Expressway missing traffic state estimation method based on physical information guide neural network

Abstract

The invention discloses an expressway missing traffic state estimation method based on a physical information guide neural network, and the method comprises the steps: carrying out the time-space discretization of two detectors and a middle non-detection road segment of an expressway, and enabling the cellular states of the installation positions of the two detectors to be observable traffic states; the states of all cells in the non-detection area are to-be-estimated traffic states; a bidirectional traffic state estimation framework from upstream to downstream and from downstream to upstream is provided, a neural network is designed based on a traffic state estimation model, a downstream boundary cellular state is utilized to carry out iterative estimation on all upstream cellular states, and an upstream boundary cellular state is utilized to carry out iterative estimation on all downstream cellular states. And the bidirectional estimation result is fused to form a final estimation result. According to the method, the accuracy and reliability of missing traffic state estimation can be improved, meanwhile, the interpretability of the model is ensured, the expressway traffic flow time-space evolution mechanism can be accurately grasped, and the full-time-space domain traffic state of the expressway target area can be estimated in real time.

Description

Technical Field

[0001] This invention relates to a method for estimating missing traffic states on highways based on a physical information-guided neural network, belonging to the technical field of the intersection of highway traffic control technology and data information processing technology. Background Technology

[0002] Accurate and reliable macroscopic traffic flow models and missing traffic state estimation methods are crucial for modeling and interpreting the spatiotemporal evolution of traffic flow, estimating traffic states, perceiving states across the entire time and space domain, quantifying emissions and fuel consumption, optimizing ramp control, and managing highway emergencies. An effective missing traffic state estimation model should possess three key characteristics: (1) strong interpretability in estimating missing traffic states; (2) high accuracy in estimating key traffic state variables such as flow rate, speed, and density; and (3) universal applicability under various traffic conditions.

[0003] The key to constructing a reliable model for estimating missing traffic states on highways lies in an estimation method with a solid theoretical foundation. Existing missing traffic state estimation methods can be roughly divided into three categories: (1) models based on traffic flow theory; (2) models based on neural networks; and (3) hybrid models that integrate traffic flow and neural networks. Models based on traffic flow theory perform well in describing the evolution process and mechanism of traffic states and estimating missing states under ideal conditions. In existing studies, researchers qualitatively describe free-flow and congested flows and use fixed parameters to represent the state correlation and state estimation model under free-flow and congested flow states. This allows for the estimation of traffic states in intermediate undetected areas using upstream and downstream observations, making the estimation method simple and effective. Models based on neural networks start from the data itself and use the data mining capabilities of neural networks to extract the correlation of traffic states between different spatiotemporal locations for traffic state estimation. Models based on neural networks perform well when there is sufficient training data, but they have high requirements for the quality and quantity of training data.

[0004] Although there are currently limited hybrid models that explore how to model traffic flow and neural networks, they mainly focus on the design of loss functions for neural networks. In this case, the model estimation results conform to a certain traffic flow physical model, but the interpretability of the model itself is poor. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to propose a method for estimating missing traffic states on highways based on physical information-guided neural networks, so as to improve the interpretability, accuracy and generalization ability of missing traffic state estimation on highways, accurately grasp the spatiotemporal evolution mechanism of highway traffic flow, and help traffic design and management departments optimize highway design and reconstruction plans and formulate reasonable and effective real-time control and guidance strategies.

[0006] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] A method for estimating missing traffic states on highways based on physical information-guided neural networks includes the following steps:

[0008] For traffic state detectors at two cross-sections of a highway and the undetected areas within the two detectors, the road is discretized in time and space. The traffic state of the upstream and downstream boundary cells at different time periods is statistically analyzed to estimate the traffic state of cells in the undetected areas.

[0009] Based on the relationship between the change of cell density over a time period and the state of the cell itself and the inflow and outflow traffic volume over a time period, a spatiotemporal evolution model of the traffic state of a cell over a time period is constructed. Based on the spatiotemporal evolution model of the traffic state, a traffic state estimation model is established for four roles: upstream cell of the core cell, downstream cell of the core cell, current time of the core cell, and next time of the core cell.

[0010] A neural network is designed based on the constructed traffic state estimation model. It iterative estimation of the states of all upstream cells is performed using the states of downstream boundary cells, and iterative estimation of the states of all downstream cells is performed using the states of upstream boundary cells. The estimation results from downstream boundary to upstream and from upstream boundary to downstream are then fused to form the final estimation result. In the neural network, corresponding relation matrices are designed for target cells with different roles to describe the relationship between the target cell state and other potential traffic state parameters. An attention neural network for estimating the state of the target cell is designed based on the relation matrices.

[0011] Design a neural network loss function and use gradient descent to optimize the neural network model; the loss function considers bidirectional estimation bias and the error between the estimation and the observation.

[0012] Preferably, the step of designing corresponding relationship matrices for target cells with different roles to describe the relationship between the target cell state and other potential traffic state parameters includes:

[0013] When estimating the state of an upstream cell using the observed states of downstream neighboring cells, if the target cell is an upstream cell of the core cell, a first relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a first neural network for estimating the target cell state is designed accordingly. When the target cell is the core cell at the current time, a second relationship matrix is ​​defined to describe the target cell state and the other potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a second neural network for estimating the target cell state is designed. When the target cell is the core cell at the next time step, a third relation matrix is ​​defined to describe the target cell state and the remaining potential traffic state parameters. The relationship is established, and a third neural network for estimating the state of the target cell is designed; where i and j are used to label the cell number and time number, respectively, X represents the traffic state, ω represents the traffic wave velocity, Δx and Δt represent the spatial length and time length of each unit after spatiotemporal discretization, respectively, DU is used to label the direction from downstream to upstream, UA is used to label the upstream cell, C is used to label the core cell, and TS is used to label the next time step.

[0014] When estimating the state of downstream cells using the observed states of upstream neighboring cells, if the target cell is a downstream cell of the core cell, a fourth relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a fourth neural network for estimating the target cell state is designed. When the target cell is the core cell at the current time, a fifth relation matrix is ​​defined to describe the target cell state and the remaining potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a fifth neural network for estimating the target cell state is designed. When the target cell is the core cell at the next time step, a sixth relation matrix is ​​defined to describe the target cell state and the remaining potential traffic state parameters. The relationship is established, and a sixth neural network for estimating the state of the target cell is designed; UD is used to label the direction from upstream to downstream, and DA is used to label the downstream cell.

[0015] As a preferred approach, when estimating the state of the upstream cell using the observed states of the downstream neighboring cells, the state estimation results are obtained when the target cell is used as the upstream cell of the core cell, the current time of the core cell, and the next time of the core cell. and Define the final estimated state of the target cell and three initial states. The seventh relation matrix between them is used to design a fusion neural network from downstream to upstream.

[0016] When using the observed states of upstream neighboring cells to estimate the state of downstream cells, the state estimation results are obtained when the target cell is used as the downstream cell of the core cell, at the current time of the core cell, and at the next time of the core cell. and Define the final estimated state of the target cell and three initial states. The eighth relation matrix between them is used to design a fusion neural network from upstream to downstream.

[0017] Preferably, the iterative estimation of the states of all upstream cells using the states of downstream boundary cells includes: traversing from the downstream boundary cells to the upstream boundary cells, and simultaneously traversing all time steps in each cell state estimation. For the state of any traversed cell in any time period, it is respectively assigned to three roles: the upstream cell of the core cell, the current state of the core cell, and the state of the core cell at the next time, participating in the corresponding spatiotemporal evolution of traffic state. When the cell is assigned to three different roles, three different estimation results are obtained, and the three different estimation results are fused to obtain the final estimation result.

[0018] The method of iteratively estimating the states of all downstream cells using the states of upstream boundary cells includes: traversing from upstream boundary cells to downstream boundary cells, and simultaneously traversing all time steps in each cell state estimation. For any traversed cell in any time period, the state is assigned to three roles: the downstream cell of the core cell, the current state of the core cell, and the state of the core cell at the next time step, respectively, and participates in the spatiotemporal evolution of the three corresponding traffic states. When the cell takes on three different roles, three different estimation results are obtained, and the three different estimation results are fused to obtain the final estimation result.

[0019] Preferably, in the traffic state estimation model that establishes the target cell as one of four roles—upstream cell of the core cell, downstream cell of the core cell, current time of the core cell, and next time of the core cell—the estimation model for the cell at different positions during a single state transition, combined with the cellular automaton state transition model and the traffic wave propagation model, is as follows:

[0020] When the upstream cell density of the core cell is missing, the estimation model is as follows:

[0021]

[0022] When the core cell density is missing, the estimation model is:

[0023]

[0024] When the downstream cell density of the core cell is missing, the estimation model is as follows:

[0025]

[0026] When the density of the core cell is missing in the next time step, the estimation model is:

[0027]

[0028] Where i and j are used to mark the cell number and time number respectively, k represents the density, ω represents the traffic wave velocity, Δx and Δt represent the spatial length and time length of each unit after spatiotemporal discretization respectively, UA is used to mark the upstream cell, C is used to mark the core cell, DA is used to mark the upstream cell, TS is used to mark the next time, f is used to characterize the functional relationship, and the superscript number is used to distinguish different functions.

[0029] As a preferred embodiment, the first to sixth neural networks adopt the following form:

[0030]

[0031] in, The state estimation result for the target cell; I i,j These are the corresponding traffic state parameters; A i,j This is the corresponding relation matrix; W1, W2, b1, and b2 are the neural network parameters; W ONE T Let Γ be a parameter matrix consisting entirely of 1s; Γ(·) is the activation function of the neural network.

[0032] As a preferred option, the downstream-to-upstream fusion neural network is as follows:

[0033]

[0034] The upstream-to-downstream fusion neural network is as follows:

[0035]

[0036] in, and These are the final state estimation results in two directions, respectively; and These are the corresponding relation matrices; and as well as and For neural network parameters; W ONE T Let Γ be a parameter matrix consisting entirely of 1s; Γ(·) is the activation function of the neural network.

[0037] As a preferred method, utilize two-way estimation bias. and the error between the estimated and observed values The loss function is loss = α × loss m +(1-α)×loss o The model parameters are updated; where N represents the number of cells and J represents the number of time steps. and Let represent the estimated flow rate, density, and velocity, respectively. DU is used to label the direction from downstream to upstream, UD is used to label the direction from upstream to downstream, ub and db are used to label the corresponding cells of the upstream and downstream detectors, respectively, q, k, and v represent the observed flow rate, density, and velocity, respectively, and α is the weight.

[0038] A computer system includes a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, wherein the computer program / instructions, when executed by the processor, implement the steps of the method for estimating missing traffic states of a highway based on a physical information-guided neural network.

[0039] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the described method for estimating missing traffic states on highways based on a physical information-guided neural network.

[0040] Beneficial Effects: This invention proposes a method for estimating missing traffic states on highways based on a physically guided neural network. It presents an iterative estimation framework from downstream boundary cells to upstream cells and from upstream boundary cells to downstream cells, fusing bidirectional results to form the optimal state estimation result. In each bidirectional iteration step, a traffic state estimation model for any missing cell is constructed based on a discretized traffic flow model cellular automata, improving model interpretability. Simultaneously, an attention neural network is introduced for modeling the estimation method, better uncovering the spatiotemporal correlation between the cell to be estimated and the observed cells while conforming to the spatiotemporal evolution of traffic states, thus improving the model's accuracy and generalization ability. The bidirectional estimation bias and the error between the estimated and observed values ​​are used as loss functions to adjust and optimize model parameters, thereby obtaining the optimal missing state estimation model. The proposed method can effectively improve the interpretability, accuracy, and generalization ability of missing traffic state estimation on highways, accurately grasp the spatiotemporal evolution mechanism of highway traffic flow, and help traffic design and management departments optimize highway design and renovation schemes, formulate reasonable and effective real-time control and guidance strategies, thus having practical application value for alleviating highway traffic congestion. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the overall process of an embodiment of the present invention.

[0042] Figure 2 This is a flowchart of the bidirectional missing traffic state estimation method used in this embodiment of the invention. Detailed Implementation

[0043] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0044] like Figure 1 As shown in the embodiment of the present invention, a method for estimating missing traffic states on highways based on a physical information-guided neural network is disclosed. First, for traffic state detectors at two cross-sections of the highway and the undetected areas within those detectors, the road is spatiotemporally discretized. The traffic states of upstream and downstream boundary cells at different time periods are statistically analyzed to estimate the traffic states of cells in the undetected areas. Next, based on the relationship between cell density changes over a time period, cell states, and inflow / outflow traffic volume, a spatiotemporal evolution model of the traffic state of a cell over a time period is constructed. Based on this model, a target cell is established as the upstream cell of the core cell, the downstream cell of the core cell, the current time of the core cell, and the core cell itself. The system first constructs a traffic state estimation model for each of the four roles at the next time step. Then, based on this model, a neural network is designed to iteratively estimate the states of all upstream cells using the downstream boundary cell state, and vice versa. The estimation results from the downstream boundary to the upstream and from the upstream boundary to the downstream are then fused to form the final estimation result. Within this neural network, a corresponding relation matrix is ​​designed for each target cell with a different role to describe the relationship between the target cell state and other potential traffic state parameters. An attention neural network for estimating the state of the target cell is then designed based on this relation matrix. Finally, a loss function for the neural network is designed, and the gradient descent method is used to optimize the neural network model.

[0045] Specifically, the highway missing traffic state estimation method based on physical information-guided neural networks described in this embodiment includes the following steps:

[0046] The first step is to perform spatiotemporal discretization of the road for the two traffic condition detectors at the two cross-sections of the highway and the undetected areas within the two detectors.

[0047] In this embodiment, based on the cellular automata model, the two detectors on the highway and the undetected area between them are divided into cells of the same length Δx. The cells corresponding to the upstream and downstream detectors are numbered ub and db, respectively, and the cells corresponding to the area where the traffic state is to be estimated are numbered 1, 2, ..., N. The traffic state of the upstream and downstream boundary cells at different time periods, including the flow rate q, is statistically analyzed at certain time intervals Δt. x,t Density k x,t and speed v x,tWe use the traffic states of two boundary cells to estimate the traffic states of undetected region cells at all times.

[0048] The second step is to construct a spatiotemporal evolution model of traffic status for any given cell over a given time period.

[0049] Specifically, for any target cell core at any time, the change in its density over a time period (k) TS -k core The state of the cell itself and the inflow and outflow traffic volume within a certain time period are both factors. and It is determined that the core cell density change process can be represented as: That is, the density change of the core cell from the current time to the next time is related to the inflow and outflow traffic flow of the core cell in the current time period. At the same time, the flow, density and speed conform to the basic graph relationship. Therefore, during a state transition process, the flow, density, speed and traffic wave speed of different cells influence each other. Here, Δx and Δt represent the spatial length and time length of each cell after spatiotemporal discretization, respectively.

[0050] The inflow and outflow traffic flow calculation model for the core cells is designed as follows: and That is, the inflow traffic volume of the core cell is related to the core cell density, the upstream cell density, and the core cell traffic wave, where ω represents the traffic wave velocity of the cell. Simultaneously, in the core cell traffic wave ω... core When the core cell is greater than or equal to 0, the inflow of traffic is... Only with the upstream cell density k UA The outflow traffic volume of the core cell is related to the core cell density, the downstream cell density, and the downstream cell traffic wave. Simultaneously, the downstream cell traffic wave ω... DA When the core cell outflow is greater than or equal to 0, the outflow of traffic is... Only the density k of the core cell itself core Related; based on the calculation of inflow and outflow traffic volume in the core cells, the current density k of the core cells. core The density k of the core cell at the next time step TS The density k of downstream adjacent cells DA Traffic wave velocity ω DA The density k of the upstream adjacent cells UA Core cell traffic wave velocity ω core The relationship model can be represented as:

[0051]

[0052] in, This represents the number of traffic flow transfers occurring between adjacent upstream and downstream cells when the traffic wave velocity of the downstream cell is less than 0. This represents the number of traffic flow transfers occurring between adjacent upstream and downstream cells when the traffic wave velocity of the downstream cell is greater than or equal to 0, and the transfer flow is only related to the density of the upstream cell.

[0053] The third step is to design an estimation model for the missing state of any cell by using a spatiotemporal evolution model of traffic state within a time period.

[0054] In this embodiment, based on the spatiotemporal evolution model of traffic state, traffic state estimation models are established for four roles: upstream cell of core cell, downstream cell of core cell, current time of core cell, and next time of core cell.

[0055] Based on the spatiotemporal evolution model of traffic conditions, when the upstream cell density of the core cell is missing, it can be estimated using the states of the remaining cells. The estimation model is as follows:

[0056]

[0057] Where i and j are used to mark the cell number and time number respectively, k represents the density, and ω represents the traffic wave velocity. This refers to a method for estimating the upstream cell density of the core cell when the traffic wave velocities of upstream cells i+1 and i+2 are both less than 0. This describes a method for estimating the upstream cell density of the core cell when the traffic wave velocity in upstream cell i+1 is less than 0 and the traffic wave velocity in cell i+2 is greater than or equal to 0. This describes a method for estimating the upstream cell density of the core cell when the traffic wave velocity in upstream cell i+1 is greater than or equal to 0 and the traffic wave velocity in cell i+2 is less than 0. This refers to a method for estimating the upstream cell density of the core cell when the traffic wave velocities of upstream cells i+1 and i+2 are both greater than or equal to 0.

[0058] Based on the spatiotemporal evolution model of traffic conditions, when the core cell density is missing, it can be estimated using the states of the remaining cells. The estimation model is as follows:

[0059]

[0060] in, This refers to a core cell density estimation method when the traffic wave velocities of both core cell i and downstream cell i+1 are less than 0. This describes a core cell density estimation method when the traffic wave velocity of core cell i is less than 0 and the traffic wave velocity of downstream cell i+1 is greater than or equal to 0. This describes a core cell density estimation method when the traffic wave velocity of core cell i is greater than or equal to 0 and the traffic wave velocity of downstream cell i+1 is less than 0. This refers to a core cell density estimation method when the traffic wave velocities of both core cell i and downstream cell i+1 are greater than or equal to 0.

[0061] Based on the spatiotemporal evolution model of traffic conditions, when the density of downstream cells of the core cell is missing, it can be estimated through the states of the remaining cells. The estimation model is as follows:

[0062]

[0063] in, This describes a method for estimating the density of core cells and downstream cells when the traffic wave velocities of both core cell i-1 and downstream cell i are less than 0. This describes a method for estimating the density of core cells and downstream cells when the traffic wave velocity of core cell i-1 is greater than or equal to 0 and downstream cell i is less than 0.

[0064] Based on the spatiotemporal evolution model of traffic conditions, when the density of the core cell in the next time step is missing, it can be estimated using the states of the remaining cells. The estimation model is as follows:

[0065]

[0066] in, This refers to the method for estimating the density of the core cell at the next time step when the traffic wave velocities of both the core cell i and the downstream cell i+1 are less than 0 at time j-1. This refers to the method for estimating the density of the core cell at the next time step when the traffic wave velocity of the core cell i is less than 0 and the traffic wave velocity of the downstream cell i+1 at time j-1 is greater than or equal to 0. This refers to the method for estimating the density of the core cell at the next time step when the traffic wave velocity of the core cell i at time j-1 is greater than or equal to 0 and the traffic wave velocity of the downstream cell i+1 at time j-1 is less than 0. This refers to the density estimation method for the core cell at the next time step when the traffic wave velocities of both the core cell i and the downstream cell i+1 at time j-1 are greater than or equal to 0.

[0067] The fourth step is to use the downstream boundary cell state to iteratively estimate the states of all upstream cells.

[0068] In this embodiment, as Figure 2On the left side, traverse from the downstream boundary cell to the upstream boundary cell, and at the same time, traverse all time steps in the state estimation of each cell. For the state of any cell traversed at any time period, it can serve as the upstream cell of the core cell, the current state of the core cell, and the next state of the core cell, respectively, and participate in three traffic state spatio-temporal evolution processes. When the cell serves as three different roles, three different estimation results are obtained using the corresponding estimation models. When the cell is the upstream cell of the core cell, when estimating the upstream adjacent cell i = N of the downstream boundary cell, the cell db+1 cannot be observed. At this time, its density estimation is as follows:

[0069]

[0070] The traffic parameters of flow, density, and speed conform to the fundamental diagram model of traffic flow, that is, q = k × v, and at the same time, v = FD(k), where FD(·) represents the relationship between speed and density. Therefore, speed and flow can be obtained from density, and the estimation of the cell traffic state (flow, density, and speed) is as follows: <​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0079] Table 1 Applicable Conditions for Various Traffic Condition Estimation Methods

[0080]

[0081] The final estimation result is obtained by combining the three estimation results:

[0082]

[0083] Among them, h D-U,1 (·) represents the fusion model of traffic state estimation results when the traffic wave velocity of cell i+1 is less than 0 at times j and j-1; h D-U,2 (·) represents the fusion model of traffic state estimation results when the traffic wave velocity of cell i+1 at time j is less than 0 and the traffic wave velocity at time j-1 is greater than or equal to 0; h D-U,3 (·) represents the fusion model of traffic state estimation results when the traffic wave velocity of cell i+1 at time j is greater than or equal to 0 and the traffic wave velocity at time j-1 is less than 0; h D-U,4 (·) represents the traffic state estimation result fusion model when the traffic wave velocity of cell i+1 is greater than or equal to 0 at times j and j-1;

[0084] The fifth step is to estimate the states of all downstream cells to be estimated using the same framework, starting from the upstream boundary states.

[0085] Similar to step four, such as Figure 2 To the right, traversing from the upstream boundary cell to the downstream boundary cell, and simultaneously traversing all time steps in each cell state estimation, the state of any traversed cell in any time period can be assigned one of three roles: downstream cell of the core cell, current state of the core cell, and next state of the core cell, participating in the spatiotemporal evolution of the three traffic states. When a cell plays one of these three different roles, three different estimation results are obtained using the corresponding estimation model. When the cell is a downstream cell of the core cell, and when estimating the upstream neighboring cell i=1 of the downstream boundary cell, cell ub-1 is unobservable. In this case, its density estimation is as follows:

[0086]

[0087] Traffic parameters flow rate, density, and speed conform to the basic graphical model of traffic flow, i.e., q = k × v, where v = FD(k), and FD(·) represents the relationship between speed and density. Therefore, speed and flow rate can be obtained from density. The cellular traffic state (flow rate, density, and speed) is estimated as follows:

[0088]

[0089] When the upstream neighboring cell i>1 of the downstream boundary cell is estimated, all cells are observable. At this time, the state of the target cell is estimated as follows:

[0090]

[0091] When the target cell is the core cell at the current moment, only the state of the upstream cell of the core cell can be observed. and After removing unobservable inputs, the final target cell state estimate is as follows:

[0092]

[0093] When this cell is the next time step of the core cell, only the state of the cell upstream of the core cell can be observed. and After removing unobservable inputs, the final state estimate is as follows:

[0094]

[0095] The estimation methods and conditions for upstream boundary estimation and downstream cell estimation are shown in Table 2:

[0096] Table 2 Applicable Conditions for Various Traffic State Estimation Methods

[0097]

[0098] The final estimation result is obtained by combining the three estimation results:

[0099]

[0100] Among them, h U-D,1 (·) represents the fusion model of traffic state estimation results when the traffic wave velocity of cell i at time j is less than 0; h D-U,2 (·) represents the fusion model of traffic state estimation results when the traffic wave velocity of cell i at time j is greater than or equal to 0.

[0101] The sixth step is to merge the estimation results from the downstream boundary to the upstream boundary and the estimation results from the upstream boundary to the downstream boundary to form the final estimation result.

[0102] Estimate results from downstream boundary to upstream estimation results from upstream boundary to downstream The fusion model is as follows:

[0103]

[0104] in, and The weights of the states estimated at the downstream boundary and the states estimated at the upstream boundary are respectively assigned.

[0105] Step 7: Introduce an attention neural network to perform the traffic state estimation calculations described above.

[0106] In this embodiment, a corresponding relation matrix is ​​designed for the target cells with different roles to describe the relationship between the target cell state and other potential traffic state parameters, and an attention neural network for estimating the state of the target cell is designed based on the relation matrix.

[0107] The neural network design is as follows when estimating the possible states of all upstream cells from the downstream boundary cell:

[0108] When the target cell is an upstream cell of the core cell, a first relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship is as follows:

[0109]

[0110] The target cell state estimation neural network is designed as follows:

[0111]

[0112] in, The state estimation result is when the target cell is an upstream cell of the core cell; It is the correlation matrix of input parameters; and For neural network parameters; W ONE T Let be a parameter matrix consisting entirely of 1s; softmax(·) is a function that calculates the output values ​​using an exponential distribution and then calculates the proportion of each calculated value to the total size; Γ(·) is the activation function of the neural network; ⊙ represents the Hadamard product of matrices, which is the direct multiplication of corresponding elements of two matrices, resulting in a matrix with the same dimension as the input. This represents the Kronecker product, which is the complete multiplication of each element of the previous matrix with the next matrix. The resulting matrix has dimensions of "number of rows in the previous matrix × number of rows in the next matrix" × "number of columns in the previous matrix × number of columns in the next matrix".

[0113] When the target cell is the core cell at the current time, a second relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship is as follows:

[0114]

[0115] The target cell state estimation neural network is designed as follows:

[0116]

[0117] in, The state estimation result is given when the target cell is used as the core cell. It is the correlation matrix of input parameters; and For neural network parameters;

[0118] When the target cell is the core cell at the next time step, a third relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship is as follows:

[0119]

[0120] The target cell state estimation neural network is designed as follows:

[0121]

[0122] in, The state estimation result for the target cell as the core cell at the next time step; It is the correlation matrix of input parameters; and For neural network parameters;

[0123] Obtain the state estimation results of the target cell as the upstream cell of the core cell, the current time step of the core cell, and the next time step of the core cell. and Define the final estimated state of the target cell and three initial states. The relationship between them is:

[0124]

[0125] The fusion model design for the final state estimation results is as follows:

[0126]

[0127] in, This is the final state estimation result; It is the correlation matrix of input parameters; and For neural network parameters;

[0128] When estimating the possible states of all downstream cells from the upstream boundary cell, the neural network design is as follows:

[0129] When the target cell is a downstream cell of the core cell, a fourth relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship is as follows:

[0130]

[0131] The target cell state estimation neural network is designed as follows:

[0132]

[0133] in, The state estimation result is given when the target cell is a downstream cell of the core cell. It is the correlation matrix of input parameters; and These are the parameters of the neural network.

[0134] When the target cell is the core cell at the current time, a fifth relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship is as follows:

[0135]

[0136] The target cell state estimation neural network is designed as follows:

[0137]

[0138] in, The state estimation result is given when the target cell is used as the core cell. It is the correlation matrix of input parameters; and For neural network parameters;

[0139] When the target cell is the core cell at the next time step, the sixth relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship is as follows:

[0140]

[0141] The target cell state estimation neural network is designed as follows:

[0142]

[0143] in, The state estimation result for the target cell as the core cell at the next time step; It is the correlation matrix of input parameters; and For neural network parameters;

[0144] Obtain the state estimation results of the target cell as a downstream cell of the core cell, at the current time step of the core cell, and at the next time step of the core cell. and Define the final estimated state of the target cell and three initial states. The relationship between them is:

[0145]

[0146] The fusion model design for the final state estimation results is as follows:

[0147]

[0148] in, This is the final state estimation result; It is the correlation matrix of input parameters; and For neural network parameters;

[0149] Step 8: Design the neural network loss function and optimize the neural network model using gradient descent.

[0150] In this embodiment, the loss function considers both-way estimation bias and the error between the estimation and the observed values. Specifically:

[0151] The first type of loss function for designing neural networks is the error of bidirectional estimation:

[0152]

[0153] The second type of loss function for designing neural networks is the observation error:

[0154]

[0155] The total error of the neural network design is:

[0156] loss = α × loss m +(1-α)×loss o

[0157] Based on the obtained error, the gradient descent method is used to update the model parameters until the error converges to a steady state, at which point the optimal traffic state estimation model is obtained.

[0158] To demonstrate the effectiveness of this invention, this embodiment uses trajectory data collected by six roadside millimeter-wave radars on the Chengdu Expressway for case analysis.

[0159] Trajectory data acquisition: Roadside millimeter-wave radar was used as the data acquisition device. Six sections of the Chengdu Expressway were selected as target areas, and the six target areas were divided into 10 experiments. The traffic state division intervals for the first five experiments were 50 meters and 1 second, and for the last five experiments, the intervals were 50 seconds and 5 seconds. The number of cells to be estimated for the target areas in experiments 1 to 5 were 10, 20, 35, 100, and 180, respectively, and the number of cells to be estimated for the target areas in experiments 6 to 10 were 20, 35, 80, 200, and 360, respectively. The flow rate, density, and velocity of each cell within each time interval were calculated using the following model:

[0160] q x,t =k x,t ×v x,t

[0161]

[0162] Where i represents the target vehicle number; d i This represents the headway between the i-th vehicle and the vehicle in front within the t-th time interval of the x-th interval of the road segment; v i Let A represent the driving speed of the i-th vehicle in the x-th interval and the t-th time period of the road segment; let A represent the total number of vehicles detected in the x-th interval and the t-th time period of the road segment.

[0163] Calculation Results: This paper presents a method for estimating missing traffic states on highways based on a physically-informed guided neural network. A bidirectional estimation framework is designed, iteratively estimating from downstream boundary observation cells to upstream cells and from upstream boundary observation cells to downstream cells. In the estimation process in both directions, a theoretical model is constructed based on a discretized traffic flow model cellular automata. The evolution of traffic state within a core cell over a time period is used as a basis. For any missing cell state, a model is designed to estimate the missing cell state using the states of the remaining cells. By introducing nonlinear modeling with an attention neural network, the model better uncovers the latent spatiotemporal relationships between cells while adhering to traffic flow principles, thus improving the accuracy and reliability of the model. The difference between the bidirectional estimations and the error between the estimated and observed values ​​at the two boundaries are used as loss functions to adjust and optimize the model parameters.

[0164] To verify the robustness of the model, five different base graphs were used in Experiments 1 to 5: the Underwood model, the Drake model, the S3 model, the 4PL model, and the Pipe's model. The corresponding estimated percentage errors of the relative loss are shown in Table 3.

[0165] Table 3 compares the performance of traffic state estimation results under different basic graphical models selected in Experiments 1-5.

[0166]

[0167]

[0168] Based on the S3 model, the estimation results of the physical information-guided neural network under congested and uncongested conditions in Experiments 1-5 are presented in Table 4.

[0169] Table 4. Estimation results of the physical guidance neural network under different unobstructed and congested flow conditions in Experiments 1-5.

[0170]

[0171] Based on the S3 model, the estimation results of the physical information-guided neural network under congested and uncongested conditions in Experiments 1-5 are presented in Table 5.

[0172] Table 5. Estimation results of the physical guidance neural network under different unobstructed and congested flow conditions in Experiments 6-10

[0173]

[0174]

[0175] Table 6 shows the traffic flow parameter estimation results based on classical linear interpolation (LIM), three-detector model (TDM), adaptive smoothing method model (ASM), and physical information neural network (PINN), as well as the traffic state estimation results of the physical guidance neural network method (PIML) proposed in this invention.

[0176] Table 6. Results of Highway Missing Traffic Condition Estimation in Experiments 1-10

[0177]

[0178]

[0179] An embodiment of the present invention discloses a computer system, including a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor. When the computer program / instructions are executed by the processor, they implement the steps of a method for estimating the missing traffic state of a highway based on a physical information-guided neural network, as described in the foregoing embodiment.

[0180] The present invention discloses a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of a method for estimating missing traffic states of a highway based on a physical information-guided neural network, as described in the foregoing embodiments.

[0181] The program / instruction code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program / instruction code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program / instruction code causes the steps of the methods of the present invention to be performed. The program / instruction code can be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a standalone software package, or entirely on a remote machine or server. All aspects not detailed in this invention are well-known to those skilled in the art.

Claims

1. A method for estimating missing traffic states of a freeway based on a physical information guided neural network, the method comprising: The method comprises the following steps: The road space-time discretization is performed for two-section traffic state detectors and two detector-free areas in the expressway, and the traffic states of the cells at the upstream and downstream boundaries in different time periods are counted to estimate the traffic states of the detector-free areas; A traffic state space-time evolution model of a cell in a time period is constructed based on the relationship between the change of the cell density in the time period, the state of the cell itself, and the inflow and outflow traffic volume in the time period, and a traffic state estimation model corresponding to the four roles of the target cell as the upstream cell of the core cell, the downstream cell of the core cell, the current time of the core cell, and the next time of the core cell is established based on the traffic state space-time evolution model; A neural network is designed based on the constructed traffic state estimation model, the state of the downstream boundary cell is used to iteratively estimate the states of all the upstream cells, the state of the upstream boundary cell is used to iteratively estimate the states of all the downstream cells, and the final estimation result is obtained by fusing the estimation result from the downstream boundary to the upstream and the estimation result from the upstream boundary to the downstream; In the neural network, a corresponding relationship matrix is designed for the target cell in different roles to describe the relationship between the state of the target cell and the remaining potential traffic state parameters, and an attention neural network for the state estimation of the target cell is designed based on the relationship matrix. A neural network loss function is designed, and the gradient descent method is used to optimize the neural network model; the loss function considers the bias of the bidirectional estimation and the error between the estimation and the observation value.

2. The method of claim 1, wherein the method is based on physical information guided neural network for freeway missing traffic state estimation. The corresponding relationship matrix is designed for the target cell in different roles to describe the relationship between the state of the target cell and the remaining potential traffic state parameters, which comprises: When estimating the state of an upstream cell using the observed states of downstream neighboring cells, if the target cell is an upstream cell of the core cell, a first relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a first neural network for estimating the target cell state is designed accordingly. When the target cell is the core cell at the current time, a second relationship matrix is ​​defined to describe the target cell state and the other potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a second neural network for estimating the target cell state is designed. When the target cell is the core cell at the next time step, a third relation matrix is ​​defined to describe the target cell state and the remaining potential traffic state parameters. The relationship is established, and a third neural network for estimating the state of the target cell is designed; where i and j are used to label the cell number and time number, respectively, X represents the traffic state, ω represents the traffic wave velocity, Δx and Δt represent the spatial length and time length of each unit after spatiotemporal discretization, respectively, DU is used to label the direction from downstream to upstream, UA is used to label the upstream cell, C is used to label the core cell, and TS is used to label the next time step. When estimating the state of downstream cells using the observed states of upstream neighboring cells, if the target cell is a downstream cell of the core cell, a fourth relation matrix is ​​defined to describe the state of the target cell and the remaining potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a fourth neural network for estimating the target cell state is designed. When the target cell is the core cell at the current time, a fifth relation matrix is ​​defined to describe the target cell state and the remaining potential traffic state parameters. The relationship between the target cell and the core cell is determined, and a fifth neural network for estimating the target cell state is designed. When the target cell is the core cell at the next time step, a sixth relation matrix is ​​defined to describe the target cell state and the remaining potential traffic state parameters. The relationship is established, and a sixth neural network for estimating the state of the target cell is designed; UD is used to label the direction from upstream to downstream, and DA is used to label the downstream cell.

3. The method of claim 1, wherein: The state estimation results of the target cell as the upstream cell of the core cell, the current time of the core cell and the next time of the core cell are obtained and Define the seventh relationship matrix between the final estimated state of the target cell and the three initial states The seventh relationship matrix is used to design the fusion neural network from the downstream to the upstream. When the state of the downstream cell is estimated by using the state of the upstream adjacent cell, the state estimation result of the target cell at the downstream cell of the core cell, the current time of the core cell and the next time of the core cell is obtained respectively and Define the eighth relationship matrix between the final estimated state of the target cell and the three initial states Based on the eighth relationship matrix, a fusion neural network in the upstream-to-downstream direction is designed.

4. The method of claim 1, wherein: The state of the downstream boundary cell is used to iteratively estimate the states of all the upstream cells, which comprises traversing the downstream boundary cell to the upstream boundary cell, and traversing all the time steps in each cell state estimation; for the state of any cell in any time period, the state is used as the upstream cell of the core cell, the current time of the core cell, and the next time of the core cell, respectively, to participate in the corresponding traffic state space-time evolution process; when the cell is used as the three different roles, three different estimation results are obtained, and the final estimation result is obtained by fusing the three different estimation results. The state of the upstream boundary cell is used to iteratively estimate the states of all the downstream cells, which comprises traversing the upstream boundary cell to the downstream boundary cell, and traversing all the time steps in each cell state estimation; for the state of any cell in any time period, the state is used as the downstream cell of the core cell, the current time of the core cell, and the next time of the core cell, respectively, to participate in the corresponding traffic state space-time evolution process; when the cell is used as the three different roles, three different estimation results are obtained, and the final estimation result is obtained by fusing the three different estimation results.

5. The method of claim 1, wherein: The establishment target cell as the core cell upstream cell, core cell downstream cell, core cell current time and core cell next time four roles corresponding traffic state estimation model, combined with the state transition model and traffic wave transmission model of cellular automata, the estimation model of the cell in different positions in a state transition process is as follows: When the density of the upstream cell of the core cell is missing, the estimation model is: When the density of the core cell is missing, the estimation model is: When the density of the downstream cell of the core cell is missing, the estimation model is: When the density of the next time of the core cell is missing, the estimation model is: Where i and j are used to mark the cell number and time number respectively, k represents the density, ω represents the traffic wave speed, Δx and Δt represent the space length and time length of each unit after space-time discretization respectively, UA is used to mark the upstream cell, C is used to mark the core cell, DA is used to mark the upstream cell, TS is used to mark the next time, f is used to represent the function relationship, and the superscript number is used to distinguish different functions.

6. The method of claim 2, wherein the method is based on a physical information guided neural network for freeway missing traffic state estimation. The first to the sixth neural networks adopt the following form: where, is the state estimation result of the target cell; I i,j is the corresponding traffic state parameter; A i,j is the corresponding relationship matrix; W1, W2, b1 and b2 are neural network parameters; W ONE T is a parameter matrix with all 1s; Γ(·) is an activation function of the neural network.

7. The method of claim 3, wherein the method is characterized by: The fusion neural network from downstream to upstream is as follows: The fusion neural network from upstream to downstream is as follows: where, and are the final state estimation results in two directions respectively; and are the corresponding relationship matrices respectively; and and and are the neural network parameters; W ONE T is a parameter matrix with all 1s; and Γ(·) is an activation function of the neural network.

8. The method of claim 1, wherein: Using two-way estimation bias and the estimation error from the observation As the loss function loss = a x loss m + (1-a) x loss o , to update the model parameters; where N represents the number of cells, J represents the number of time points, and respectively represent the estimated flow, density and velocity, D-U is used to mark the direction from downstream to upstream, U-D is used to mark the direction from upstream to downstream, ub and db are used to mark the corresponding cells of the upstream and downstream detectors, respectively, q, k and v represent the observed flow, density and velocity, respectively, and a is the weight.

9. A computer system comprising a memory, a processor, and a computer program / instructions stored on the memory and executable on the processor, wherein, The computer program / instructions are executed by the processor to realize the steps of the highway missing traffic state estimation method based on the physical information guided neural network according to any one of claims 1-8.

10. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions are executed by the processor to realize the steps of the highway missing traffic state estimation method based on the physical information guided neural network according to any one of claims 1-8.

Images