## 4 Multidimensional Integration and Visualization of Road Operational Resilience Evaluation  
This chapter employs the methods introduced in Section 3 to quantify the pressure, state, response, and road operational resilience under emergency scenarios. The pressure resilience, \(\rm Y_{P}(t)\), is quantified by the probability of changes in the pressure resilience state. Similarly, the state resilience \(\rm Y_{S}(t)\) and response resilience \(\rm Y_{R}(t)\) are measured by the probability of changes in their respective resilience states. These probabilities are obtained through DBN network learning and parameter learning based on resilience state judgment on the emergency event dataset, as described in Section 3. The pressure resilience, \(\rm Y_{P}(t)\) at time \(\rm x=t\) is not only affected by the factors under the corresponding dimension at time \(\rm x=t-1\) but is also related to the pressure resilience \(\rm Y_{P}(t-1)\) at time \(\rm x=t-1\). The factors \((H_{1}(t-1),H_{2}(t-1),\ldots,H_{n}(t-1))\), and \(\rm Y_{P}(t-1)\) are used as parent nodes of the pressure resilience \(\rm Y_{P}(t)\), and the impact strength between nodes is measured by conditional probability. Therefore, the calculation of pressure resilience \(\rm Y_{P}(t)\) is shown in Equation (16). Similarly, the calculation of state resilience \(\rm Y_{S}(t)\) and response resilience \(\rm Y_{R}(t)\) is shown in Equations (17) and (18). \[\rm Y_{P}(t)=P(H_{1}(t),H_{2}(t),...,H_{i}(t))=\prod_{i=1}^{n}P(H_{i}(t)\mid Pa (H_{i}(t-1)),Y_{P}(t-1)), \tag{16}\]  
\[\rm Y_{S}(t)=P(S_{1}(t),S_{2}(t),...,S_{i}(t))=\prod_{i=1}^{n}P(S_{i}(t)\mid Pa (S_{i}(t-1)),Y_{S}(t-1)), \tag{17}\]  
\[\rm Y_{R}(t)=P(R_{1}(t),R_{2}(t),...,R_{i}(t))=\prod_{i=1}^{n}P(R_{i}(t)\mid Pa (R_{i}(t-1)),Y_{R}(t-1)), \tag{18}\]  
\(\rm Y_{P}(t)\), \(\rm Y_{S}(t)\), and \(\rm Y_{R}(t)\) represent the probability that the status of the pressure resilience, the state resilience, and the response resilience at time \(\rm t\). \(\rm H_{n}\), \(\rm S_{n}\), and \(\rm R_{n}\) represent the nth elements that affect pressure resilience, state resilience, and response resilience. The road operational resilience, Resilience(t), at time \(\rm t\) is affected by the pressure resilience \(\rm Y_{P}(t-1)\), the state resilience \(\rm Y_{S}(t-1)\), the response resilience \(\rm Y_{R}(t-1)\) at time \(\rm t-1\), and the road operational resilience, Resilience(t-1), at the previous time, calculated as Equation (19):  
\[\rm Resilience(t)=P(Y_{P}(t-1),Y_{S}(t-1),Y_{R}(t-1),Resilience(t-1)). \tag{19}\]  
Figure 8: D-S + BWM process for judging node resilience status in Bayesian networks among different levels. In order to achieve quantitative visualization of multidimensional resilience with weight information at different stages in space, this paper proposes a method of multidimensional resilience evaluation, integration, and visualization. The two-dimensional x-y coordinate plane of the resilience curve model is expanded into an x-y-z spatial coordinate system. In this system, the x-axis (horizontal axis) represents time, and the y-axis (vertical axis) replaces the system performance value in the resilience curve model with the probability of dimension node resilience status being in good condition. By introducing a weight for each dimension of resilience, the degree of impact on road operational resilience can be quantified. The z-axis (depth axis) is incorporated to depict changes in the weight of each dimension of resilience over time. In the resilience curve model, the area of the function curve envelope of system performance concerning time represents the resilience for a certain period. As for the three-dimensional space constructed in this paper, by expanding the two-dimensional curves of the different dimensions of resilience with the corresponding weight in the z-axis direction, the spatial geometric bodies with each dimension of resilience are formed. The volume of spatial geometric bodies can reflect multidimensional resilience for a certain period, such as in Equations (20) and (21).