## 3 Crash Prediction Testing Methodology
### Validation Tests  
Validation tests are performed in virtual simulations based on the developed test scenario catalog, and contain the crash severity prediction algorithm as well as the virtual vehicles and the environment. For this purpose, the software IPG CarMaker and the clustered GIDAS collision configuration scenarios were utilized. Concrete collision scenarios were extracted as cluster representatives and the case number was searched in the GIDAS PCM database. Since not every GIDAS case contains a GIDAS PCM case, the k-NN algorithm was used here again and the closest cases to the cluster center were considered as representatives of those that can be found in the GIDAS PCM database. This also covered the diversity of the different Pre-Crash phases, since the clustering represents the collision configuration, but the Pre-Crash phase may be different. The GIDAS PCM scenarios were converted into the IPG CarMaker scenario formats. In addition to real accident scenarios from the GIDAS PCM database, generic accident scenarios were created for the identified representative collision configurations.  
The tests pursued the goal of verifying the predicated outputs with regard to a defined ground truth. Each predicted variable was compared against the nominal ground truth value from the database, at each prediction timestep in the Pre-Crash phase. This is shown exemplary in Table 2, where VREL is a GIDAS variable for the collision velocity.  
Thus, each predicted variable can be verified as decoupled from others. The time before \(t_{0}\), known as TTC, for a sufficiently good prediction performance should be determined. However, a purely quantitative assessment of the prediction performance is not sufficient without a connection to the targeted Pre-Crash system. Crash severity prediction contains a predicted distribution of potential collision configurations and their severity values. Methods to generate fire, may fire and no fire signals from these distributions must be developed. As a result, the requirements for prediction performance must be determined  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Prediction Time**} & **Simulation** & **Simulation** & **Prediction Error** \\  & **Nominal Velocity** & **Predicted Velocity** & **Prediction Error** \\ \hline \(t_{1}\) & \(VREL_{nominal}=70\)\(\frac{\text{km}}{\text{h}}\) & \(VREL_{\left(t_{1}\right)}=50\)\(\frac{\text{km}}{\text{h}}\) & \(\Delta VREL\left(t_{1}\right)=20\)\(\frac{\text{km}}{\text{h}}\) \\ \(t_{2}\) & \(VREL_{nominal}=70\)\(\frac{\text{km}}{\text{h}}\) & \(VREL_{\left(t_{2}\right)}=57\)\(\frac{\text{km}}{\text{h}}\) & \(\Delta VREL\left(t_{2}\right)=13\)\(\frac{\text{km}}{\text{h}}\) \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \(t_{coll}\) & \(VREL_{nominal}=70\)\(\frac{\text{km}}{\text{h}}\) & \(VREL_{\left(coll\right)}=67\)\(\frac{\text{km}}{\text{h}}\) & \(\Delta VREL\left(t_{coll}\right)=3\)\(\frac{\text{km}}{\text{h}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulative assessment of predicted outputs.  
by the Pre-Crash systems. Moreover, simulations composed of the complete system under test, including the individual components, such as vehicle sensors, controllers, data transmission and processing, crash severity prediction and Pre-Crash actuators, are required for reliable validation.