## 2 Related Work  
### Runway Overrun  
As mentioned above, current studies on the risk of runway overrun can be roughly divided into two categories, i.e., studies based on real historical accident data and studies based on QAR data. In this section, we give a brief overview of the related work in these two categories.  
For studies based on historical accident data, [PERSON] et al. [8] attempted to normalize historical accident data to facilitate future research. They further adopted bivariate analysis to build a probabilistic model for the risk factors of runway overrun incidents [9]. Their model mainly considers factors such as the aircraft weight, tailwind, light conditions, weather, approach speed, and touchdown point. [PERSON] et al. [10] added factors such as the aircraft type, airport elevation, and safety area length to their probabilistic model. [PERSON] et al. [11] built a probabilistic model that considers the spatial distribution of accident locations to describe runway overrun and excursion accidents. [PERSON] et al. [12] studied the severity of accident consequences using logistic regression and Bayesian logistic regression methods based on over 1400 runway overrun and excursion data from an ACRP databasefrom 1970 to 2009, which included five types of accidents: runway overrun and runway excursion in both takeoff and landing phases and undershoot.  
For studies based on QAR data, machine learning and risk assessment models are mainly employed to analyze QAR data, thereby identifying key factors contributing to the runway overrun risk. [PERSON] et al. [13; 14] analyzed long landing incidents with a risk of runway overrun and used variance analysis and linear regression (LR) methods based on QAR data to analyze different factors of long landing. Subsequently, [PERSON] et al. [15; 16] proposed a runway overrun risk assessment model based on QAR data, defining the long landing risk as the product of the probability of a certain landing distance and the severity of risk corresponding to that landing distance. [PERSON] et al. [17; 18] investigated the long landing problem and proposed a deep sequence-to-sequence model to predict the landing speed and distance. [PERSON] et al. [19] defined runway overrun risk as a function related to the remaining runway distance and touchdown speed, dividing flights into high-risk and low-risk flights based on the magnitude of the risk indicator. They ultimately employed machine learning algorithms for high-risk flight classification. [PERSON] et al. [20] took the remaining runway distance when the aircraft's ground speed reaches 80 knots as a measure of runway overrun risk. They used Bayesian networks to analyze the influencing factors of runway overrun risk, including the crosswind, tailwind, surface contamination, approach mode, autobrake usage, and entry altitude. To address the problem of a lack of positive samples for runway overrun, [PERSON] et al. [21] employed subset simulation methods to calculate the changes in the probability of runway overrun incidents based on selected factor distributions, thereby identifying relevant risk factors.  
The limitations of the existing studies are as follows: For studies based on historical accident data, they can only provide coarse-grained information, such as the weather condition, aircraft weight, aircraft age, etc. Therefore, compared to QAR data, the available information from historical accident data are very limited, and it is difficult to uncover valuable in-flight information to support flight safety analysis. For studies based on QAR data, the current risk assessment metrics are usually oversimplistic and they failed to consider the dynamic runway overrun risk of the pilot's deceleration operation after touchdown.