# Safety Evaluation Method and Management Strategy for Aviation Flight Plans
## 3 Method
### Safety Evaluation of Flight Plans
#### 3.2.4 Quantification of the Flight Plan Safety Index  
After the conflict probability of the flight plan is obtained, the safety level of the flight plan must be determined. In this paper, we propose a flight plan safety index to quantify the safety level. Aircraft safety index factors include special airspace, weather-influenced airspace, and aircraft conflict areas. Figure 6: Raster method for modelling the airspace environment (The green and red squares represent the start and end of the discretized route). Figure 7: Spatial division of airspace planning. Aircrafts are not permitted to enter special airspaces or weather-influenced airspaces. If the spatiotemporal track intersects with a special airspace or a weather-influenced airspace, there will be a very high cost, and the corresponding safety quantification value will be extremely low. Therefore, in the construction of the safety index, the penalty factor for an aircraft entering a special airspace and a weather-influenced airspace can take a maximum value. Since the aircraft is to avoid potential space movement with other aircrafts, it is not completely forbidden to enter one of these. If there is an intersection between the spatiotemporal trajectory and the potential conflict area of other aircraft, then a relatively large cost will be incurred, and the corresponding safety index will be low. The safety index of the intersection depends on the probability of the aircraft entering the conflict area so the penalty factor for the aircraft entering other potential motion spaces should be smaller than that for the former. The safety index depends on the probability of the aircraft being at the intersection point. If the spatiotemporal track does not intersect with any special airspace, weather-influenced airspace, or accessible areas for other aircrafts, the distance of the spatiotemporal track from these areas can be used as a quantitative criterion for safety evaluation; the further the distance from the threat area is, then the safer the track is. The spatiotemporal track is discretized at a certain time intervals to obtain a series of point sets including longitude, latitude, and time coordinates, which are denoted as \(T=[(x_{1},y_{1},t_{1}),\ldots(x_{i},y_{i},t_{i}),\ldots(x_{n},y_{n},t_{n})]\), respectively. The flight plan safety index \(I_{\text{safe}}\) is calculated as follows:  
\[I_{\text{safe}}=\left\{ \begin{array}{ll}\frac{1}{\sum\limits_{a=1}^{n}x_{a} P_{1}+\sum\limits_{a=1}^{n}\beta_{a}P_{2}+\sum\limits_{a=1}^{n}\frac{1}{(x_{a}-x_{n}) ^{2}+(y_{a}-y_{n})^{2}}}&\left(\sum\limits_{a=1}^{n}\alpha_{a}P_{1}+\sum \limits_{a=1}^{n}\beta_{a}P_{2}+\sum\limits_{a=1}^{n}\frac{1}{(x_{a}-x_{n})^{2 }+(y_{a}-y_{n})^{2}}>0\right)\\ +\infty&\left(\sum\limits_{a=1}^{n}\alpha_{a}P_{1}+\sum\limits_{a=1}^{n}\beta _{a}P_{2}+\sum\limits_{a=1}^{n}\frac{1}{(x_{a}-x_{n})^{2}+(y_{a}-y_{n})^{2}}=0 \right)\end{array} \right., \tag{2}\]  
where \(P_{1}\) represents the penalty factor for aircraft entering special airspace or weather-influenced airspace, and takes the maximum value;  
\(P_{2}\) represents the penalty factor for the aircraft to enter other aircraft-accessible areas, and its value is smaller than that of \(P_{1}\);  
\((x_{n},y_{n},t_{n})\) refers to points that are located in a special airspace, a weather-influenced airspace, and the aircraft-accessible area;  
\(\beta_{a}\) represents the probability that the aircraft is at point \(a\) (probability density function). \(\alpha_{a}\) represents the coefficient of determination of the penalty factor \(P_{1}\), whose formula is as follows:  
\[\left\{ \begin{array}{l}\alpha_{a}=1,(x_{a},y_{a},t_{a})\in STSAorSTWIA\\ \alpha_{a}=0,(x_{a},y_{a},t_{a})\
otin STSAorSTWIA^{\prime}\end{array}