## 4 Results
### Risk Coupling Probability Calculation  
Based on the risk combination frequencies in the previous section, the risk coupling probabilities for one to four risk types in different ACs were calculated according to Equations (7), (8), (10), and (12). There was no need to calculate for five types, as all factors were coupled. For clarity, the calculation process for the coupling probabilities of different risk types is provided below.  
The risk probabilities of single risks in different ACs are shown in Figure 8. Taking \(P(h)\) in PA as an example, if  
cannot analyze the coupling relationships between risk types, this result can be attributed to the insufficient number of accident samples involving weather-related factors.  
The risk coupling probabilities of two risks in different ACs are shown in Figure 9. Taking \(P(h,v)\) in PA as an example, if \(h=0\) and \(v=0\), \(r,w,m\in\{0,1\}\), \(P(h,v)\) is the sum of all \(P_{hverum}\) with \(h=0\) and \(v=0\) shown in Figure 6, resulting in \(P_{00***}=0.0055\). Similarly, it can be concluded that \(P_{01***}=0.0577\), \(P_{10***}=0.3599\), and \(P_{11***}=0.5769\). The results showed that when the two risk type statuses were 1, the risk coupling probability of the human-vehicle factors were the highest across different ACs. This indicates that, regardless of how the risk scenario evolves, human and vehicle factors are the main sources of danger and tend to occur together. An interesting phenomenon occurred in SA, where the road-weather risk coupling frequency is the lowest. This suggests that poor weather and poor road environment are less likely to coexist. This seems counterintuitive, as adverse weather typically leads to a poor road environment. This contradiction can be attributed to the classification of risk factors. In the road risk type, only slippery roads and icy roads are caused by weather, while the other risk factors in the road type are not significantly associated with those in the weather type.  
The risk coupling probabilities of three risks in different ACs are shown in Figure 10. Taking \(P(h,v,r)\) in PA as an example, if \(h=0\), \(v=0\), and \(r=0\), \(w,m\in\{0,1\}\), \(P(h,v)\) is the sum of all \(P_{hverum}\) with \(h=0\), \(v=0\), and \(r=0\) shown in Figure 6, resulting in \(P_{000**}=0\). Similarly, it can be concluded that \(P_{001**}=0.0055\), \(P_{010**}=0.033\), \(P_{011**}=0.0247\), \(P_{100**}=0.2115\), \(P_{101**}=0.1484\), and \(P_{110**}=0.294\), because \(P_{000**}+P_{001**}+P_{010**}+P_{011**}+P_{100**}+P_{101**}+P_{110**}+P_{111**}=1 \), \(P_{111**}=0.283\). The results showed that when the three risk type statuses were 1, the risk coupling probability of the human-vehicle-management factors was the highest across the different ACs. This indicates that, compared with road and weather factors, insufficient management is more likely to lead to accidents and exacerbate the evolution of those accidents.  
Figure 8: Risk probabilities of single risk types in different accident categories: (**a**) probabilities of single risks in PA; (**b**) probabilities of single risks in SA. Risk coupling probability values greater than 0.35 are highlighted with a black border.  
\(P_{1100*}+P_{1101*}+P_{1110*}+P_{1111*}=1\), \(P_{1111*}=0.044\). The results show that when the four risk type statuses were 1, the risk coupling probability of the human-vehicle-road-management factors was the highest and human-vehicle-weather-management was the lowest across the different ACs. This indicates that, in both PA and SA, road factors are more critical in complex coupling scenarios, while the impact of weather factors diminishes.