## 3 Crash Prediction Testing Methodology
### Test Scenario Catalog Development
#### 3.5.1 Machine Learning Scenario Extraction
While the distortion score is continuously reduced with an increasing number of clusters, the silhouette score reaches the peak at four clusters and drops rapidly with an increasing number of clusters. According to the elbow method on the distortion score plot, the optimal number of clusters is about 15 clusters. This would also be a very rudimentary representation of the diversity of all vehicle to vehicle collision configurations. From the silhouette score plot, four clusters show the best clustering structure. Obviously, only four clusters cannot represent all relevant vehicle to vehicle collisions. Similar results have been obtained with various clustering algorithms on the same dataset. It is clear that common distance and similarity-based clustering evaluation metrics, such as distortion or silhouette scores, are  
Figure 7: Distortion score (**left**) and silhouette score (**right**) on GIDAS vehicle to vehicle collisions clustering. not sufficient to validate the traffic scenario clustering results in detail. However, it can help to show a tendency. Nevertheless, the evaluation of the clusters by expert knowledge is required. The current GIDAS clustering results already allow the reduction of thousands of collision configurations to less than 50 representative test cases. For this study, a catalog of 35 clusters representing car to car collision configurations was created. The clustered collision configurations were evaluated by experts based on the system definition and concrete testing requirements. In doing so, the collision velocity, impact points, collision angle, delta-v values and injury severity of the cluster representatives have been examined. To better understand the results, the collision configurations of all the accident cases within the clusters were visualized. A few examples of the clusters are presented. Figure 8 shows, on the left, the cluster C1 with the highest number of cases, which represents low speed rear-end collisions. The blue box is the host vehicle, and the red boxes are all the opponent vehicles within the cluster. By determining the cluster center, a concrete collision configuration for this cluster is derived. The median velocity speed in this cluster is 15 \(\frac{\text{km}}{\text{h}}\), the delta-v is 9 \(\frac{\text{km}}{\text{h}}\) and the percentage of serious injured passengers in the host vehicle is 2%. On the right of Figure 8 is the cluster C2, which represents the most severe accidents on the database. The median velocity speed in this cluster is 132 \(\frac{\text{km}}{\text{h}}\), the delta-v value is 61 \(\frac{\text{km}}{\text{h}}\) and the percentage of serious injured passengers is 52%. However, the implemented clustering algorithm also manages to form unique clusters for some critical accident constellations. This is shown in Figure 9 by cluster C3. This is a cluster with accidents at a very high collision velocity; however, the percentage of serious injuries is in the low-medium range. The median velocity speed in this cluster is 130 \(\frac{\text{km}}{\text{h}}\), the delta-v value is 15 \(\frac{\text{km}}{\text{h}}\) and the percentage of serious injured passengers is 12%. This can be explained by sliding effects during collision. This cluster is a proof that, by the precise selection of the correct clustering parameterization and the relevant input features, such special cases can be identified as test cases. Nevertheless, clustering can still blur some rare and unique scenarios. That is why we used a k-NN algorithm that helps to create the logical test scenario catalog. The use of logical test scenarios in the defined clusters parameter space prevents the disappearance of the corner cases as test cases. Figure 8: Visualization of clusters C1 (**left**) and C2 (**right**). Figure 9: Visualization of cluster C3. Regular driving scenarios do not necessarily require machine learning analysis. For the baseline, a sufficiently large number of driving hours and the diversity of different driving conditions should be represented.