Method for Measuring the Relationship between Urban Spatial Structure and Traffic Congestion Based on Persistent Homology

Abstract

An embodiment of the present invention provides a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology, belonging to the technical field of traffic control. Specifically, it includes: Step 1, matching the target data of the target area with the road network and identifying the urban spatial structure characteristics and traffic congestion characteristics; Step 2, substituting the urban spatial structure characteristics and traffic congestion characteristics into a multi-scale geographically weighted regression model for regression analysis to generate an analysis result; Step 3, measuring the relationship between the urban spatial structure and traffic congestion according to the analysis result and the persistent homology method. Through the solution of the present invention, considering the coupling and topological properties of the interaction of multiple urban spatial structure characteristics in the real environment, using multi-scale geographically weighted regression to calculate the relationship between multiple urban spatial structure characteristics and traffic congestion, and applying the method of persistent homology to measure the relationship between urban spatial structure characteristics and traffic congestion characteristics, it has stronger reality and interpretability.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of traffic control, and particularly to a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology. Background Art

[0002] At present, with the continuous development of urban space, people's travel demands are also increasing day by day, resulting in the increasingly serious problem of urban traffic congestion. Reasonably understanding the relationship between urban spatial structure and traffic congestion is the key to solving the traffic congestion problem.

[0003] When evaluating the measurement of the relationship between urban spatial structure and traffic congestion, there are also mainly two evaluation methods, namely relationship reliability evaluation and relationship spatial distribution evaluation. Relationship reliability evaluation mainly uses methods such as model goodness-of-fit test and significance test to evaluate the reliable degree of the explanation of urban spatial structure to traffic congestion. This evaluation method is limited to the current research area and can only test a single feature, so there are limitations in the generalization and transferability of the analysis results. Relationship spatial distribution evaluation mainly shows the non-stationary characteristics of spatial relationships through the visualization of influence factor coefficients and interprets them in combination with geographical meanings. This method has certain advantages in showing spatial relationships, but this method mainly focuses on the visualization analysis of a single feature and ignores the complexity of the interaction between multiple elements in the traffic system. In addition, the existing methods lack the ability to quantitatively analyze these interactions and cannot comprehensively capture the spatial distribution characteristics of traffic flow.

[0004] It can be seen that there is an urgent need for a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology with high interpretability and adaptability. Summary of the Invention

[0005] In view of this, the embodiments of the present invention provide a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology, which at least partially solves the problem of poor interpretability and adaptability in the prior art.

[0006] The embodiments of the present invention provide a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology, including:

[0007] Step 1, matching the target data of the target area with the road network, and identifying urban spatial structure features and traffic congestion features;

[0008] Step 2, substituting the urban spatial structure features and traffic congestion features into a multi-scale geographically weighted regression model for regression analysis to generate an analysis result;

[0009] Step 3, measuring the relationship between urban spatial structure and traffic congestion according to the analysis result and the persistent homology method.

[0010] According to a specific implementation manner of an embodiment of the present invention, step 1 specifically includes:

[0011] Step 1.1: Perform topological inspection and vectorization on the road network, process double-line roads into single lines, determine the buffer radius accordingly, generate a buffer of the road network as a research unit, perform data cleaning on the POI data in the target data and match it with the research unit, and match the vehicle trajectories in the target data with the research unit by using a preset map matching algorithm in combination with the geometric structure, topological information, and vehicle speed constraints of the road network;

[0012] Step 1.2: Extract the physical attributes and social attributes of the urban structure characteristics respectively from the target data after matching with the research unit to form urban spatial structure characteristics;

[0013] Step 1.3: Calculate the average congestion index of each road in the research unit to form traffic congestion characteristics.

[0014] According to a specific implementation manner of an embodiment of the present invention, step 2 specifically includes:

[0015] Take the urban spatial structure characteristics as the independent variable X and the average congestion index as the dependent variable Y and substitute them into a multi-scale geographically weighted regression model to perform multi-scale geographically weighted regression analysis on the urban spatial structure characteristics and traffic congestion characteristics, and generate an analysis result.

[0016] According to a specific implementation manner of an embodiment of the present invention, the expression of the multi-scale geographically weighted regression model is

[0017] ;

[0018] Wherein, is the dependent variable of the th observation point, is the th independent variable of the th observation point, is the spatial coordinate of the th observation position, is the intercept term at the position , is the regression coefficient of the independent variable at the position , which depends on the spatial coordinate, is the error term;

[0019] ;

[0020] Wherein, is the spatial bandwidth parameter of the th independent variable, is the position and the space weight between positions is calculated based on the spatial bandwidth parameter of the th independent variable where is the value of the th independent variable at the jth position, and is the value of the dependent variable at the th position

[0021] According to a specific implementation manner of an embodiment of the present invention, step 3 specifically includes:

[0022] Step 3.1: Extract the regression coefficients of the independent variables in the analysis results as the high-dimensional coordinates of each road, and construct a VR complex for this set of point cloud data;

[0023] Step 3.2: Draw persistence diagrams of topological features in different dimensions according to the VR complex, and calculate the persistence times of all two-dimensional features accordingly;

[0024] Step 3.3: Sort the two-dimensional features in descending order of persistence time, select a preset number of two-dimensional features from top to bottom, extract the road groups corresponding to each two-dimensional feature, and output the spatial distribution results corresponding to each road group

[0025] The urban spatial structure and traffic congestion relationship measurement scheme based on persistent homology in the embodiments of the present invention includes: Step 1, match the target data of the target area with the road network, and identify the urban spatial structure features and traffic congestion features; Step 2, substitute the urban spatial structure features and traffic congestion features into a multi-scale geographically weighted regression model for regression analysis to generate an analysis result; Step 3, measure the relationship between the urban spatial structure and traffic congestion according to the analysis result and the persistent homology method

[0026] The beneficial effects of the embodiments of the present invention are as follows: Through the solution of the present invention, considering that multiple urban spatial structure features in the real environment interact with each other to jointly cause the coupling and topological properties of traffic congestion and urban spatial structure, the relationship between multiple urban spatial structure features and traffic congestion calculated by multi-scale geographically weighted regression is utilized, and the method of persistent homology is innovatively applied to measure the relationship between urban spatial structure features and traffic congestion features, developing a measurement method for the relationship between urban spatial structure and traffic congestion based on persistent homology, which has stronger realism and interpretability BRIEF DESCRIPTION OF THE DRAWINGS

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0028] Figure 1 It is a schematic flowchart of a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology provided by an embodiment of the present invention;

[0029] Figure 2 It is a schematic diagram of the specific implementation process of a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology provided by an embodiment of the present invention;

[0030] Figure 3 It is a schematic diagram of a partial taxi trajectory and a research area provided by an embodiment of the present invention;

[0031] Figure 4 It is a schematic diagram of the duration barcode of the two-dimensional feature with the longest duration provided by an embodiment of the present invention;

[0032] Figure 5 It is a schematic diagram of the spatial distribution result of a road group provided by an embodiment of the present invention. Detailed implementation manners

[0033] The following will describe the embodiments of the present invention in detail with reference to the drawings.

[0034] The following illustrates the embodiments of the present invention through specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. The present invention can also be implemented or applied through other different specific implementation manners. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0035] It should be noted that the following describes various aspects of embodiments within the scope of the appended claims. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present invention, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement a device and / or practice a method. Additionally, this device can be implemented and this method can be practiced using other structures and / or functionality in addition to one or more of the aspects set forth herein.

[0036] It should also be noted that the diagrams provided in the following embodiments only schematically illustrate the basic concept of the present invention. The diagrams only show the components related to the present invention and are not drawn according to the number, shape, and size of the components in actual implementation. The type, quantity, and ratio of each component in actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0037] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the aspects can be practiced without these specific details.

[0038] With the continuous development of urban space, people's travel demands are also increasing day by day, resulting in an increasingly serious urban traffic congestion problem. Reasonably understanding the relationship between urban space structure and traffic congestion is the key to solving the traffic congestion problem.

[0039] Traditional research believes that there are mainly two relationships between urban space structure and traffic congestion, namely the spatial homogeneous relationship and the spatial heterogeneous relationship. The former refers to the relationship between the urban space structure characteristics at different locations within the study area and traffic congestion being the same, mainly including correlation analysis, multiple linear regression analysis, and land use - traffic models. The characteristic of these models is that the estimated value of the regression coefficient represents the global average value, and they are usually analyzed from a macroscopic perspective. The latter refers to the relationship between the urban space structure and traffic congestion at different locations within the study area varying with location. Typical models for studying the spatial heterogeneous relationship include locally weighted regression, spatially varying parameter regression, and geographically weighted regression models. They consider the locality and heterogeneity of spatial data and can more accurately depict the complex relationships within the urban space.

[0040] When evaluating the relationship measurement between urban spatial structure and traffic congestion, there are also mainly two evaluation methods, namely relationship reliability evaluation and relationship spatial distribution evaluation. Relationship reliability assessment mainly uses methods such as model goodness-of-fit test and significance test to evaluate the reliability of the explanation of traffic congestion by urban spatial structure. This evaluation method is limited to the current research area and can only test single features, so there are limitations in the generalization and transferability of the analysis results. Relationship spatial distribution assessment mainly shows the non-stationary characteristics of spatial relationships through the visualization of influence factor coefficients and interprets them in combination with geographical meanings. This method has certain advantages in showing spatial relationships, but this method mainly focuses on the visualization analysis of single features and ignores the complexity of the interactions among multiple elements in the traffic system. In addition, the existing methods lack the ability to quantitatively analyze these interactions and cannot comprehensively capture the spatial distribution characteristics of traffic flow.

[0041] It can be seen that the disadvantages of the prior art are as follows:

[0042] (1) Traditional relationship assessment studies mainly focus on relationship reliability assessment and qualitative assessment of relationship spatial distribution, and there are limitations in the generalization and transferability of the analysis results, or only focus on the visualization analysis of single features and ignore the complexity of the interactions among multiple elements in the traffic system.

[0043] (2) In the traditional research on the relationship between urban spatial structure and traffic congestion, only the impact of spatial structure on traffic congestion is evaluated from a single dimension of physical distance, without considering other attributes such as the topology of urban spatial structure characteristics.

[0044] An embodiment of the present invention provides a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology, and the method can be applied to the traffic control process of urban management scenarios.

[0045] See Figure 1 , which is a schematic flowchart of a method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology provided by an embodiment of the present invention. As Figure 1 and Figure 2 shown, the method mainly includes the following steps:

[0046] Step 1: Match the target data of the target area with the road network and identify the urban spatial structure characteristics and traffic congestion characteristics;

[0047] Further, the specific steps of Step 1 include:

[0048] Step 1.1, perform topological check and vectorization on the road network, process the double-lane road into a single-lane road, determine the buffer radius accordingly, generate the buffer of the road network as the research unit, clean the POI data in the target data and match it with the research unit, and, based on the road network geometry, topological information and vehicle speed constraints, use the preset map matching algorithm to match the vehicle trajectory in the target data with the research unit;

[0049] Step 1.2, extract the physical attributes and social attributes of urban structural characteristics according to the target data matched with the research unit to form the urban spatial structural characteristics;

[0050] Step 1.3, calculate the average congestion index of each road in the study unit to form the traffic congestion characteristics.

[0051] In the specific implementation, the data used is cleaned and matched with the road network, and the characteristics of urban spatial structure and traffic congestion are identified. Specifically, it includes:

[0052] 1.1 Data processing and road network matching

[0053] First, the road network is topologically checked and vectorized, and the double-line roads are processed as single-line roads. On this basis, the buffer radius is determined to generate the buffer zone of the road network as the research unit. Secondly, the classification errors in the POI data caused by individual word meaning analysis during the data crawling process are solved, and the POI types that have almost no impact on the research, such as "maintenance department" and "agent" data, are deleted. Then, the coordinate correction and projection conversion processing are performed on the remaining data, and the POI data are divided into six categories: public services, commercial services, offices, and accommodation services. Next, the data with an average price of less than 500 yuan per square meter and other data anomalies in the collected second-hand residential data are removed. Finally, the trajectory data outside the research area, with time anomalies and repeated records are deleted, and then the points where the front and rear coordinates of the same vehicle drift or the state is abnormal are eliminated.

[0054] Taking into account the road network geometry, topology information and vehicle speed constraints, a map matching algorithm for low sampling rate trajectory points - ST-Matching is used to match vehicle trajectories with urban road networks.

[0055] 1.2 Calculation of urban spatial structure characteristic indicators

[0056] The physical attributes of urban structural characteristics are the external manifestations of the urban spatial structure. The external characteristics of the urban structure are selected as urban scale, spatial pattern, land use structure, and urban density, and the built-up area, central vitality, land use mix, and floor area ratio are used as the indicators of these characteristics respectively. The social attributes of the urban structural characteristics are the internal connections of the urban spatial structure. The external characteristics of the urban structure are selected as the distribution of economic development level and the distribution of population space, and the distribution of housing prices and the distribution of population density are used as the two indicators to characterize the internal connections of the city.

[0057] 1.3 Calculation of traffic congestion characteristic indicators

[0058] The traffic congestion characteristics of the research unit are characterized by the average congestion index of the road. Given a directed road, the traffic congestion index at time t is:

[0059] ;

[0060] In the formula is the actual average speed of the vehicle at moment, is the 85th percentile after ascending order within a working day. Calculate the average value of all unique trajectory points per hour on the directed road as the average driving speed to ensure the stability of the road driving speed. At the same time, the calculation of requires at least 5 vehicles to pass through this section per hour, the calculation of

[0061] Step 2: Substitute the urban spatial structure characteristics and traffic congestion characteristics into the multi-scale geographically weighted regression model for regression analysis to generate the analysis results;

[0062] Based on the above embodiments, the specific content of the said Step 2 includes:

[0063] Take the urban spatial structure characteristics as the independent variable X and the average congestion index as the dependent variable Y and substitute them into the multi-scale geographically weighted regression model to conduct multi-scale geographically weighted regression analysis on the urban spatial structure characteristics and traffic congestion characteristics, and generate the analysis results.

[0064] Furthermore, the expression of the multi-scale geographically weighted regression model is

[0065] ;

[0066] Among them, is the The dependent variable of the spatial coordinates of the intercept term at the position regression coefficient of the independent variable is the error term;

[0067] ;

[0068] Among them, spatial bandwidth parameter of the spatial weight between the position calculated based on the spatial bandwidth parameter of the independent variable, is the value of the independent variable at the j-th position, dependent variable value at the

[0069] In specific implementation, the urban spatial structure characteristics and traffic congestion characteristics are substituted into the multi-scale geographically weighted regression model for regression analysis, where the urban spatial structure characteristics are the independent variable X and the average congestion index is the dependent variable Y.

[0070] The multi-scale geographically weighted regression model is an extended version of the geographically weighted regression model, which can more precisely capture the characteristics that different explanatory variables may play roles at different spatial scales. The formula of the multi-scale geographically weighted regression model is:

[0071] ;

[0072] In the formula, dependent variable of the independent variable of the spatial coordinates of the intercept term at the position regression coefficient of the independent variable, depending on the spatial coordinates,​​​​​​​​​​​​​​​​​​ is the error term.

[0073] Different from the traditional geographically weighted regression model, each regression coefficient in the multi-scale geographically weighted regression model corresponds to a different bandwidth , that is, the regression coefficient of each independent variable can have different smoothing scales in space:

[0074] ;

[0075] In the formula, is the spatial bandwidth parameter of the th independent variable, is the spatial weight between location and location , calculated based on the spatial bandwidth parameter of the th independent variable, is the value of the th independent variable at the jth location, is the value of the dependent variable at the th location.

[0076] Step 3, measure the relationship between the urban spatial structure and traffic congestion according to the analysis results and the persistent homology method.

[0077] Based on the above embodiments, step 3 specifically includes:

[0078] Step 3.1, extract the regression coefficients of the independent variables in the analysis results as the high-dimensional coordinates of each road, and construct a VR complex for this set of point cloud data;

[0079] Step 3.2, draw the persistence diagrams of topological features in different dimensions according to the VR complex, and calculate the persistence time of all two-dimensional features accordingly;

[0080] Step 3.3, sort the two-dimensional features in descending order of persistence time, select a preset number of two-dimensional features from top to bottom, extract the road groups corresponding to each two-dimensional feature, and output the spatial distribution results corresponding to each road group.

[0081] Specifically in implementation, the process of detecting the relationship between the urban spatial structure and traffic congestion is as follows:

[0082] 3.1 Construct a topological graph

[0083] Extract the independent variable regression coefficients in the results of the multi-scale geographically weighted regression analysis in Step 2 as the high-dimensional coordinates of each road, that is, regard each research unit as a six-dimensional point. Construct a VR complex for this set of point cloud data, where the nodes represent the relationship between spatial structure features and traffic congestion, and the edges represent the relationship distance between them. Given a distance threshold parameter, generate a set of increasing distance parameters with an inclusion relationship , and construct a series of simplicial complexes with an inclusion relationship. As the distance parameter increases, the original simplicial complex will not be affected, but will be included in the new simplicial complex formed by a larger distance parameter. Suppose the simplicial complex generated at the distance parameter is , and the generated sequence of simplicial complexes is shown as follows:

[0084] ;

[0085] In the formula, is the point cloud data group, is the increasing distance parameter, is the simplicial complex generated at the distance parameter , and indicates that the previous simplicial complex is included in the next simplicial complex.

[0086] 3.2 Calculate the feature persistence duration

[0087] During the construction of the filtered nested complex, as the distance parameter continuously increases, topological features will experience the processes of "birth" and "death". Therefore, for each topological feature , its life cycle can be defined. Suppose first appears at this distance parameter and disappears at this distance parameter. Then it is said that the topological feature "is born" at the former and "dies" at the latter, and the duration is also called the life cycle of this feature, that is, the persistence duration. Calculate the persistence duration of all features.

[0088] 3.3 Extract the road groups corresponding to long-persistence features

[0089] During the process of persistent homology, features with a longer persistence duration mean that there is a stable topological structure among the elements that make up this feature and need special attention; while topological features with a shorter persistence duration are usually regarded as noise and can be ignored. The process of persistent homology can extract the topological feature information of the data without changing the original data structure, that is, it can extract the topological features of the data without dimensionality reduction and reveal its life cycle by describing the birth and death of the topological features.

[0090] ​Sort the two-dimensional features in descending order of duration, select three features from top to bottom, and extract their corresponding roads. The duration of the continuous homophonic two-dimensional features of these three groups of roads is the longest among all the two-dimensional features, so their internal structure is stable.

[0091] The method for measuring the relationship between urban spatial structure and traffic congestion based on continuous coherence provided in this embodiment takes into account that multiple urban spatial structure characteristics in a real environment will interact with each other to jointly cause traffic congestion and the coupling and topological properties of the urban spatial structure, calculates the relationship between multiple urban spatial structure characteristics and traffic congestion using multi-scale geographically weighted regression, and innovatively applies the continuous coherence method to measure the relationship between urban spatial structure characteristics and traffic congestion characteristics, thereby developing a method for measuring the relationship between urban spatial structure and traffic congestion based on continuous coherence, which is more realistic and interpretable.

[0092] The method of the present invention will be further described below through a specific embodiment, using the 2019 road data, building outline data, second-hand housing price data, POI data, population density spatial distribution data and taxi trajectory data from September 23, 2019 to September 29, 2019 in District B of City A to illustrate the specific implementation process of the present invention:

[0093] (1) In the embodiment, District B of City A is selected as the research area, and the data used are taxi trajectory data, road data, building outline data, second-hand housing price data, POI data and population density spatial distribution data. The time of road data, building outline data, second-hand housing price data, POI data and population density spatial distribution data is 2019, and the time of taxi trajectory data is from 6:00 to 23:59 every day from September 23, 2019 to September 29, 2019, with a sampling interval of 15 seconds. Some trajectory data are related to the research area as shown in Figure 2. Figure 3 shown.

[0094] (2) The road network in Area B is processed into a single line. On this basis, a buffer zone with a radius of 120 meters is generated as the research unit. The misclassified data in the POI data is modified and invalid data is eliminated. The data with an average price of less than 500 yuan per square meter and other data anomalies in the collected second-hand residential data are removed. The remaining POI data and second-hand residential data are processed by coordinate correction and projection transformation. The POI data is deleted. Trajectory data outside the study area, with time anomalies and repeated records are deleted. Points where the front and rear coordinates of the same vehicle drift or have abnormal states are eliminated. ST-Matching is used to match vehicle trajectories with urban road networks.

[0095] (3) Calculate the urban spatial structure characteristics and traffic congestion characteristics in Area B. The spatial structure characteristics include urban scale characteristics, spatial pattern characteristics, land use structure characteristics, urban density characteristics, urban economic level distribution characteristics, and urban population spatial distribution characteristics. The corresponding indicators are the area of the research unit, the central vitality value of the research unit, the land use mixing degree, the plot ratio, the average price of second-hand housing, and the average population density; the indicator corresponding to traffic congestion is the average congestion index of the research unit.

[0096] Directly calculate the area of each research unit to obtain the scale characteristics. Conduct kernel density analysis on six types of POI data respectively, perform weighted superposition after normalization processing, and calculate the mean value of each research unit to obtain the spatial pattern characteristics. Count the number of six types of POIs in each research unit, and use the calculation method of Shannon entropy to represent the land use mixing degree. The calculation formula is as follows:

[0097] ;

[0098] In the formula, represents the value of Shannon entropy, refers to different elements within the research unit, refers to the type of elements within the research unit, refers to within the research unit the proportion of elements in all research units of the total amount of elements.

[0099] The calculation method of the plot ratio is as follows:

[0100] ;

[0101] In the formula, refers to the plot ratio, refers to the total number of buildings in the research unit, refers to a certain building within the research unit, refers to the floor area of the building, refers to the number of floors of the building.

[0102] Use the ordinary Kriging interpolation method to predict the surface of the second-hand housing price, and calculate the mean value of the interpolation results in each research unit as the economic level distribution of the research unit. Calculate the average population density in each research unit as the population spatial distribution of the research unit.

[0103] Given a directed road, the traffic congestion index at time t is:

[0104] ;

[0105] In the formula is the vehicle at The actual average speed at a moment, is the 85th percentile after ascending order within a working day. The average congestion index is calculated as the average of the congestion indices at all time periods of this road section.

[0106] (4) Take the urban spatial structure characteristics as the independent variable X and the average congestion index as the dependent variable Y and substitute them into the multi-scale geographically weighted regression model to conduct multi-scale geographically weighted regression analysis on the urban spatial structure characteristics and traffic congestion characteristics.

[0107] (5) Extract the regression coefficients of the independent variables in the results of the multi-scale geographically weighted regression analysis as the high-dimensional coordinates of each road, and construct a VR complex for this set of point cloud data, where the nodes represent the relationship between the spatial structure characteristics and traffic congestion, and the edges represent the relationship distance between them.

[0108] (6) Draw the persistence diagrams of topological characteristics in different dimensions, calculate the persistence times of all two-dimensional characteristics, and arrange them in descending order of the persistence times. The persistence time barcode of the two-dimensional characteristic with the longest persistence time is as Figure 4 shown.

[0109] (7) Select three characteristics from top to bottom, extract the corresponding road groups, and the spatial distribution results of the three road groups are as Figure 5 shown in (a), (b), and (c) of. Visualize the characteristics of the urban spatial structure and traffic congestion calculated in (3) on the spatial distribution of the three road groups, and it is found that the congestion indices of the three road groups are relatively high, the average area and housing price are high, and the average values of the central vitality, land utilization rate, floor area ratio, and population density are relatively small.

[0110] It should be understood that each part of the present invention can be implemented by hardware, software, firmware, or a combination thereof.

[0111] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for measuring the relationship between urban spatial structure and traffic congestion based on persistent homology, characterized in that, Including: Step 1: Match the target data of the target area with the road network, and identify the urban spatial structure features and traffic congestion features; The specific steps of Step 1 include: Step 1.1: Conduct a topological check and vectorization on the road network, process the double-line roads into single lines, determine the buffer radius accordingly, generate the buffer of the road network as the research unit, match the POI data in the target data after data cleaning with the research unit, and, in combination with the geometric structure, topological information, and vehicle speed constraints of the road network, use a preset map matching algorithm to match the vehicle trajectories in the target data with the research unit; Step 1.2: Extract the physical attributes and social attributes of the urban structure features from the target data after matching with the research unit to form the urban spatial structure features; Step 1.3: Calculate the average congestion index of each road in the research unit to form the traffic congestion features; Step 2: Substitute the urban spatial structure features and traffic congestion features into the multi-scale geographically weighted regression model for regression analysis to generate the analysis results; Step 3: Measure the relationship between the urban spatial structure and traffic congestion according to the analysis results and the persistent homology method; The specific steps of Step 3 include: Step 3.1: Extract the independent variable regression coefficients in the analysis results as the high-dimensional coordinates of each road, and construct a VR complex for this set of point cloud data; Step 3.2: Draw the persistent diagrams of topological features in different dimensions according to the VR complex, and calculate the persistence time of all two-dimensional features accordingly; Step 3.3: Sort the two-dimensional features in descending order of persistence time, select a preset number of two-dimensional features from top to bottom, extract the road groups corresponding to each two-dimensional feature, and output the spatial distribution results corresponding to each road group.

2. The method according to claim 1, characterized in that, The specific steps of Step 2 include: Take the urban spatial structure features as the independent variable X and the average congestion index as the dependent variable Y and substitute them into the multi-scale geographically weighted regression model to conduct multi-scale geographically weighted regression analysis on the urban spatial structure features and traffic congestion features to generate the analysis results.

3. The method according to claim 2, characterized in that The expression of the multi-scale geographically weighted regression model is ； wherein, is the dependent variable of the th observation point, is the th th independent variable of the th observation point, are the spatial coordinates of the th observation position, is the intercept term at the position is the th regression coefficient of the independent variable at the position, depending on the spatial coordinates, is the error term; ； Among them, is the spatial bandwidth parameter of the th independent variable, is the spatial weight between position and position , calculated based on the spatial bandwidth parameter of the th independent variable . is the th value of the th independent variable at the th position, is the dependent variable value at the th position.

Images