# Model Validation and Scenario Selection for Virtual-Based Homologation of Automated Vehicles
## 3 Methodology
### Data-Driven Application Scenarios  
We present a data-driven approach to extract scenarios from data that meet the requirements of the regulation. The data processing pipeline follows a rule-based algorithm:  
1. It partitions the scenario space into 1D acceleration bins and contiguous velocities. 2. It filters the noisy lateral acceleration signal using a Butterworth filter according to [17]. 3. It calculates a reference lateral acceleration signal. 4. It transforms the continuous time signals via thresholds to binary masks by applying condition checks. 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 resulting mask and represents them with start and stop time indices. 8. It transforms each binary event to a scenario with mean velocity and bin-centered lateral acceleration. We also refer to the algorithm as the event finder to highlight the data-driven condition checks. The steps of the event finder algorithm are illustrated in Figure 3 and will be explained in detail in the following. This is accompanied by the respective equations to ensure the reproducability of this paper. We define symbols for the scenario and assessment quantities of Sections 3.2-3.4 inspired by their written names. The longitudinal velocity is called \(v_{x}\), the lateral acceleration \(a_{y}\), the road radius \(r\), the curvature \(\kappa\), the lateral distance to line \(y\), the time \(t\), a binary mask \(b\) and the lower and upper acceleration ranges \(r_{l}\) and \(r_{u}\). Further indices are required to make distinctions. Vectors are denoted as bold symbols and matrices as upper case letters. In the first step, we partition the lateral acceleration dimension into stationary interval ranges (bins) \([r_{l,i},r_{u,i}]\) with  
\[r_{l,i}\in\mathbf{r}_{l}=[0.1,0.2,\ldots,0.9]\;\;\forall\;\;i \in\{1,\ldots,9\} \tag{1}\] \[r_{u,i}\in\mathbf{r}_{u}=\mathbf{r}_{l}+0.1\;\;\forall\;\;i\in \{1,\ldots,9\} \tag{2}\]  
consisting of 10% steps of \(a_{y,smax}=2.5\,\mathrm{m}/\mathrm{s}^{2}\) in the manner of R-79. We dispense with an analog partitioning into velocity bins, since it can be set very precisely in the experiment. Figure 3a contains the lateral acceleration signal \(a_{y}(t)\) of the vehicle after applying the Butterworth filter of the second step and the \"necessary lateral acceleration to follow the curve\" [4]. We refer to the latter as reference lateral acceleration  
\[a_{y,ref}(t)=\frac{v_{x}^{2}(t)}{r(t)}=v_{x}^{2}(t)\cdot\kappa(t)\text{ with }\kappa(t)=\frac{1}{r(t)}\,. \tag{3}\]Figure 3: Data-driven condition checks and assessment at the exemplary application scenario \(v_{x}=107\,\mathrm{km}/\mathrm{h}\) and \(a_{y,ref}~{}=~{}0.85\cdot a_{y,smax}\). The continuous signals in (**a**) are inputs to the conditions checks, whereas the binary signals in (**b**) are its outputs. The signals shown in (**c**) refer to the distance of the vehicle edges to the left and right lane markings and their minimum value over time. For decision making, we only consider the global minimum highlighted in red. In contrast to the former, it is not based on the vehicle trajectory, but on the road radius \(r\) and curvature \(\kappa\) from maps. We aggregate all time steps in vectors and denote them as bold symbols, for example, \(\mathbf{a}_{y,ref}\in\mathbb{R}^{N_{l}}\) with \(N_{l}\) time steps. Figure 2(b) contains multiple binary mask signals \(\mathbf{b}\in\mathbb{B}^{N_{l}}\) from the fourth processing step. The velocity mask  
\[\mathbf{b}_{v}=(\mathbf{v}_{x}\geq v_{x,smin})\ \wedge\ (\mathbf{v}_{x}\leq v_{x, smax}) \tag{4}\]  
is derived by comparing the velocity signal \(\mathbf{v}_{x}\) with the lower and upper velocity limits \(v_{x,smin}\) and \(v_{x,smax}\) from the vehicle manufacturer.