Urban traffic network resilience assessment method based on neural attention controlled differential equation

Abstract

The present invention relates to the field of intelligent transportation, and proposes an urban traffic network resilience assessment method based on a neural attention controlled differential equation, which includes three steps: Step 1: functional indicator prediction based on original traffic speed data; Step 2: structural indicator calculation based on original traffic speed data; Step 3: integrating functional and structural indicators to construct a comprehensive evaluation index system, and combining a multi-index resilience assessment algorithm to achieve urban traffic network resilience assessment. The present invention inherits the efficient memory utilization and robustness of processing missing observations during neural controlled differential equation training, and demonstrates special advantages in processing long-term mutation jitter signals. It is particularly sensitive to the trend characteristics of time series data and is competent for modeling dynamic long-term traffic speed data prediction. In addition, the designed comprehensive resilience evaluation index system and multi-index resilience assessment algorithm can achieve accurate assessment of urban traffic network resilience.

Description

Technical Field

[0001] The present invention relates to the field of intelligent transportation, and in particular to an urban transportation network resilience assessment method based on a neural attention controlled differential equation. Background Art

[0002] The urban traffic network is the link and artery of urban social and economic activities, and is the basis for ensuring the operation of the economy and society. However, in recent years, affected by factors such as global warming, natural disasters such as heavy rainfall have occurred frequently, resulting in prominent problems such as traffic congestion, loss of accessibility, traffic safety, and traffic pollution. Therefore, when the urban traffic network faces interference from emergencies, effective evaluation of its anti-interference and recovery capabilities has become an urgent requirement for promoting social and economic development and improving people's livelihood. Previous researchers mainly relied on indicators such as reliability, vulnerability, and robustness to evaluate the performance of urban traffic networks. However, there are differences in the focus and perspective of the above indicators, and they cannot comprehensively evaluate the performance of urban traffic networks, resulting in the concept of traffic resilience. For the performance evaluation of urban traffic networks, traffic resilience has the characteristics of a wide range of evaluation, which can be used to measure the resistance, recovery, and adaptability of urban traffic systems to external shocks, and can comprehensively evaluate the reliability, vulnerability, and robustness of traffic systems in the face of interference from emergencies.

[0003] At present, traffic resilience has gradually become a hot research topic at home and abroad, and has become an innovative thinking paradigm in safety science research and practice. In addition, countries around the world have introduced corresponding policies to support the research on traffic resilience. Comprehensive and effective evaluation of traffic resilience will become the key to the management and control of urban transportation systems. Therefore, modeling resilience assessment methods for urban transportation networks is of great significance and value in reducing road network operating costs, improving urban sustainable development, improving people's livelihood, avoiding traffic congestion, and maintaining traffic safety.

[0004] Traffic speed data is an important observation indicator for resilience assessment. It is a time series data that is continuously recorded by sensors deployed at different spatial locations at fixed time intervals. Taking speed as an observation indicator and predicting the speed of the traffic network can intuitively reflect the operating conditions of the urban traffic network before and after the rainstorm, thereby realizing the assessment of the resilience of the traffic network. Early methods regarded traffic parameter prediction as a conventional linear time series prediction problem, such as autoregressive model, Kalman filter, and integrated moving average model. However, these traditional methods did not consider the spatial characteristics of the traffic network. Therefore, some machine learning models for traffic prediction were born, such as Bayesian network and K nearest neighbor method. Although this type of method takes the spatial characteristics of the traffic network into account, its prediction accuracy is still low and the effect is poor when applied in actual scenarios. Furthermore, traffic prediction methods based on deep learning have become a research hotspot in recent years. For example, researchers combine recurrent neural networks with graph neural networks, use recurrent neural networks to extract the time-dependent features of the road network, use graph neural networks to extract the spatial-dependent features of the road network, and fuse time and space features to achieve traffic parameter prediction. Compared with previous machine learning methods, this type of method has greatly improved the accuracy of traffic forecasting. It is worth noting that extreme weather events such as heavy rains can damage sensors that provide speed information, resulting in possible information loss in the speed data of the traffic network at the temporal or spatial level. However, the prediction performance of traditional traffic prediction models such as graph neural networks and recurrent neural networks will drop significantly when data is missing. Therefore, enabling the model to maintain good prediction performance in the absence of data will be crucial for evaluating the resilience of urban traffic networks. In addition, in the field of spatiotemporal traffic parameter prediction, the current mainstream methods are all discrete feature extraction, which results in discontinuous and insufficient spatiotemporal feature extraction.

[0005] In recent years, more and more researchers have combined dynamics theory with deep learning theory to form a neural differential equation model. This type of model is different from the traditional neural network model. It has the natural characteristics of continuous feature extraction and can realize the ability to pre-process spatiotemporal data. Specifically, the neural differential equation will first interpolate the original spatiotemporal data into continuous data to make up for the data loss in the original data, and then further input it into the feature extraction module for feature extraction. The reason is that the model applies the idea of ​​calculus, divides the integrand area into infinitely small blocks, and realizes continuous spatiotemporal feature extraction. Therefore, the traffic network is regarded as a dynamic system, and the changes in speed indicators are described by differential equations. Based on the neural network, the time and space vector fields are built for training, and a neural differential equation model for speed prediction can be constructed to capture the dynamic change process of the speed indicator. At the same time, the resilience assessment of the urban traffic network is realized, which plays an important role in the subsequent traffic resilience improvement and route planning and other transportation services.

[0006] In addition, the speed data in a rainstorm scene is different from the speed data in normal weather. Vehicles in the traffic network will be affected by the amount of rainfall and the duration of rainfall, causing the vehicle speed values ​​to fluctuate irregularly. The attention mechanism can focus on capturing useful information, which is one of the most successful concepts in deep learning. The idea of ​​the attention mechanism comes from the human visual perception system, which can selectively focus on important information while ignoring irrelevant information. Here, the attention mechanism is introduced into the neural controlled differential equation, which can not only focus on the spatiotemporal speed changes of vehicles in the road network during the rainy period, but also effectively extract continuous spatiotemporal dependency features to achieve accurate evaluation of the resilience of the urban traffic network. Summary of the invention

[0007] In order to solve the problem that the urban traffic network resilience assessment method under heavy rain scenes is affected by factors such as incomplete data source input, inability to effectively extract continuous spatiotemporal dependency features, inability to capture key features of rainy periods, and inaccurate assessment algorithms, resulting in inaccurate assessment results, the present invention proposes an urban traffic network resilience assessment method based on neural attention controlled differential equations. First, a neural attention controlled differential equation model is designed to achieve accurate prediction of vehicle speed; it first uses a cubic natural spline interpolation strategy to interpolate incomplete discrete raw data into a continuous path, solving the problem of incomplete data source input; and then through initial, time, and space attention vector field processing, it not only achieves continuous spatiotemporal dependency feature extraction, but also can accurately capture the key features of vehicle speed during rainy periods. Secondly, in order to comprehensively consider the functional and structural factors of the road network, the speed index output by the neural attention controlled differential equation model is combined with the physical topological structure of the road network, and a comprehensive evaluation index system is designed. Finally, the urban traffic network resilience assessment under heavy rain scenes is realized based on the designed multi-index resilience assessment algorithm.

[0008] The present invention is achieved through the following technical solutions:

[0009] The urban traffic network resilience assessment method based on neural attention controlled differential equations consists of three steps:

[0010] 1) Predict functional indicators based on raw traffic speed data;

[0011] 2) Calculate structural indicators based on raw traffic speed data;

[0012] 3) Integrate functional and structural indicators to construct a comprehensive evaluation index system, and combine multi-index resilience assessment algorithm to realize urban transportation network resilience assessment.

[0013] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0014] (1) Previous methods were affected by incomplete data source input, unable to accurately extract continuous spatiotemporal dependency features, and unable to capture key features of rainy periods, resulting in the inability to accurately predict traffic speed indicators. The present invention designs a neural attention controlled differential equation model, which first uses a cubic natural spline interpolation strategy to interpolate incomplete discrete raw data into a continuous path, solving the problem of incomplete data source input. Then, through initial, temporal, and spatial attention vector field processing, not only is continuous spatiotemporal dependency feature extraction achieved, but the key features of vehicle speed during rainy periods can also be accurately captured to achieve accurate prediction of vehicle speed, providing effective support for subsequent resilience calculations.

[0015] (2) Previous methods only considered functional or structural index factors for the calculation of resilience, but failed to combine the two. The present invention comprehensively considers the functional and structural factors of the road network, combines the speed index output by the neural attention controlled differential equation model with the physical topological structure of the road network, and designs a comprehensive evaluation index system.

[0016] (3) The resilience calculation of previous methods is not accurate. The present invention fully considers factors such as multiple indicators and the periodic characteristics of vehicle speed, and constructs a multi-indicator resilience evaluation algorithm to realize the resilience evaluation of urban traffic road networks under heavy rain scenarios.

[0017] The experimental results conducted on the public dataset PEMS-BAY show that the present invention has obvious advantages over other latest and well-known methods and can effectively evaluate the resilience of traffic networks.

[0018] The present invention inherits the efficient memory utilization and robustness of processing missing observations during neural controlled differential equation training, and also demonstrates the special advantage of processing long-term mutation jitter signals. It is particularly sensitive to the trend characteristics of time series data and is competent for modeling dynamic long-term traffic speed data prediction. In addition, the designed comprehensive resilience evaluation index system and multi-index resilience evaluation algorithm can realize the accurate evaluation of urban traffic network resilience. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a system flow chart of the urban traffic network resilience assessment method based on the neural attention controlled differential equation of the present invention.

[0020] Figure 2 Schematic diagram of the ASTG-NCDE model structure.

[0021] Figure 3 It is a visual topological structure diagram of the urban traffic network.

[0022] Figure 4 This is a fitting curve diagram of the predicted value and the actual value of PEMS-BAY at node 12 under normal weather and heavy rain weather.

[0023] Figure 5 This is a heat map of the predicted and true values ​​of PEMS-BAY in heavy rain weather.

[0024] Figure 6 The resilience assessment results of urban traffic road network in PEMS-BAY. DETAILED DESCRIPTION

[0025] The evaluation accuracy of urban traffic network resilience depends not only on functional observation indicators such as vehicle speed, flow, density, etc., but also on structural observation indicators such as road network node centrality and road network maximum connected subgraph. In order to improve the evaluation accuracy of the method, the present invention uses the most intuitive vehicle speed as a functional observation indicator, and combines the road network structural factors to propose an urban traffic network resilience evaluation method based on neural attention controlled differential equations. Figure 1 As shown in the figure, it generally includes three steps: 1) predicting functional indicators based on the original traffic speed data; 2) calculating structural indicators based on the original traffic speed data; 3) integrating functional and structural indicators to construct a comprehensive evaluation index system, and combining the designed multi-index evaluation algorithm to realize the resilience evaluation of the urban traffic network.

[0026] The technical solution provided by the present application will be further described below in conjunction with specific embodiments and accompanying drawings. The advantages and features of the present application will become more apparent with the following description.

[0027] Example

[0028] Step 1: Based on the original traffic speed data, a neural attention controlled differential equation model (ASTG-NCDE) is designed, whose structure is as follows: Figure 2 As shown. The model includes four submodules, namely, interpolation module, initial attention neural controlled differential equation module, time attention processing module, and space attention processing module; the time attention processing module and the space attention processing module respectively contain time attention controlled differential equations and space attention controlled differential equations to extract time and space dependent features. The model first uses the cubic natural spline interpolation method to interpolate the original traffic speed data into a continuous path, solving the problem of incomplete data source input. Then the continuous path is transmitted to the initial attention neural controlled differential equation module and processed into spatiotemporal speed data based on the attention coefficient, focusing on the data characteristics of the rainy period, and the output speed prediction result is solved by the solver.

[0029] The input of the neural attention controlled differential equation model is the speed data of the Los Angeles road network in the United States, which is provided by the California Department of Transportation. It contains speed data of 325 different spatial locations in Los Angeles, captured by 325 sensors. Specifically, the model contains three serial neural controlled differential equations, namely the initial attention neural controlled differential equation, the time attention neural controlled differential equation, and the space attention neural controlled differential equation, as shown in equations (1), (2), and (3), respectively. The model can effectively extract the spatiotemporal dependence characteristics of the road network and focus on the speed change of each vehicle during the rainy period.

[0030]

[0031]

[0032]

[0033] Where X(t):t∈[0,T] is the continuous path obtained after interpolation of the original speed data; a(t):t∈[0,T] is the spatiotemporal data based on the attention coefficient obtained after processing the continuous path X(t); and represents two types of matrix multiplication; Y(t): t∈[0,T] is the constructed time and space level attention coefficient value; s(a(t); θ s )、f(H(t);θ f ) and g(Z(t);θ g ) represent the initial attention vector field, the temporal attention vector field and the spatial attention vector field respectively, and the internal structure includes θ s ,θ f and θ g Trainable parameters used to form the gradient module of the controlled differential equation; a(T), H(T), and Z(T) represent the feature dependencies of the T time period obtained after processing the initial attention vector field, the temporal attention vector field, and the spatial attention vector field, respectively, and cover the feature dependencies at any time t (t∈[0,T]); a(0) represents the initial value of the feature state obtained after processing the initial attention vector field.

[0034] In order to facilitate the subsequent solution of equations, equations (1), (2), and (3) can be combined, that is, the neural attention controlled differential equation model is shown in equation (4):

[0035]

[0036] Secondly, to solve equation (4), it needs to be transformed into an ordinary differential dynamic system, as shown in equation (5). Its training and prediction are attributed to the solution process of ordinary differential equations. Then, equation (6) is used as the input of the solver and trained by the adjoint sensitivity method to output the prediction result of vehicle speed.

[0037]

[0038]

[0039] Step 1.1: Interpolate the original traffic speed data into continuous paths using the cubic natural spline interpolation method

[0040] The cubic natural spline interpolation method transforms multidimensional discrete spatiotemporal data into a continuous path X:[0,T]→R V , which provides support for subsequent integration. Compared with other interpolation methods, the reason why ASTG-NCDE uses cubic natural spline interpolation is that it not only considers all discrete time points in the interpolation process, but also ensures that the derivatives at each point are equal, so that cubic natural spline interpolation can better adapt to ASTG-NCDE.

[0041] Step 1.2: Initial attention The neural controlled differential equation module processes the continuous path into spatiotemporal velocity data based on the attention coefficient, focusing on the data characteristics of the rainy period

[0042] The continuous path generated by cubic natural spline interpolation is transmitted to the initial attention neural controlled differential equation module, which has two functions: 1) Generate spatiotemporal data a(t) based on the attention coefficient, focusing on the speed characteristics of the rainy period, and providing a reference for the subsequent spatiotemporal feature dependency extraction; 2) Obtain the initial spatiotemporal value a(0) with attention, and use it in the subsequent time and space attention differential equations, effectively improving the feature extraction performance at the spatiotemporal level. Among them, the calculation method of a(t) is shown in formula (8):

[0043] a(t)=sigmoid(X(t)), (8)

[0044] Where sigmoid(·) is the Sigmoid activation function, and X(t) is the continuous path obtained by cubic natural spline interpolation. The initial spatiotemporal value a(0) is obtained by taking the value of a(t) at the moment t=0.

[0045] The initial attention neural controlled differential equation operates on the spatiotemporal level based on the attention coefficient a(t) as shown in formula (9):

[0046]

[0047] In the formula, FC represents the fully connected operation. In addition, it is worth noting that if the initial attention neural controlled differential equation acts on the time level, a(t) is a single element; if the initial attention neural controlled differential equation acts on the space level, a(t) is a vector.

[0048] Step 1.3: Temporal Attention Processing Module Extracts Time-Dependent Features

[0049] The temporal attention processing module contains the designed temporal attention controlled differential equation, which has a temporal attention vector field and can effectively extract the time-dependent characteristics of the rainy period.

[0050] The function of the temporal attention neural controlled differential equation is to further extract the temporal feature dependency of the spatiotemporal attention data generated by the initial attention neural controlled differential equation. The specific operation is shown in formula (2), that is, it is a controlled signal a(t), the vector field is f(H(t); θ f ) is the controlled differential equation. Among them, f(H(t); θ f ) vector field is a conventional multi-layer perceptron, which includes 3 layers of fully connected operations and uses Sigmoid and LeakyReLu as activation functions. The initial fully connected layer maps the hidden state H(t) at the current moment to a higher dimension. In order to make the model focus on the characteristics of the rainy period, the SE attention module is embedded in the middle, which assigns weight parameters to the data features of the hidden layer for feature extraction. The final fully connected layer maps and aligns the hidden layer to ensure that the output performs matrix multiplication with the control signal at the current moment.

[0051] Specifically, f(H(t);θ f ) is the designed time attention vector field, which includes full connection, activation, and attention processing. The specific operations are as follows:

[0052]

[0053]

[0054] A 2 =(Att Temporal (A 1 )), (12)

[0055]

[0056] In the formula, A 0 , A 1 and A 2 represents the feature result obtained after being processed by a neural layer. Equations (10) and (11) respectively represent that the fully connected layer converts the hidden state H(t) and A at the current moment into 0 Perform dimensional mapping. Where |K| represents the continuous path set of traffic network nodes, dim(h (k) ) represents the hidden features of node k in a certain feature layer. FC input_size→output_sizerepresents the fully connected operation, input_size represents the size of the input feature, and output_size represents the size of the output feature. In addition, σ(·) represents the Sigmoid activation function. Formula (12) uses Att Temporal (·) The temporal attention operation further processes the hidden features, making the model focus on the rainy period. Formula (13) further 2 Mapping alignment is performed to ensure that the output performs matrix multiplication with the current control signal. is the LeakyReLu activation function.

[0057] Step 1.4: Spatial attention processing module extracts spatial dependency features

[0058] The spatial attention processing module contains the designed spatial attention controlled differential equation, which has a spatial attention vector field and can effectively extract the spatial dependence characteristics of the rainy period.

[0059] The role of the spatial attention neural controlled differential equation is to further realize the feature dependency extraction at the spatial level. The specific operation is shown in formula (3), that is, it is a controlled signal H(t), the vector field is g(Z(t); θ f ) is the controlled differential equation. Among them, g(Z(t); θ f ) and f(H(t);θ f ) is similar to the above, except that g(Z(t); θ f ) introduced an adaptive graph convolution operation, which performs adaptive node embedding representation on road network nodes, obtains the corresponding adjacency matrix through matrix self-multiplication and transposition operation, and uses Chebyshev polynomials as graph convolution kernels.

[0060] Specifically, g(Z(t);θ g ) is the designed spatial attention vector field, which includes full connection, activation, adaptive graph convolution, and attention processing. The specific operations are as follows:

[0061]

[0062] B 1 =α(I+φ(σ(E·E T )))B 0 W spatial , (15)

[0063] B 2 =(Att Spatial (B 1 )), (16)

[0064]

[0065] In the formula, B0 , B 1 and B 2 represents the feature result obtained after processing by a neural layer. Formula (14) represents the dimension-up mapping of the hidden state Z(t) by the full connection operation. Similarly, |K| represents the continuous path set of the traffic network node, dim(z (k) ) represents the hidden features of node k in a certain feature layer. Formula (15) uses adaptive graph convolution operation to extract spatial dependency features. Where I is the unit matrix calculated by |K|×|K|. E is the trainable node embedding matrix, E T is the transposed matrix of E, W spatial is a trainable weight matrix. Formula (16) contains Att Temporal (·) spatial attention operation to focus on the spatial dependence characteristics of the rainy period; Formula (17) further adds 2 Mapping alignment is performed to ensure that the output performs matrix multiplication with the control signal at the current moment.

[0066] Step 1.5: Solver solves the neural attention controlled differential equation

[0067] In order to solve the neural attention controlled differential equation, the initial, temporal, and spatial attention controlled differential equations can be integrated into an ordinary differential equation, as shown in equation (5). The neural controlled differential equation is trained by the adjoint sensitivity method, and the final hidden state obtained by solving the equation is solved. The solution process of the solver is shown in equation (6). Finally, nonlinear mapping is performed through the output layer to output the prediction result.

[0068] Step 2: Calculate structural indicators based on the original traffic speed data, construct the spatial physical topological structure of the traffic network, and calculate two types of structural observation indicators: the centrality of the road network nodes and the maximum connected subgraph of the road network.

[0069] Step 2.1: Construct the spatial physical topology of the transportation network

[0070] In order to calculate the two structural indicators of road network node centrality and road network maximum connected subgraph, it is necessary to model the physical topology of the original traffic network and visualize it as follows: Figure 3 The physical topology of the traffic network is a directed graph, which can be represented as G(N,δ), where N represents the set of sensors in the traffic network and δ represents the set of edges connecting the sensors.

[0071] Step 2.2: Calculate the network node centrality and the largest connected subgraph of the network

[0072] The node centrality of the road network and the maximum connected subgraph of the road network are used to measure the importance of the node and the traffic efficiency of the road network respectively. The calculation methods of the two are shown in formulas (18) and (19) respectively:

[0073]

[0074]

[0075] In the formula, δ o,d represents the number of connected routes with node o as the starting point, K as the set of network nodes, and node d as the end point; δ o,d|k N represents the number of connected routes starting from node o, ending at node d and passing through node k; A Indicates the number of road network nodes; N M Indicates the number of network nodes in the maximum connectivity case.

[0076] Step 3: Integrate functional and structural indicators to construct a comprehensive evaluation index system, and combine it with the resilience assessment algorithm to realize the resilience assessment of the urban transportation network.

[0077] Specifically, the speed prediction results of step 1 and the road network node centrality and the road network's largest connected subgraph of step 2 are integrated to construct a comprehensive evaluation system for road network resilience indicators covering functional and structural observation indicators; and a multi-indicator resilience evaluation algorithm is designed to realize the evaluation of road network resilience.

[0078] Step 3.1: Construct a comprehensive evaluation system for road network resilience indicators

[0079] In order to improve the accuracy of the model's assessment of the resilience of urban transportation road networks, it is necessary to comprehensively consider the changes in the functional and structural indicators of the road network. Therefore, a comprehensive evaluation system for road network resilience indicators was constructed.

[0080] The speed index of step 1 is integrated into the road network topology of step 2 to generate a weighted graph structure. The time-varying characteristics of the speed index make the weighted graph change dynamically in time and space. The calculation methods of the speed-weighted node centrality SNC and the speed-weighted maximum connected subgraph SMS of the road network are shown in formulas (20) and (21), respectively:

[0081]

[0082]

[0083] Where V mean Represents the average speed of the entire road network node, V o,d , represents the speed from node O to node d,δ o,d represents the number of connected routes with node o as the starting point, K as the set of network nodes, and node d as the end point; δ o,d|k N represents the number of connected routes starting from node o, ending at node d and passing through node k; A Indicates the number of road network nodes; N M Indicates the number of nodes in the road network under maximum connectivity.M It represents the speed of the vehicle at node M. By multiplying the node centrality or the maximum connected subgraph with the speed index, the speed-weighted SNC and SMS can be obtained.

[0084] In addition, in order to further evaluate the resilience of the road network, the calculation methods of the comprehensive resilience value resilience and the comprehensive resilience capacity value capability are shown in formulas (22) and (23).

[0085] resilience=SNC+SMS, (22)

[0086]

[0087] In the formula, resilience normal and resilience rainy Represent the comprehensive resilience capability values ​​of normal weather and rainy weather respectively. Among them, capability∈(0,1], the closer it is to 1, the stronger the resilience capability of the road network is, that is, the road network is less disturbed by rainy days; the closer it is to 0, the weaker the resilience capability of the road network is, that is, the road network is more disturbed by rainy days.

[0088] Step 3.2: Based on the constructed comprehensive evaluation system of road network resilience indicators, design a multi-indicator resilience evaluation algorithm to realize the evaluation of road network resilience.

[0089] In order to accurately calculate the road network resilience loss, a multi-index resilience evaluation algorithm was designed.

[0090] The input of the multi-index resilience assessment algorithm is the label value of the urban traffic road network, the predicted value of the ASTG-NCDE model and the rainfall of the urban traffic road network. Among them, the label value of the urban traffic road network is the true value of the speed obtained by 325 sensors distributed at each node of the road network. The rainfall data is obtained from the official website of the National Weather Service of the United States, which contains the rainfall in each area of ​​the road network. The multi-index resilience assessment algorithm calculates the comprehensive resilience capacity value resilience under the influence of non-rainstorm based on the input data. normal And the comprehensive resilience value under the influence of heavy rain rainy , and then calculate the comprehensive resilience capability value capability according to formula (23) to evaluate the resilience of the urban traffic network. The specific details of the multi-index resilience evaluation algorithm are shown in the following algorithm:

[0091]

[0092]

[0093] Verification Example

[0094] To prove the speed prediction performance of this example in normal weather and rainstorm weather, the present invention conducts experiments on the public data set PEMS-BAYS. The data set contains 308 road section nodes, and the speed data is statistically observed every 5 minutes. Node 12 is selected as the test node. The prediction results of the present invention in normal and rainstorm weather are compared with the true value fitting curve as shown in the figure. Figure 4 As shown. And from Figure 4 It can be seen that the model has excellent performance in predicting road network traffic speed, whether in normal weather or rainstorm weather, and is basically consistent with the actual value changes. In particular, the prediction effect of this model is better in rainstorm weather, which is attributed to the introduction of the attention mechanism. Among them, the initial attention neural controlled differential equation module generates spatiotemporal data based on the attention coefficient, focusing on the speed characteristics of the rainy period, providing a reference for the subsequent spatiotemporal feature dependency extraction. The time and space attention controlled differential equation module further effectively extracts the spatiotemporal dependency correlation of the rainy period, causing the model to focus on the feature extraction of the rainy period.

[0095] When the urban traffic network is affected by heavy rain, each spatial node will be affected to varying degrees due to the different rainfall amounts and durations, resulting in deviations in the prediction accuracy of the model at different spatiotemporal levels. Therefore, in order to prove the robustness and generalization ability of the speed prediction of the present invention at different temporal and spatial levels, the network nodes were tested at different temporal and spatial levels, and the prediction results were visualized to more intuitively show the spatiotemporal prediction effect of the model on the speed of the road network, and a heat map of the predicted value and the true value was drawn, as shown in Figure 1. Figure 5 shown. Figure 5 In the figure, the vertical axis represents 0 to 308 road network nodes, the horizontal axis represents the time point, and the color depth represents the speed value. Figure 5 It can be seen that the predicted speed value of this model is basically consistent with the actual speed value at the temporal and spatial levels, which effectively proves the accuracy of this model in predicting the traffic speed of the road network at the temporal and spatial levels.

[0096] In addition, to prove the superiority of the present invention over other prediction methods, the latest and well-known prediction models were selected to conduct comparative experiments on the public data set PEMS-BAYS. The experimental results show that the invented ASTG-NCDE model is superior to similar models in terms of mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), as shown in Table 2.

[0097] Table 2 Comparison of experimental results with the latest and well-known models

[0098]

[0099] As can be seen from Table 2, compared with the current mainstream and advanced methods, the prediction performance of the present invention is almost fully ahead in all evaluation indicators, whether in normal weather or rainstorm weather. Among them, the Graph-WaveNet[1] model combines graph convolutional neural network and diffuse causal convolution to extract the spatiotemporal dependency information of traffic data. On the basis of Graph-WaveNet, ASTGCN[2] incorporates the attention mechanism to improve the model's ability to capture key information. STGODE[3] incorporates time and space vector fields into ordinary differential equations to achieve the extraction of time and space continuous feature dependencies. Compared with STGODE, ANCDE[4] introduces the attention mechanism, which improves its prediction performance in rainstorm weather to a certain extent. However, compared with STGODE, ANCDE lacks the ability to extract spatial features, resulting in its prediction effect in normal weather being slightly worse than that of STGODE. As the most advanced spatiotemporal feature extraction model, STG-NCDE[5] introduces controlled signals compared with STGODE, and introduces spatial feature extraction compared with ANCDE, which greatly improves its performance. However, the prediction performance of the STG-NCDE model is still inferior to that of the ASTG-NCDE model of the present invention. The ASTG-NCDE model designs and introduces the initial attention controlled differential equation, and redesigns the time and space vector fields based on the attention mechanism, which greatly improves the model's ability to capture the spatiotemporal dependent features in rainstorm weather. At present, the ASTG-NCDE has achieved the best speed prediction accuracy in normal and rainstorm weather.

[0100] Finally, the road network resilience is evaluated by combining the comprehensive resilience evaluation index system and the multi-index resilience evaluation algorithm. The comprehensive resilience index changes and the comprehensive resilience capacity curve are shown in the figure. Figure 6 As shown in the figure, under the influence of rainfall before, during and after, the comprehensive resilience index of the road network shows a trend of sharp decline (resistance stage), short-term recovery (absorption stage), oscillation (self-adjustment stage) and slow recovery (self-recovery stage), which is in line with the time-varying evolution mechanism of urban traffic road network resilience.

[0101] The above content is a further detailed description of the present invention. It cannot be determined that the specific implementation methods of the present invention are limited to these. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the scope of protection of the invention determined by the claims of the present invention.

[0102] References are as follows:

[0103] [1]Z.Wu,S.Pan,G.Long,J.Jiang,and C.Zhang,“Graph wavenet for deepspatial-temporal graph modeling”,in Proc.ofIJCAI,2019.

[0104] [2]Guo S,Lin Y,FengN,“Attention based spatial-temporal graphconvolutional networks for traffic flow forecasting”,Proceedings of the AAAIconference on artificial intelligence,33(01):922-929,2019.

[0105] [3]Fang Z,Long Q,Song G,“Spatial-temporal graph ode networks fortraffic flow forecasting”,Proceedings of the 27th ACM SIGKDD conference onknowledge discovery&data mining,364-373,2021.

[0106] [4]Jhin S Y,Shin H,Hong S,“Attentive neural controlled differentialequations for time-series classification and forecasting”,IEEE InternationalConference on Data Mining,250-259,2021.

[0107] [5]Choi J,Choi H,Hwang J,“Graph neural controlled differentialequations for traffic forecasting”,Proceedings of the AAAI Conference onArtificial Intelligence,36(6):6367-6374,2022。

Claims

1. An urban traffic network resilience assessment method based on neural attention controlled differential equations, characterized in that: There are three steps involved: Step 1: Predict functional indicators based on raw traffic speed data; Step 2: Calculate structural indicators based on the original traffic speed data; Step 3: Integrate functional and structural indicators to build a comprehensive evaluation index system, and combine the multi-index resilience assessment algorithm to realize the resilience assessment of urban transportation network; Step 1: Construct a neural attention controlled differential equation model to accurately predict vehicle speed; The model comprises four submodules, namely, an interpolation module, an initial attention neural controlled differential equation module, a time attention processing module, and a space attention processing module; the time attention processing module and the space attention processing module respectively comprise a time attention controlled differential equation and a space attention controlled differential equation for extracting time and space dependent features; The processing steps are: Step 1.1: Use the cubic natural spline interpolation method to interpolate the original traffic speed data into a continuous path; Step 1.2: The initial attention neural controlled differential equation module processes the continuous path into spatiotemporal velocity data based on the attention coefficient, focusing on the data characteristics of the rainy period; Step 1.3: The temporal attention processing module further extracts time-dependent features; Step 1.4: The spatial attention processing module further extracts spatial dependency features; Step 1.5: The solver solves the neural attention controlled differential equation; The initial attention neural controlled differential equation, the temporal attention neural controlled differential equation, and the spatial attention neural controlled differential equation are respectively shown in equations (1), (2), and (3): Where X(t):t∈[0,T] is the continuous path obtained by interpolating the original velocity data through cubic natural spline; a(t):t∈[0,T] is the spatiotemporal data based on the attention coefficient obtained after processing the continuous path X(t); and represents two types of matrix multiplication; Y(t): t∈[0,T] is the constructed time and space level attention coefficient value; s(a(t); θ s )、f(H(t);θ f ) and g(Z(t);θ g ) represent the initial attention vector field, the temporal attention vector field and the spatial attention vector field respectively, and the internal structure includes θ s ,θ f and θ g Trainable parameters, used to form the gradient module of the controlled differential equation; a(T), H(T), and Z(T) represent the feature dependencies of the T time period obtained after processing the initial attention vector field, the temporal attention vector field, and the spatial attention vector field, respectively, and cover the feature dependencies at any time t (t∈[0,T]); a(0) represents the initial value of the feature state obtained after processing by the initial attention vector field; In order to facilitate the subsequent solution of equations, equations (1), (2), and (3) are combined, that is, the neural attention controlled differential equation model is shown in equation (4): Secondly, to solve equation (4), it needs to be transformed into an ordinary differential dynamic system, as shown in equation (5). Its training and prediction are attributed to the solution process of ordinary differential equations. Then, equation (6) is used as the input of the solver and trained by the adjoint sensitivity method to output the prediction result of vehicle speed:

2. The method according to claim 1, characterized in that In step 1.2: The continuous path generated by cubic natural spline interpolation is transmitted to the initial attention neural controlled differential equation module to generate spatiotemporal data a(t) based on the attention coefficient, focusing on the speed characteristics of the rainy period, providing a reference for the subsequent spatiotemporal feature dependency extraction; the initial spatiotemporal value a(0) with attention is obtained and used in the subsequent time and space attention differential equations, effectively improving the feature extraction performance at the spatiotemporal level; where a(t) is calculated as shown in formula (8): a(t)=sigmoid(X(t)), (8) Where sigmoid(·) is the Sigmoid activation function, X(t) is the continuous path obtained by cubic natural spline interpolation; the initial spatiotemporal value a(0) is obtained by taking the value of a(t) at the moment t is 0; The initial attention neural controlled differential equation operates on the spatiotemporal level based on the attention coefficient a(t) as shown in formula (9): Where FC represents the fully connected operation; if the initial attention neural controlled differential equation acts on the time level, a(t) is a single element; if the initial attention neural controlled differential equation acts on the space level, a(t) is a vector.

3. The method according to claim 1, characterized in that In step 1.3: The temporal attention neural controlled differential equation further extracts the temporal feature dependency of the spatiotemporal attention data generated by the initial attention neural controlled differential equation, and is a controlled signal a(t) and a vector field f(H(t); θ f ) controlled differential equations; Among them, f(H(t);θ f ) is the temporal attention vector field, which includes full connection, activation, and attention processing. The specific operations are as follows: A2=(To Temporal (A1)), (12) In the formula, A0, A1 and A2 represent the feature results obtained after processing by a certain neural layer; Formulas (10) and (11) respectively represent that the fully connected layer maps the hidden state H(t) and A0 at the current moment to a higher dimension; where |K| represents the continuous path set of the traffic network nodes, dim(h (k) ) represents the hidden feature of node k in a certain feature layer; FC input_size→output_size represents the fully connected operation, input_size represents the size of the input feature, output_size represents the size of the output feature; σ(·) represents the Sigmoid activation function; Formula (12) uses Att Temporal (·) The temporal attention operation further processes the hidden features to make the model focus on the rainy period; Formula (13) further maps and aligns A2 to ensure that the output performs matrix multiplication with the current control signal; where is the LeakyReLu activation function.

4. The method according to claim 1, characterized in that In step 1.4: The spatial attention neural controlled differential equation further realizes the feature dependency extraction at the spatial level, which is a controlled signal H(t), a vector field g(Z(t); θ f ) controlled differential equations; Among them, g(Z(t);θ g ) is the designed spatial attention vector field, which includes full connection, activation, adaptive graph convolution, and attention processing. The specific operations are as follows: B1=α(I+φ(σ(EE T )))B0W spatial , (15) B2=(To Spatial (B1)), (16) In the formula, B0, B1 and B2 represent the feature results obtained after processing by a certain neural layer; Formula (14) represents the fully connected operation to map the hidden state Z(t) to a higher dimension. Similarly, |K| represents the continuous path set of the traffic network nodes, dim(z (k) ) represents the hidden features of node k in a certain feature layer; Formula (15) uses adaptive graph convolution operation to extract spatial dependency features; where I is the unit matrix calculated by |K|×|K|; E is the trainable node embedding matrix, E T is the transposed matrix of E, W spatial is a trainable weight matrix; Formula (16) contains Att Spatial (·) Spatial attention operation to focus on the spatially dependent features of the rainy period; Formula (17) further aligns the mapping of B2 to ensure that the output performs matrix multiplication with the control signal at the current moment.

5. The method according to claim 1, characterized in that The step 2 comprises: Step 2.1: Construct the spatial physical topological structure of the transportation network; Step 2.2: Calculate the node centrality of the road network and the largest connected subgraph of the road network; The node centrality of the road network and the maximum connected subgraph of the road network are used to measure the importance of the node and the traffic efficiency of the road network respectively. The calculation methods of the two are shown in formulas (18) and (19) respectively: In the formula, δ o,d represents the number of connected routes with node o as the starting point, K as the set of network nodes, and node d as the end point; δ o,d|k N represents the number of connected routes starting from node o, ending at node d and passing through node k; A Indicates the number of network nodes; N M Indicates the number of network nodes in the maximum connectivity case.

6. The method according to claim 1, characterized in that The step 3 comprises: Step 3.1: Construct a comprehensive evaluation system for road network resilience indicators The speed index is integrated into the road network topology to generate a weighted graph structure. The time-varying characteristics of the speed index make the weighted graph change dynamically in time and space. The calculation methods of the speed-weighted node centrality and the speed-weighted maximum connected subgraph of the road network are shown in equations (20) and (21), respectively: Where V mean Represents the average speed of the entire road network node, V o,d , represents the speed from node o to node d,δ o,d represents the number of connected routes with node o as the starting point, K as the set of network nodes, and node d as the end point; δ o,d|k N represents the number of connected routes starting from node o, ending at node d and passing through node k; A Indicates the number of network nodes; N M Indicates the number of network nodes in the maximum connectivity case; V M represents the speed of the vehicle at node M; The calculation methods of comprehensive resilience index and comprehensive resilience capacity are shown in formulas (22) and (23): resilience=SNC+SMS, (22) In the formula, resilience normal and resilience rainy Represent the comprehensive resilience capability values ​​of normal weather and rainy weather respectively; where capability∈(0,1], the closer it is to 1, the stronger the resilience capability of the road network is, that is, the road network is less disturbed by rainy days; the closer it is to 0, the weaker the resilience capability of the road network is, that is, the road network is more disturbed by rainy days; Step 3.2: Based on the constructed comprehensive evaluation system of road network resilience indicators, a multi-indicator resilience evaluation algorithm is designed to evaluate road network resilience; The multi-index resilience evaluation algorithm calculates the comprehensive resilience capacity value resilience under the influence of non-rainstorm according to the urban traffic road network speed label value, urban traffic road network speed prediction value, and urban traffic road network rainfall input parameters. normal and the comprehensive resilience value under the influence of heavy rain rainy , and then the comprehensive resilience capability value capability is calculated according to formula (23).

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