Dynamic Evaluation of Road Network Resilience to Traffic Accidents: An Emergency Management Perspective for Sustainable Cities in China

Abstract

When assessing road network resilience, emergency management behavior should be considered, as this represents the road network’s capacity to adapt to and recover from traffic accidents. Given the timeliness and variability of emergency management behavior, deterministic approaches seem inadequate to represent real road network performance. Thus, this paper innovatively designs an emergency management perspective-based dynamic evaluation method of road network resilience to traffic accidents. Firstly, based on four stages of emergency management, a road network resilience evaluation index system encompassing resilience capabilities, resilience attributes and traffic accident emergency management ability indicators is constructed. Afterwards, the gray relational technique for order preference by similarity to the ideal solution (GRA-TOPSIS) evaluation method based on combination weighting, which integrates factor analysis with hesitant intuitionistic fuzzy expert scoring, is designed to quantify resilience. Finally, the obstacle degree model is utilized for identifying resilience constraints as the input of a long short-term memory (LSTM) model to predict the resilience variation trend. The fast road network of Shanghai in China is adopted as a case study, and the results indicate that road network resilience embodies significant spatial distribution characteristics. Road length, number of tractors, perception and response and disposal time of traffic accidents cast notable effects on resilience. Additionally, some roads are forecast to show descending resilience. The proposed method is valuable for helping policymakers identify current and potential vulnerable roads and to formulate proposals to effectively improve the resilience of urban agglomerations and promote sustainable cities.

1. Introduction

As a pivotal part of the transportation system constituting a city’s lifeline, a resilient road network serves as the key to achieving sustainable cities [1,2]. According to World Health Organization statistics [3], road traffic accidents resulted in global annual deaths upwards of 1.35 million and direct economic losses of up to 3 percent of the world’s gross domestic product. Therefore, increasing attention has been given to road network resilience under traffic accidents in recent years. Although the understanding of road network resilience varies, there is a consensus that it refers to a system’s return to normal conditions after a disturbance through adaptation, absorption and quick recovery [4].

Typically, in the current literature, the most common approach to evaluate road network resilience is to study network topology and assess its structural characteristics. Certain metrics, such as the maximum connected subgraph size, average shortest path, intermediate centrality and connectivity, are commonly used to measure road network resilience [5]. At the same time, complex network analysis provides researchers with the means to simulate the impact of disasters and monitor the remaining capacity of the road network after a disturbance [4,6,7]. When traffic accidents happen, road network resilience is mainly ensured by technological and organizational means, which are often referred to as emergency management behavior. There are obvious links between emergency management behavior and road network resilience, as emergency management behavior greatly affects the road network’s capacity to operate with acceptable performance under a disruptive event.

However, previous works mainly focus on road network “hard resilience”, equipped by road physical properties like structure, function and capacity; limited efforts have been devoted to investigate road network “soft resilience” to resist disturbances brought on by emergency management behavior [8,9]. Furthermore, current studies mainly involve a single index weighting and evaluation method of road network resilience, and they rarely dynamically explore the variation trend in resilience [10].

Therefore, the research objectives of this paper are as follows: (1) To operationalize the road network resilience concept from the perspective of emergency management, the first contribution of this study is to establish a road network resilience evaluation index system incorporating resilience capabilities, resilience attributes and indicators of traffic accident emergency management ability based on four emergency management stages. (2) To tackle the challenge of low accuracy owing to the single index weighting and evaluation method, the second contribution lies in combining objective factor analysis with subjective hesitant intuitionistic fuzzy expert scoring to determine the weights of resilience indexes and designing the gray relational technique for order preference by similarity to the ideal solution (GRA-TOPSIS) evaluation method to quantify resilience. (3) To fulfill the gap in dynamic resilience prediction, the third contribution of this study is to predict the resilience variation trend by substituting main resilience constraints obtained by an obstacle degree model into a long short-term memory (LSTM) model.

The remainder of this paper is organized as follows. Section 2 introduces the concept and evaluation method of road network resilience. Section 3 builds up a road network resilience evaluation index system from the perspective of emergency management. Section 4 devises a dynamic evaluation method of road network resilience to traffic accidents. Section 5 presents the application and results analysis of the research method on Shanghai fast roads. Section 6 concludes with a summary and the implications of the research findings as well as outlooks for future research.

2. Literature Review

2.1. Road Network Resilience

The application fields of resilience theory have evolved from ecological systems and social–ecological systems to transportation systems. As an instrumental component of transportation systems, the concept of road network resilience was initially introduced by Hansen and Sutter [11] in a study of road damage under earthquake scenarios. Since then, numerous scholars have defined road network resilience as the ability of a road to resist, absorb and recover from a disaster risk during emergencies [12,13,14,15].

Based on this definition of road network resilience, scholars have interpreted resilience capabilities and resilience attributes from different angles. From the viewpoint of disaster occurrence stages, Nogal and Honfi [16] divided road network resilience into preparedness capability in the precrisis stage, response capability in the crisis stage and recovery capability in the postcrisis stage. Specifically, preparedness capability was reflected through accessibility, redundancy and vulnerability. Response capability was reflected through mobility, adaptability and robustness. Recovery capability was reflected through recoverability. Chen et al. [17] set up a road network resilience evaluation framework covering the stages of before, during and after the disturbance, corresponding to a road’s absorption, restoration and adaptation abilities. Specifically, absorption ability was characterized by robustness and redundancy. Restoration ability was characterized by reliability, vulnerability and rapidity. Adaptation ability was characterized by resourcefulness and adaptability. Based on the phases of during and after floods, Shi et al. [18] segmented road network resilience into absorption and restoration abilities depicted by robustness and rapidity, respectively.

From the viewpoint of time-varying stages of road network status, Jiang et al. [19] refined road network resilience into rapid response capability during the preparation phase, sustained resistance capability during the resistance phase, continuous running capability during the adaptation phase, rapid convergence capability during the recovery phase and dynamic evolution capability during the evolution phase. Considering the variation in road status from preparation to mitigation, response and recovery during emergencies, Borghetti et al. [20] separated road network resilience into prediction ability, resistance ability, response ability and recovery ability. To be specific, resources availability, resourcefulness, acquisition speed of resources and node robustness were used for describing these four abilities. By means of classifying road status under an earthquake into initially stable, destructing, destroyed, recovery and post-recovery stages, Chen and Huang [21] selected reliability, robustness, responsiveness, recoverability and learnability for characterizing road network resilience under different statuses. Lu et al. [22] considered the significant impact of traffic accidents on urban road network resilience and selected redundancy, reduction, rapidity, robustness, reinforcement and recovery to depict the road network’s status during a traffic accident. Tao et al. [23] divided road network status under a traffic accident into the resistance stage and the recovery stage, obtaining resilience results by calculating rescue time and recovery time. Caliendo et al. [24] divided road status during the process of traffic accidents into a loss-of-functionality stage, disruptive stage and recovery stage, calculating the resilience of the road network based on its resilience curve.

2.2. Evaluation Method of Road Network Resilience

To address the issue of evaluating road network resilience, scholars have conducted extensive research on methods for assigning weights to resilience evaluation indexes and quantifying resilience [22].

In terms of approaches for weighting road network resilience evaluation indexes, Bao et al. [25] utilized the analytic hierarchy process to calculate the subjective weights of first-level indicators, composed of resilient road network constituents, and second-level indicators, consisting of realistic metrics within the road network resilience evaluation index system. Tang et al. [26] employed the fuzzy analytic hierarchy process to obtain the subjective weights of a road network resilience evaluation index system composed of road emergency management capabilities. Considering the superiority of genetic algorithms in optimizing initial weights and thresholds of neural networks, Jiao et al. [27] came up with a neural network improved by a genetic algorithm for determining objective weights of road network resilience evaluation indicators. To acquire indexes weights conveniently and objectively, Chen et al. [28] resorted to an entropy weighting method for calculating the objective weights of a multilayer road network resilience evaluation index system. Ma et al. [29] recognized the limitations of a single index weighting method and adopted composite weighting via the blending of the Delphi method and entropy weighting.

Regarding quantitative methods of road network resilience, Chen et al. [30] noted the paucity of dynamic measurement of road network resilience in existing research and put forward a dynamic Bayesian network (DBN) to achieve a more flexible quantification of resilience. To comprehensively analyze the periodic characteristics of a road network during a disturbance, Chen et al. [17] used the weighted membership degree matrix of a fuzzy comprehensive evaluation (FCE) method to arrive at the overall resilience score. Given the low accuracy of traditional quantitative methods in managing fuzzy information, Su et al. [31] associated FCE with a cloud model to calculate road network resilience. Li et al. [32] noted the high efficiency and accuracy of cloud models in converting qualitative concepts into numerical values and thereby applied a cloud model to quantify a road network resilience evaluation framework containing qualitative indicators. Based on the road network resilience evaluation system constructed from functional, feature and element layers, Zhao et al. [33] used the DBN to accomplish calculations and trend analyses of road network resilience in different cities.

As for the prediction of the resilience variation trend, LSTM has been widely used due to its accuracy and efficiency. Zhu et al. [34] applied an LSTM model to capture the temporal correlations in the original resilience data and obtained accurate predictions of resilience for the next three months. Ashraf et al. [35] innovatively used LSTM to predict the time required for a system to recover from a disturbance and derived the predicted resilience to guide the operation of the system. Cuong et al. [36] dynamically predicted the variation trend in resilience by utilizing LSTM to capture the underlying mechanisms in the original resilience data.

2.3. Knowledge Gaps

The above review of the existing literature suggests the following knowledge gaps:

• Most previous works have elected to use resilience capabilities and attributes enabled by road physical characteristics like structure, function and capacity to portray road network resilience from the perspective of disaster occurrence stages or time-varying stages of road status. However, the effect of emergency management behavior such as risk management, timely response and rapid disposal on road network resilience has not been considered.
• Most previous works have employed single index weighting and quantitative methods of road network resilience, which may result in significant biases in indicator weights and low precision in evaluation results on account of relying solely on expert opinions or improper treatment of outliers.
• The variation trend in road network resilience has not been fully investigated in previous works, which fails to further enhance the foresight of emergency management.

Therefore, this study innovatively proposes an emergency management perspective-based dynamic evaluation method of road network resilience under traffic accidents. Based on four stages of road emergency management, a road network resilience index system incorporating resilience capabilities, resilience attributes and traffic accident emergency management ability indicators is constructed. The gray relational technique for order preference by similarity to the ideal solution (GRA-TOPSIS) evaluation method based on combination weighting, which integrates factor analysis with hesitant intuitionistic fuzzy expert scoring, is designed to quantify resilience. The dynamic prediction of resilience variation trend is achieved by utilizing an obstacle degree model for identifying resilience constraints as the input of a long short-term memory (LSTM) model.

3. Establishment of Road Network Resilience Evaluation Index System

In this study, road network resilience refers to advance road preparedness, resistance, absorption, adaptation, recovery and evolutionary capacity in response to traffic accidents by virtue of emergency management behavior like risk management, timely response and rapid disposal. To conduct a thorough and precise dynamic evaluation of resilience, this study abides by the indicator selection principles of being scientific, systematic, representative, independent and measurable to construct a road network resilience evaluation index system (

Table 1. The evaluation index system of road network resilience.

Evaluation Perspective	Functional Layer	Feature Layer	Element Layer	Unit	Effect on Resilience
Mitigation and Preparedness stage	Preparedness capacity (B1)	Preparedness (C1)	Frequency of road patrols per month (D1)	times	Positive
			Total investment in road construction (D2)	CNY	Positive
			Total investment in road maintenance per month (D3)	CNY	Positive
			Frequency of road emergency exercises per month (D4)	times	Positive
Response stage	Resistance capability (B2)	Robustness (C2)	Total length of road (D5)	meter	Positive
			Width per lane (D6)	meter	Positive
	Absorption capability (B3)	Redundancy (C3)	Number of lanes (D7)	lane	Positive
			Number of ramps (D8)	ramp	Positive
		Vulnerability (C4)	Frequency of vehicle breakdowns per month (D9)	times	Negative
			Frequency of vehicle fires per month (D10)	times	Negative
			Frequency of rollovers per month (D11)	times	Negative
			Frequency of rear-end collisions per month (D12)	times	Negative
			Property loss due to accidents per month (D13)	CNY	Negative
			Number of deaths per month (D14)	person	Negative
			Number of severe injuries per month (D15)	person	Negative
			Number of minor injuries per month (D16)	person	Negative
			Number of involved vehicles per month (D17)	vehicle	Negative
	Adaptation capability (B4)	Reliability (C5)	Predetermined traffic flow per hour (D18)	vehicle	Negative
			Number of emergency parking strips (D19)	strip	Positive
	Recovery capability (B5)	Rapidity (C6)	Average accident perception time per month (D20)	minute	Negative
			Average accident response time per month (D21)	minute	Negative
			Average accident disposal time per month (D22)	minute	Negative
		Resourcefulness (C7)	Number of tractors (D23)	tractor	Positive
			Number of towing personnel (D24)	person	Positive
			Number of fire stations within 15 min (D25)	station	Positive
			Number of hospitals within 15 min (D26)	hospital	Positive
Recovery stage	Evolutionary capability (B6)	Acquisition (C8)	Average travel time (D27)	minute	Negative
			Frequency of using emergency parking strips per month (D28)	times	Positive

). Starting from the perspective of emergency management stages and referencing relevant articles, an evaluation index system is formed with a functional layer composed of resilience capabilities, a feature layer composed of resilience attributes and an element layer composed of indicators of traffic accident emergency management ability [17,19,20,21]. The strong correlation among element layer indicators is eliminated by a Pearson correlation test, which is conducted before the resilience evaluation process to ensure the rationality and independency of indicators, reducing the influence of strong indicator correlation on the precision of resilience evaluation.

The emergency management of road traffic accidents can be divided into the four stages of mitigation, preparation, response and recovery [37]. The mitigation and preparation stages include actions taken before accidents to reduce the occurrence probability of emergencies and improve the efficiency of emergency response. This study selects preparedness capacity as the functional layer indicator to measure road network resilience during the mitigation and preparation stages. Preparedness is leveraged as the feature layer indicator to describe the ability to cope with potential accidents through road safety investment. As the primary means of detecting accidents, the higher frequency of road patrols can raise the possibility of disposing of accidents in time, improving road preparedness to potential accidents [38]. In terms of the significant impact of road layout and facilities’ health conditions on accident occurrence possibility, more investment in road construction and maintenance can reduce accident risk and enhance road preparedness [39]. The timeliness of delivering emergency resources serves as the key to enhancing a road’s capability of handling potential accidents, which can be effectively improved by increasing road emergency exercises [39]. Thus, frequency of road patrols per month (D1), total investment in road construction (D2), total investment in road maintenance per month (D3), and frequency of road emergency exercises per month (D4) are chosen as indicators to quantify preparedness.

The response stage includes measures implemented during accidents to prevent a situation from deteriorating. This study selects resistance, absorption, adaptation and recovery capabilities to evaluate road network resilience during the response stage. Robustness is utilized for depicting the ability to conduct emergency organization work, which enables a road to withstand a certain level of disturbance. As the main factor influencing the number of accidents, a road’s basic properties have a direct bearing on the difficulty of carrying out emergency organization work, thereby affect the road’s ability to withstand disturbances. Considering data accessibility, total length of road (D5) and width per lane (D6) are employed to measure robustness.

Redundancy and vulnerability, respectively, reflect the road’s ability to facilitate the use of alternative means to sustain functionality and ease the impact of accidents via implementing traffic dispersion. Acting as key factors affecting the number of accidents, a road’s layout and basic properties have a direct effect on the difficulty of diverting congested traffic. The higher the efficiency of conducting a traffic diverting plan, the stronger the ability of a road to maintain functionality using alternative means. In view of data availability, number of lanes (D7) and number of ramps (D8) are exploited to quantify redundancy. The frequency of traffic accidents, number of casualties and amount of property loss can indirectly reflect the capability of implementing traffic dispersion to mitigate the impact of accidents [40]. The higher the frequency of accidents and the higher the number of casualties and the amount of property loss, the weaker the ability of the road to absorb disturbances via traffic dispersion. Considering data accessibility, frequency of vehicle breakdowns per month (D9), frequency of vehicle fires per month (D10), frequency of rollovers per month (D11), frequency of rear-end collisions per month (D12), property loss due to accidents per month (D13), number of deaths per month (D14), number of severe injuries per month (D15), number of minor injuries per month (D16) and number of involved vehicles per month (D17) are chosen to measure vulnerability.

Reliability indicates the ability to allow a road to provide basic transportation services by conducting control plans of an accident scene. The larger the predetermined traffic flow of the road, the more difficult it is to disperse vehicles at the accident site [41], which leads to the deterioration of the road’s ability to provide basic transportation services. The employment of road emergency parking strips as temporary parking areas for accident vehicles plays a crucial role in restoring traffic flow [42], which has a direct effect on the road’s ability to provide basic services. Therefore, predetermined traffic flow per hour (D18) and number of road emergency parking strips (D19) are chosen to quantify reliability.

Rapidity and resourcefulness, respectively, represent the ability of enabling a road to quickly restore the normal service level and satisfying rescue needs through responding to accident site requirements and dispatching emergency resources. Accident perception, response and disposal time refer to the total time from accident occurrence to detection, detection to the arrival of emergency resources and arrival to the completion of accident disposal [42,43]. Given that total time can intuitively reflect whether the road promptly returns to the normal service level, average accident perception time per month (D20), average accident response time per month (D21) and average accident disposal time per month (D22) are chosen to measure rapidity. Since the abundance and variety of emergency resources exert a profound impact on the safety of accident victims [44], thereby indicating the ability to meet rescue needs by the agency that dispatches emergency resources, number of tractors (D23), number of towing personnel (D24), number of fire stations within 15 min (D25) and number of hospitals within 15 min (D26) are selected as indicators to measure resourcefulness.

The recovery stage involves actions taken after accidents to restore a road to a stable state. This study selects evolutionary capability to depict road network resilience during the recovery stage. Acquisition is applied to characterize the ability to deal with unknown risks by learning from historical accident-handling experiences. The shorter average travel time indicates better traffic conditions [31], which can reflect the stronger ability of the road to cope with unknown risks. In terms of the impact of using emergency parking strips on mitigating accident risks [45], the higher frequency of using parking strips can reduce the possibility of traffic congestion and improve the road’s ability to cope with potential risks. Therefore, average travel time (D27) and frequency of using emergency parking strips per month (D28) are selected to quantify acquisition.

4. Dynamic Evaluation Method of Road Network Resilience

To address the issues of large weight deviation and inaccurate evaluation results found in single index weighting and evaluation methods, as well as the lack of resilience variation trend prediction, this study sets forth a dynamic evaluation method of road network resilience from the emergency management perspective. Firstly, based on the established evaluation index system and original data of the element layer indicators, objective factor analysis is integrated with subjective hesitant intuitionistic fuzzy expert scoring to attain combination weighting. Then, the GRA-TOPSIS model is applied to accomplish more scientific and precise resilience evaluation. After that, a self-organizing map (SOM) clustering algorithm is employed to the classification of road network resilience levels. Finally, the prediction of the resilience variation trend is actualized through an agency of obstacle degree and LSTM model. The methodology framework is shown in Figure 1. The detailed description of the variables in the methodology can be found in

Table A6. Explanations for variables in the dynamic evaluation method.

Variable	Explanation
$W_j^{D-objective}$	Objective element layer weights
$w_j^D$	Initial objective element layer weight
$w_h^C$	Objective feature layer weight
$w_g^B$	Objective function layer weight
$W_j^{D-subjective}$	Subjective element layer weights
$p_{s_k}\left(x\right)$	Term’s support strength
$T_{s_i}\left(x\right)$	The times that experts use or do not use term $s_k$ to describe the importance of index $x$
$T$	The number of experts
$l_M\left(x\right)$$, l_N\left(x\right)$	The number of evaluation terms in membership and non-membership sets
$W_j^{D-combined}$	Element layer combination weights
$R$	Correction coefficient
$Z$	Weighted normalization matrix
$Z^{+}$$, Z^{-}$	Positive and negative ideal solutions
$D_i^{+}$$, D_i^{-}$	Euclidean distance between evaluation object to the positive and negative ideal solutions
$r_i^{+}$$, r_i^{-}$	Gray relational degree between evaluation object to the positive and negative ideal solutions
$C_i^{+}$, $C_i^{-}$	Relative closeness degree of evaluation object to the positive and negative ideal solutions
$R_i$	Resilience of evaluation object
$M_{ij}$	Obstacle degree of index $j$ of road $i$
$I_{ij}$	Deviation from index $j$ of road $i$ to the ideal solution of index $j$
$F_1^t,F_2^t,F_3^t,F_4^t,F_5^t$	Five main resilience constraining factors at time $t$
$f_t$	Forget gate coefficient
$c_{t-1}$	Previous cell state
$c_t$	Current cell state
$i_t$	Input gate coefficient
${\tilde{c}}_t$	Current candidate cell state
$h_t$	Current memory block
$o_t$	Output gate coefficient
${\widehat{R}}_t$	Predicted road network resilience for time $t$

.

4.1. Determination of Indicator Weights

This study determines the objective and subjective weights of resilience evaluation indexes based on factor loadings [46] and the membership and non-membership sets composed of linguistic evaluation terms [47]. The advantage of factor analysis lies in objectively weighting indicators by extracting information from original data, but it fails to consider the reality factors [48]. The expert scoring method is able to obtain authoritative indicator weight by synthesizing opinions from field experts; however, the subjective bias is difficult to eliminate [49]. By using a correction coefficient method to blend objective weights with subjective weights, the absence of subjective judgment in objective weighting and the strong arbitrariness of subjective weighting are compensated for. The specific steps are as follows:

Step 1: Use factor analysis to calculate objective element layer weights $W_j^{D-objective}$.

1. Calculate the factor score coefficients and variance contribution rate based on the factor loadings of the element layer to obtain initial objective element layer weight $w_j^D$ and feature layer weight $w_h^C$.

$$w_h^C={\displaystyle \frac{varianc{e}_h}{{\displaystyle \sum _{h=1}^{p}varianc{e}_h}}}={\displaystyle \frac{{\displaystyle \sum _{j=1}^{n}loadin{g}_{jh}^2}}{{\displaystyle \sum _{h=1}^p{\displaystyle \sum _{j=1}^{n}loading{s}_{jh}^2}}}},h=1,2,\dots ,p;j=1,2,\dots ,n$$

(1)

$$w_j^D=cor{r}^{-1}\left(X_{j\times j}\right)\times loadin{g}_{j\times h}$$

(2)

2. Calculate the variance contribution rate based on factor loadings of the feature layer to obtain functional layer weight $w_g^B$ and determine the final objective element layer weights using $w_g^B$, $w_h^C$ and $w_j^D$.

$$W_j^{D-objective}={\displaystyle \frac{w_{g-h}^B\times w_{h-j}^C\times w_j^D}{{\displaystyle \sum w_{g-h}^B\times w_{h-j}^C\times w_j^D}}}$$

(3)

$w_{g-h}^B$, $w_{h-j}^C$ denote the weight of functional layer index $g$ to which feature layer index $h$ is affiliated and the weight of feature layer index $h$ to which element layer index $j$ is affiliated.

Step 2: Apply hesitant intuitionistic fuzzy expert scoring to calculate subjective element layer weights $W_j^{D-subjective}$.

1. Derive the membership and non-membership sets composed of linguistic evaluation terms that experts will and will not use to describe index importance on road network resilience, based on the hesitant intuitionistic fuzzy expert scoring matrix extracted from the questionnaire. Then, calculate the occurrence probability of each evaluation term in membership and non-membership sets, respectively, as the term’s support strength $p_{s_k}\left(x\right)$.

$$p_{s_k}\left(x\right)={\displaystyle \frac{T_{s_k}\left(x\right)}{T}},k=1,2,\dots ,l$$

(4)

$T_{s_i}\left(x\right)$ denotes the times that experts use or do not use term $s_k$ to describe the importance of index $x$.

$T$ denotes the number of experts.

2. Use the linguistic scale function to transform the evaluation term into numerical values.

$$f\left(s_k\right)=\left\{\begin{array}{l}{\displaystyle \frac{a^{\frac{l}{2}}-a^{\left(\frac{l}{2}-k\right)}}{2a^{\frac{g}{2}}-2}}, k=0,1,\dots ,{\displaystyle \frac{l}{2}}\hfill \\ {\displaystyle \frac{a^{\frac{l}{2}}-a^{\left(\frac{l}{2}-k\right)}-2}{2a^{\frac{l}{2}}-2}}, k={\displaystyle \frac{l}{2}}+1,{\displaystyle \frac{l}{2}}+2,\dots ,l\hfill \end{array}\right.$$

(5)

3. Calculate subjective element layer weights $W_j^{D-subjective}$ based on accuracy function $A_j^D$.

$$A_j^D={\displaystyle \frac{1}{l}}\times \left({\displaystyle \sum _{s_k\in M_j}\frac{f\left(s_k\right)\times p_{s_k}\left(j\right)}{l_M\left(j\right)}+{\displaystyle \sum _{s_k\in N_j}\frac{f\left(s_k\right)\times p_{s_k}\left(j\right)}{l_N\left(j\right)}}}\right)$$

(6)

$$W_j^{D-subjective}={\displaystyle \frac{A_{g-h}^B\times A_{h-j}^C\times A_j^D}{{\displaystyle \sum A_{g-h}^B\times A_{h-j}^C\times A_j^D}}}$$

(7)

$l_M\left(x\right)$, $l_N\left(x\right)$ denote the number of evaluation terms in membership and non-membership sets, respectively.

Step 3: Apply the correction coefficient method to determine element layer combination weights $W_j^{D-combined}$.

$$R=({\displaystyle \frac{2}{n}}(1\times {W_1^{D-objective}}^{\prime }+2\times {W_2^{D-objective}}^{\prime }+\dots +n\times {W_n^{D-objective}}^{\prime })-{\displaystyle \frac{n+1}{n}} )\times {\displaystyle \frac{n}{n+1}}$$

(8)

$$W_j^{D-combined}=R\times W_j^{D-objective}+\left(1-R\right)\times W_j^{D-subjective}$$

(9)

$R$ denotes the correction coefficient.

${W_1^{D-objective}}^{\prime },{W_2^{D-objective}}^{\prime },\dots ,{W_n^{D-objective}}^{\prime }$ denote the ascending order of objective element layer weights.

4.2. Determination of Evaluation Model

TOPSIS embodies the merits of determining the priority of objects conveniently, based on the Euclidean distance between objects and ideal solutions. However, it fails to obtain accurate results when several objects show close distance to the ideal solutions [50]. This study determines the priority of an evaluation object by measuring its Euclidean distance from the ideal solution as well as the similarity to the shape of the ideal solution curve [10], which can make up for the limitation of TOPSIS. The specific steps are as follows:

Step 1: Calculate the weighted normalization matrix $Z$ based on interval numerical matrix $X$ and combination weights $W^{D-combined}$.

$$Z=X\times W^{D-\mathrm{combined}}=\left[\begin{array}{cccc}{x}_{11}^{\prime }\times W_1^{D-\mathrm{combined}}& x_{12}^{\prime }\times W_2^{D-\mathrm{combined}}& \cdots & x_{1n}^{\prime }\times W_n^{D-\mathrm{combined}}\\ x_{21}^{\prime }\times W_1^{D-\mathrm{combined}}& x_{22}^{\prime }\times W_2^{D-\mathrm{combined}}& \cdots & x_{2n}^{\prime }\times W_n^{D-\mathrm{combined}}\\ ⋮& ⋮& ⋮& ⋮\\ x_{m1}^{\prime }\times W_1^{D-\mathrm{combined}}& x_{m2}^{\prime }\times W_2^{D-\mathrm{combined}}& \cdots & x_{mn}^{\prime }\times W_n^{D-\mathrm{combined}}\end{array}\right]=\left[\begin{array}{cccc}{z}_{11}& z_{12}& \cdots & z_{1n}\\ z_{21}& z_{22}& \cdots & z_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ z_{m1}& z_{m2}& \cdots & z_{mn}\end{array}\right]$$

(10)

$$x_{ij}^{\prime }=\{\begin{array}{l}a+(b-a)\times \frac{x_{ij}-\min \left(x_j\right)}{\max \left(x_j\right)-\min \left(x_j\right)},x_j \mathrm{is\; positive\; indicator}\\ a+(b-a)\times \frac{\max \left(x_j\right)-x_{ij}}{\max \left(x_j\right)-\min \left(x_j\right)},x_j \mathrm{is\; negative\; indicator}\end{array}$$

(11)

Step 2: Determine the positive and negative ideal solutions based on the weighted normalization matrix.

$$\begin{gathered} Z^{+}=\left[z_1^{+},z_2^{+},\cdots ,z_n^{+}\right]=\left[\max \left\{z_{11},z_{21},\cdots ,z_{m1}\right\},\cdots ,\max \left\{z_{1n},z_{2n},\cdots ,z_{mn}\right\}\right] \\ {Z}^{-}=\left[z_1^{-},z_2^{-},\cdots ,z_n^{-}\right]=\left[\min \left\{z_{11},z_{21},\cdots ,z_{m1}\right\},\cdots ,\min \left\{z_{1n},z_{2n},\cdots ,z_{mn}\right\}\right] \end{gathered}$$

(12)

Step 3: Calculate the distance between the evaluation object to the positive and negative ideal solutions based on Euclidean distance.

$$\begin{gathered} D_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^n{\left(z_{ij}-z_j^{+}\right)}^2}} \\ {D}_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^n{\left(z_{ij}-z_j^{-}\right)}^2}} \end{gathered}$$

(13)

Step 4: Determine the gray relational degree between the evaluation object to the positive and negative ideal solutions based on the gray relational coefficient.

$$\begin{gathered} r_i^{+}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{j=1}^n{r}_{ij}^{+}}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{j=1}^n\left(\frac{\underset{i}{\min }\underset{j}{\min }\left|z_j^{+}-z_{ij}\right|+\rho \underset{i}{\max }\underset{j}{\max }\left|z_j^{+}-z_{ij}\right|}{\left|z_j^{+}-z_{ij}\right|+\rho \underset{i}{\max }\underset{j}{\max }\left|z_j^{+}-z_{ij}\right|}\right)} \\ {r}_i^{-}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{j=1}^n{r}_{ij}^{-}=\frac{1}{n}{\displaystyle \sum _{j=1}^n\left(\frac{\underset{i}{\min }\underset{j}{\min }\left|z_j^{-}-z_{ij}\right|+\rho \underset{i}{\max }\underset{j}{\max }\left|z_j^{-}-z_{ij}\right|}{\left|z_j^{-}-z_{ij}\right|+\rho \underset{i}{\max }\underset{j}{\max }\left|z_j^{-}-z_{ij}\right|}\right)}} \end{gathered}$$

(14)

Step 5: Calculate the relative closeness degree of the evaluation object to the positive and negative ideal solutions based on the dimensionless values of $D_i^{{+}^{\prime }}$, $D_i^{{-}^{\prime }}$, $r_i^{{+}^{\prime }}$, $r_i^{{-}^{\prime }}$.

$$\begin{gathered} C_i^{+}={\alpha }_1{D}_i^{{-}^{\prime }}+{\beta }_1{r}_i^{{+}^{\prime }} \\ {C}_i^{-}={\alpha }_2{D}_i^{{+}^{\prime }}+{\beta }_2{r}_i^{{-}^{\prime }} \end{gathered}$$

(15)

Step 6: Obtain the resilience of the evaluation object according to its degree of closeness.

$$R_i={\displaystyle \frac{C_i^{+}}{C_i^{+}+C_i^{-}}}$$

(16)

Step 7: Use SOM to classify the resilience level of the road.

SOM achieves classification by mapping high-dimensional input to the low-dimensional competitive layer that is closest in distance and has a simple structural relationship. The basic principle is shown in Figure 2. Given that SOM exhibits high efficiency in processing high-dimensional data, this study takes road network resilience at each moment as the input of SOM. Through iteratively learning the distribution characteristics of input data, the positions and weight vectors of neurons in the competitive layer are adjusted. The output results automatically classify roads into three levels according to resilience, namely, high-resilient, medium-resilient and low-resilient.

4.3. Determination of Prediction Model

This study substitutes the evaluation results of road network resilience and five main factors identified by the obstacle degree model that constrain the improvement of resilience into LSTM, achieving more accurate resilience forecasting to promptly recognize a road with low resilience. The specific steps are as follows:

Step 1: Identify the main factors restricting resilience using an obstacle degree model based on the evaluation results of road network resilience.

$$M_{ij}={\displaystyle \frac{W_j\times I_{ij}}{{\displaystyle \sum _{i=1}^m{W}_j\times I_{ij}}}}$$

(17)

$$I_{ij}=z_j^{+}-z_{ij}$$

(18)

$M_{ij}$ denotes the —obstacle degree of index $j$ of road $i$.

$I_{ij}$ denotes the —deviation from index $j$ of road $i$ to the ideal solution of index $j$. The greater the deviation, the higher the impact of index $j$ on road $i$.

Step 2: Based on road network resilience evaluation results and the corresponding influencing factors of resilience, construct a multivariate multistep LSTM model to predict future resilience (see Figure 3). The specific steps are as follows:

1. Identify five element layer indexes with the highest obstacle degree at time $t$ as the main resilience constraining factors at time $t$. With a time step of 12 months, the resilience evaluation results of the previous 12 months and the corresponding five main factors are substituted into the LSTM. The outputs involve the predicted road network resilience of the current and following two months, creating a series of input–output sample pairs.

$$Inputdata=\left[\begin{array}{c}{x}_t\\ x_{t+1}\\ ⋮\\ x_{t+11}\\ ⋮\\ x_{t+14}\end{array}\right]=\left[\begin{array}{c}{F}_1^t{F}_2^t{F}_3^t{F}_4^t{F}_5^t{R}^t\\ F_1^{t+1}{F}_2^{t+1}{F}_3^{t+1}{F}_4^{t+1}{F}_5^{t+1}{R}^{t+1}\\ ⋮\\ F_1^{t+11}{F}_2^{t+11}{F}_3^{t+11}{F}_4^{t+11}{F}_5^{t+11}{R}^{t+11}\\ ⋮\\ F_1^{t+14}{F}_2^{t+14}{F}_3^{t+14}{F}_4^{t+14}{F}_5^{t+14}{R}^{t+14}\end{array}\right]$$

(19)

$F_1^t,F_2^t,F_3^t,F_4^t,F_5^t$ denote the five main resilience constraining factors at time $t$.

2. The sample pairs are fed into the hidden layer of the LSTM. Each memory block first uses forget gate coefficient $f_t$ to retain information $f_t\cdot c_{t-1}$ from previous cell state $c_{t-1}$ to current cell state $c_t$. Then it uses input gate coefficient $i_t$ to keep information $i_t\cdot {\tilde{c}}_t$ from current candidate cell state ${\tilde{c}}_t$ and move it to current cell state $c_t$. Finally, it determines the output of current memory block $h_t$ using output gate coefficient $o_t$.

$$\begin{array}{l}{f}_t=sigmoid\left(W_f\cdot \left[h_{t-1},x_t\right]+b_f\right)\\ i_t=sigmoid\left(W_i\cdot \left[h_{t-1},x_t\right]+b_i\right)\\ {\tilde{c}}_t=\tan \mathrm{h}\left(W_c\cdot \left[h_{t-1},x_t\right]+b_c\right)\\ c_t=f_t\cdot c_{t-1}+i_t\cdot {\tilde{c}}_t\\ o_t=sigmoid\left(W_o\cdot \left[h_{t-1},x_t\right]+b_o\right)\\ h_t=o_t\cdot \tan \mathrm{h}\left(c_t\right)\end{array}$$

(20)

3. After training the LSTM model, outputs are processed by inverse normalization to serve as the predicted road network resilience for the next three months.

$${\widehat{R}}_t=Min+h_t\times \left(Max-Min\right)$$

(21)

$Min$ denotes the minimum value of road network resilience

$Max$ denotes the maximum value of road network resilience.

5. Case Study

5.1. Study Area

Shanghai is one of the first cities to build fast roads in China [51]. By the end of 2020, Shanghai completed 19 fast roads, including Inner Ring, Yixian and South–North Elevated roads, with a total length of 392 km. Shanghai fast roads are classified as high-grade roads with an average driving speed of 80 km/h and generally contain six to eight lanes in two directions [51]. With highway interchanges serving as intersections connecting traffic flows from different fast roads and traffic lights connected to roads helping to guide the entering and exiting of traffic flows, Shanghai fast roads provide long-distance and rapid transport service for large traffic flows [52]. The detailed topological structure of Shanghai fast roads can be seen in Figure 4. While providing safe, fast and efficient transport service as the main artery of urban transportation operation, Shanghai fast roads are faced with challenges such as frequent traffic accidents and emergency management difficulties caused by the rapid increase in the number of vehicles. According to statistics, 426,904 traffic accidents occurred on Shanghai fast roads in 2021, resulting in 88,463 casualties and property losses of up to CNY 69,728, which severely affected road service levels [53]. Circular road sections formed by Yanan, Humin and South–North are the most severe areas affected by traffic accidents [53]. The reasons for the increasingly frequent accidents are partly due to the topological structure of fast roads, for example, narrow and crowded lanes, disturbances brought about by the entering traffic flow and queuing near the off-ramps.

5.2. Data Source and Processing

This study selected representative sections of Inner Ring, Yixian, South–North, Yanan and Humin Elevated roads as the subjects for road network resilience evaluation. The original data for the element layer indicators of evaluation subjects were sourced from the Shanghai Fast Roads Emergencies Dataset, Shanghai Elevated Road Vehicle Towing Emergency Disposal Plan and OpenStreetMap (https://www.openstreetmap.org) (accessed on 18 June 2024). Considering data availability, this study applied data from January 2019 to July 2022 for dynamic resilience evaluation (

Table A1. Raw data samples in July 2022.

Road	D1	D2	D3	……	D25	D26	……
Inner Ring-Mainline01-Inner Circle	90	9980	76,768	……	0	16	……
Inner Ring-Mainline01-Outer Circle	60	10,560	84,896	……	0	14	……
Inner Ring-Mainline02-Inner Circle	60	3467	25,069	……	0	16	……
Inner Ring-Mainline02-Outer Circle	60	2477	22,334	……	0	14	……
Inner Ring-Mainline03-Inner Circle	90	21,713	188,955	……	3	16	……
……	……	……	……	……	……	……	……
Yanan Elevated Road-Mainline04-North Side	90	1471	10,368	……	20	20	……
Yanan Elevated Road-Mainline04-Sorth Side	60	2246	19,780	……	20	19	……
Yanan Elevated Road-Mainline05-North Side	60	26,857	205,861	……	20	19	……
Yanan Elevated Road-Mainline05-South Side	90	24,192	192,347	……	20	11	……

).

Firstly, the original data were standardized to calculate the objective weights of element layer indicators based on the factor analysis method described in Section 4.1. Then, a questionnaire was designed to obtain subjective judgments from domain experts on the importance of functional, feature and element layer indicators on road network resilience. The domain experts comprised 50 experts in the field of urban road emergency management. The questionnaire was divided into two sections, where experts could choose any number of evaluation terms from a seven-point linguistic set ranging from “very unimportant” to “very important” to answer specific questions in each section. The first section asked which evaluation terms from the linguistic set the experts would use to describe the importance of functional, feature and element layer indicators. The second section asked which evaluation terms the experts would not use from the linguistic set to describe the importance of indicators. The results of the questionnaire were used to calculate subjective element layer weights based on the hesitant intuitionistic fuzzy expert scoring method described in Section 4.1. The objective and subjective weights were combined to attain element layer combination weights (

Table A2. Indicator weights in July 2022.

Element Layer	Subjective Weights	Objective Weights	Combined Weights
D1	0.0057	0.0203	0.0073
D2	0.0066	0.3253	0.0406
D3	0.0067	0.2700	0.0348
D4	0.0053	0.0020	0.0050
D5	0.0450	0.1615	0.0574
D6	0.0485	0.1908	0.0637
D7	0.0459	0.0125	0.0423
D8	0.0438	0.0048	0.0397
D9	0.0308	0.0001	0.0275
D10	0.0328	0.0001	0.0293
D11	0.0312	0.0001	0.0279
D12	0.0271	0.0001	0.0242
D13	0.0283	0.0001	0.0252
D14	0.0369	0.0043	0.0333
D15	0.0360	0.0001	0.0322
D16	0.0299	0.0043	0.0271
D17	0.0314	0.0001	0.0281
D18	0.0303	0.0016	0.0272
D19	0.0322	0.0001	0.0288
D20	0.0739	0.0007	0.0661
D21	0.0867	0.0001	0.0775
D22	0.0847	0.0004	0.0757
D23	0.0457	0.0004	0.0409
D24	0.0453	0.0003	0.0405
D25	0.0477	0.0001	0.0426
D26	0.0489	0.0001	0.0436
D27	0.0064	0.0004	0.0058
D28	0.0064	0.0001	0.0058

) using the correction coefficient method described in Section 4.1. Afterwards, the weighted standardization matrix derived from multiplying standardized original data with combination weights was substituted into GRA-TOPSIS, described in Section 4.2, to calculate the resilience of Shanghai fast roads from January 2019 to July 2022 (

Table A3. Evaluation results of road network resilience from January 2019 to July 2022.

Road	January 2019	February 2019	March 2019	……	May 2022	June 2022	July 2022
Inner Ring-Mainline01-Inner Circle	0.4030	0.4030	0.4033	……	0.3944	0.4154	0.3992
Inner Ring-Mainline01-Outer Circle	0.4696	0.4687	0.4804	……	0.4820	0.4223	0.4371
Inner Ring-Mainline02-Inner Circle	0.4652	0.4815	0.4889	……	0.4902	0.4873	0.4926
Inner Ring-Mainline02-Outer Circle	0.4804	0.4966	0.5023	……	0.4755	0.4725	0.4779
Inner Ring-Mainline03-Inner Circle	0.5335	0.5432	0.5592	……	0.5585	0.4554	0.5110
……	……	……	……	……	……	……	……
Yanan Elevated Road-Mainline04-North Side	0.4730	0.4640	0.4721	……	0.5376	0.5349	0.4231
Yanan Elevated Road-Mainline04-Sorth Side	0.5157	0.5262	0.4394	……	0.5048	0.5020	0.5072
Yanan Elevated Road-Mainline05-North Side	0.5160	0.5292	0.5529	……	0.6172	0.6145	0.4897
Yanan Elevated Road-Mainline05-South Side	0.4748	0.5107	0.4932	……	0.5870	0.5845	0.5889

). Finally, the resilience of each road section was substituted into the obstacle degree model described in Section 4.3 to obtain five main constraints and the corresponding constraining levels of resilience (

Table A4. Constraining factors of samples in July 2022.

Road	Factor 1	Factor 2	Factor 3	Factor 4	Factor 5
Inner Ring-Mainline01-Inner Circle	D6 (0.1023)	D20 (0.0988)	D7 (0.0848)	D23 (0.0816)	D5 (0.0813)
Inner Ring-Mainline01-Outer Circle	D23 (0.1063)	D24 (0.1051)	D5 (0.1035)	D20 (0.0858)	D2 (0.0843)
Inner Ring-Mainline02-Inner Circle	D5 (0.1662)	D24 (0.1414)	D24 (0.1398)	D2 (0.1355)	D8 (0.1179)
Inner Ring-Mainline02-Outer Circle	D5 (0.1542)	D23 (0.1291)	D24 (0.1276)	D2 (0.1266)	D8 (0.1076)
Inner Ring-Mainline03-Inner Circle	D20 (0.2521)	D5 (0.1052)	D22 (0.1026)	D8 (0.0868)	D2 (0.0834)
……	……	……	……	……	……
Yanan Elevated Road-Mainline04-North Side	D22 (0.1687)	D21 (0.1274)	D5 (0.1092)	D20 (0.1053)	D2 (0.0896)
Yanan Elevated Road-Mainline04-Sorth Side	D5 (0.1794)	D23 (0.1575)	D24 (0.1556)	D2 (0.1498)	D8 (0.1111)
Yanan Elevated Road-Mainline05-North Side	D21 (0.2626)	D22 (0.2563)	D20 (0.1599)	D13 (0.0855)	D17 (0.0680)
Yanan Elevated Road-Mainline05-South Side	D23 (0.4274)	D24 (0.4225)	D28 (0.0602)	D27 (0.0601)	D4 (0.0298)

). This was followed by forming input sample pairs for the LSTM model to predict the resilience variation trend in each road section for the next three months (

Table A5. Prediction results of road network resilience from August 2022 to October 2022.

Road	August 2022	September 2022	October 2022
Inner Ring-Mainline01-Inner Circle	0.4087	0.4182	0.4287
Inner Ring-Mainline01-Outer Circle	0.4310	0.5024	0.5068
Inner Ring-Mainline02-Inner Circle	0.5044	0.4999	0.4977
Inner Ring-Mainline02-Outer Circle	0.4884	0.4875	0.4872
Inner Ring-Mainline03-Inner Circle	0.5086	0.5063	0.5032
……	……	……	……
Yanan Elevated Road-Mainline04-North Side	0.5501	0.5453	0.5309
Yanan Elevated Road-Mainline04-Sorth Side	0.4843	0.4871	0.4729
Yanan Elevated Road-Mainline05-North Side	0.5368	0.6121	0.5079
Yanan Elevated Road-Mainline05-South Side	0.5579	0.5477	0.5420

).

5.3. Results and Discussion

5.3.1. Calculation Results of Indicator Weights and Road Network Resilience

According to the indicator weights in Table A2, the subjective weights of the total investment in the road (D2), total investment in road maintenance per month (D3) and width per lane (D6) are relatively large, whereas the objective weights and combined weights are all greater for average accident response time per month (D21), average accident disposal time per month (D22) and average accident perception time per month (D20). This implies that perception, response and disposal efficiency have a significant impact on the resilience of fast roads under traffic accidents. The potential reason for the larger subjective weights of D2, D3 and D6 lies in the greater original numerical values of these indicators, which can cause bias in objective weighting. This also reflects the rationale of the combination weighting adopted by this study to diminish the shortcomings of single objective weighting in relying heavily on raw data.

Based on the resilience evaluation results from Figure 5a to Figure 5e, based on the overall resilience of Shanghai fast roads, Yixian possessed the highest average resilience from January 2019 to July 2022, reaching 0.5363 (Figure 5b). In contrast, Inner Ring showed the lowest average resilience with only 0.4931 (Figure 5a). This suggests that Yixian had a stronger comprehensive emergency management capability in the face of traffic accidents.

In terms of the resilience of each road section, Figure 5a displays that Inner Ring Elevated Road—Mainline 01—Inner Circle had the lowest overall resilience from January 2019 to July 2022, with only 0.31 in April 2022. This indicates that the comprehensive emergency management capability of Inner Ring Elevated Road—Mainline 01—Inner Circle was the weakest under traffic accidents. Therefore, it is of necessity to improve accident preparedness, mitigation, response and recovery measures in this area to enhance its overall road network resilience.

Observing the resilience fluctuations, the resilience of each road section shows fluctuations from January 2019 to July 2022. Among them, Figure 5d demonstrates that Yanan Elevated Road—Mainline 03—South Side experienced the largest upward fluctuation from March 2022 to April 2022. The potential reason is the significant reduction in accident response and disposal time during this period, which enhanced the road’s ability to restore a normal service level rapidly during the emergency response phase, resulting in a significant increase in resilience. Conversely, as shown in Figure 5d, Yanan Elevated Road—Mainline 03—South Side experienced the largest downward fluctuation from May 2022 to June 2022. The potential explanation lies in the significant increase in accident response and disposal time during this period, which weakened its ability to restore a normal service level quickly during the emergency response phase, leading to a significant decrease in resilience.

5.3.2. Spatial Distribution in Road Network Resilience

It is apparent in Figure 6 that the resilience of Shanghai fast roads under traffic accidents has notable spatial distribution characteristics, as follows:

1. As can be seen from Figure 6a, with regard to the distribution of road sections with different resilience levels, high-resilient sections are mainly located on South–North and Yanan, with both having four high-resilient road sections. The potential cause is that South–North and Yanan were constructed relatively late, resulting in better road health and structural conditions as well as more completed emergency response mechanisms, which contribute to higher resilience. Medium-resilient sections are primarily found on Inner Ring and Humin, with 11 and 10 road sections rated as medium-resilient, respectively. Low-resilient sections are mainly distributed on Inner Ring and South–North, with both having six low-resilient road sections. The underlying reason is that Inner Ring and South–North carry a large volume of traffic on a daily basis, raising the likelihood of traffic accidents. Additionally, the high-density traffic flow and a few narrow lanes also escalate the difficulty of emergency management, thereby reducing resilience.

2. As can be found in Figure 6b, considering the orientation of road sections with different resilience levels, low-resilient sections of Inner Ring are predominantly located on the outer circle. There are more medium-resilient sections on the inner circle than the outer circle, suggesting that the overall resilience of the outer circle is lower than the inner circle. This calls for enhancing the emergency management capability of the outer circle of Inner Ring.

Figure 6c demonstrates that low-resilient sections of South–North are mainly on the east side. The potential reason is that the east side of North–South acts as the essential route for north-to-south traffic flow, resulting in a higher probability of traffic accidents and greater difficulty in emergency management, thereby lowering the resilience of the east side.

It is visible in Figure 6d that low-resilient sections of Yanan are entirely located on the south side. The overall resilience of the north side is better than the south side. The underlying reason is that the south side of Yanan is an important route for west-to-east traffic flow, leading to a rising probability of traffic accidents, thus decreasing the resilience of the south side.

As can been viewed from Figure 6f, both the east and west sections of Humin are deemed as medium-resilient, indicating that Humin possesses a comparatively excellent emergency management ability under traffic accidents.

5.3.3. Constraining Factors of Resilience

According to the statistical results of constraining factors presented in Figure 7, total length of road (D5), average accident response time per month (D21), average accident perception time per month (D20), number of tractors (D23) and average accident disposal time per month (D22) exert remarkable impact on the resilience of fast roads. This reveals that the efficiency of emergency organization work, perception, response and disposal of accidents, as well as the dispatching of emergency resources during the emergency response phase, can significantly affect a road’s ability to resist a certain level of disturbance, meet the needs at an accident site and quickly recover normal traffic flow.

The statistical analysis of constraints for Inner Ring shown in Figure 8a suggests that accident disposal time (D22) exerts the greatest impact on the improvement of its resilience. By dispatching necessary emergency resources from nearby locations and coordinating rescue vehicles and personnel to carry out emergency organization work in an orderly way, the efficiency of accident disposal can be improved and the resilience of Inner Ring will be enhanced.

The statistical analysis of constraints for Yixian in Figure 8b and South–North in Figure 8c depict that the main factor restricting the improvement of their resilience is accident perception time (D20). Elevating the monitoring of traffic accidents during peak hours by road surveillance and video inspections can reduce the time to detect accidents and enhance the resilience of Yixian and North–South.

Observed from Figure 8d,e, the leading factor restricting the enhancement of the resilience of Yanan and South–North is the number of tractors (D23). By planning the number and distribution of tractors rationally, the timeliness of satisfying the demand at an accident site can be guaranteed and the resilience of Yanan and South–North will be improved.

5.3.4. Variation Trend in Road Network Resilience

Based on the predicted road network resilience shown in Figure 9e, Humin Elevated Road sections showed the least variation in resilience from August 2022 to October 2022, revealing that Humin can maintain a stable resilience level over a certain period under traffic accidents.

It is evident in Figure 9a that some sections of Inner Ring are expected to experience an ascending or increasing trend after an initial drop in the next three months. Therefore, it is of great importance to focus on sections of Inner Ring that show a downward trend in resilience to enhance the road’s preparedness for potential accidents.

Figure 9b illustrates that the resilience levels of all sections of Yixian are expected to follow a decreasing trend before increasing. In contrast, Figure 9c,d indicate that the majority of the South–North and Yanan sections are expected to exhibit an increasing resilience trend followed by a decrease in the next three months. Thus, it is necessary to pay attention to sections with s descending trend in resilience to identify vulnerable roads in time and enhance emergency management ability, which will effectively minimize the descending extent of resilience.

6. Conclusions

Dynamic evaluation of road network resilience in traffic accident scenarios is crucial for administrators and practitioners to identify current and potential vulnerable road sections as well as weak links in emergency management, fundamentally enhancing emergency management capability and reducing the negative impact of traffic accidents on resilient and sustainable cities. Given the critical role of Shanghai fast roads in providing urban transport services and the increasingly significant randomness and destructiveness of traffic accidents, it is crucial to evaluate the resilience of Shanghai fast roads dynamically. To concretize the road network resilience concept from an emergency management perspective, this study first selected indicators of resilience capability, resilience attributes and traffic accident emergency management capabilities to construct a road network resilience evaluation index system. Subsequently, considering the high arbitrariness and lack of experienced judgment in single subjective and objective weighting methods, as well as the low precision in single evaluation methods, this study designed a combination weighting integrating factor analysis with hesitant intuitionistic fuzzy expert scoring for GRA-TOPSIS and an obstacle degree model with LSTM to achieve the dynamic evaluation of resilience. Finally, the method was applied to an evaluation of Shanghai fast road resilience under traffic accidents. The results showed that the proposed method can accomplish scientific and precise resilience evaluation, indicating that the combination of subjective and objective weighting methods can compensate for the large weight bias in single weighting methods, and the hybrid evaluation model can effectively solve the low precision of single evaluation models when judging the superiority of similar evaluation objects.

The dynamic evaluation results of road network resilience provided by this study are helpful for government and road operators to improve emergency management work pertinently and enhance the comprehensive road emergency management ability under traffic accidents. According to the results of our case study, there are significant spatial distribution characteristics in road network resilience. Accident perception, response and disposal time, the number of tractors and total length of road have a remarkable impact on road network resilience. Some road sections are expected to show a notable descending trend in resilience. As a result, based on resilience evaluation results, administrators can turn to information technology to elevate the accident perception capability of low-resilient road sections and promote accident response and disposal efficiency by quickly organizing and dispatching nearby emergency resources. Moreover, by referring to resilience prediction results, road operators can anticipate and identify roads with a downward resilience trend, thereby strengthening emergency mitigation and preparation work for roads with potential low resilience and reducing the negative impact of accidents. The method proposed by this study is applicable to the resilience evaluation of road networks in other cities with similar network topological structures and road operating characteristics, which requires further study to validate the generalizability of the proposed method.

However, the dynamic evaluation method of road network resilience in this study has certain limitations and can offer avenues for future research. First, due to data availability, there is a lack of evaluation indicators in the emergency recovery phase, which can be enriched in future research to construct a more comprehensive index system. Second, this study only uses GRA-TOPSIS with combination weighting for road network resilience evaluation as a default to compare the results of different models. Outlooks for future research lie in employing different hybrid models for road network resilience evaluation to test the robustness of this research method.