A cross-domain-oriented urban traffic road network resilience pre-judgment evaluation method

Abstract

The present application relates to the field of intelligent transportation, and proposes a cross-domain-oriented urban traffic network resilience prediction and evaluation method, which contains three steps: step 1: based on the input source domain and target domain urban traffic data, a time-space cross-domain traffic prediction model is constructed, the traffic state migration learning and generalization prediction between different cities are realized, and the traffic prediction and the corresponding traffic graph structure under the cross-domain scene are generated; step 2: combining the prediction result and the traffic graph structure, a hysteresis resilience index is designed, the structure-function resilience and hysteresis resilience factors are fused, and the resilience index reflecting the performance evolution mechanism of the road network is formed; step 3: based on the hysteresis resilience index, a time-space fine-grained resilience quantification algorithm is established, which is used for quantifying the node-level resilience of the road network. The present application effectively solves the three major problems of the existing evaluation method: lack of predictability and cross-domain generalization ability, single resilience index representation and rough resilience quantification, and significantly improves the forward-looking, adaptability and accuracy of the road network resilience evaluation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent transportation, in particular to a cross-domain-oriented urban traffic network resilience prediction and evaluation method. BACKGROUND

[0002] As a key infrastructure, urban traffic network is an important support for ensuring the normal operation of the city. With the expansion of the city size and the growth of traffic demand, the road network is more vulnerable to large-scale service capacity decline when facing extreme weather, sudden accidents or local failures. Therefore, how to accurately predict and evaluate the resilience of the road network under the disturbance situation is of great significance for resource scheduling and emergency response. However, there are differences in road network structure and operation characteristics among different cities, and the resilience evaluation method constructed in a single scenario is difficult to be directly migrated to other cities. Further, it is of great significance to study a cross-domain-oriented urban traffic network resilience prediction and evaluation method to improve the forward-looking and generalization of the model, and to improve the urban traffic management.

[0003] Existing traffic network resilience evaluation methods mainly include three types: topological model, simulation model and data-driven model. Topological model focuses on the structure of the road network, and uses structural indicators such as road network connectivity, node centrality and shortest path to represent the resilience of the road network. However, in real scenarios, structural resilience indicators usually only change significantly when large-scale structural damage (such as earthquakes, floods, etc.) occurs, and it is difficult to effectively evaluate the resilience of the road network under general traffic accidents or sudden congestion and other functional disturbances.

[0004] Simulation model introduces node attack, link failure and other simulation strategies, and combines functional indicators such as traffic speed, flow or occupancy to quantify the resilience of the road network. However, such methods usually need to rely on a large number of preset assumptions and are mainly used for fixed road networks, which are difficult to realistically depict the real evolution of the road network under disturbance situations, resulting in poor flexibility and scalability.

[0005] With the popularity of deep learning techniques and large-scale traffic sensor data, data-driven methods have become mainstream. Based on spatio-temporal traffic data, these methods combine convolutional neural networks, graph neural networks, and neural differential equations to model road network states. They not only accurately depict the evolution of road networks during disturbances but also significantly improve the accuracy of resilience quantification. However, these methods still face three common problems. First, they lack predictive ability and cross-domain generalization. Existing methods are mostly based on historical observation data for post-evaluation, which cannot effectively predict future road network resilience. Moreover, they can only analyze a single city or a fixed road network scenario, lacking cross-domain migration and generalization ability. Second, the resilience index representation is single-dimensional. The road network has a hysteresis effect during disturbances, and existing methods generally ignore the evolution mechanism of road network performance with disturbance intensity, leading to distorted resilience index representation. Third, there is a lack of spatio-temporal fine-grained resilience quantification. Existing methods usually focus on the overall change of road network performance at the beginning and end of the disturbance, without conducting fine-grained analysis by stages (such as resistance and recovery). In the spatial dimension, they do not refine to the node or road segment level, making it difficult to identify local vulnerable units and limiting the guiding value of evaluation results for resource allocation and fine-grained management. SUMMARY

[0006] To solve the problems of existing urban traffic road network resilience evaluation methods, such as lack of predictive ability and cross-domain generalization, single-dimensional resilience index representation, and lack of spatio-temporal fine-grained resilience quantification, the present invention proposes a cross-domain-oriented urban traffic road network resilience prediction and evaluation method, including a spatio-temporal cross-domain traffic prediction model, a hysteresis resilience index, and a spatio-temporal fine-grained resilience quantification algorithm. The spatio-temporal cross-domain traffic prediction model uses a pre-training-fine-tuning framework. It first learns general spatio-temporal features on source domain urban traffic data, then adapts to target domain data through the fine-tuning stage while inheriting the source domain spatio-temporal pattern, achieving traffic prediction in cross-city scenarios. The hysteresis resilience index is constructed based on the prediction results, integrating structural, functional resilience indices, and hysteresis resilience factors to comprehensively represent multi-dimensional resilience characteristics during disturbances. The spatio-temporal fine-grained resilience quantification algorithm considers the performance retention rate, average resistance index, and maximum recovery rate of the road network, segmentally depicts the disturbance process in the time dimension, and refines to the node level in the spatial dimension, dynamically outputting fine-grained resilience evaluation results.

[0007] The present invention is achieved by the following technical solutions:

[0008] A cross-domain-oriented urban traffic road network resilience prediction and evaluation method includes the following steps:

[0009] Step 1: Based on source domain and target domain urban traffic data, construct a spatio-temporal cross-domain traffic prediction model to generate traffic prediction and traffic graph structure in cross-city scenarios.

[0010] The construction of the spatiotemporal cross-domain traffic prediction model includes a pre-training stage and a fine-tuning stage. First, it is pre-trained on source domain urban traffic data to learn general spatiotemporal characteristics. Then, the fine-tuning stage adapts it to the target domain data. Both stages share: a constant-to-differential time-series module, a lightweight spatial memory module, and a decoder module. Additionally, a refined spatiotemporal distillation module is introduced in the fine-tuning stage.

[0011] Therefore, the working process of the spatiotemporal cross-domain traffic prediction model is as follows:

[0012] First, historical velocity data of source cities are selected for pre-training. The general pre-trained spatiotemporal features of source cities are captured through a constant-dissimilar time series module, a lightweight spatial memory module, and a decoder.

[0013] Then, historical speed data of the target domain city is selected for fine-tuning. The same module is used to capture the fine-tuned spatiotemporal features of the target domain city. At the same time, the source domain features are effectively transferred to the target domain through a refined spatiotemporal distillation device.

[0014] Finally, the speed prediction and corresponding traffic map structure of the target domain city under the disturbance scenario are generated.

[0015] Step 2: Based on the prediction results and traffic map structure, design the hysteresis resilience index;

[0016] The hysteresis toughness index includes structural-functional toughness and hysteresis toughness factor.

[0017] The establishment process is as follows: First, considering both the road network spatial structure and traffic speed characteristics, a structural-functional resilience index is designed. Second, the hysteresis characteristics of the road network during disturbance phases are analyzed, and a hysteresis resilience factor is designed. Finally, the hysteresis resilience factor is integrated into the structural-functional resilience to construct the hysteresis resilience index.

[0018] Step 3: Based on the hysteresis toughness index, establish a spatiotemporal fine-grained toughness quantification algorithm and output the toughness results.

[0019] First, based on the target domain city traffic speed label values, the target domain city traffic speed prediction values, and disturbance events, the hysteresis resilience index under non-disturbance conditions is calculated respectively. Hysteresis resilience index under disturbance .

[0020] Secondly, based on and Quantifying the performance retention rate of the road network during the disturbance phase from a macro perspective. .

[0021] Then, calculate the average resistance index separately. and maximum recovery rate .

[0022] Finally, the three-part toughness quantification results are weighted and fused to obtain:

[0023] ,

[0024] wherein, , and are weight coefficients, R is the final spatiotemporal fine-grained toughness quantification result.

[0025] Advantages

[0026] The present application aims at the three major problems faced by the existing city traffic network toughness evaluation method: lack of predictability and cross-domain generalization ability, single toughness index representation dimension, and lack of fine-grained toughness quantification. Based on deep learning technology, the adaptability and accuracy of road network toughness evaluation under cross-city market scenarios are effectively improved, which provides guidance for resource scheduling, emergency scheduling and strategy optimization, as follows:

[0027] (1) Based on the pre-training-fine-tuning framework, a spatiotemporal cross-domain traffic prediction model is designed, which fully utilizes the source domain spatiotemporal pattern for transfer learning, improves the traffic prediction ability of the target domain, and realizes the predictability and cross-domain generalization of toughness evaluation.

[0028] (2) On the basis of traditional structure-function toughness index, a hysteresis toughness factor is designed, and the two are fused to build a hysteresis toughness index, which more comprehensively and accurately represents the dynamic evolution of the road network in the disturbance period.

[0029] (3) A spatiotemporal fine-grained toughness quantification algorithm is proposed, which segments the whole disturbance process in the time dimension and refines to the node level in the space dimension, realizing the toughness evaluation of local fragile units. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is the flowchart of the cross-domain city traffic network toughness prediction and evaluation method of the present application;

[0031] Figure 2 is the structural schematic diagram of the spatiotemporal cross-domain traffic prediction model of the embodiment of the present application;

[0032] Figure 3 is the visual traffic node diagram of the city traffic network of the embodiment of the present application;

[0033] Figure 4 is the hysteresis evolution mechanism diagram of the road network performance of the embodiment of the present application;

[0034] Figure 5 is the road network toughness evaluation result diagram of the embodiment of the present application in San Jose, USA;

[0035] Figure 6 Fig. 9 is a graph showing the resilience evaluation results of Beijing road network in an embodiment of the present application. DETAILED DESCRIPTION

[0036] The technical solutions provided by the present application will be further described below with reference to specific embodiments and the accompanying drawings. The advantages and features of the present application will become more apparent in light of the following description.

[0037] A cross-domain-oriented urban traffic road network resilience prediction and evaluation method, as shown in FIG. 1, comprises the following steps: Figure 1

[0038] Step 1: Based on the source domain and target domain urban traffic data, a spatio-temporal cross-domain traffic prediction model is constructed to generate traffic prediction and traffic graph structure under cross-city market scenarios.

[0039] Step 2: According to the prediction results and traffic graph structure, a hysteresis resilience index is designed.

[0040] Step 3: Based on the hysteresis resilience index, a spatio-temporal fine-grained resilience quantification algorithm is established to output the resilience results.

[0041] EMBODIMENT

[0042] Taking cross-domain urban traffic road network resilience prediction and evaluation as the application scenario:

[0043] Step 1: Construct a spatio-temporal cross-domain traffic prediction model, as shown in FIG. 2. Figure 2

[0044] The design of the spatio-temporal cross-domain traffic prediction model includes a pre-training stage and a fine-tuning stage. First, pre-train on the source domain urban traffic data to learn general spatio-temporal features, and then adapt to the target domain data through the fine-tuning stage. Among them, the two stages share the common-heterochronous module (1), the lightweight spatial memory module (2) and the decoder module (3). At the same time, the fine-tuning stage additionally introduces the fine-grained spatio-temporal distiller module (4). Figure 2 Figure 2 Figure 2 Figure 2

[0045] The working process of the spatio-temporal cross-domain traffic prediction model:

[0046] First, select the historical speed data of the source domain city for pre-training, and capture the general pre-training spatio-temporal features of the source domain city through the common-heterochronous module, the lightweight spatial memory module and the decoder.

[0047] Second, select the historical speed data of the target domain city for fine-tuning, and capture the fine-tuning spatio-temporal features of the target domain city using the same modules, while realizing the effective migration of the source domain features to the target domain through the fine-grained spatio-temporal distiller. ​​​​​​

[0048] Finally, the speed prediction of the target domain city under the disturbance scenario and the corresponding traffic graph structure are generated.

[0049] In this embodiment, the source domain city data is the speed data of the California road network in the United States, containing historical observation values of hundreds of different spatial sensors. The target domain city is the speed data of the Beijing road network in China, also containing historical observation values of hundreds of different spatial sensors.

[0050] Step 1.1: Constructing traffic graph structure;

[0051] Based on the theory of topological network structure, the road sensor is regarded as the node of the traffic network, and the connection relationship between the sensors is regarded as the edge of the traffic network, thereby constructing the spatial physical topological structure of the traffic network, i.e. the traffic graph structure. The traffic graph can be defined as:

[0052] (1)

[0053] In the formula, represents a set of nodes; is a set of edges connecting the nodes; is an adjacency matrix. When node is connected to node , then ; otherwise, . Based on , the spatiotemporal traffic data can be represented as a sequence ; wherein is the length of the time series; is the traffic feature (such as speed, flow and occupancy).

[0054] For the source domain and the target domain city, the traffic graph structure is constructed.

[0055] Taking the San Jose city road network in the United States as an example, the traffic graph visualization is shown in Figure 3 . The horizontal coordinate is the longitude value, and the vertical coordinate is the latitude value. The maximum rainfall information of the regional position is used as the attribute feature of the traffic node, which can be used for road network evaluation when the traffic node appears rainfall.

[0056] Step 1.2: Normal-Abnormal Time Sequence Module;

[0057] Urban traffic network not only exists periodicity and other normal time dependence, but also often accompanied by sudden fluctuations superimposed by disturbance effect. In order to fully capture the normal and abnormal time dependence of traffic pattern, a normal-abnormal time sequence module is designed, including: time scale decomposition, patch processing, global time attention convolution and gated time convolution;

[0058] Step 1.2.1: Time-scale decomposition;

[0059] Traffic time series generally exhibit multi-scale characteristics, including both long-term seasonal variations and short-term trend changes. Long-term seasonality reflects the periodicity of the road network and other normal traffic conditions, while short-term trend reflects abnormal traffic conditions caused by nonlinear fluctuations due to disturbances. To facilitate the subsequent capture of multi-scale time dependencies, scale decomposition is necessary first.

[0060] Specifically, spatiotemporal traffic data Perform a Fast Fourier Transform to convert the spatiotemporal data X The signal is converted to the frequency domain, and then the K most significant frequency components with the largest amplitudes are selected. The inverse fast Fourier transform is then used to restore the signal to low-frequency and high-frequency sequences. This process is represented as follows:

[0061] (2)

[0062] (3)

[0063] (4)

[0064] (5)

[0065] (6)

[0066] In equation (2), Represents spatiotemporal traffic data (source or target domain); It is the Fast Fourier Transform function; For the frequency domain signal. In equation (3), It is the amplitude function; Indicates before selecting amplitude K Large salient frequency domain components. In equation (4), Indicates from the previous K A frequency domain subset composed of components. In equation (5), It is the inverse fast Fourier transform function; This represents a low-frequency sequence, reflecting the long-term characteristics of the time series, and is used to characterize normal traffic conditions. Equation (6) It is a high-frequency sequence that focuses on short-term irregular fluctuations in time series and is used to characterize abnormal traffic conditions.

[0067] Step 1.2.2: Patch processing;

[0068] In the field of traffic prediction methods, 'Patch' refers to a local data unit formed after structuring and blocking traffic time series data, containing traffic state features (such as flow, speed, density, etc.) within a continuous time window, with clear time series continuity and feature aggregation.

[0069] Since the original input spatiotemporal traffic data often covers a long time span, directly training it will lead to feature redundancy and high computational complexity. Therefore, the present application performs Patch processing on low-frequency sequences and high-frequency sequences , that is, dividing continuous sequences ( or ) into coarse-grained time blocks. This operation helps to improve the efficiency of long sequence processing while preserving key sequence information, represented as:

[0070] ,(7)

[0071] In formula (7), represents the Patched sequence; is the window length of the Patch; , and represents the number of Patch blocks.

[0072] Secondly, the linear layer is used to map the Patch sequence to the required dimension of the model, represented as:

[0073] ,(8)

[0074] Further, to preserve the periodicity and trend context information of spatiotemporal data, an embedding item is introduced for each Patch block, which represents the time position information of the Patch.

[0075] It should be noted that is the linear mapping result of the original Patch sequence, only containing the mapped feature information, not the chronological order relationship of the Patch in the overall time sequence, i.e. the time position information, which is represented by .

[0076] The time information covers the periodic characteristics of the Patch corresponding data in the time series dimension, including daily and weekly cycles. The position information refers to the chronological order relationship of the Patch in the overall time sequence, which is used to reflect the chronological logic between Patches to provide cross-Patch context information. It is represented as:

[0077] ,(9)​

[0078] ,(10)

[0079] Formula (9) represents a broadcast operation; formula (10) represents feature fusion, Patch sequence representing superimposed position information, including Patched low-frequency sequence and Patched high-frequency sequence .

[0080] Step 1.2.3: Global time attention convolution;

[0081] Patched low-frequency sequence The change frequency is low in unit time, and the normal periodic change of the road network is focused on. Therefore, the global time attention convolution is designed, and the normal periodic information of the traffic mode is supplemented by combining the (source domain or target domain) normal time mode library. The process is represented as:

[0082] ,(11)

[0083] Formula (11) represents the Hadamard product of the Patched low-frequency sequence and the (source domain or target domain) normal time mode library . .

[0084] Wherein, is an adaptive matrix. In the model training stage, the dynamic parameter updating mechanism is continuously optimized, based on the mode (such as the typical traffic flow change of the morning and evening peak of weekdays, the stable speed distribution of the regular period, etc.) conforming to the normal characteristics in the input traffic data, combined with the error back propagation gradient of the model prediction and the real normal performance, the matrix parameters are updated iteratively using the Adam optimizer, so that the matrix can adaptively capture and store different types of traffic normal mode characteristics. is the Patched low-frequency sequence after explicit adaptive update. .

[0085] ,(12)

[0086] ,(13)

[0087] ,(14)

[0088] In formula (12), is a trainable parameter; respectively represent Query, Key and Value matrices, which are respectively used to learn the feature mapping of query, key and value between time blocks.

[0089] is a activation function; is a transpose of Key matrix; is a feature dimension; denotes an attention matrix.

[0090] Equation (14) is a global time attention convolution operation . denotes normal time dependence (of source domain or target domain) captured via .

[0091] Step 1.2.4: Gated time convolution

[0092] Patch high-frequency sequence The frequency of change in a unit of time is high, and the focus is on reflecting the violent abnormal fluctuations of the road network under disturbance, which needs to fully capture its time dependence from a local perspective. Therefore, the invention designs a gated time convolution, and combines the abnormal time mode library (of source domain or target domain) to explicitly supplement the abnormal fluctuation information of the traffic mode, which is represented as:

[0093] ,(15)

[0094] Equation (15) represents the Hadamard product of the Patch high-frequency sequence and the abnormal time mode library (of source domain or target domain) . , is also an adaptive matrix. In the model training stage, through a dynamic parameter updating mechanism, based on the abnormal features (such as sudden surge of traffic flow, sudden drop of abnormal speed, etc.) deviating from the normal mode library in the input traffic data, combined with the back propagation gradient of the model prediction error, the matrix parameters are updated iteratively using the Adam optimizer, so that the matrix can adaptively capture and store different types of traffic abnormal mode features. is the Patch high-frequency sequence after explicit adaptive update.

[0095] ,(16)

[0096] In equation (16), is a dilated convolution operation; denotes an expansion factor; is the size of the convolution kernel;

[0097] ,(17)

[0098] In equation (17), ​​for gated time convolution operation; and are activation functions; denotes time convolution operation; denotes time convolution operation; captures abnormal time dependence (source domain or target domain).

[0099] Further, the normal and abnormal time dependence are fused to obtain comprehensive (pre-training or fine-tuning) time features:

[0100] , (18)

[0101] In formula (18), denotes feature fusion; denotes pre-training time features (pre-training stage) or fine-tuning time features (fine-tuning stage).

[0102] Step 1.3: lightweight space memory module;

[0103] The existing method often faces two aspects of shortcomings in the space feature modeling method: one is that the memory ability of the space dependence between traffic nodes is weak, and it is difficult to continuously pay attention to the key space mode information before and after the disturbance occurs. The second is that in the pre-training-fine-tuning cross-domain scene, when facing large-scale traffic network nodes, the parameter quantity of the traditional model is large, the training cost is high, and the migration generalization ability is limited.

[0104] Therefore, the lightweight space memory module is designed to enhance the dynamic memory ability of the space relationship and reduce the parameter overhead.

[0105] The lightweight space memory module comprises a space memory module and a LoRA enhanced training strategy.

[0106] Step 1.3.1: space memory module;

[0107] For the (pre-training or fine-tuning) time features captured by the normal-abnormal time sequence module, the space memory module is used to further extract the space features between traffic nodes, and the space pattern library (source domain or target domain) is combined to enhance the memory of the model to the space relationship, which is represented as:

[0108] ,(19)

[0109] ,(20)

[0110] ,(21)

[0111] In formula (19), are trainable parameters; Query, Key and Value matrices respectively used for learning the feature mapping of query, key and value of the spatial pattern. Equation (20) represents obtaining the intermediate layer spatial dependency with attention mechanism is an activation function; , , and are trainable parameters; represents the spatial dependency captured by the spatial memory module; is a spatial pattern library, .

[0112] Specifically, the spatial pattern library is obtained by iteratively updating the matrix parameters based on the traffic speed characteristics of different spatial positions (such as different road segments, intersections, and regions) in the input traffic data, combining the error backpropagation gradient of the model's spatial traffic speed prediction result and the true situation, and using the Adam optimizer. The spatial pattern library stores diversified spatial relationship templates of the road network, and can be updated adaptively with training, helping the model to share key spatial dependency patterns when facing different disturbance events and different urban scenes.

[0113] Step 1.3.2: LoRA enhanced training strategy;

[0114] Since the trainable matrices of Query and Value Under a large-scale spatial graph, the parameter quantity is large, which easily leads to high model training overhead. Therefore, the present application introduces LoRA low-rank decomposition to reduce the trainable parameters and reduce the cost of model transfer learning across cities. The low-rank decomposition is represented as:

[0115] ,(22)

[0116] (23)

[0117] In equation (22), represents a low-rank matrix; in equation (23), and are incremental terms.

[0118] Based on the low-rank matrix and the incremental term, the original weight is updated and represented as:

[0119] (24)

[0120] Further, the enhanced Query and Value are represented as:

[0121] (25)

[0122] Finally, the spatial dependency after LoRA enhancement training changes from equations (20) and (21) to equations (26) and (27):

[0123] (26)

[0124] (27)

[0125] In equation (26), This represents the intermediate layer spatial dependency after LoRA optimization; in equation (27), This represents pre-trained spatial features captured via a lightweight spatial memory module. Or fine-tune spatial features .

[0126] Step 1.4: Refined space-time distillation apparatus;

[0127] In pre-training-fine-tuning cross-domain scenarios, the time taken to learn the source domain... and spatial characteristics The data often contains noise that is unusable for the target city, and direct transfer can easily reduce the model's adaptability. Therefore, this invention designs a refined spatiotemporal distiller to improve the consistency and effectiveness of spatiotemporal features during the pre-training and fine-tuning stages, including: pre-training-fine-tuning spatiotemporal distillation and pre-training spatiotemporal feature refinement.

[0128] Step 1.4.1: Pre-training - Fine-tuning spatiotemporal distillation;

[0129] Distillation using temporal feature similarity: Pre-trained temporal features obtained using KL divergence loss to evaluate equation (18) and fine-tuning time characteristics The similarity is represented as:

[0130] (28)

[0131] In equation (28), Promote and Feature alignment; M This represents the number of samples.

[0132] Distillation using spatial feature similarity: Pre-trained spatial features enhanced using contrastive learning loss (27) and fine-tuning spatial characteristics Consistency is represented as:

[0133] (29)

[0134] In equation (29), It is a similarity measurement function; Represents an exponential function; Able to align effectively and .

[0135] The updated distillation time features are obtained by minimizing the distillation loss utilizing temporal feature similarity and the distillation loss utilizing spatial feature similarity. Characteristics of distillation space This provides input for subsequent pre-training spatiotemporal feature refinement.

[0136] Step 1.4.2: Refinement of pre-trained spatiotemporal features;

[0137] Refine the temporal features captured during pre-training using adaptive filters. and spatial characteristics :

[0138] (30)

[0139] In equation (30), and These represent adaptive temporal and spatial filters, respectively. , Respectively with time characteristics Spatial features Element-wise multiplication is used to optimize parameters in a task-oriented manner during pre-training, automatically identifying and discarding noise while retaining relevant features. Specifically, during pre-training, the filter parameters... and The optimization is achieved through joint optimization using task-related loss functions (KL divergence loss and contrastive learning loss). The parameter update direction is determined by the task objective function, thereby automatically suppressing noise and preserving relevant features.

[0140] Step 1.5: Decoder

[0141] The decoder is used to adjust the number of feature channels and output traffic prediction results. The decoder of this invention consists of a multilayer perceptron. The components, taking the decoder in the fine-tuning stage as an example, are represented as follows:

[0142] (31)

[0143] In equation (31), This indicates a Concat operation; The cross-city traffic prediction result (traffic speed prediction result in this embodiment) output by the spatio-temporal cross-domain traffic prediction model. Step 2 can be based on the speed prediction result to construct the hysteresis resilience index.

[0144] Step 2: design the hysteresis resilience index, as shown in Figure 1

[0145] The construction of the hysteresis resilience index includes structural-functional resilience and hysteresis resilience factors.

[0146] The establishment process of the hysteresis resilience index: first, considering the spatial structure of the road network and the traffic speed characteristics, the structural-functional resilience index is designed. Second, the hysteresis characteristics of the road network in the disturbance stage are analyzed, and the hysteresis resilience factor is designed. Finally, the hysteresis resilience factor is integrated into the structural-functional resilience to construct the hysteresis resilience index.

[0147] Step 2.1: structural-functional resilience index;

[0148] Traditional resilience indicators focus on single attributes of road network structure or function, and cannot comprehensively reflect the coupling effect of the two. Therefore, the structural-functional resilience index is constructed, which includes speed coupling node accessibility, speed coupling node importance, local diffusion congestion index, speed coupling connectivity integrity and speed fluctuation index, which are defined as:

[0149] ,(32)

[0150] ,(33)

[0151] ,(34)

[0152] ,(35)

[0153] ,(36)

[0154] ,(37)

[0155] In formula (32), is the speed coupling node accessibility of node n at time t represents the number of accessible road segments between node o and d represents the number of accessible road segments between node o and d and passing through node n is a function of calculating node degree; ​​​​representing a node m with n whether connected, 1 if connected, otherwise 0; is a normalization function; representing a node n at t moment.

[0156] representing a node n at t moment. .

[0157] in equation (34), representing a node n at t moment. is a node n at diffusion step k . representing the total number of nodes in the road network.

[0158] in equation (35), representing the velocity-coupled connected integrity of the road network at t moment. is the number of nodes in the largest connected subgraph; representing the average velocity of all nodes in the road network at t moment.

[0159] in equation (36), is the velocity fluctuation index of the road network at t moment. representing the velocity set of all nodes in the road network at t moment. and represent the standard deviation and mean of the velocity set, respectively.

[0160] in equation (37), representing the structure-function resilience index of the road network at t moment. is a weight coefficient, which is obtained by entropy method, and . Specifically, the indexes are first standardized, then the entropy values are calculated (the smaller the entropy value, the more significant the difference in index data and the more important the information carried), and finally the weights are allocated according to the proportion of information importance.

[0161] in equations (32)~(37), , , , , , and reflect the spatial structure characteristics of road network, while and and their derivatives correspond to traffic speed characteristics. The combined effects of the two types of characteristics ensure that the structure-function resilience index can comprehensively characterize the spatial topology properties and functional operation characteristics of road network.

[0162] Step 2.2: Hysteresis resilience factor;

[0163] During the disturbance, existing methods usually only focus on the performance-time variation process of road network, ignoring the hysteresis effect, such as Figure 4 (a). To characterize the non-ideal fluctuation of road network performance with disturbance intensity during the disturbance phase, this embodiment constructs a road network hysteresis performance variation diagram, as shown in Figure 4 (b), and further establishes a hysteresis resilience factor.

[0164] Specifically, first, define the hysteresis time point of road network performance, denoted as:

[0165] ,(38)

[0166] In formula (38), is the hysteresis time point, representing the inflection point where the road network performance changes from decline to recovery; represents the lower bound value of the set; is the time search window step; is the performance value of the road network at t’ time; represents the minimum value of road network performance; is the tolerance threshold.

[0167] Secondly, divide the original road network performance variation curve into resistance-recovery process:

[0168] ,(39)

[0169] In formula (39), and are the performance curves of the resistance and recovery stages, respectively; and represent the time points when the road network starts to be disturbed and the road network recovers to the steady state, respectively.

[0170] In addition, since the resistance and recovery times are usually asymmetric, an interpolation method is used to realize curve continuity and time dimension alignment, denoted as:

[0171] , ,(40)

[0172] wherein, is a cubic spline interpolation function; and The resistance and recovery stage performance curves are processed by cubic spline interpolation. The hysteretic performance variation diagram of the road network is constructed based on the above formula, as shown in (b) in Figure 4 .

[0173] Then, the hysteretic factor is established according to the hysteretic performance variation diagram of the road network, as follows:

[0174] ,(41)

[0175] ,(42)

[0176] ,(43)

[0177] In formula (41), represents the hysteretic index of the road network, which is measured from the hysteresis area.

[0178] In formula (42), is the ideal hysteretic effect of the road network; and are maximum and minimum value calculation functions, respectively.

[0179] In formula (43), is the hysteretic factor, which comprehensively considers the resistance decay and hysteresis recovery evolution mechanism of the road network under the influence of disturbance intensity.

[0180] Finally, the hysteretic factor is fused with the structure-function resilience index to generate the hysteretic resilience index :

[0181] ,(44)

[0182] Step 3: Establishing a spatio-temporal fine-grained resilience evaluation algorithm;

[0183] Therefore, the design process of the spatio-temporal fine-grained resilience evaluation algorithm is as follows: first, according to the target domain city traffic speed label value, the target domain city traffic speed prediction value and the disturbance event, the hysteretic resilience index under non-disturbance and the hysteretic resilience index under disturbance are calculated, respectively.

[0184] Secondly, based on and , the performance retention rate of the road network in the disturbance stage is quantified from a macroscopic perspective, which is expressed as:

[0185] ,(45)

[0186] Formula (45) calculates the performance retention rate of the road network from the beginning of the disturbance to the end of the disturbance ​ .

[0187] Then, the average resistance index and the maximum recovery rate are calculated respectively, and the resistance and recovery stage resilience are quantified from the fine-grained level, which are denoted as:

[0188] ,(46)

[0189] ,(47)

[0190] In formula (46), is the hysteresis point, which is calculated by formula (38); denotes the average resistance index of the road network in the time period to ; formula (47) measures the maximum recovery rate of the road network in the time period to .

[0191] Finally, the three-part resilience quantification results are weighted and fused:

[0192] ,(48)

[0193] In formula (48), , and are weight coefficients. From the hyperparameter analysis experiment, , and the optimal values of R , and

[0194] are 0.4, 0.3 and 0.3 respectively. is the final spatio-temporal fine-grained resilience quantification result.

[0195] Verification Example

[0196] To demonstrate the superiority of the spatiotemporal cross-domain traffic prediction model of this invention, the following prediction models were selected for comparison: DGCRN, ST-Wave, BigST, FlashST, and OpenCity. DGCRN is based on a dynamic graph convolutional recurrent network, combining graph convolution and recurrent units to simultaneously model the dynamic spatial dependencies and temporal characteristics of the traffic network. ST-WAVE employs spatiotemporal wavelet transform to extract multi-scale spatiotemporal features, enhancing the model's ability to express complex traffic patterns. BigST is a distributed spatiotemporal prediction framework designed for large-scale urban road networks, emphasizing computational efficiency and multi-regional data collaboration. FlashST achieves rapid response and prediction of sudden traffic events through a lightweight structure and fast training mechanism. OpenCity, based on open-domain multi-source traffic data, supports multi-task cross-city traffic state prediction and generalization capability verification.

[0197] Evaluation metrics include Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). MAE reflects the average deviation between predicted and actual values; a smaller value indicates a smaller overall deviation. RMSE represents the square root of the average of the squares of the differences between predicted and actual values, and is more sensitive to extreme deviations, highlighting the impact of large errors; a smaller value indicates better prediction stability. MAPE expresses relative error as a percentage, is unaffected by dimensions, and is easy to understand intuitively as an error proportion. These three metrics evaluate model accuracy from different dimensions; the smaller the values ​​of all three, the better the model performance.

[0198] This embodiment conducts a comparative experiment on the PEMS-Rainy dataset, and the results are shown in Table 1.

[0199] Table 1 shows the experimental results compared with the latest prediction model.

[0200]

[0201] As can be seen from Table 1, regardless of whether it is a cross-domain scenario in the United States or China, the MAE, RMSE and MAPE in this invention are all superior to similar models.

[0202] To visually verify the effectiveness of the method of this invention in assessing urban road network resilience, heavy rainfall was used as a sudden disturbance event, and the assessment results of this invention were visualized on the PEMS-Rainy dataset, as shown below. Figure 5 As shown, the darker the color, the stronger the toughness. Figure 5 The data showcases fine-grained road network resilience before, during, and after rainfall. From a macro perspective, during periods of sustained heavy rainfall, road network resilience in various regions exhibits a dynamic evolution trend of first decreasing and then recovering. From a local perspective, urban centers demonstrate strong resilience, while coastal areas show relatively weaker resilience.

[0203] With the snowfall event as a sudden disturbance event, the effectiveness of the method of the application for evaluating the resilience of the urban road network is verified. Specifically, as shown in Figure 6 The fine-grained road network resilience of Beijing road network before snowfall, during snowfall and after snowfall is shown. From the results, it can be seen that the traffic resilience of Beijing road network presents obvious difference and dynamic evolution characteristics in space. The core urban road network has high density and strong traffic capacity, reflecting good resilience level. However, when snowfall occurs, the resilience of the main road section in the core area decreases, but benefits from the high redundancy of the road network and the preferential protection of snow removal resources, and the resilience recovers quickly after snowfall. The western suburban area is significantly restricted by the terrain, and the road network structure is relatively single. In addition, some roads are close to mountains and rivers, which are easily affected by snow and ice, and the resilience recovers slower than the urban area. The road network in the southern suburb is relatively sparse and mainly in the form of radial channels. The resilience before snowfall is at a medium level. The resilience decreases significantly during snowfall, and the recovery speed is also relatively slower than that in the core area. Zhongguancun is a typical high-density working area. The resilience of this area is high before snowfall, but when snowfall occurs, the commuting flow is superimposed with disturbance effect, and the resilience of local ring roads and connecting roads decreases significantly. After snowfall, the resilience recovers quickly with the decrease of traffic demand and the improvement of road conditions, but there are still some nodes that recover slowly, indicating that high-density office areas are sensitive to extreme weather disturbance.

[0204] Therefore, the application can accurately depict the spatiotemporal resilience change of the road network during the disturbance period and identify local fragile units in time, providing support for the traffic management department to carry out infrastructure construction and external intervention.

[0205] The above description is only a description of the preferred embodiments of the application, and does not limit the scope of the application in any way. Any modification or modification made by any person skilled in the art according to the above disclosed technical content shall be regarded as an equivalent effective embodiment, and shall fall within the scope of the technical scheme protected by the application.

[0206] The references are as follows:

[0207] [1] F. Li, J. Feng, H. Yan, et al, “Dynamic graph convolutional recurrent network for traffic prediction: Benchmark and solution,” ACM Transactions on Knowledge Discovery from Data, 2023, 17(1): 1-21.

[0208] [2] Y. Fang, Y. Qin, H. Luo, F. Zhao, B. Xu, L. Zeng, and C. Wang,“When spatio-temporal meet wavelets: Disentangled traffic forecasting via efficient spectral graph attention networks,” in 2023 IEEE 39th International Conference on Data Engineering (ICDE). IEEE, 2023, pp. 517–529.

[0209] [3] J. Han, W. Zhang, H. Liu, et al. “Bigst: Linear complexity spatio-temporal graph neural network for traffic forecasting on large-scale road networks,” in Proceedings of the VLDB Endowment, 2024, 17(5): 1081-1090.

[0210] [4] Z. Li, L. Xia, Y. Xu, and C. Huang, “Flashst: A simple and universal prompt-tuning framework for traffic prediction,” in International Conference on Machine Learning (ICML), ser. ICML’24. JMLR.org, 2024.

[0211] [5] Z. Li, L. Xia, L. Shi, Y. Xu, D. Yin, and C. Huang, “Opencity: Open spatio-temporal foundation models for traffic prediction,” 2024.

Claims

1. A method for predicting and assessing the resilience of cross-regional urban transportation networks, characterized in that, Includes the following steps: Step 1: Based on urban traffic data from the source and target domains, construct a spatiotemporal cross-domain traffic prediction model to generate traffic predictions and traffic map structures for cross-city scenarios; The traffic map is defined as follows: ,(1) In the formula, express A set of nodes; This is the set of edges connecting nodes; Given an adjacency matrix, when the node With nodes If connected, then ; otherwise, ;based on Spatiotemporal traffic data is represented as a sequence. ;in, The length of the time series; Traffic characteristics; The construction of the spatiotemporal cross-domain traffic prediction model includes a pre-training stage and a fine-tuning stage: first, it is pre-trained on the source domain urban traffic data to learn general spatiotemporal features, and then the target domain data is adapted through the fine-tuning stage; the two stages share the constant-heterogeneous time series module, the lightweight spatial memory module and the decoder module; at the same time, the fine-tuning stage introduces an additional refined spatiotemporal distillation module. The working process of the spatiotemporal cross-domain traffic prediction model: First, historical velocity data of source cities are selected for pre-training. The general pre-trained spatiotemporal features of source cities are captured through a constant-dissimilar temporal sequence module, a lightweight spatial memory module, and a decoder. Then, historical velocity data of the target domain city is selected for fine-tuning. The fine-tuned spatiotemporal features of the target domain city are captured through the constant-dissimilar time series module, the lightweight spatial memory module and the decoder. At the same time, the source domain features are effectively transferred to the target domain through the refined spatiotemporal distiller. Finally, the speed prediction and corresponding traffic map structure of the target domain city under the disturbance scenario are generated; Step 2: Based on the prediction results and traffic map structure, design the hysteresis resilience index; The hysteresis toughness index includes structural-functional toughness and hysteresis toughness factor; The establishment process is as follows: First, considering both the spatial structure of the road network and the traffic speed characteristics, design the structural-functional resilience index; second, analyze the hysteresis characteristics of the road network during the disturbance phase and design the hysteresis resilience factor; finally, integrate the hysteresis resilience factor into the structural-functional resilience to construct the hysteresis resilience index. Step 3: Based on the hysteresis toughness index, establish a spatiotemporal fine-grained toughness quantification algorithm and output the toughness results; First, based on the target domain city traffic speed label value, the target domain city traffic speed prediction value, and the disturbance event, the hysteresis resilience index under non-disturbance conditions is calculated respectively. Hysteresis resilience index under disturbance ; Secondly, based on and Quantifying the performance retention rate of the road network during the disturbance phase from a macro perspective. ; Then, calculate the average resistance index separately. and maximum recovery rate ; Finally, the three resilience quantification results are weighted and fused to obtain: , in, , and These are the weighting coefficients. R This is the final result for spatiotemporal fine-grained toughness quantification.

2. The method according to claim 1, characterized in that, The constant-dissimilar temporal module includes: temporal scale decomposition, patching processing, global temporal attention convolution, and gated temporal convolution; specifically as follows: Step 1.2.1: Time-scale decomposition spatiotemporal traffic data Perform a Fast Fourier Transform to convert the spatiotemporal data X The signal is converted to the frequency domain, and then the K most significant frequency components with the largest amplitudes are selected. The inverse fast Fourier transform is then used to restore the signal to low-frequency and high-frequency sequences. This process is represented as follows: ,(2) ,(3) ,(4) ,(5) ,(6) In equation (2), Represents spatiotemporal traffic data from the source or target domain; It is the Fast Fourier Transform function; For frequency domain signals; in equation (3), It is the amplitude function; Indicates before selecting amplitude K Large salient frequency domain components; in equation (4), Indicates from the previous K A frequency domain subset composed of components; in equation (5), It is the inverse fast Fourier transform function; This represents a low-frequency sequence, reflecting the long-term characteristics of the time series, and is used to characterize normal traffic conditions; Equation (6) It is a high-frequency sequence that focuses on short-term irregular fluctuations in time series and is used to characterize abnormal traffic conditions; Step 1.2.2: Patch Processing For low-frequency sequences and high frequency sequences Patch processing is performed on continuous sequences. Divided into coarse-grained time blocks, for or , is represented as; ,(7) In equation (7), This represents the patched sequence; The window length for the patch; This indicates the number of patch blocks; Use linear layers Map the patch sequence to the dimensions required by the model. , represented as: ,(8) Furthermore, to preserve the periodicity and trend contextual information of spatiotemporal data, embedding terms are introduced for each patch block. This indicates the time and location information of the Patch; Time information encompasses the periodic characteristics of the data corresponding to a patch in the time series dimension, including daily and weekly periods; location information refers to the sequential relationship of patches within the overall time series, used to reflect the temporal logic between patches and provide cross-patch contextual information; represented as: ,(9) ,(10) Equation (9) represents the broadcast operation; Equation (10) represents feature fusion. The patch sequence represents the overlay location information, including the patched low-frequency sequence. and Patch-based high-frequency sequences ; Step 1.2.3: Global Time Attention Convolution A global temporal attention convolution was designed, and the regular periodic information of traffic patterns was explicitly supplemented by a normal temporal pattern library of the source or target domain. This process is represented as follows: ,(11) Equation (11) represents the process of combining the patched low-frequency sequence with a source or target domain normal time pattern library. Perform Hadamard accumulation ;in, It is an adaptive matrix; For the The patched low-frequency sequence after explicit adaptive update; ,(12) In equation (12), These are trainable parameters; These represent the Query, Key, and Value matrices, respectively, which are used to learn the feature mappings of queries, keys, and values ​​across time blocks. ,(13) In equation (13), For activation functions; This is the transpose of the Key matrix; For feature dimensions; Represents the attention matrix; ,(14) Equation (14) represents the global-time attention convolution operation. ; Indicates via Captured source or target domain normal time dependency ; Step 1.2.4: Gated Temporal Convolution Gated temporal convolution, combined with anomaly time pattern libraries in the source or target domain, explicitly supplements the information on anomalous fluctuations in traffic patterns. This process is represented as follows: ,(15) Equation (15) represents the combination of patched high-frequency sequences with a source or target domain anomalous time pattern library. Perform Hadamard accumulation; It is an adaptive matrix. For the Explicitly adaptively updated patched high-frequency sequences; ,(16) In equation (16), This is a dilated convolution operation; Indicates the expansion factor; It is the size of the convolution kernel; ,(17) In equation (17), This is a gated-time convolution operation; and For activation functions; Indicates a temporal convolution operation; Indicates Capture anomalous time dependencies in the source or target domain; Furthermore, normal and abnormal time dependencies are fused to obtain comprehensive time characteristics: ，(18) in," "Indicates feature fusion; Representing pre-training time features Or fine-tune the time characteristics .

3. The method according to claim 2, characterized in that, The lightweight spatial memory module includes: a spatial memory module and a LoRA-enhanced training strategy; specifically as follows: Step 1.3.1: Spatial Memory Module Pre-training or fine-tuning temporal features captured by constant-discrete time-series modules The spatial memory module further extracts spatial features between traffic nodes and combines them with a spatial pattern library of the source or target domain to enhance the model's memory of spatial relationships, as shown below: ,(19) ,(20) ,(21) In equation (19), These are trainable parameters; Let represent the Query, Key, and Value matrices, respectively, which are used to learn the feature mappings of the query, key, and value in the spatial pattern; Equation (20) represents the acquisition of the intermediate spatial dependency with attention mechanism. In equation (21), For activation functions; , ,and These are trainable parameters; This indicates the spatial dependencies captured by the spatial memory module; For spatial pattern library, ; Step 1.3.2: LoRA Enhancement Training Strategy LoRA low-rank decomposition is introduced to reduce the number of trainable parameters and lower the transfer learning cost of the model across cities. The low-rank decomposition is expressed as: ,(22) (23) In equation (22), Denotes a low-rank matrix; in equation (23), and It is an incremental term; Update the original weights based on the low-rank matrix and the increment term. , represented as: (24) Therefore, the enhanced Query and Value are represented as follows: ,(25) Finally, the spatial dependency after LoRA enhancement training changes from equations (20) and (21) to equations (26) and (27): ,(26) ,(27) In equation (26), This represents the intermediate layer spatial dependency after LoRA optimization; in equation (27), This represents pre-trained spatial features captured via a lightweight spatial memory module. Or fine-tune spatial features .

4. The method according to claim 3, characterized in that, The refined spatiotemporal distillation apparatus includes: pre-trained and fine-tuned spatiotemporal distillation and pre-trained spatiotemporal feature refining; Step 1.4.1: Pre-training - Fine-tuning spatiotemporal distillation; Distillation using temporal feature similarity: Evaluating pre-trained temporal features using KL divergence loss and fine-tuning time characteristics The similarity is represented as: ,(28) In equation (28), Promote and Feature alignment; M The number of samples; Distillation using spatial feature similarity: Evaluating pre-trained spatial features using contrastive learning loss and fine-tuning spatial characteristics Consistency is represented as: ,(29) In equation (29), It is a similarity measurement function; Represents an exponential function; Able to align effectively and ; The updated distillation time features are obtained by minimizing the distillation loss utilizing temporal feature similarity and the distillation loss utilizing spatial feature similarity. Characteristics of distillation space This provides input for subsequent pre-training spatiotemporal feature refinement; Step 1.4.2: Refinement of pre-trained spatiotemporal features; Refine the temporal features captured during pre-training using adaptive filters. and spatial characteristics , represented as: ,(30) In equation (30), and These represent adaptive temporal and spatial filters, respectively. , Respectively with time characteristics Spatial features Element-wise multiplication is performed to optimize parameters in a task-oriented manner during pre-training.

5. The method according to claim 4, characterized in that, The decoder consists of a multilayer perceptron. The decoder, which consists of components and is fine-tuned, is represented as follows: ,(31) in, This indicates a Concat operation; This refers to the cross-city traffic prediction results output by the spatiotemporal cross-domain traffic prediction model.

6. The method according to claim 5, characterized in that, Step 2 is as follows: Step 2.1: Structural-functional resilience index The structural-functional resilience indices include: velocity-coupled node accessibility, velocity-coupled node importance, local diffusion congestion index, velocity-coupled connectivity integrity, and velocity fluctuation index, which are defined as follows: ,(32) ,(33) ,(34) ,(35) ,(36) ,(37) In equation (32), For nodes n exist t Moment-time velocity coupling node accessibility; Represents a node o and d The number of accessible road segments between them; Represents a node o and d Between, and through nodes n The number of accessible road sections; This is a function for calculating node degree; Represents a node m and n Whether the connection is connected is indicated by a value of 1 if connected and 0 otherwise. This is the normalization function; Represents a node n exist t The speed of time; Equation (33) represents the node n exist t Importance of velocity coupling nodes at time intervals ; In equation (34), Represents a node n exist t Localized congestion index at any given time; For nodes n At a diffusion step size of k The number of reachable nodes at that time; This represents the total number of nodes in the road network; In equation (35), Indicates the road network in t Moment-time velocity coupling connectivity integrity; The number of nodes in the largest connected subgraph; Indicates that all nodes in the road network are t Average velocity at time; In equation (36), For the road network in t The velocity fluctuation index at any given moment; Indicates the road network in t The set of velocities of all nodes at any given moment; and Let these represent the standard deviation and mean of the velocity set, respectively. In equation (37), Indicates the road network in t The structure-functional resilience index at any given time; These are the weighting coefficients, obtained using the entropy method, and ; In equations (32) to (37), , , , , , and Reflecting the spatial structural characteristics of the road network, and and its derived terms corresponding to traffic speed characteristics; Step 2.2: Hysteresis Toughness Factor The hysteresis time point of road network performance is defined as follows: ,(38) In equation (38), The hysteresis point represents the inflection point at which the road network performance changes from decline to recovery; This indicates taking the lower bound of the set; The time search window step size; For the road network in t’ Performance values ​​at any given time; This represents the minimum performance value of the road network. This is the tolerance threshold; Secondly, the original road network performance change curve is divided into a resistance-recovery process: ,(39) In equation (39), and These are the performance curves for the resistance and recovery phases, respectively. and These represent the points in time when the road network begins to be disturbed and the points in time when the road network returns to a steady state, respectively. Using interpolation methods to achieve curve continuity and time-dimensional alignment is represented as follows: , ,(40) In equation (40), It is a cubic spline interpolation function; and The resistance and recovery performance curves are obtained after cubic spline interpolation. Then, the hysteresis factor is established based on the road network hysteresis performance change diagram: ,(41) ,(42) ,(43) In equation (41), The hysteresis index represents the road network, measured by the loop area; in equation (42), The ideal hysteresis effect of the road network; and These are the functions for calculating the maximum and minimum values, respectively; in equation (43), As a hysteresis factor, it comprehensively considers the counter-degradation and hysteresis recovery evolution mechanism of the road network under the influence of disturbance intensity; Finally, the hysteresis factor is fused with the structure-function resilience index to generate the hysteresis resilience index. : ,(44)。 7. The method according to claim 6, characterized in that, In step 3, The performance retention rate during the disturbance phase is expressed as: ,(45) Equation (45) calculates the road network at the start of the disturbance. Until the end Performance retention rate ; Resilience during the resistance and recovery phases is represented as: ,(46) ,(47) In equation (46), The hysteresis point Indicates the road network during the time period to The average resistance index; Equation (47) measures the road network in time period to Maximum recovery rate .

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