## 3 Road Operational Resilience Evolution Based on DBN
### DBN Parameter Learning Based on Node Resilience Status  
In addition to defining the network structure, it is essential to learn the parameters of a Dynamic Bayesian Network (DBN) to implement road operational resilience evolution based on dynamic Bayesian methods. DBN parameter learning involves determining the unconditional and conditional probabilities [45]. If a node in the network is not influenced by its parent nodes, it has an unconditional probability; on the other hand, if its parent nodes influence it, it has a conditional probability. The resilience status of input layer nodes can be gauged based on actual data and domain expertise, and their unconditional probability can be calculated based on the frequency of their resilience status. However, the resilience status of middle and output layer nodes cannot be directly obtained from recorded real-world data, making it crucial to initially determine the resilience status of these nodes before using data containing their resilience status to calculate their conditional probability. Given the multiple factors that impact road operational resilience, two issues need to be addressed when determining the resilience status of each node. The first issue is determining the weightage of each influencing factor on the node's resilience status. The second issue is how to incorporate numerous factors' effects into determining the node's resilience status. This paper proposes a method that utilizes the Best Worst Method (BWM) algorithm to convert domain knowledge into node weights and employs the Dempster-Shafer (DS) evidence theory to assess the resilience status of Bayesian network nodes by combining historical data on emergency events. Additionally, we have realized the BN parameter learning technique based on data. Figure 7: DBN of road operational resilience considering the time characteristics of the elements. response resilience is chosen as the most important node, and state resilience is chosen as the least important node. The importance of response resilience is compared with that of pressure and state resilience, respectively, and the importance of pressure and response resilience is also compared with that of state resilience. Finally, the ratios between nodes are transformed into weights using Equations (3) and (4). The process of evaluating node weights is presented in Table 4. The weight calculation process for other nodes follows a similar approach. After obtaining the node weights, the challenge is integrating multiple factors' impacts on a node's resilience state. Determining the resilience state requires integrating diverse information on influencing factors, which is inherently subjective and thus generates uncertainty [48]. However, the Dempster-Shafer (DS) evidence theory can overcome this issue by combining evidence [29]. DS evidence theory is precious when assessing road operational resilience, which involves multiple elements and hierarchical data [49]. This paper adopts a layered approach based on the DS evidence theory to tackle this challenge. First, the resilience-related variables of secondary-element nodes are combined at the factor node level. Then, the resilience state of factor nodes is integrated into the resilience state of dimension nodes. Finally, the resilience state of dimension nodes is merged into the resilience state of road operational resilience nodes. This comprehensive evaluation enables the determination of the resilience states of all nodes. The process includes the following steps:  
1. Determine the identification framework \(\Theta\) and construct a non-empty set of resilience element states. In this paper, the states of road operational resilience elements are conducive to resilience (H) and detrimental to resilience evaluation (L). All sets of identification framework \(\Theta=\{\mathrm{L},\mathrm{H}\}\) are called the power set \(2^{\Theta}\), and their subsets are called focal elements. \[2^{\Theta}=\{\varphi,\mathrm{L},\mathrm{H},\{\mathrm{L},\mathrm{H}\}\};\] (5)
2.