation, and finally, applies a spatio-temporal clustering algorithm to pinpoint the most critical hotspot segments for collisions involving battery electric vehicles.
2. Methodology and Theoretical Framework
The core of our methodology is a three-stage process: first, characterizing the spatio-temporal distribution using a weighted density estimate; second, identifying spatial clusters; and third, refining these into spatio-temporal clusters. We ground our analysis in a dataset comprising 717 validated collisions between battery electric vehicles and pedestrians or non-motorized vehicles over an 11-month period in a major city.
2.1 Weighted Network Kernel Density Estimation for Spatial Tendency
To move beyond simple point mapping, we employ a Network Kernel Density Estimation (NetKDE) method. Standard KDE applied to road networks can identify areas of high event concentration. However, it treats all events equally. A collision resulting in a fatality is fundamentally more significant than a minor property-damage-only incident for hotspot analysis aimed at saving lives and reducing severe injuries. Therefore, we introduce a Composite Influence Index $U_i$ for each collision event $i$. This index aggregates weighted contributing factors:
$$U_i = k_1 R_i + k_2 W_i + k_3 A_i + k_4 S_i$$
where:
- $R_i$ represents the road type factor (e.g., highway, urban arterial, local street).
- $W_i$ represents the weather condition factor (e.g., clear, rainy).
- $A_i$ represents the age factor of the involved VRU, as older pedestrians/cyclists are typically at higher risk of severe injury.
- $S_i$ represents the severity outcome of the collision (e.g., property damage, injury, fatality).
- $k_1, k_2, k_3, k_4$ are the corresponding weights determined via the Analytic Hierarchy Process (AHP).
The AHP pairwise comparison matrix was constructed with expert judgment, prioritizing collision severity ($S$) as the most critical factor, followed by VRU age ($A$), road type ($R$), and weather ($W$). The calculated weights were $k_1=0.090$, $k_2=0.042$, $k_3=0.216$, and $k_4=0.652$. The consistency ratio (CR) was 0.076, indicating acceptable consistency.
This weighted index $U_i$ is then integrated into the NetKDE formula. The density estimate $\hat{\lambda}(d_i)$ at a network location is given by:
$$\hat{\lambda}(d_i) = \frac{1}{r} \sum_{i=1}^{n} K\left(\frac{d_i}{r}\right) U_i \quad \text{for} \quad d_i < r$$
where $n$ is the total number of events, $r$ is the search bandwidth (kernel radius), $K(\cdot)$ is the Gaussian kernel function, and $d_i$ is the network distance from the estimation point to event $i$. Events beyond distance $r$ have zero influence. This weighted approach ensures that areas with clusters of high-severity collisions involving battery electric vehicles are more prominently highlighted than areas with frequent but minor incidents.
2.2 Spatial Clustering using Density Peaks Clustering (DPC)
The density map reveals tendencies, but for precise identification of discrete hotspot segments, we apply clustering algorithms. We first evaluate spatial clustering. The Density Peaks Clustering (DPC) algorithm is particularly suitable for our data, which may form clusters of arbitrary shape and density. DPC operates on two intuitive assumptions: cluster centers are surrounded by neighbors with lower local density, and they are at a relatively large distance from points with higher density.
For each data point $i$, we compute its local density $\rho_i$ and its minimum distance $\delta_i$ to any point with a higher density:
$$\rho_i = \sum_j \chi(d_{ij} – d_c), \quad \text{where} \quad \chi(x) = \begin{cases} 1 & \text{if } x \leq 0 \\ 0 & \text{otherwise} \end{cases}$$
$$\delta_i = \min_{j: \rho_j > \rho_i} (d_{ij})$$
Here, $d_{ij}$ is the Euclidean distance between points $i$ and $j$, and $d_c$ is a cutoff distance. Points with high $\rho_i$ and high $\delta_i$ are identified as cluster centers. This method is effective for preliminary spatial segmentation of battery electric vehicle collision hotspots.
2.3 Spatio-Temporal Clustering using ST-DBSCAN
To incorporate the continuous time dimension, we adapt the DBSCAN algorithm into a Spatio-Temporal DBSCAN (ST-DBSCAN). Traditional DBSCAN finds spatial clusters based on a spatial radius ($eps$) and a minimum number of points ($MinPts$). ST-DBSCAN extends the neighborhood search from a circle (2D) to a cylinder or sphere in 3D, where the third dimension is time. It requires two distance parameters: a spatial radius ($eps_1$) and a temporal radius ($eps_2$). A point is a core point if within its $eps_1$ spatial distance AND $eps_2$ temporal distance, there are at least $MinPts$ points (including itself).
The spatio-temporal distance between two events $i$ and $j$ is evaluated conjunctively: they must be close in both space and time to be considered part of the same cluster. This is crucial for identifying hotspots like “the intersection near the school between 3:00 PM and 4:00 PM,” which would be missed by a purely spatial analysis that aggregates all-day data or a purely temporal analysis that aggregates city-wide data. This model is perfectly suited to pinpoint the precise spatio-temporal signatures of risk for battery electric vehicle interactions with VRUs.
| Factor Category | Specific Indicator | Description / Quantified Value |
|---|---|---|
| Road & Environment | Road Type (R) | Highway (1), Urban Arterial (2), Local Street (3) |
| Central Isolation | Present (1), Absent (0) | |
| Bike Lane | Present (1), Absent (0) | |
| Signal Density | Actual value per zone | |
| Weather (W) | Clear (1), Non-Clear (e.g., Rainy) (2) | |
| Road User | VRU Age (A) | Under 25 (1), 25-45 (2), Over 45 (3) |
| — | — | |
| Socio-Economic Context | Regional GDP | Actual value |
| Elderly Population Ratio | Actual value | |
| — | — | |
| Outcome | Collision Severity (S) | Property Damage (1), Injury (4), Fatality (6) |
3. Empirical Analysis and Results
3.1 Spatio-Temporal Distribution Characteristics
Initial analysis of the 717 battery electric vehicle collisions with VRUs reveals distinct patterns. Temporally, the total number of collisions exhibits a triple-peak pattern throughout the day, differing from the classic bimodal peak of general traffic congestion. Peaks occur during 8:00-11:00, 14:00-15:00, and 18:00-19:00. Notably, fatal collisions show a different rhythm, concentrating in the early morning (7:00-8:00) and late evening (20:00-22:00). The evening fatal peak may be exacerbated by the low-noise operation of the battery electric vehicle combined with reduced pedestrian visibility.
Spatially, the application of the weighted NetKDE provided a more accurate risk surface compared to unweighted KDE. The results showed pronounced clustering in central urban areas, with more dispersed but significant clusters in suburban regions. The weighting caused several areas with lower raw collision counts but higher average severity to be elevated to hotspot status. This confirms that the unique risk profile of a battery electric vehicle collision with a VRU is not solely about frequency but critically about severity.
3.2 Performance of Spatial Clustering Models
We compared the performance of DPC against other common spatial clustering algorithms (DBSCAN, OPTICS, Mean Shift) for identifying spatial hotspots. The evaluation was based on three metrics: Silhouette Coefficient (higher is better), Davies-Bouldin Index (DBI, lower is better), and Calinski-Harabasz Index (CHI, higher is better).
| Algorithm | Silhouette Coefficient | Davies-Bouldin Index (DBI) | Calinski-Harabasz Index (CHI) |
|---|---|---|---|
| DBSCAN | 0.41 | 2.16 | 184.38 |
| OPTICS | 0.17 | 5.51 | 32.14 |
| Mean Shift | 0.42 | 1.06 | 144.26 |
| DPC | 0.60 | 0.27 | 204.77 |
The DPC algorithm demonstrated superior performance, achieving a 42.9% higher Silhouette Coefficient, a 74.5% lower DBI, and an 11.1% higher CHI compared to the best alternative values. This indicates that DPC produced clusters with significantly better internal cohesion and separation, making it the optimal choice for defining the spatial extent of battery electric vehicle collision hotspots.
3.3 Identification of Spatio-Temporal Hotspots with ST-DBSCAN
For the final and most granular identification, we applied ST-DBSCAN and compared it to other algorithms extended into the time dimension (ST-OPTICS, ST-DPC, ST-Mean Shift).
| Algorithm | Silhouette Coefficient | Davies-Bouldin Index (DBI) | Calinski-Harabasz Index (CHI) |
|---|---|---|---|
| ST-OPTICS | 0.14 | 1.57 | 15.61 |
| ST-DPC | 0.13 | 1.36 | 70.63 |
| ST-Mean Shift | 0.16 | 1.17 | 156.28 |
| ST-DBSCAN | 0.52 | 1.47 | 245.79 |
The results are compelling. While the DBI values were relatively close, the ST-DBSCAN algorithm achieved a Silhouette Coefficient 2.25 times greater and a CHI 57.3% higher than the best-performing alternative. This decisive advantage confirms that ST-DBSCAN is exceptionally effective at finding dense, well-separated clusters in the combined space-time domain of battery electric vehicle collision data. The resulting hotspots are not just areas on a map but specific locations active during specific time windows (e.g., a commercial district intersection during the mid-afternoon peak, or a suburban arterial late at night), providing highly actionable intelligence for dynamic countermeasure deployment.
4. Discussion and Implications
The proposed framework successfully transitions from general spatial trend analysis to the precise identification of actionable spatio-temporal hotspot segments for collisions between battery electric vehicles and VRUs. The weighted NetKDE proved essential for ensuring that high-severity events appropriately influenced the initial risk landscape. The superior performance of the DPC algorithm for spatial clustering validates its utility in handling the irregular, dense clusters typical of urban collision data. Most importantly, the significant outperformance of ST-DBSCAN for spatio-temporal clustering underscores the critical importance of processing time as a continuous, integrated dimension rather than a separate, aggregated factor.
The identified triple-peak pattern for battery electric vehicle collisions suggests that risk is not confined to traditional rush hours but extends into broader daytime activity periods, possibly related to complex urban mobility patterns and the continuous quiet operation of the battery electric vehicle fleet. The spatial concentration in central urban areas aligns with high VRU exposure, while the identification of severe suburban hotspots highlights areas where higher speeds and the quiet approach of a battery electric vehicle may have particularly dangerous consequences.
From a practical standpoint, the output of the ST-DBSCAN model provides transportation and safety agencies with a prioritized list of location-time pairs. This enables targeted interventions such as:
- Dynamic Infrastructure: Installing or enhancing pedestrian-activated warning lights, raised crosswalks, or speed humps at locations identified as hotspots during specific high-risk hours.
- Focused Enforcement: Deploying traffic enforcement resources to hotspot segments during their active time windows to deter speeding or failure-to-yield violations from drivers of battery electric vehicles and other vehicles.
- Public Awareness Campaigns: Tailoring educational messages for both battery electric vehicle drivers (emphasizing extra caution in quiet mode) and VRUs (highlighting the need for visual checks) specific to known hotspot areas and times.
- Vehicle Technology Integration: The spatio-temporal hotspot maps can inform the geofencing parameters for Automated Vehicle Sounding Systems (AVAS) on battery electric vehicles, potentially triggering enhanced auditory alerts in these high-risk zones.
5. Conclusion
This study presents a comprehensive methodological framework for the advanced identification of spatio-temporal hotspot segments specific to collisions involving battery electric vehicles and vulnerable road users. By integrating a severity-weighted network kernel density estimation with a two-stage clustering approach—using DPC for spatial segmentation and ST-DBSCAN for final spatio-temporal pinpointing—we achieve a nuanced and accurate characterization of risk. The empirical analysis demonstrates that the collision patterns of battery electric vehicles have unique temporal signatures (triple-peak) and that clustering in the combined space-time domain is vastly more informative than spatial analysis alone. The ST-DBSCAN algorithm, in particular, showed marked superiority in defining these complex clusters.
The findings emphasize that safety strategies for the evolving fleet of battery electric vehicles must be equally evolved, moving from static, location-based interventions to dynamic, time-sensitive strategies. The methodology is generalizable and can be applied to other cities or to dissect collision patterns for other vehicle types. Future research should integrate real-time traffic flow and pedestrian volume data to further refine the risk model, and conduct causal analysis on the identified hotspots to determine the specific contributing factors (e.g., specific sightline obstructions, signal timing issues) at each location. This will enable the design of even more precise and effective countermeasures, ensuring that the transition to battery electric vehicles proceeds alongside a commitment to enhanced safety for all road users.