# Model Validation and Scenario Selection for Virtual-Based Homologation of Automated Vehicles
## 4 Results and Discussion
### Coverage-Based Validation Scenarios  
The coverage-based validation scenarios are based on an offline scenario design that has to be executed afterwards at the real road and the virtual environment. Therefore, it is important to analyze whether there are significant deviations between the planned and observed conditions. After the test execution, we used the data-driven event finder to check whether the measured velocity and the calculated reference lateral acceleration matches the planned bin. Due to oscillations in the curvature of the real road and in the velocity, a couple of test repetitions were lost due to the condition checks. Nevertheless, the coverage-based design was accurate enough to preserve all distinct validation scenarios with at least two repetitions and in some scenarios with more than ten repetitions. This fits to the recommendation by [24] as described in Section 3.3. The number of validation scenarios is smaller than the number of application scenarios to legitimize the model-based process. The distribution of validation scenarios is shown in Figure 4. It is selected based on maximizing both scenario coverage and scenario duration to obtain representative and reproducible scenarios for a fair comparison between simulation and reality. The scenariosare distributed across the entire space with small holes in between and with gaps at the edges at low velocities and low lateral accelerations. The validation methodology including prediction intervals should be capable of dealing with this degree of interpolation and extrapolation.  
Furthermore, we analyze the reproducability of the hybrid test environment including hardware components. There are many factors that have an influence on the repetitions, such as the scenario environment and the localization of the event within the measurement files by using the event finder. We illustrate the reproducability analysis in this paper both with a qualitative comparison of time series and histogram data in Figure 8, as well as with quantitative measures in Table 1. The similarity of the time signals in general and the similarity in characteristic points like minima and maxima is clearly recognizable. This demonstrates that the localization works accurately and the lateral driving behavior correlates between repetitions. The distribution of the lateral acceleration in the histogram shows narrow bands in the order of magnitude of the bins from the scenario design. The similar values of the quantitative measures mean value, standard deviation and variance reinforce the qualitative statements.  
Figure 8: Correlation analysis with (**a**) time series and (**b**) derived histogram data (15 bins). On the one hand, both subplots contain the lateral acceleration signals \(\mathbf{a}_{y}\) of three repetitions. On the other hand, they contain the averaged reference lateral acceleration signal \(\mathbf{a}_{y,ref}\), as the three repetitions almost coincide. The peaks at the beginning of the signals are caused by the transient passage between the straight line and the curve entrance at the validation scenario \(v_{x}=118\,\mathrm{km/h}\) and \(a_{y,ref}=0.85\cdot a_{y,smax}\).