A method for locating a motor vehicle exhaust remote sensing station based on minimum cut

Abstract

The application discloses a motor vehicle exhaust remote sensing station site selection method based on a minimum cut, and comprises the following steps: S1, converting a city traffic network into a directed graph, and searching the directed graph by a depth-first search algorithm to obtain a city road section set, wherein the city road section set comprises a directed loop road section, a directed non-loop road section and a boundary point distribution road section; S2, performing a point distribution operation on the directed loop road section; converting a motor vehicle exhaust remote sensing station site selection problem into a minimum cut problem, finding a minimum cut set based on a path segmentation algorithm of the minimum cut, optimizing by a local search algorithm, obtaining a result and outputting. The method only needs to use traffic network topological structure and traffic flow direction information, converts the motor vehicle remote sensing station site selection problem into a minimum cut problem, thereby obtaining a minimum road section set covering the traffic network, and enables all on-road motor vehicles in the city traffic network to be monitored at least once.

Description

Technical Field

[0001] The present invention relates to the technical field of layout of motor vehicle telemetry sites, and in particular to a minimum cut-based site selection method for motor vehicle exhaust telemetry sites. Background Art

[0002] In recent years, as governments around the world attach great importance to environmental protection, more and more high-pollution factories originally located in and around urban areas have been gradually relocated to suburbs. This measure has greatly improved the urban atmospheric environment. However, with the improvement of people's living standards, the number of motor vehicles is increasing sharply, making motor vehicle exhaust emissions one of the main causes of air pollution in urban areas. Motor vehicles driving on urban roads consume fuel and produce a variety of emissions, such as carbon oxides, nitrogen oxides and PM. 2.5 These emissions can, to some extent, harm public health. Reports indicate that living near major traffic routes significantly increases the risk of asthma, lung disease, and deep vein thrombosis. Therefore, taking necessary measures to effectively monitor vehicle exhaust emissions within traffic networks, identify and screen out high-emission vehicles on the roads, and thereby reduce vehicle emissions, is a pressing issue. Remote sensing systems for vehicle exhaust emissions, used to monitor emissions from road vehicles that contribute to urban air pollution, are a promising approach. However, their practical application in traffic networks is significantly limited by the location and number of monitoring stations. Because remote sensing monitoring station equipment is extremely expensive, their deployment in actual traffic networks is often constrained by budget constraints. It is often not possible to deploy enough monitoring stations to fully meet the performance requirements of the remote sensing system within the traffic network. Therefore, devising an effective site selection strategy for monitoring station placement is crucial for the performance of remote sensing systems.

[0003] Currently, research on the site selection and deployment of vehicle exhaust remote sensing systems is still in its infancy, significantly limiting their practical application. To enable the system to quickly monitor exhaust emissions concentrations from on-road vehicles in urban traffic networks, further research is needed on the site selection and deployment of telemetry stations. Summary of the Invention

[0004] The present invention aims to overcome the shortcomings of existing technologies by providing a minimum-cut-based method for selecting vehicle exhaust telemetry station sites, utilizing only the topology of the traffic network and traffic flow direction information. First, a depth-first search algorithm is used to distinguish directed non-loop segments from directed loop segments in a directed graph, and boundary segments are obtained as a set of boundary segments exiting the traffic network. Then, a point placement operation is performed on the directed loop segments, transforming the vehicle telemetry station site selection problem into a minimum-cut problem. This method results in a minimum set of segments covering the traffic network, enabling all vehicles on the road in the urban network to be monitored at least once.

[0005] In order to solve the above technical problems, the technical solution of the present invention is:

[0006] A method for selecting a site for a motor vehicle exhaust telemetry station based on minimum cut includes the following steps:

[0007] S1. Converting the urban traffic road network into a directed graph, and searching the directed graph using a depth-first search algorithm to obtain a set of urban road segments, wherein the set of urban road segments includes directed loop segments, directed non-loop segments, and boundary distribution segments;

[0008] S2. Perform point placement operations on directed loop sections

[0009] The method of the point placement operation is as follows: the inflow of vehicles in the balance node of the urban traffic road network is equal to the outflow of vehicles, so a virtual node is introduced in the directed loop section to separate the inflow and outflow relationship of vehicles from one node, and a minimum vertex set covering the directed loop section in the directed graph is selected and transformed to obtain the corresponding virtual node, and each two transformed nodes are regarded as an OD pair, which are respectively regarded as the source node O and the sink node D; the site selection problem of the motor vehicle exhaust telemetry station is converted into a minimum cut problem, and the minimum cut set is found based on the minimum cut path segmentation algorithm; optimization is performed through a local search algorithm, and the result is obtained and output.

[0010] Preferably, in step S1, the specific method for converting the urban traffic road network into a directed graph is: first, the topological structure and traffic flow direction displayed by the urban traffic road network are abstracted into a directed graph.

[0011] Preferably, the depth-first search algorithm is specifically:

[0012] (1) Abstracting urban traffic network information into an adjacency data matrix based on a directed graph;

[0013] (2) Starting from a vertex in the directed graph according to the adjacency data matrix, a directed path is searched along the directed segments and adjacent vertices of the directed graph until the next vertex cannot be accessed. Then, a determination is made as to whether the directed path constitutes a directed loop. If so, its directed segment is recorded in the directed loop segment set; otherwise, it is recorded in the directed non-loop segment set.

[0014] (3) Go back to the last visited vertex of the directed path in step (2), continue searching and expanding the directed path until the next vertex cannot be visited, and determine whether the directed path constitutes a directed loop. If so, record its directed segment in the directed loop segment set; otherwise, record it in the directed non-loop segment set.

[0015] (4) Repeat step (3) until you return to the initial traversal vertex;

[0016] (5) Repeat steps (2), (3), and (4) with other vertices as initial vertices to obtain the result set of all directed loop sections, directed non-loop sections, and boundary distribution sections.

[0017] Preferably, the adjacency data matrix is ​​as follows:

[0018]

[0019] Among them, v1, v2, ..., v m represents all intersections in the urban traffic network, m is the total number of intersections in the network; A ij ,i=1,2,…m,j=1,2,…,m represents the intersection v i and intersection v j If the two are connected, then A ij = 1. If not connected, then A ij =INF.

[0020] Preferably, in step S2, the directed graph separates OD pairs through an integer programming model, and the data expression of the integer programming model is as follows:

[0021] minz=∑ a∈A z a ###(1)

[0022] Subject to:

[0023]

[0024]

[0025] Among them, z a∈{0,1} is a binary variable, which means whether a vehicle emission remote sensing monitor is on road section a. If the monitor is on road section a, then z a =1; otherwise z a =0, w∈W,a∈A,p∈P w represents one of the paths of a certain OD pair. If segment a is on the path p of the connected OD pair w, then otherwise The objective function (1) aims to minimize the total investment in the vehicle exhaust remote sensing system in the traffic network and minimize the number of vehicle exhaust remote sensing monitoring stations required to separate all OD pairs in the network. Constraint (2) ensures that at least one monitoring station is installed on each feasible path p of each OD pair w. Constraint (3) represents the feasible domain of the decision variable.

[0026] Preferably, the minimum cut path segmentation method is introduced in step S2: according to the weight coefficient corresponding to each road section, the two sets of starting points and ending points in the urban traffic road network are blocked to achieve a complete segmentation of an 0-D pair, and the cut set that can lead from point set C to point set T in the original road network directed graph is selected, where point set C is the set where the starting point O is located, and point set T is the set where the end point D is located;

[0027] Repeat the above steps until all OD pairs are blocked in the same way.

[0028] Preferably, the implementation process of the minimum cut algorithm is as follows:

[0029] First, the maximum capacity of each edge in the traffic network directed graph G is set as the weight value of the road, and the flow of all edges is initialized to 0. The cost of placing a remote sensing monitoring station on each road section is used as the weight value of each road section. Therefore, the weight value of each road section is set to 1.

[0030] The flow value of an edge must meet the following conditions:

[0031] (a)0≤flow≤Capacity;

[0032] (b) Except for the starting point O and the ending point D, the inflow rate of all nodes is equal to the outflow rate;

[0033] Search for a path p from the starting point O to the end point D that satisfies the restrictions. The path p needs to meet the following requirements: before the path passes, flow ≠ Capacitye; it can pass through unoccupied edges in the reverse direction;

[0034] After calculating the minimum capacity Δ on path p and updating the path, increase the flow of all edges in the path by an increase Δ until there is no path that meets the conditions;

[0035] Delete the edge a that is fully occupied in the directed graph G of the traffic network, and use the path search method to find the set C of the most points that can be passed from the starting point O, so that the set T containing the end point D = VC;

[0036] Select the edge set that is fully occupied by the flow in the edge set that can lead from the point set C to the point set T in the original road network directed graph.

[0037] The present invention has the following characteristics and beneficial effects:

[0038] The present invention only needs to utilize the topological structure of the traffic network and the traffic flow direction information, and the invention can effectively deal with the problems of redundancy and insufficient monitoring rate.

[0039] The present invention can effectively deal with the boundary problems caused by unbalanced nodes in the traffic network, is more in line with the actual situation, and is applicable to any traffic network and has strong universality.

[0040] It lays the foundation for monitoring the exhaust gas of all motor vehicles in the urban road network, and then facilitates the control of motor vehicles based on the pollution emitted by automobiles, thereby protecting the urban environment and greatly improving the urban atmospheric environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0042] Figure 1 Flow chart of the method of the present invention;

[0043] Figure 2 Part of the transportation network of a city;

[0044] Figure 3 It is a directed graph of part of the traffic road network of a city;

[0045] Figure 4 This figure shows the changes before and after the introduction of virtual nodes. DETAILED DESCRIPTION

[0046] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0047] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0048] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed connections, detachable connections, or integral connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0049] In order to make the technical innovations achieved by the present invention easier to understand, Figure 1 , the implementation of the present invention is further described in detail, and the specific implementation is as follows:

[0050] A method for selecting a site for a motor vehicle exhaust telemetry station based on minimum cut includes the following steps:

[0051] S1, such as Figure 2 As shown in the figure, according to the topological structure and traffic flow of a city's traffic network, it is abstracted into Figure 3 The directed graph shown is converted into an adjacency matrix as follows:

[0052]

[0053] Where V = {v1, v2, ..., v m} represents all intersections in the urban traffic network, m is the total number of intersections in the network; A ij ,i=1,2,…m,j=1,2,…,m represents the intersection v i and intersection v j If the two are connected, then A ij = 1. If not connected, then A ij=inf.

[0054] exist Figure 3 In the process, the depth-first search algorithm is used to distinguish the directed non-loop segments and directed loop segments in the directed graph, and the boundary distribution segments are obtained as the set of boundary segments leaving the traffic network. The specific process is as follows:

[0055] (1) First, according to Figure 2 The traffic topology structure and traffic flow direction information are obtained. Figure 3 ;

[0056] (2) Taking v1 as the initial vertex, find its directed path P = {v1, ...v p , v q}, p<q<m, until the next vertex can no longer be visited, determine the directed path Is it a directed loop? If so, record its directed arcs in the directed loop arc set; otherwise, record it in the directed non-loop arc set.

[0057] (3) Return to the last visited vertex v p , continue searching and expanding the directed path until the next vertex can no longer be accessed, and determine whether the directed path constitutes a directed loop. If so, record its directed arc into the directed loop arc set, otherwise record it into the directed non-loop arc set;

[0058] (4) Repeat step (3) until returning to the initial traversal vertex v1;

[0059] (5) Repeat steps (2)(3)(4) with other vertices as initial vertices to obtain the result set of all directed loop segments and directed non-loop segments. The result set of directed non-loop segments is {a 27 ,a 28 ,a 29 ,a 30}, and then the boundary distribution road section is the set of the boundary road sections leaving the traffic network is {a 29 ,a 30}.

[0060] S2. Based on the search results of step S1, separate the directed non-loop sections and then perform point placement on the directed loop sections, transforming the motor vehicle telemetry station location problem into a minimum cut problem. The virtual node transformation process in this step is as follows: Figure 4 As shown, vertex v2 represents a selected vertex, (b) is the result of the virtual transformation of (a), and after the transformation, v2 and v4 are a pair of 0-D pairs.

[0061] Furthermore, the directed graph separates the OD pairs through an integer programming model, and the data expression of the integer programming model is as follows:

[0062] minz=∑ a∈A z a ###(1)

[0063] Subject to:

[0064]

[0065]

[0066] Among them, z a ∈{0,1} is a binary variable, which means whether a vehicle emission remote sensing monitor is on road section a. If the monitor is on road section a, then z a =1; otherwise z a =0, w∈W,a∈A,p∈P w represents one of the paths of a certain OD pair. If segment a is on the path p of the connected OD pair w, then otherwise The objective function (1) aims to minimize the total investment in the vehicle exhaust remote sensing system in the traffic network and minimize the number of vehicle exhaust remote sensing monitoring stations required to separate all OD pairs in the network. Constraint (2) ensures that at least one monitoring station is installed on each feasible path p of each OD pair w. Constraint (3) represents the feasible domain of the decision variable.

[0067] The specific process of solving the minimum cut set is as follows:

[0068] S2-1, select one of the minimum vertex sets (v1, v3, v6, v 12 ), transform it to get the corresponding virtual node, and take every two transformed nodes as an OD pair.

[0069] S2-2. Based on the OD pair set obtained in step S2-1, the minimum cut path segmentation method is introduced. According to the weight coefficient corresponding to each road section, the two sets of starting points and ending points are blocked to achieve a complete segmentation of an 0-D pair. The cut set that can lead from point set C (the set where the starting point O is located) to point set T (the set where the end point D is located) in the original road network directed graph is selected.

[0070] The implementation process of the minimum cut algorithm is as follows:

[0071] 1. First, set the maximum capacity of each edge in the directed graph G as the weight of the road, and initialize the flow of all edges to 0. Here, the cost of placing a remote sensing monitoring station on each road segment is used as the weight of each road segment, so the weight of each road segment is set to 1.

[0072] The flow value of an edge must meet the following conditions:

[0073] (a)0≤flow≤Capacity;

[0074] (b) Except for the starting point O and the ending point D, the inflow rate of all nodes is equal to the outflow rate.

[0075] 2. Search for a path p from the starting point O to the end point D that satisfies the restrictions. The path p needs to meet the following requirements: (a) flow ≠ Capacitye before the path passes; (a) it can pass through unoccupied edges in the reverse direction.

[0076] 3. After calculating the minimum capacity Δ on path p and updating the path, increase the flow of all edges in the path by an increase Δ until there is no path that meets the conditions.

[0077] 4. Delete the edge a with full traffic in the directed graph G of the traffic network, and use the path search method to find the set C of the most points that can be passed from the starting point O, so that the set T containing the end point D = VC.

[0078] 5. Select the edge set with full flow from the point set C to the point set T in the original road network directed graph.

[0079] (3) Repeat step (2) until all OD pairs are blocked in the same way.

[0080] (4) In order to avoid the situation in step (3) where a small number of redundant points appear due to the path length being less than the set value β, a local search algorithm based on depth-first traversal is introduced for optimization, and the set of road sections {a2, a5, a8, a 12 ,a 23 ,a 26}.

[0081] Since after a vehicle leaves any position of any road section in the traffic network, there are only two situations: still in the traffic network and leaving the traffic network. The boundary distribution road section obtained by step 1 is the set of boundary road sections leaving the traffic network {a 29 ,a 30}, according to the set of points of the directed loop segment in step 2, in this example the set of points is {a2,a5,a8,a 12 ,a 23 ,a 26 ,a 29 ,a 30}.

[0082] Whether vehicles on other sections of road without monitoring points can be monitored when passing through sections with monitoring points can be determined by the monitoring rate M. rate Calculated.

[0083]

[0084] Among them, R sa The number of road sections where monitoring stations can monitor vehicles on the road can be determined by removing the sections where monitoring stations are deployed and calculating the number of sections that form directed loops and directed paths that leave the traffic network. A is the number of all road sections in the traffic network. rate The value of reflects that each vehicle on the road can be monitored at least once. rate =30 / 30×100%=100%. It can be seen that this method can ensure that each vehicle on the road can be monitored at least once.

[0085] In summary, the present invention is more feasible and universal. Compared with the existing site selection and layout methods of motor vehicle exhaust telemetry stations, the present invention only needs to utilize the topological structure of the traffic network and the traffic flow direction information. While ensuring the monitoring rate, the results obtained are free of redundancy and can also effectively deal with the boundary problems caused by unbalanced nodes in the traffic network. It is suitable for the traffic network of any city and provides new ideas and methods for the study of site selection and layout methods of motor vehicle exhaust telemetry stations.

[0086] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. It will be apparent to those skilled in the art that various changes, modifications, substitutions, and variations of these embodiments, including components, without departing from the principles and spirit of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for selecting vehicle exhaust telemetry sites based on minimum cut, characterized in that: The steps include: S1. Converting the urban traffic road network into a directed graph, and searching the directed graph using a depth-first search algorithm to obtain a set of urban road segments, wherein the set of urban road segments includes directed loop segments, directed non-loop segments, and boundary distribution segments; S2. Perform point placement operations on directed loop sections The method for the point placement operation is as follows: the inflow of vehicles in the balance node of the urban traffic road network is equal to the outflow of vehicles, so a virtual node is introduced in the directed loop section to separate the inflow and outflow relationship of vehicles from one node, and a minimum vertex set covering the directed loop section in the directed graph is selected and transformed to obtain the corresponding virtual node, and each two nodes after the transformation are regarded as an OD pair, which are respectively regarded as the source node O and the sink node D; the site selection problem of the motor vehicle exhaust telemetry station is converted into a minimum cut problem, and the minimum cut set is found based on the minimum cut path segmentation algorithm; optimization is performed through a local search algorithm, and the result is obtained and output; The directed graph separates OD pairs through an integer programming model, and the data expression of the integer programming model is as follows: ； in, Is a binary variable, which means whether a vehicle emission remote sensing monitor is on the road section If the monitor is on the road On, then ;otherwise , , , , Indicates one of the paths of an OD pair. If the segment In the connected OD On the path p, then ,otherwise , the objective function (1) aims to minimize the total investment of the vehicle exhaust remote sensing system in the traffic network and minimize the number of vehicle exhaust remote sensing monitoring stations required to separate all OD pairs in the network. The constraint (2) ensures that each OD pair Every feasible path There is at least one monitoring station installed on the network, and constraint (3) represents the feasible domain of the decision variables; The minimum cut path segmentation method is as follows: according to the weight coefficient corresponding to each road section, the two sets of starting points and ending points in the urban traffic road network are blocked to achieve a complete segmentation of a 0-D pair, and the points in the original road network directed graph that can be represented by the point set are selected. Towards a point set The cut set of is the set where the starting point O is located, the point set For the end Repeat the action until all OD pairs are blocked in the same way.

2. The method for selecting vehicle exhaust remote sensing sites based on minimum cut according to claim 1, characterized in that: In step S1, the specific method of converting the urban traffic road network into a directed graph is: first, the topological structure and traffic flow direction displayed by the urban traffic road network are abstracted into a directed graph.

3. The method for selecting vehicle exhaust remote sensing sites based on minimum cut according to claim 1, characterized in that: The depth-first search algorithm is specifically: (1) Abstracting urban traffic network information into an adjacency data matrix based on a directed graph; (2) Starting from a vertex in the directed graph according to the adjacency data matrix, a directed path is searched along the directed segments and adjacent vertices of the directed graph until the next vertex cannot be accessed. The directed path is judged to see whether it constitutes a directed loop. If so, its directed segment is recorded in the directed loop segment set; otherwise, it is recorded in the directed non-loop segment set. (3) Go back to the last visited vertex of the directed path in step (2), continue searching and expanding the directed path until the next vertex cannot be visited, and determine whether the directed path constitutes a directed loop. If so, record its directed segment in the directed loop segment set; otherwise, record it in the directed non-loop segment set. (4) Repeat step (3) until you return to the initial traversal vertex; (5) Repeat steps (2), (3), and (4) with other vertices as initial vertices to obtain the result set of all directed loop segments, directed non-loop segments, and boundary point segments.

4. The method for selecting a site for a vehicle exhaust remote sensing station based on minimum cut according to claim 3, characterized in that: The adjacency data matrix is ​​as follows: ； in, Represents all intersections of the urban traffic network, is the total number of intersections in the road network; Indicates intersection and intersection If the two are connected, then If not connected, then .

5. The method for selecting vehicle exhaust remote sensing sites based on minimum cut according to claim 1, characterized in that: The implementation process of the minimum cut algorithm is as follows: First, transform the traffic network directed graph The maximum capacity of each edge in Set the weight value of the road and initialize the flow of all edges is 0, and the cost of placing a remote sensing monitoring station on each road section is used as the weight value of each road section. Therefore, the weight value of each road section is set to 1. The flow value of an edge must meet the following conditions: （a） ； (b) Except the starting point O and the ending point In addition, the inflow of all nodes is equal to the outflow; Search from the starting point O to the end point Paths that satisfy the constraints ,path The following requirements need to be met: Before the path passes, ; You can go back through the unoccupied edges; Calculate Path After finding the minimum capacity Δ on the path and updating the path, the flow of all edges in the path is increased by an increase Δ until there is no path that meets the conditions; In the traffic network directed graph Delete the edge a that is full of traffic, and use the path search method to find the set of the most points that can be passed from the starting point O , so that it contains the termination point Collection ; Select the point set in the original road network directed graph Towards a point set In the edge set, the edge set is filled with traffic.

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