# Applying Heuristics to Generate Test Cases for Automated Driving Safety Evaluation
## 4 Assessment of Generated Cut-In Test Cases  
### Evaluation of Criticality of Severity and Exposure Test Suites  
The evaluation of criticality for both test suites was conducted based on two different metrics: RPF (Figure 3a) and a newly developed independent criticality metric, denoted as required deceleration, \(\mathrm{a_{x}}\) (Figure 3b). For both metrics, the generated test suites severity and exposure are opposed to the original scenario database. Accordingly, the performance of the heuristics, to create critical test cases out of the original database, can be evaluated.  
Figure 3a shows the comparison of the RPF values from the original database and the RPF values from the severity and the exposure test cases, respectively. The comparison reveals that the RPF values of the generated severity test cases are at the edge of the RPF values from the original dataset. Accordingly, the test cases that are more critical could be synthetically generated. Contrary to that, the values of the exposure test cases show, as expected, a comparable criticality as the original scenario dataset.  
To validate the severity of both test suites, a newly defined independent criticality measure (required deceleration a\({}_{x}\)) was incorporated. The selection of this metric was justified because the established metrics, such as time to collision or time headway, do not account for criticality in longitudinal and lateral direction. The critical deceleration metric is defined as the required mean deceleration for the VuT necessary to overcome the negative relative velocity with the challenging cut-in vehicle and to achieve a longitudinal distance > 10 m, before the end of the cut-in scenario.  
Hence, a simulation framework is established, where the generated cut-in test cases are re-modelled by applying their generated characteristic parameter values.  
To calculate the required deceleration of the VuT for a scenario, the scenario is re-modelled in simulation, according to its specified parameter characteristics. The following assumptions apply: the cut-in object is assumed to be detected by the VuT as soon as the object's left side crosses the left lane marking.  
The movement of the VuT is characterised by the initial velocity from the test case, influenced by the initial acceleration value model. The cut-in object is initially positioned and parametrized according to the initial longitudinal and lateral distance, as well as the initial velocity in the test case. The object's acceleration is modelled as a mean value over the lane change maneuver. The lateral movement for the lane change is abstracted as a second-degree polynomial function of the lateral velocity with a maximum according to the maximum lateral velocity in the test case. As the test cases were assessed in a simplified simulation environment, not the absolute but the relative values were relevant for evaluation purposes.  
Figure 3b shows the comparison of the VuT's required deceleration values between the original scenario database and the severity and exposure test cases, respectively. Even with an independently designed criticality measure, the severity test suite incorporated significantly higher risk, interpreted as higher required deceleration for the VuT than the original database. Only a few test cases show a comparable criticality to the original data. For the exposure test suite, a risk evaluation that was similar to the original scenario data can be observed.  
Figure 3: Results of criticality evaluation for severity test suite (**left** column) and exposure test suite (**right** column), based on two different criticality measures: risk potential field (**a**) and required VuT deceleration (**b**).