## 5 Sensitivity Analysis of AV to Situations and Events for the Generation of Concrete Scenarios
### Analyze the Sensitivity to Events and Define the Sensitivity Distribution Function
#### 5.2.1 Sensitivity Analysis and Gradient  
We have identified three possible levels of impact of the event:  
* Functional impact: once generated, this event leads to the transition from one functional situation to another.
* Logical impact: once generated, this event leads to the transition from one logical situation to another, within the same functional situation, fixed at the beginning.
* Concrete impact: once generated, this event leads to the transition from one concrete situation to another, within the same logical situation set at the start.  
Figure 2 illustrates the three impact levels. Consider the logical situation LS1 belonging to the functional situation FS1. The functional impact is the modification of a range of values of LS1 that switches to a logical situation of another functional situation, for instance, FS3. With the logical impact, the modification of a range of values of LS1 causes a switch to another logical situation (for instance, LS3 also belonging to FS1). Finally, at the level of the concrete impact, no range of LS1 is modified (the values that are modified by the event remain in the same value ranges).  
A range of LS1 values is considered relevant as an event if it has a non-zero sensitivity level. The drawing of a concrete event value within this range causes the AV to move from one concrete situation to another within LS1 (for instance, from CS1 to CS2). Thus, by assumption, we consider that the other events (which concern the other ranges with a null sensitivity value) are not relevant because the AV is not sensitive to these events.  
These three levels of impact of the event suggest the existence of a variation in the associated sensitivity level. When the event concerns a modification of the value of a parameter in the same range of values (impact at the concrete level), its sensitivity is obtained with the a priori sensitivity value of the AV to the range, as defined in the scale in Table 2. It will be noted that \(\Delta\)(Ax_y), with Ax_y as the value range.  
When the event is a modification with a change of the value range (logical or functional impact), it will be noted that \(\Delta\)(Ax_y, Ax_z). Its sensitivity is then calculated using a concept we call \"sensitivity gradient\". The sensitivity gradient is defined as the absolute value of the difference in sensitivity between two logical situations. It is thus associated with the event that causes the transition from the initial logical situation to an intermediate situation.  
The sensitivity gradient of the event impacting the logical level is obtained by the absolute value of the difference in sensitivity between the initial and the intermediate logical situation (within the same functional situation). Only the level 1 neighborhood of the logical situations is considered, i.e., starting from an initial logical situation (for instance, LS1), the intermediate logical situations to be considered are those which differ by only one range of values. This means that we only consider here the generation of a \"single event\".  
When generated, the event impacting the functional level takes the AV out of the FS under analysis. If this is the case, it means that the new range of values is either outside the validity conditions of the operational maneuver characterizing the FS or outside the ODD. To obtain the sensitivity gradient of this event which impacts the functional level, we are interested in the new range obtained as a result of the modification. We will first calculate the sensitivity associated with the range, using the scale in Table 2, and then add +1 to this value. Indeed, given that such an event induces a change to another FS, an additional difficulty is added to the AV decision component. To consider this, we decide to add +1 to the sensitivity obtained for the change in the range of values.