Expressway traffic state estimation method and system fusing traffic flow model and graph neural network

Abstract

The invention discloses an expressway traffic state estimation method and system fusing a traffic flow model and a graph neural network, and the method comprises the steps: discretizing an expressway into cells with a fixed length, and representing the traffic state of each cell through three parameters: flow, density and speed; determining an active influence region and a region which will be influenced of the cells in a time period by using the traffic wave velocity between any two cells, and establishing a cell traffic state space-time evolution model; converting the discretized cellular traffic state and the adjacency information into graph structure data, and designing a graph neural network to update all cellular traffic states; and based on the updated cellular traffic state, optimizing the cellular traffic state space-time evolution model by using a gradient descent method to obtain a highway traffic state estimation result. The expressway traffic flow time-space evolution modeling method can effectively improve interpretability, accuracy and generalization ability of expressway traffic flow time-space evolution modeling, and accurately grasp an expressway traffic flow time-space evolution mechanism.

Description

Technical Field

[0001] The present invention belongs to the field of traffic control, relates to the estimation of highway traffic states, and particularly relates to a method and system for estimating highway traffic states by integrating a traffic flow model and a graph neural network. Background Art

[0002] An accurate and reliable macroscopic traffic flow spatio-temporal evolution model is crucial for the modeling and interpretation of traffic flow phenomena, the estimation and prediction of traffic states, the deduction of congestion propagation, the optimization of ramp control, and the management of highway emergencies. An effective traffic flow model should possess three key characteristics: (1) strong interpretability in capturing the spatio-temporal evolution of traffic flow; (2) high accuracy in estimating and predicting key traffic state variables such as flow rate, speed, and density; (3) general applicability under various different traffic conditions.

[0003] The key to constructing a reliable macroscopic highway traffic flow model lies in a modeling method with a solid theoretical foundation. Existing macroscopic traffic flow modeling methods can be roughly divided into three categories: (1) models based on physical principles; (2) models based on machine learning; (3) hybrid models. Models based on physical principles perform well in describing the evolution of traffic states, capturing a wide range of traffic flow phenomena, and estimating traffic states when historical data is scarce. Historically, researchers have derived macroscopic models based on fluid dynamics principles by analogy between highway traffic flow and fluid dynamics. These models conceptualize highway traffic as a continuous flow with specific properties and use aggregated variables such as flow rate, average speed, and density to model traffic operation at the macroscopic level, which helps to derive mathematical formulas for traffic dynamics. Models based on machine learning, on the other hand, start from the data itself and use the data mining ability of machine learning to extract the spatio-temporal correlations between traffic flow parameters for traffic state estimation. Models based on machine learning perform excellently when there is sufficient training data, but have high requirements for the quality and quantity of training data.

[0004] Although there are currently limited hybrid models that have explored how to combine traffic flow models and machine learning-based models, this mainly reflects in the exploration of the loss function of machine learning-based models. In this case, the results obtained by the model conform to a certain traffic flow physical model, but the interpretability of the model itself is poor. Summary of the Invention

[0005] Objective of the Invention: In order to overcome the deficiencies in the prior art, the present invention provides a method and system for estimating the traffic state of expressways that integrates traffic flow models and graph neural networks, which can effectively improve the interpretability, accuracy, and generalization ability of the spatio-temporal evolution modeling of expressway traffic flow, accurately grasp the spatio-temporal evolution mechanism of expressway traffic flow, and help traffic design and management departments optimize expressway design and renovation plans, formulate reasonable and effective real-time control and guidance strategies, and have practical application value for alleviating expressway traffic congestion.

[0006] Technical Solution: To achieve the above objective, the present invention provides a method for estimating the traffic state of expressways that integrates traffic flow models and graph neural networks, including the following steps:

[0007] S1: Discretize the expressway into cells of a fixed length, and represent the traffic state of each cell by three parameters: flow, density, and speed;

[0008] S2: Determine the active influence area and the area that will be affected within a time period for each cell by using the traffic wave speed between any two cells;

[0009] S3: Convert the discretized cell traffic state and adjacency information into graph-structured data, design a graph neural network to update the traffic state of all cells, and establish a spatio-temporal evolution model for the cell traffic state;

[0010] S4: Based on the updated cell traffic state, use the gradient descent method to optimize the spatio-temporal evolution model of the cell traffic state, and obtain the expressway traffic state estimation result.

[0011] Furthermore, in step S1, according to the cellular automaton model, the main road of the expressway is cut into cells of the same length ΔX, numbered 1, 2,..., N; the vehicle movement trajectories on the road section are cut into a continuous time series at time intervals ΔT, and the traffic state X of each cell is calculated according to the vehicle trajectory information in each cell x,t , including density k x,t , speed v x,t and flow q x,t .

[0012] Furthermore, step S2 specifically includes:

[0013] For any cell x, use the density k x,t and flow q x,t of adjacent cells to calculate the transmission directions {x - 1:x}, {x:x + 1} and speed of the traffic wave between the cell and its upstream and downstream cells and accordingly determine the upstream and downstream spatial influence ranges D of each cell within a time period u,x,t = ωx-1:x,t ×ΔT and D d,x,t = ω x:x+1,t ×ΔT; thus obtaining the corresponding number of upstream and downstream influencing cells and The corresponding upstream influencing cell region is {x - 1, …, x - m u,x,t}}, and the downstream influencing region is {x + 1, …, x + m d,x,t};

[0014] For any cell y, traverse cells 1, 2, …, x, …, y - 1. If the downstream influencing region {x + 1, …, x + m d,x,t} of cell x contains cell y, then the farthest upstream influencing cell x of cell y is found, and thus the number of upstream cells n affecting cell y is obtained u,y,t , and the traversal stops; for any cell y, traverse cells N, N - 1, …, x, …, y + 1. If the upstream influencing region {x - 1, …, x - m u,x,t} of cell x contains cell y, then the farthest downstream influencing cell x of cell y is found, and thus the number of downstream cells n affecting cell y is obtained d,y,t , and the traversal stops;

[0015] For the number of upstream cells n u,y,t and the number of downstream cells n d,y,t of any cell y, calculate the longest number of influencing cells n corresponding to the cell y,t = max{n u,y,t n d,y,t}, traverse the number of upstream and downstream influencing cells of all cells, and determine the farthest number of influencing cells n among all cells update,t = max{n u,1,t , …, n u,N,t , n d,1,t , …, n d,N,t}.

[0016] Furthermore, in step S3, for any cell, updating the traffic state of the cell by using the traffic states of all cells that will affect the cell within a time period specifically includes:

[0017] Combining the methods for updating density, speed, and flow in the cellular automaton, a hybrid model with a cyclic traffic state update structure is proposed Determine the number of cyclic updates through the longest influence number n update,t ;

[0018] In an update i, if it is the first update, then it is to use the traffic state X of all cells observed at the previous moment 1:N,tAs the input for subsequent updates, the output of the previous update i-1 is used. As the input for this update i, the output is Among them, the output of the update consists of and During the update process, for each cell y, the traffic state of the cell itself the traffic states of adjacent cells and the traffic wave speed and are used to calculate the change in the upstream and downstream traffic states of cell y: and Then, the traffic state of the cell itself the change in the upstream and downstream traffic states of cell y and are used to update the cell state

[0019] After completing the update, all cells are traversed. If the current iteration i reaches the maximum number of influential cells n y,t of cell y, then the traffic state update of cell y is completed

[0020] Furthermore, the specific method for the graph neural network to update the traffic states of all cells in step S3 is as follows:

[0021] A graph neural network that conforms to the upstream and downstream adjacency relationships of cells is proposed. The traffic states and adjacency relationships of cells on the road segment are transformed into a graph structure G=(V,E), and a message passing and update network consistent with the spatio-temporal transfer of traffic states is constructed in the graph neural network; on the basis of conforming to the traffic state transfer logic, the spatio-temporal correlations hidden in the data are extracted, so as to complete the modeling of traffic flow evolution within a time period and the estimation of cell states X y,t+1 ;

[0022] For each update, the traffic states X 1:N,t of all cells observed at the previous moment are used as the input. For subsequent updates, the output of the previous update i-1 is used as the input for this update i; in update i, a cell connection relationship matrix is first initialized, where represents a directed edge of a cell connection relationship, where M represents the number of directed connection edges of all cells; and represent the starting cell and the ending cell of the directed edge e, respectively. Denote the traffic wave speed of the directed edge e; Denote the traffic state transfer quantity of the directed edge e; then calculate the traffic wave speed and traffic state transfer quantity of each directed edge connected to the cells in the cell connection relationship matrix. The expression for the traffic wave speed of the directed edge is:

[0023]

[0024] The expression for the traffic state transfer quantity of each directed edge connected to the cell is:

[0025]

[0026] where W1, b1, W2, b2, W3, and b3 are the parameter matrices of the three-layer fully connected neural network;

[0027] Finally, transform the connection relationship matrix into a matrix with dimensions R×R The expression for the state update calculation process of all cells is as follows:

[0028]

[0029] where ⊙ represents matrix dot multiplication; W h and b h are the parameter matrices; W ONE represents a matrix of all 1s;

[0030] After completing the update of i, traverse all cells. If the current number i reaches the maximum number n of cells that affect cell y y,t , then the traffic state update of cell y is completed

[0031] Furthermore, in step S4, the gradient descent method is used to optimize the spatio-temporal evolution model of the cell traffic state, specifically including:

[0032] First, use the observed state values X of all cells x,t to calculate the average values μ(k), μ(v), σ(q) of flow, density, and speed, and the standard deviations σ(q), σ(k), σ(v). Then, normalize the estimated values and observed values for the t+1 time period. The normalization calculation is as follows:

[0033]

[0034]

[0035] where, represents the estimated value of flow for the t+1 time period; represents the estimated value of density for the t+1 time period; represents the estimated speed value in the time period of t + 1; represents the observed traffic flow value in the time period of t + 1; represents the observed density value in the time period of t + 1; represents the observed speed value in the time period of t + 1;

[0036] Use the normalized traffic state values to calculate the mean absolute error Calculate. According to the obtained error, use the gradient descent method to update the parameters of the model f(·|θ) until the error is reduced to a stable state. At this time, the best traffic state spatio-temporal evolution model is obtained.

[0037] The present invention also provides a highway traffic state estimation system integrating a traffic flow model and a graph neural network, including:

[0038] A discretization module for discretizing the highway into cells of a fixed length and representing the traffic state of each cell by three parameters: traffic flow, density, and speed;

[0039] A model establishment module for determining the active influence area and the area that will be affected of a cell within a time period based on the traffic wave speed between any two cells, and establishing a spatio-temporal evolution model of the cell traffic state;

[0040] A state update module for converting the discretized cell traffic state and adjacency information into graph structure data and designing a graph neural network to update the traffic state of all cells;

[0041] A model optimization module for optimizing the spatio-temporal evolution model of the cell traffic state using the gradient descent method to obtain the highway traffic state estimation result.

[0042] The present invention also provides a computer storage medium, and the computer storage medium stores a program for a method for estimating highway traffic state integrating a traffic flow model and a graph neural network. When the program for the method for estimating highway traffic state integrating a traffic flow model and a graph neural network is executed by at least one processor, the steps of a method for estimating highway traffic state integrating a traffic flow model and a graph neural network are implemented.

[0043] The present invention constructs a theoretical model based on the cellular automaton model to improve the interpretability of the model. The purpose of interpretability is to make the model more understandable, with explicit parameter relationships and change processes, and to have a trend description of the traffic flow evolution process, avoiding being affected by the small amount of training set data, resulting in overfitting of the model, and guiding the model to learn in line with the trend.

[0044] Meanwhile, transform the discretized cellular traffic states and adjacency information into graph-structured data, design the message passing and update mechanism of the graph neural network to complete the computational design of the theoretical model, and adjust and optimize the model parameters using the error between the traffic state estimated by the model at the next moment and the observed traffic state.

[0045] Through the introduction of the non-linear modeling of the graph neural network, the present invention can better explore the latent spatio-temporal relationships of all cells on the basis of conforming to the traffic flow, improving the accuracy and generalization ability of the model. Determine the mean and standard deviation corresponding to each traffic flow parameter using the flow, density, and speed of the training data, normalize the traffic state estimated by the model at the next moment and the observed traffic state, calculate the mean absolute error between the normalized estimated value and the observed value, and use this to adjust and optimize the model parameters, thereby eliminating the imbalance caused by the numerical size of the traffic flow parameters themselves.

[0046] Beneficial effects: Compared with the prior art, the present invention can effectively improve the interpretability, accuracy, and generalization ability of the spatio-temporal evolution modeling of highway traffic flow, accurately grasp the spatio-temporal evolution mechanism of highway traffic flow, and help traffic design and management departments optimize highway design and renovation plans, and formulate reasonable and effective real-time control and guidance strategies, which has practical application value for alleviating highway traffic congestion. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is the framework flowchart of the present invention;

[0048] Figure 2 is the flowchart for quantifying the influence area of cells within a unit time period adopted. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] The present invention will be further clarified below with reference to the drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art to the present invention fall within the scope defined by the appended claims of this application.

[0050] Embodiment 1:

[0051] As Figure 1 shown, this embodiment provides a highway traffic state estimation method integrating a traffic flow model and a graph neural network, including the following steps:

[0052] S1: Discretize the highway into cells of a fixed length, and represent the traffic state of each cell with three parameters: flow, density, and speed;

[0053] In this embodiment, the highway arterial road is cut into cells of the same length ΔX according to the cellular automaton model, and their numbers are 1, 2, …, N; the vehicle movement trajectories on the road section are cut into a continuous time series at time intervals ΔT, and the traffic states X of the cells at different time periods are calculated according to the vehicle trajectory information in each cell x,t , including density k x,t , speed v x,t and flow q x,t , and a data set is constructed, where 80% is divided into the training data set and 20% is divided into the test data set

[0054] S2: Determine the active influence area and the area that will be affected of a cell within a time period by using the traffic wave speed between any two cells

[0055] Refer to Figure 2 , for any cell x, use the density k x,t and flow q x,t of the adjacent cells to calculate the transmission directions {x - 1:x}, {x:x + 1} and speed of the traffic waves between the cell and the upstream and downstream cells and accordingly determine the upstream and downstream spatial influence ranges D u,x,t = ω x-1:x,t ×ΔT and D d,x,t = ω x:x+1,t ×ΔT; thus obtaining the corresponding number of upstream and downstream influencing cells and the corresponding upstream influencing cell area is {x - 1, …, x - m u,x,t} and the downstream influence area is {x + 1, …, x + m d,x,t}

[0056] For any cell y, traverse cells 1, 2, …, x, …, y - 1. If the downstream influence area {x + 1, …, x + m d,x,t} of cell x contains cell y, then the farthest upstream influencing cell x of cell y is found, and thus the number n of upstream cells affecting cell y is obtained u,y,t , and the traversal stops; for any cell y, traverse cells N, n - 1, …, x, …, y + 1. If the upstream influence area {x - 1, …, x - m u,x,t} of cell x contains cell y, then the farthest downstream influencing cell x of cell y is found, and thus the number n of downstream cells affecting cell y is obtained d,y,t , and the traversal stops

[0057] For the number n u,y,t of upstream cells and the number nd,y,t , calculate the maximum number n of influencing cells corresponding to the cell y,t = max{n u,y,t n d,y,t}}, traverse the number of upstream and downstream influencing cells of all cells, and determine the maximum number n of the farthest influencing cells among all cells update,t = max{n u,1,t ,…,n u,N,t ,n d,1,t ,…,n d,N,t}}.

[0058] S3: Based on the cell area determination method in step S2, transform the discretized cell traffic state and adjacency information into graph structure data, design a graph neural network to update the traffic state of all cells, and establish a spatio-temporal evolution model of the cell traffic state;

[0059] For any cell, update the traffic state of the cell by using the traffic states of all cells that will affect the cell within a time period, specifically including:

[0060] Combining the methods for updating density, speed, and flow in the cellular automaton, propose a hybrid model with a cyclic traffic state update structure Determine the number of cyclic updates through the maximum influence number n update,t ;

[0061] In an update i, if it is the first update, then use the traffic states X of all cells observed at the previous moment 1:N,t as the input. For subsequent updates, use the output of the previous update i - 1 as the input for this update i, and the output is where the output of the update is composed of and ; During the update process, for each cell y, use the traffic state of the cell itself the traffic states of adjacent cells and the traffic wave velocity and to calculate the change amounts of the upstream and downstream traffic states of cell y: and Then use the traffic state of the cell itself the change amounts of the upstream and downstream traffic states of cell y and to update the cell state

[0062] After the update is completed, traverse all cells. If the current iteration i reaches the maximum number of influential cells n of cell y y,t , then the traffic state update of cell y is completed

[0063] The specific way for the graph neural network to update the traffic states of all cells is as follows:

[0064] Propose a graph neural network that conforms to the adjacency relationship of upstream and downstream cells of the cell. Convert the traffic states and adjacency relationships of cells on the road segment into a graph structure G=(V, E), and construct a message passing and update network in the graph neural network that is consistent with the spatio-temporal transfer of traffic states; on the basis of conforming to the traffic state transfer logic, extract the spatio-temporal correlations hidden in the data, so as to complete the modeling of traffic flow evolution within a time period and the estimation of cell states X in the next time period y,t+1 ;

[0065] For each update, the traffic states X of all cells observed at the previous moment are used as the input. For subsequent updates, the output of the previous update i - 1 is used as the input for this update i; in update i, first initialize a cell connection relationship matrix 1:N,t where represents a directed edge of a cell connection relationship, where M represents the number of directed connection edges of all cells; and represent the starting cell and the arriving cell of the directed edge e respectively; and represent the traffic wave speed of the directed edge e; represents the traffic state transfer amount of the directed edge e; then calculate the traffic wave speed and traffic state transfer amount of each cell connection directed edge in the cell connection relationship matrix. The expression for the traffic wave speed of the directed edge is: The expression for the traffic state transfer amount of each cell connection directed edge is:

[0066]

[0067] where W1, b1, W2, b2, W3 and b3 are the parameter matrices of the three-layer fully connected neural network;

[0068]

[0069] Finally, convert the connection relationship matrix

[0070] into a matrix with dimensions R×R The expression for the calculation process of the state update of all cells is as follows:

[0071] ​

[0072] where ⊙ represents matrix dot product; W h and b h are parameter matrices; W ONE represents a matrix of all 1s;

[0073] After completing the update of i, traverse all cells. If the current iteration i reaches the maximum number of influential cells n y,t of cell y, then the traffic state update of cell y is completed

[0074] S4: Based on the updated traffic states of the cells, use the gradient descent method to optimize the spatio-temporal evolution model of the traffic states of the cells to obtain the estimated results of the highway traffic states;

[0075] First, use the observed state values X x,t of all cells to calculate the average values μ(k), μ(v), σ(q) and standard deviations σ(q), σ(k), σ(v) of flow, density, and speed. Then, normalize the estimated values and observed values for the time period t + 1. The normalization calculation is as follows:

[0076]

[0077] where, represents the estimated flow value for the time period t + 1; represents the estimated density value for the time period t + 1; represents the estimated speed value for the time period t + 1; represents the observed flow value for the time period t + 1; represents the observed density value for the time period t + 1; represents the observed speed value for the time period t + 1;

[0078] Use the normalized traffic state values to calculate the mean absolute error Calculate. According to the obtained error, use the gradient descent method to update the parameters of the model f(·|θ) until the error shrinks to a stable state. At this time, the optimal spatio-temporal evolution model of the traffic states is obtained.

[0079] Embodiment 2:

[0080] Based on the method of Embodiment 1, this embodiment provides a highway traffic state estimation system that integrates a traffic flow model and a graph neural network, including:

[0081] A discretization module for discretizing the highway into cells of a fixed length and representing the traffic state of each cell by three parameters: flow, density, and speed;

[0082] A model establishment module, which is used to determine the active influence area and the area that will be affected of a cell within a time period by using the traffic wave speed between any two cells, and establish a spatio-temporal evolution model of the traffic state of the cells.

[0083] A state update module, which is used to transform the discretized traffic state and adjacency information of the cells into graph structure data, and design a graph neural network to update the traffic state of all cells.

[0084] A model optimization module, which is used to optimize the spatio-temporal evolution model of the traffic state of the cells by using the gradient descent method, and obtain the estimation result of the highway traffic state.

[0085] This embodiment also provides a computer storage medium, which stores a computer program. When the processor executes the computer program, the above-described method can be implemented. The computer-readable medium can be considered tangible and non-transitory. Non-limiting examples of non-transitory tangible computer-readable media include non-volatile memory circuits (such as flash memory circuits, erasable programmable read-only memory circuits, or mask read-only memory circuits), volatile memory circuits (such as static random access memory circuits or dynamic random access memory circuits), magnetic storage media (such as analog or digital magnetic tapes or hard disk drives), and optical storage media (such as CDs, DVDs, or Blu-ray discs), etc. The computer program includes processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer program may also include or rely on stored data. The computer program may include a basic input / output system (BIOS) that interacts with the hardware of a dedicated computer, device drivers that interact with specific devices of a dedicated computer, one or more operating systems, user applications, background services, background applications, etc.

[0086] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or means for implementing the functions specified in multiple blocks.

[0088] Embodiment 3:

[0089] To prove the effectiveness of the present invention, this embodiment uses the trajectory data collected by the millimeter-wave radar on the side of the Chengdu Expressway for case analysis, as follows:

[0090] Trajectory data collection: Using the roadside millimeter-wave radar as the data collection device, two sections of the Chengdu Expressway are used as the target areas. Two millimeter-wave radars respectively cover a detection area of 525 meters. The 5-day trajectory data collected is used as the experimental data source;

[0091] The lengths of the two target sections are 525 meters. The sections are discretized with a spatial interval of 25 meters ΔX to form 21 cells. The trajectory data is divided with a time interval of 5 seconds ΔT. The traffic flow, density, and speed of each cell within each time interval are calculated using the following model:

[0092] q x,t = k x,t × v x,t

[0093]

[0094] After obtaining the traffic flow, density, and speed of each cell for all time periods, 2 experiments are designed to verify the accuracy of the method of the present invention. In Experiment 1, the traffic flow parameter data of the first 4 days of Section 1 is used as the training data set, and the data of the 5th day of Section 1 is used as the test data set. In Experiment 2, the traffic flow parameter data of the first 4 days of Section 1 is used as the training data set, and the data of the 5th day of Section 2 is used as the test data set.

[0095] Table 1 shows the comparison results of the traditional Cell Transmission Model (CTM), Gated Recurrent Unit (GRU) model, Graph Convolutional Network (GCN) model, and the proposed hybrid model in the free flow state and the congestion state. In the free flow state and the congestion state, the hybrid model performs excellently in all evaluation metrics.

[0096] In the free flow state, the mean absolute error (MAE) of the hybrid model is the lowest: the MAE of speed is 4.29 km / h, the MAE of density is 2.11 vehicles / km / lane, and the MAE of flow is 127.16 vehicles / hour / lane. Its mean absolute percentage error (MAPE) in terms of speed, density, and flow is also the lowest, at 5.87%, 17.67%, and 14.82% respectively. In terms of speed estimation, compared with the traditional CT model, GRU model, and GCN model, the MAE of the hybrid model is reduced by 34.8%, 42.8%, and 17.7% respectively, and the MAPE values are reduced by 1.99%, 3.24%, and 0.72% respectively. In terms of density estimation, the MAE of the hybrid model is reduced by 23.6%, 31.7%, and 8.3% respectively, and the MAPE values are reduced by 6.81%, 8.27%, and 2.12% respectively. In terms of flow estimation, the MAE of the hybrid model is reduced by 26.2%, 33.3%, and 4.4% respectively, and the MAPE values are reduced by 7.06%, 7.55%, and 1.39% respectively.

[0097] In the congested state, the hybrid model also performs excellently in all evaluation metrics. The MAE of the hybrid model is the lowest: the MAE of speed is 1.66 km / h, the MAE of density is 3.48 vehicles / km / lane, and the MAE of flow is 84.43 vehicles / hour / lane. Its MAPE in terms of speed, density, and flow is also the smallest, at 14.66%, 6.13%, and 9.97% respectively. In terms of speed estimation, compared with the traditional CTM model, GRU model, and GCN model, the MAE of the hybrid model is reduced by 23.1%, 25.9%, and 10.3% respectively, and the MAPE values are reduced by 8.03%, 12.68%, and 1.58% respectively. In terms of density estimation, compared with the three baseline models, the MAE of the hybrid model is reduced by 41.3%, 38.3%, and 7.2% respectively, and the MAPE values are reduced by 1.98%, 1.71%, and 0.5% respectively. In terms of flow estimation, the MAE of the hybrid model is reduced by 24.8%, 30.2%, and 9.4% respectively, and the MAPE values are reduced by 7.98%, 12.17%, and 3.15% respectively.

[0098] Table 1 Comparison of the effects of the hybrid model and the basic model in Experiment 1

[0099]

[0100] Table 2 shows the comparison results of the traditional traffic flow model (CTM), gated recurrent unit (GRU) model, graph convolutional network (GCN) model, and the proposed hybrid model under free flow and congested states. Under both free flow and congested states, the hybrid model performs excellently in all evaluation metrics. Under free flow, the hybrid model has the lowest mean absolute error (MAE): the MAE of speed is 4.29 km / h, the MAE of density is 2.11 vehicles / km / lane, and the MAE of flow is 127.16 vehicles / hour / lane. It also achieves the lowest mean absolute percentage error (MAPE) in terms of speed, density, and flow, which are 5.87%, 17.67%, and 14.82% respectively. In terms of speed estimation, compared with the traditional CTM, GRU model, and GCN model, the hybrid model reduces the MAE by 34.8%, 42.8%, and 17.7% respectively, and reduces the MAPE value by 1.99%, 3.24%, and 0.72% respectively. In terms of density estimation, the hybrid model reduces the MAE by 23.6%, 31.7%, and 8.3% respectively, and reduces the MAPE value by 6.81%, 8.27%, and 2.12% respectively. In terms of flow estimation, the hybrid model reduces the MAE by 26.2%, 33.3%, and 4.4% respectively, and reduces the MAPE value by 7.06%, 7.55%, and 1.39% respectively.

[0101] Under the congested state, the hybrid model demonstrates excellent performance in all evaluation metrics. The hybrid model has the lowest MAE: the MAE of speed is 1.66 km / h, the MAE of density is 3.48 vehicles / km / lane, and the MAE of flow is 84.43 vehicles / hour / lane. It also has the lowest MAPE in terms of speed, density, and flow, which are 14.66% for speed, 6.13% for density, and 9.97% for flow. In terms of speed estimation, compared with the traditional CTM, GRU model, and GCN model, the hybrid model reduces the MAE by 23.1%, 25.9%, and 10.3% respectively, and reduces the MAPE value by 8.03%, 12.68%, and 1.58% respectively. In terms of density estimation, compared with the three baseline models, the hybrid model reduces the MAE by 41.3%, 38.3%, and 7.2% respectively, and reduces the MAPE value by 1.98%, 1.71%, and 0.5% respectively. In terms of flow estimation, the hybrid model reduces the MAE by 24.8%, 30.2%, and 9.4% respectively, and reduces the MAPE value by 7.98%, 12.17%, and 3.15% respectively. The results show that integrating machine learning methods into the spatio-temporal discretized traffic flow model can improve the estimation accuracy under different traffic conditions.

[0102] Table 2 Comparison Effect Table of the Hybrid Model and Basic Models in Experiment 2

[0103]

Claims

1. A freeway traffic state estimation method integrating a traffic flow model and a graph neural network, characterized in that It includes the following steps: S1: Discretize the highway into cells of a fixed length, and represent the traffic state of each cell with three parameters: flow, density, and speed; S2: Use the traffic wave speed between any two cells to determine the active influence area and the area that will be affected by a cell within a time period; S3: Transform the discretized cell traffic state and adjacency information into graph-structured data, design a graph neural network to update the traffic state of all cells, and establish a spatio-temporal evolution model of the cell traffic state; S4: Based on the updated cell traffic state, use the gradient descent method to optimize the spatio-temporal evolution model of the cell traffic state, and obtain the highway traffic state estimation result.

2. The freeway traffic state estimation method integrating a traffic flow model and a graph neural network according to claim 1, wherein In the step S1, the main road of the highway is cut into cells of the same length ΔX according to the cellular automaton model, and their numbers are 1, 2, …, N; the vehicle movement trajectories on the road section are cut into a continuous time series at time intervals ΔT, and the traffic state X of the cells in different time periods is calculated according to the vehicle trajectory information in each cell x,t , including density k x,t , speed v x,t and flow q x,t .

3. The freeway traffic state estimation method integrating a traffic flow model and a graph neural network according to claim 2, characterized in that The specific content of step S2 includes: For any cell x, use the density k of adjacent cells x,t and the flow q x,t to calculate the propagation directions {x - 1:x} and {x:x + 1} and the speed of the traffic wave between the cell and its upstream and downstream cells and accordingly determine the upstream and downstream spatial influence ranges D u,x,t = ω x-1:x,t ×ΔT and D d,x,t = ω x:x+1,t ×ΔT; thus obtaining the corresponding number of upstream and downstream influencing cells and The corresponding upstream influencing cell region is {x - 1, …, x - m u,x,t}, and the downstream influence region is {x + 1, …, x + m d,x,t}; For any cell y, traverse cells 1, 2, … x, …, y - 1. If the downstream influence region of cell x {x + 1, …, x + m d,x,t} contains cell y, then the farthest upstream influencing cell x of cell y is found, and thus the number n of upstream cells influencing cell y is obtained u,y,t , and the traversal stops; for any cell y, traverse cells N, N - 1, … x, …, y + 1. If the upstream influence region of cell x {x - 1, …, x - m u,x,t} contains cell y, then the farthest downstream influencing cell x of cell y is found, and thus the number n of downstream cells influencing cell y is obtained d,y,t , and the traversal stops; For the number n of upstream cells of any cell y u,y,t and the number n of downstream cells d,y,t , calculate the maximum number n of cells that can have an impact corresponding to the cell y,t = max{n u,y,t n d,y,t}. Traverse the number of upstream and downstream cells that can have an impact on all cells to determine the maximum number n of cells that can have the farthest impact among all cells update,t = max{n u,1,t ,…, n u,N,t , n d,1,t ,…, n d,N,t}.

4. A freeway traffic state estimation method integrating a traffic flow model and a graph neural network according to claim 3, characterized in that In step S3, for any cell, use the traffic states of all cells that will affect this cell within a time period to update the traffic state of this cell. The specific content includes: Combined with the density, speed, and flow update methods in cellular automata, a hybrid model with a circular traffic state update structure is proposed. Through the longest influence quantity n update,t Determine the number of circular updates; In an update i, if it is the first update, the traffic states X of all cells observed at the previous moment are used as the input. For subsequent updates, the output of the previous update i - 1 is used as the input for this update i, and the output is 1:N,t where the output of the update is composed of and During the update process, for each cell y, the traffic state of the cell itself , the traffic states of adjacent cells , the traffic wave speed and are used to calculate the change in the upstream and downstream traffic states of cell y: and Then, the traffic state of the cell itself , the change in the upstream and downstream traffic states of cell y , andare used to update the cell state ​ After the update is completed, traverse all cells. If the current count i reaches the maximum number n of cells affected by cell y y,t , then the traffic state update of cell y is completed 5. The freeway traffic state estimation method integrating a traffic flow model and a graph neural network according to claim 4, characterized in that The specific way for the graph neural network in step S3 to update the traffic states of all cells is: A graph neural network that conforms to the upstream and downstream adjacency relationships of cells is proposed. The traffic states and adjacency relationships of cells on a road section are transformed into a graph structure G=(V, e), and a message passing and updating network consistent with the spatio-temporal transfer of traffic states is constructed in the graph neural network. On the basis of conforming to the traffic state transfer logic, the spatio-temporal correlations hidden in the data are extracted, so as to complete the modeling of traffic flow evolution within a time period and the estimation of cell states X in the next time period y,t+1 ; For each update, the traffic states X of all cells observed at the previous moment are used 1:N,t as the input. For subsequent updates, the output of the previous update i - 1 is used as the input for this update i. In update i, first, a cell connection relationship matrix is initialized where represents a directed edge of a cell connection relationship, where M represents the number of directed connection edges of all cells; and represent the departure cell and the arrival cell of the directed edge e, respectively; represents the traffic wave speed of the directed edge e; represents the traffic state transfer amount of the directed edge e. Then, the traffic wave speed and traffic state transfer amount of each cell connection directed edge in the cell connection relationship matrix are calculated. The expression for the traffic wave speed of the directed edge is: The expression of the traffic state transfer amount of the directed edge connected to each cell is: where W1, b1, W2, b2, W3, and b3 are the parameter matrices of the three-layer fully connected neural network; Finally, the connection relationship matrix is converted into a matrix with dimensions R×R The expression for calculating the state update of all cells is as follows: where ⊙ represents matrix dot product; W h and b h are parameter matrices; W ONE represents a matrix of all 1s; After completing the update of i, traverse all cells. If the current count i reaches the maximum number of influencing cells n of cell y y,t , then the traffic state update of cell y is completed 6. The freeway traffic state estimation method integrating a traffic flow model and a graph neural network according to claim 5, characterized in that In step S4, use the gradient descent method to optimize the spatio-temporal evolution model of the cell traffic state. The specific content includes: First, use the observed state values X of all cells x,t Calculate the average values μ(k), μ(v), σ(q) of flow, density, and velocity, and the standard deviations σ(q), σ(k), σ(v). Then, normalize the estimated and observed values for the time period t+1. The normalization calculation is as follows: Among them, represents the traffic estimation value in the time period of t + 1; represents the density estimation value in the time period of t + 1; represents the speed estimation value in the time period of t + 1; represents the traffic observation value in the time period of t + 1; represents the density observation value in the time period of t + 1; represents the speed observation value in the time period of t + 1; Calculate the mean absolute error using the normalized traffic state values. Based on the obtained error, use the gradient descent method to update the parameters of the model f(·|θ) until the error is reduced to a stable state, at which point the best spatio-temporal evolution model of the traffic state is obtained. ​ 7. A highway traffic state estimation system integrating a traffic flow model and a graph neural network, characterized in that, It includes: A discretization module, which is used to discretize the highway into cells of a fixed length, and represent the traffic state of each cell with three parameters: flow, density, and speed; A model establishment module, which is used to use the traffic wave speed between any two cells to determine the active influence area and the area that will be affected by a cell within a time period, and establish a spatio-temporal evolution model of the cell traffic state; A state update module, which is used to transform the discretized cell traffic state and adjacency information into graph-structured data, and design a graph neural network to update the traffic states of all cells; A model optimization module, which is used to use the gradient descent method to optimize the spatio-temporal evolution model of the cell traffic state, and obtain the highway traffic state estimation result.

8. A computer storage medium, characterized in that: The computer storage medium stores a program for a highway traffic state estimation method that fuses a traffic flow model and a graph neural network. When the program for the highway traffic state estimation method that fuses a traffic flow model and a graph neural network is executed by at least one processor, it implements the steps of the highway traffic state estimation method described in any one of claims 1 to 6.

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