# Model Validation and Scenario Selection for Virtual-Based Homologation of Automated Vehicles
## 3 Methodology
### Coverage-Based Validation Scenarios  
After the extraction of application scenarios in the last section, the focus is now on the generation of coverage-based validation scenarios. The approach uses both the requirements of the regulation with regard to the scenario conditions as well as road maps with radius \(r\) and curvature \(\kappa\) information. The coverage-based algorithm consists of the following steps:  
1. It partitions the velocity and acceleration dimension into 1D bins and the scenario space into 2D bins. 2. It takes full-factorial samples within each velocity bin. 3. It calculates a reference lateral acceleration signal across the entire road for each velocity sample. 4. It transforms the continuous signals into binary masks by comparison with the acceleration bins. 5. It merges neighboring events of ones in the masks via a connected components algorithm [60]. 6. It combines all binary masks using Boolean algebra. 7. It extracts events from the binary masks and represents them with start and stop time indices. 8. It selects the longest event for each 2D bin over all velocity samples and all road curves. 9. We manually select single 2D bins based on the event length and a coverage criterion. 10. It represents each selected 2D bin with its center as scenario parameters. Figure 4: Coverage-based validation scenarios and data-driven application scenarios. The 2D grid cells are used by the coverage-based algorithm. The data-driven algorithm uses only the acceleration grid and has contiguous velocities with a maximum resolution of \(1\,\mathrm{km/h}\). The steps of the coverage-based algorithm will be explained in detail in the following. The width of the velocity bins is 10 km/h and the width of the acceleration bins is 10% of \(a_{y,smax}\). We distinguish combined 2D bins and separate 1D bins of both scenario parameters. We take 10 full-factorial samples within each velocity bin to get several velocities \(v_{x,j}\). In the third step, combining the radius information from the road maps with the sampled velocities yields several reference lateral acceleration signals \(\mathbf{a}_{y,ref,j}\). The steps 4-7 are similar to the steps 4-7 from the data-driven algorithm. To avoid repetition, we refer back to the previous descriptions at this point. Due to the extension to 2D bins, we get three indices \((i,j,k)\) of the acceleration bin, the velocity bin and the event number within the bin and ultimately the start and stop time steps \(t_{s,ijk}\) and \(t_{e,ijk}\) of each event. The eighth step reduces the amount of events by performing a maximum operation  
\[\operatorname*{arg\,max}_{k}(t_{e,ijk}-t_{s,ijk}) \tag{10}\]  
over the event duration to use only the longest event per bin with the final duration \(\Delta t_{ij}\). In addition, we manually reduce the number of events by selecting individual bins that excel with a high event length and a good coverage of the entire scenario space. A coverage-based design of validation scenarios can be seen in Figure 4. The coordinates of the scenario points result from the final tenth step that represents each selected bin with its coordinate center. The distribution of points results from the availability of curves in the used segments of the German roads A7 and B19 and will be discussed in the results section in more detail. An exemplary scenario is projected on the corresponding road section in Figure 5. Each validation scenario will be repeated several times to get information about the reproducibility of the real and virtual (hybrid) experiments and to be able to apply statistical validation metrics. According to [24], we will generally use at least three repetitions if possible and ten to fifteen repetitions for individual scenarios for a detailed analysis. If only larger measurement files can be stored after the tests have been carried out, it is possible to use data-based techniques in post-processing to locate the planned coverage-based scenarios.