Lane change interaction behavior feature analysis method based on Copula

Abstract

The invention belongs to the technical field of intelligent traffic systems, and discloses a Copula-based lane change interaction behavior feature analysis method, which can effectively and automatically identify a potential change interaction mode from a large amount of original data by accurately extracting microscopic interaction features and clustering the change interaction behaviors by using three clustering algorithms, thereby improving the accuracy of lane change interaction behavior analysis. According to the method, a Copula theory is introduced to model a dependency relationship among vehicles, functions such as Clayton Copula, Normal Copula and Student-T Copula are adopted, a complex nonlinear dependency structure among the vehicles in the transformation interaction behaviors can be effectively captured, particularly the mutual relationship of key indexes such as time headway can be effectively captured, the fitting effect of a Copula model is optimized through a parameter estimation method, and the accuracy of the transformation interaction behaviors is improved. And the prediction capability is improved.

Description

Technical Field

[0001] This application belongs to the technical field of intelligent transportation systems, and specifically relates to a method for analyzing the characteristics of lane-changing interaction behavior based on Copula, which can be used to analyze the lane-changing interaction patterns of vehicles in the weaving area and provide support for autonomous driving decision-making. Background Art

[0002] In modern transportation systems, the weaving area is a key node in traffic flow. The weaving area is usually the area where highways, urban roads, and other important roads intersect. Vehicles frequently change lanes here, resulting in a shortage of road resources and unstable traffic flow. Due to the large number of lanes and heavy traffic flow in the weaving area, the lane-changing behavior of vehicles in these areas is not only affected by other vehicles but also closely related to the overall state of the traffic flow. For example, during peak traffic hours, drivers may frequently change lanes due to increased traffic pressure, further exacerbating the risk of traffic congestion and accidents. Therefore, how to effectively capture and analyze the traffic flow patterns in the weaving area has become an important research direction in traffic engineering and autonomous driving systems.

[0003] Traditional research on lane-changing behavior has mainly focused on the behavior analysis of individual vehicles. Existing studies mainly use discrete choice models based on individual driver decisions or rule-based methods to model lane-changing behavior. Rule-based models usually rely on preset driving rules and gap acceptance theory to simulate the driver's lane-changing decision-making process. However, due to the complexity and diversity of driver behavior, fixed-rule models are difficult to comprehensively and accurately describe lane-changing behavior in the actual traffic environment. Discrete choice-based models: These models are based on the theory of utility maximization and establish a lane-changing choice probability model for drivers in different situations. For example, Ahmed et al. established a vehicle lane-changing probability model, and Toledo et al. constructed an integrated model that simultaneously considers the forced lane-changing and free lane-changing processes. However, these models have limitations in dealing with the correlation between multiple choices, which may lead to estimation biases and inaccurate predictions. Cellular automaton-based models divide the road into discrete cells and simulate traffic flow by setting the movement rules of vehicles between cells. However, traditional cellular automaton models usually update the vehicle state in a fixed order and have the same transition rules, failing to fully consider the behavioral differences and diversity of different drivers, resulting in limitations in simulating vehicle lane-changing behavior in actual traffic scenarios. In these studies, the interaction between interacting vehicles before and after lane-changing is generally ignored. For example, Qu Dayi et al. proposed a classification method that divides vehicle lane-changing behavior into three types: free lane-changing, forced lane-changing, and cooperative lane-changing, and established a corresponding minimum safety distance model. However, this study mainly focuses on the interaction behavior between the lane-changing vehicle and the following vehicle in the target lane and fails to comprehensively consider the influence of all relevant vehicles. In addition, Ji Wenchao's research proposed a vehicle lane-changing model for urban roads based on driving behavior analysis. This model considers the driver's lane-changing intention and the decision-making of the following vehicle in the adjacent lane, but still has limitations in dealing with multi-vehicle interactions in complex traffic environments. These methods often ignore the mutual influence between vehicles. For example, when a vehicle changes lanes, it may be affected by the behavior of the vehicle in front, the vehicle behind, and the vehicles in front and behind in the target lane. This kind of influence is multi-level and dynamically changing. The shortcoming of existing models is that they cannot accurately model this complex interaction, often resulting in low prediction accuracy. In addition, most existing studies rely on small-scale experimental data and are difficult to cover the complexity of the real traffic environment. Traditional traffic data collection often focuses on specific road sections or time periods and fails to reflect the dynamically changing traffic flow behavior. Therefore, how to use large-scale real-time traffic data to analyze and predict traffic behavior in weaving areas has become a new challenge.

[0004] In recent years, with the development of big data, machine learning, and intelligent transportation technologies, data-driven lane-changing behavior modeling methods have gradually become a research hotspot. Methods such as deep learning and graph neural networks can model the complex interaction relationships between vehicles to a certain extent, but these methods usually rely on a large amount of labeled data and lack the ability to explicitly model statistical dependencies. Therefore, how to use unsupervised learning methods to automatically identify lane-changing patterns from data and accurately model the interaction dependencies through statistical models is an important challenge in current intelligent transportation and autonomous driving decision optimization.

[0005] Generally speaking, the traffic mobility analysis in the weaving area requires a more refined and comprehensive model to describe the complex vehicle interaction relationships therein. Combining real-time traffic data and advanced computing technologies can effectively improve the traffic management level and provide more accurate predictions for the decision-making of autonomous driving systems. Summary of the Invention

[0006] The purpose of this application is to solve the problems of the prior art and provide a Copula-based method for analyzing the characteristics of lane-changing interaction behavior.

[0007] To solve the technical problems, the technical solution of this application is: a Copula-based method for analyzing the characteristics of lane-changing interaction behavior, including the following steps: Step 1: Data collection; Obtain the video of the weaving area through drone aerial photography and identify the vehicle trajectory data of lane changes from it; Step 2: Data preprocessing; Step 2-1: Extract microscopic interaction features from the vehicle trajectory data identified in Step 1. The microscopic interaction features include absolute speed, relative speed, relative distance, and time headway; Step 2-2: Perform data cleaning and normalization processing on the microscopic interaction features; Step 3: Cluster analysis; Step 3-1: Input the preprocessed microscopic interaction features into three clustering algorithms, namely K-means, hierarchical clustering, or self-organizing feature mapping, and use the silhouette coefficient or CH index to select the best clustering algorithm; Step 3-2: Construct a feature space and use the extracted microscopic interaction features to construct a multi-dimensional feature space as the input for cluster analysis; Step 3-3: Run the clustering algorithm selected in Step 3-1 during the clustering execution stage of cluster analysis, and divide the lane-changing interaction behavior into multiple clustering categories, where each clustering category represents a specific lane-changing pattern; Step 3-4: Then use the silhouette coefficient or CH index to evaluate the clustering categories and determine the optimal number of clustering categories; Step 4: Copula Modeling, using the Copula model to model and predict the statistical dependence relationship of different transformation interaction behaviors; Step 4-1: First, perform marginal distribution fitting, analyze the marginal distribution of the headway of each clustering category, and select the distribution type that best describes the headway; Step 4-2: According to the distribution type, select the corresponding Copula function to establish a Copula model for capturing the non-linear dependence structure between variables; Step 4-3: Use the maximum likelihood estimation method to estimate the parameters of the selected Copula model; Step 4-4: Evaluate the fitting effects of different Copula models and select the optimal Copula model; Step 5: Behavior Interpretation, interpret the optimal Copula model and output the classification of transformation interaction behaviors.

[0008] Preferably, the specific content of step 1 is as follows: Use the drone aerial photography technology to take real-time traffic flow videos of the weaving area, and combine YOLOv5 and DeepSort to extract vehicle trajectories, and identify the vehicle trajectory data of lane-changing vehicles from them. The vehicle trajectory data includes vehicle position, speed, acceleration, and lane-changing behavior.

[0009] Preferably, the absolute speed in step 2-1 is the speed of the target vehicle itself, expressed as: ; Where: is the vehicle i at time t absolute speed, km / h; is the vehicle position change; is the lane-changing vehicle moment, s; The relative speed is the relative speed between adjacent vehicles, expressed as: ; Where: is the vehicle i and vehicle j relative speed between, km / h; is the vehicle j at time t absolute speed, km / h; The relative distance is the relative distance between vehicles, expressed as: ; Where: For a vehicle i With the vehicle j At time t The relative distance, m; And Are respectively the positions of the vehicle i With the vehicle j At time t The position, m; The headway is the headway between vehicles, expressed as: ; When the relative speed is zero, the headway is defined as a maximum value or supplemented by interpolation.

[0010] Preferably, the data cleaning and normalization processing of the microscopic interaction features in step 2-2 are specifically as follows: detecting the microscopic interaction features and removing outliers, and then using the min-max normalization method to convert the microscopic interaction features with different dimensions to the unified [0,1] scale range.

[0011] Preferably, the objective function of the K-means algorithm in step 3-1 is: ; In the formula: Is the n th sample, i ∈ {1, 2,..., N} , N Is the total number of samples; Is to optimize the cluster ; Is the centroid of the cluster; A Is the number of clusters.

[0012] Preferably, step 4-1 is specifically as follows: by transforming the headway of each clustering category, the corresponding marginal distribution function is obtained; ; In the formula: Is an arbitrarily given headway value; Is the probability operator, indicating the probability of the event that the headway ≤ This event occurs; Step 4-2 is specifically as follows: according to the distribution type, select the corresponding Copula function to establish a Copula model, expressed as: ; Wherein: are the parameters of the Copula model; and are two real thresholds, which are respectively used to calculate the probabilities that the headway does not exceed them; and are respectively the marginal distributions of the headways of two lane-changing modes.

[0013] Preferably, the Copula function in the step 4-2 includes Normal Copula, Student-T Copula, Clayton Copula, Gumbel Copula and Frank Copula; The basic formula of the Copula function is: ; The Normal Copula is: ; The Student-T Copula is: ; The function forms of the indicated Clayton Copula, Gumbel Copula and Frank Copula are constructed by using the following formula: ; Wherein: is the cumulative distribution function of the standard bivariate normal distribution; is the inverse function of the cumulative distribution function of the standard bivariate normal distribution; is the correlation coefficient matrix between variables; is the inverse matrix of the correlation coefficient matrix; is one of the random variables in the case of a binary variable, the marginal distribution function of the random variable, = ; is the 1,2,...,N th marginal distribution function of the random variable, i ∈ {1, 2,..., N} , is the i th marginal distribution function of the random variable; is the other random variable in the case of a binary variable; is a vector whose elements are quantiles of the standard normal distribution; is the vector transpose; is the identity matrix; is the degrees of freedom parameter used to define the shape of the distribution; is the cumulative distribution function of the univariate ρ and degrees of freedom k with the correlation coefficient matrix distribution; is the inverse cumulative distribution function of the univariate k with degrees of freedom distribution; is a generating function that satisfies strict monotonic decrease, convexity, and ; is the inverse function of the generating function.

[0014] The conditions and are compatible under the definitions of strict monotonic decrease and convexity of the generating function . The former is the normalization condition of the generating function, and the latter is the defining condition to ensure the Copula within the valid range. Together, they define the reasonable behavior of the Copula.

[0015] Preferably, the Normal Copula is applicable to describe the linear dependence relationship in lane-changing interaction behavior for smooth traffic flow; the Clayton Copula is applicable to capture left-tail dependence and is used to describe the interdependent behavior under low vehicle speed or congestion conditions; the Student-T Copula is used to capture tail dependence and is used to describe extreme behaviors.

[0016] Preferably, the specific content of step 5 is as follows: behavior interpretation, interpreting the optimal Copula model, providing an understanding of different transformation interaction behaviors from aspects such as speed, acceleration, and trajectory characteristics, interpreting and annotating different types of transformation interaction behaviors by analyzing the characteristic distribution laws of each clustering category and combining with the dependence relationship revealed by the Copula model, and finally outputting a classification result of transformation interaction behavior with clear physical meaning to support autonomous driving decision-making and traffic management.

[0017] Preferably, a method for analyzing the characteristics of lane-changing interaction behavior based on Copula includes a system for analyzing the characteristics of lane-changing interaction behavior based on Copula. The system for analyzing the characteristics of lane-changing interaction behavior based on Copula includes a data acquisition module, a data processing module, a clustering analysis module, a dependence modeling module, and a behavior interpretation module. The data acquisition module is used to collect videos of the weaving area and identify the vehicle trajectory data of lane-changing vehicles from them. The data processing module is used to extract the microscopic interaction characteristics of the vehicle trajectory data. The clustering analysis module uses K-means, hierarchical clustering, or self-organizing feature mapping to perform clustering analysis on the transformation interaction behavior. The dependence modeling module uses the Copula model to model and predict the statistical dependence relationship of different transformation interaction behaviors. The behavior interpretation module understands and interprets different transformation interaction behaviors by analyzing speed, acceleration, and trajectory characteristics.

[0018] Compared with the prior art, the advantages of this application are as follows: (1) Based on UAV aerial photography data, this application accurately extracts microscopic interaction characteristics and uses unsupervised learning methods such as K-means, hierarchical clustering, or self-organizing feature mapping to cluster the transformation interaction behavior. These methods can effectively automatically identify potential transformation interaction patterns from a large amount of raw data, classify different transformation interaction behaviors, and provide data support for subsequent behavior analysis and modeling. (2) For different transformation interaction patterns, this application introduces the Copula theory to model the dependence relationship between vehicles. By using functions such as Clayton Copula, Normal Copula, and Student-T Copula, it can effectively capture the complex non-linear dependence structure between vehicles in the transformation interaction behavior, especially the mutual relationship of key indicators such as time headway. Through parameter estimation methods, the fitting effect of the Copula model is optimized, thereby improving the prediction ability. Compared with traditional methods, the Copula theory can more accurately describe the statistical dependence between various transformation interaction patterns, thus enhancing the understanding and prediction ability of the transformation interaction behavior. (3) This application adopts a statistical-based modeling method with low computational complexity, can quickly process large-scale traffic data, is suitable for real-time traffic analysis and prediction. By optimizing the algorithm and model structure, this application can operate efficiently in the actual traffic environment, provide immediate analysis results of the transformation interaction behavior, and provide real-time support for traffic mobility management and safety warning. (4) This application is not only applicable to the analysis of traditional traffic flow data, but also can effectively process large-scale real-time data in emerging applications such as autonomous driving and intelligent transportation systems. In the field of autonomous driving, the mutual influence between vehicles and cooperative lane-changing behaviors are the keys to improving driving safety and fluency. The lane-changing interaction behavior clustering analysis method based on the Copula theory has the characteristics of high efficiency, accuracy, and real-time, and can deeply analyze the interaction patterns during the lane-changing process of vehicles, providing strong support for the optimization of intelligent transportation systems, the improvement of the safety of autonomous driving systems, and traffic flow management. (5) This application can comprehensively consider various factors, such as vehicle speed, headway, relative lane position, etc., to conduct multi-dimensional transformation interaction behavior analysis, helping to identify lane-changing risks in different scenarios and providing a scientific basis for optimizing traffic flow management in weaving areas. (6) By real-time analyzing the transformation interaction behaviors in the weaving area, this application can provide accurate traffic flow prediction, helping traffic management departments to monitor traffic conditions in real time, identify potential traffic congestion and accident risks, and provide decision-making support for intelligent transportation systems and autonomous driving vehicles; at the same time, based on the identification of transformation interaction behavior patterns, it can early warn of possible safety hazards and improve road safety. Description of the Drawings

[0019] Figure 1 It is a flowchart of a method for analyzing lane-changing interaction behavior characteristics based on Copula. Figure 2 It is a schematic diagram for extracting vehicle trajectories from UAV aerial photography. Figure 3 It is a schematic diagram for extracting microscopic interaction characteristics. Figure 4 It is a schematic diagram of the distribution of Kendall rank correlation coefficients of the results of each clustering category. Detailed Embodiments

[0020] The following describes this application in detail with reference to the drawings and specific embodiments, but this application is not limited to these embodiments. This application covers any alternatives, modifications, equivalent methods, and solutions made within the essence and scope of this application. For the public to have a thorough understanding of this application, specific details are described in detail in the following embodiments of this application, but those skilled in the art can fully understand this application without the description of these details.

[0021] As Figure 1 shown, this application discloses a method for analyzing lane-changing interaction behavior characteristics based on Copula, including the following steps: Step 1: Data collection; obtaining the video of the weaving area through UAV aerial photography and identifying the vehicle trajectory data of lane-changing from it. Step 2: Data preprocessing; Step 2-1: Extract microscopic interaction features from the vehicle trajectory data identified in Step 1. The microscopic interaction features include absolute speed, relative speed, relative distance, and time headway; Step 2-2: Perform data cleaning and normalization on the microscopic interaction features; Step 3: Cluster analysis; Step 3-1: Input the preprocessed microscopic interaction features into three clustering algorithms, namely K-means, hierarchical clustering, or self-organizing feature mapping, and select the best clustering algorithm using the silhouette coefficient or CH index; Step 3-2: Construct a feature space. Using the extracted microscopic interaction features, construct a multi-dimensional feature space as the input for cluster analysis; Step 3-3: Run the clustering algorithm selected in Step 3-1 during the clustering execution stage of cluster analysis, and divide the lane-changing interaction behaviors into multiple clustering categories. Each clustering category represents a specific lane-changing pattern; Step 3-4: Then use the silhouette coefficient or CH index to evaluate the clustering categories and determine the optimal number of clustering categories; Step 4: Copula modeling. Use the Copula model to model and predict the statistical dependence relationships of different lane-changing interaction behaviors; Step 4-1: First, perform marginal distribution fitting. Conduct marginal distribution analysis on the time headway of each clustering category and select the distribution type that best describes the time headway; Step 4-2: According to the distribution type, select the corresponding Copula function to establish a Copula model for capturing the non-linear dependence structure between variables; Step 4-3: Use the maximum likelihood estimation method to estimate the parameters of the selected Copula model; Step 4-4: Evaluate the fitting effects of different Copula models and select the optimal Copula model; Step 5: Behavior interpretation. Interpret the optimal Copula model and output the classification of lane-changing interaction behaviors.

[0022] Preferably, Step 1 is specifically: Use the drone aerial photography technology to capture the traffic flow video of the weaving area in real time, and combine YOLOv5 and DeepSort to extract vehicle trajectories, and identify the vehicle trajectory data of the vehicles that change lanes from them. The vehicle trajectory data includes vehicle position, speed, acceleration, and lane-changing behavior.

[0023] Preferably, in Step 2-1, the absolute speed is the speed of the target vehicle itself, expressed as: ; Where: For a vehicle i At time t The absolute speed of, km / h; Is the change in the position of the vehicle; Is the time of the lane-changing vehicle, s; The relative speed is the relative speed between adjacent vehicles, expressed as: ; Where: Is the vehicle i And the vehicle j The relative speed between them, km / h; Is the vehicle j At time t The absolute speed of, km / h; The relative distance is the relative distance between vehicles, expressed as: ; Where: Is the vehicle i And the vehicle j At time t The relative distance at, m; And Are respectively the vehicles i And the vehicle j At time t The positions at, m; The time headway is the time headway between vehicles, expressed as: ; When the relative speed is zero, the time headway is defined as a maximum value or supplemented by interpolation.

[0024] Preferably, the data cleaning and normalization processing of the microscopic interaction features in step 2-2 is specifically: detecting the microscopic interaction features and removing outliers, and then using the min-max normalization method to convert the microscopic interaction features with different dimensions into a unified [0,1] scale range.

[0025] Preferably, the objective function of the K-means algorithm in step 3-1 is: ; In the formula: Is the n Th sample, i ∈ {1, 2,..., N} , N Is the total number of samples; To optimize the cluster ; is the th cluster; is the centroid of the cluster; A is the number of clusters, determined by the silhouette coefficient or the CH index.

[0026] Preferably, step 4-1 is specifically: by transforming the headway of each clustering category, the corresponding marginal distribution function is obtained; ; In the formula: is an arbitrarily given headway value; is the probability operator, indicating the probability of the event that the headway ≤ occurs; Step 4-2 is specifically: according to the distribution type, the corresponding Copula function is selected to establish a Copula model, expressed as: ; In the formula: are the parameters of the Copula model; and are two real thresholds, respectively used to calculate the probabilities that the headway does not exceed them; and are the marginal distributions of the headways of two lane-changing modes respectively.

[0027] Preferably, the Copula functions in step 4-2 include Normal Copula, Student-T Copula, Clayton Copula, Gumbel Copula, and Frank Copula; The basic formula of the Copula function is: ; The Normal Copula is: ; The Student-T Copula is: ; The functional forms of the Clayton Copula, Gumbel Copula, and Frank Copula shown are constructed using the following formulas: ; where: is the cumulative distribution function of the standard bivariate normal distribution; is the inverse function of the cumulative distribution function of the standard bivariate normal distribution; is the correlation coefficient matrix between variables; is the inverse matrix of the correlation coefficient matrix; is one of the random variables in the case of bivariate variables, and the marginal distribution function of the random variable, = ; is the 1,2,...,N th marginal distribution function of the random variable, i ∈ {1, 2,..., N} , is the i th marginal distribution function of the random variable; is the other random variable in the case of bivariate variables; is a vector whose elements are the quantiles of the standard normal distribution; is the transpose of the vector ; is the identity matrix; is the degrees of freedom parameter used to define the shape of the distribution; is the cumulative distribution function of the univariate ρ distribution with the correlation coefficient matrix k and degrees of freedom ; is the inverse cumulative distribution function of the univariate k distribution with degrees of freedom ; is the generating function, which satisfies strict monotonic decrease, convexity, and ; is the inverse function of the generating function.

[0028] Preferably, the Normal Copula is applicable to describe the linear dependence relationship in lane-changing interaction behavior and is used when the traffic flow is stable; the Clayton Copula is applicable to capture left-tail dependence and is used to describe the interdependent behavior under low vehicle speed or congestion conditions; the Student-T Copula is used to capture tail dependence and is used to describe extreme behaviors.

[0029] Preferably, step 5 is specifically as follows: behavior interpretation, interpreting the optimal Copula model, providing an understanding of different transformation interaction behaviors from aspects such as speed, acceleration, and trajectory characteristics, analyzing the characteristic distribution laws of each clustering category, and combining the dependence relationship revealed by the Copula model to interpret and label different types of transformation interaction behaviors, and finally outputting a classification result of transformation interaction behaviors with clear physical meanings to support autonomous driving decision-making and traffic management.

[0030] Preferably, a method for analyzing lane-changing interaction behavior characteristics based on Copula includes a system for analyzing lane-changing interaction behavior characteristics based on Copula. The system for analyzing lane-changing interaction behavior characteristics based on Copula includes a data acquisition module, a data processing module, a clustering analysis module, a dependence modeling module, and a behavior interpretation module; the data acquisition module is used to collect videos of the weaving area and identify vehicle trajectory data of lane changes from them; the data processing module is used to extract microscopic interaction characteristics of the vehicle trajectory data; the clustering analysis module uses K-means, hierarchical clustering, or self-organizing feature mapping to perform clustering analysis on the transformation interaction behavior; the dependence modeling module uses the Copula model to model and predict the statistical dependence relationship of different transformation interaction behaviors; the behavior interpretation module understands and interprets different transformation interaction behaviors by analyzing speed, acceleration, and trajectory characteristics.

[0031] Embodiment 1 As Figure 1 shown, a method for analyzing lane-changing interaction behavior characteristics based on Copula in this embodiment includes the following steps: Step 1: Data acquisition; Drone aerial photography is used to obtain videos of the weaving area. YOLOv5 and DeepSort are used to extract vehicle trajectories, and whether the vehicle trajectories cross the lane line equations; Yes, obtain the vehicle trajectories of lane-changing vehicles and extract the moments of lane-changing vehicles; No, obtain the vehicle trajectories of non-lane-changing vehicles.

[0032] Step 2: Data preprocessing; Extract the trajectories of adjacent vehicles before and after lane-changing of lane-changing vehicles, extract microscopic interaction characteristics, perform data cleaning, and normalization processing.

[0033] Step 3: Clustering analysis; Select the best clustering algorithm from the set of clustering algorithms using the silhouette coefficient or the CH index, construct the feature space, perform clustering, and evaluate the clustering categories.

[0034] Step 4: Copula modeling; Marginal distribution fitting, select Copula function, Copula parameter estimation, Copula model evaluation, optimal Copula model.

[0035] Step 5: Behavior interpretation, interpret the optimal Copula model and output the classification of transformed interaction behaviors.

[0036] Embodiment 2 A method for analyzing the characteristics of lane-changing interaction behavior based on Copula in this embodiment includes the following steps: Step 1: Data collection; As Figure 2 shown, it is a schematic diagram for extracting vehicle trajectories by drone aerial photography. High-precision vehicle trajectory data in the weaving area is obtained through drone aerial photography technology. Specifically, when implementing, drones are deployed over the weaving area to capture traffic flow videos in real time and capture the driving trajectories of vehicles. Combine YOLOv5 and DeepSort technologies to extract all vehicle trajectories and identify the vehicle trajectory data of lane-changing vehicles from them.

[0037] The data collection module is responsible for collecting vehicle trajectory data in real time in the weaving area through high-precision GPS devices or other sensors. The collected vehicle trajectory data includes information such as the position, speed, acceleration, and lane-changing behavior of the vehicle. The time interval for data recording is Δt, usually 0.1 second or shorter.

[0038] Step 2: Data preprocessing; In this step, the collected data is preprocessed and microscopic interaction features are extracted. First, select absolute speed, relative speed, relative distance, and time headway as microscopic interaction features. Then, in the data cleaning stage, detect and remove outliers, such as data deviations caused by sensor errors, to ensure the accuracy of the data. Finally, perform normalization processing on the data using the min-max normalization method to convert feature values with different dimensions to a unified [0,1] scale range to improve the stability and convergence speed of model training.

[0039] The extracted vehicle trajectory data is transmitted to the data processing module through wireless communication technology for subsequent analysis.

[0040] Absolute speed: The speed of the vehicle itself, expressed as: ; In the formula: is the vehicle i at timet Absolute speed, km / h; Is the change in vehicle position; Is the lane-changing vehicle time, s; Relative speed: The relative speed between adjacent vehicles is defined as: ; Is vehicle i And vehicle j The relative speed between them, km / h; Is vehicle j At time t Absolute speed, km / h; Relative distance: The relative distance between vehicles is defined as: ; In the formula: Is vehicle i And vehicle j At time t The relative distance, m; And Are respectively vehicle i And vehicle j At time t Position, m; Time headway (THW): The time headway between vehicles is defined as: ; When the relative speed is zero, the time headway is defined as a maximum value or supplemented by interpolation.

[0041] As Figure 3 Shown, is a schematic diagram of microscopic interaction feature extraction. The contents represented by the parameters in the figure are as follows: Is the speed of the lane-changing vehicle i In the current lane, km / h; Is the speed of the vehicle following the lane-changing vehicle in the current lane, km / h; Is the speed of the vehicle in front of the lane-changing vehicle in the current lane, km / h; Is the speed of the vehicle following the lane-changing vehicle in the target lane, km / h; Is the speed of the vehicle in front of the lane-changing vehicle in the target lane, km / h; is the relative distance, in m, between the lane-changing vehicle on the original lane i and the following vehicle r ; is the relative distance, in m, between the lane-changing vehicle on the original lane i and the vehicle ahead f ; is the relative distance, in m, between the lane-changing vehicle on the target lane i and the following vehicle r ; is the relative distance, in m, between the lane-changing vehicle on the target lane i and the vehicle ahead f ; H c,i,f , H c,i,r , H t,i,f , H t,i,r are four headways.

[0042] Step 3: Cluster analysis; In this step, unsupervised cluster analysis is performed on the preprocessed data. First, the preprocessed microscopic interaction features are input into three clustering algorithms, namely K-means, hierarchical clustering, or self-organizing feature mapping, and the silhouette coefficient or CH index is used to select the best clustering algorithm; second, a feature space is constructed, and the extracted microscopic interaction features are used to construct a multi-dimensional feature space as the input for cluster analysis; then, the selected clustering algorithm is run in the clustering execution phase of cluster analysis to divide the transformed interaction behaviors into multiple cluster categories, each cluster category representing a specific lane-changing pattern; finally, the silhouette coefficient or CH index is used to evaluate the cluster categories to determine the optimal number of cluster categories.

[0043] The K-means clustering algorithm is used for behavior pattern classification. The goal is to divide the lane-changing behavior into K clusters, each cluster representing a specific interaction pattern. The objective function of the K-means algorithm is: ; where: is the n th sample, i ∈ {1, 2,..., N} , N is the total number of samples; is to optimize the cluster ; is the th cluster; is the centroid of the cluster; A is the number of clusters.

[0044] As Figure 4 shown, the clustering categories 0, 1, 2, 3, and 4 are obtained.

[0045] Step 4: Copula modeling; In this step, the Copula model is used to model and predict the statistical dependence relationship of different transformation interaction modes. First, the marginal distribution fitting is carried out, and the marginal distribution analysis of the headway data of each clustering category is performed to select the distribution type that can best describe the data characteristics; secondly, according to the characteristics of the marginal distribution, a suitable Copula function is selected to capture the non-linear dependence structure between variables; then, methods such as maximum likelihood estimation are used to estimate the parameters of the selected Copula model; finally, indicators such as AIC and BIC are used to evaluate the fitting effect of different Copula models, and the optimal model is selected; The Copula model is constructed through the following steps: Step 4-1: Data transformation, by transforming the headway data under each clustering category, the corresponding marginal distribution function is obtained: ; In the formula: is an arbitrarily given headway value; is the probability operator, indicating the probability of the event that the headway ≤ ; Step 4-2: Construct the Copula model, and fit the joint distribution according to the dependence structure of the data: ; In the formula: are the parameters of the Copula model; and are two real thresholds, which are used to calculate the probabilities that the headways do not exceed them respectively; and are the marginal distributions of the headways of two lane-changing modes respectively.

[0046] As shown in Table 1, the results of different copula modeling are presented. In the table, the optimal Copula for cluster category 0 is Clayton Copula, the optimal Copula for cluster category 1 is Normal Copula, the optimal Copula for cluster category 2 is Clayton Copula, the optimal Copula for cluster category 3 is Normal Copula, and the optimal Copula for cluster category 4 is Clayton Copula.

[0047] Table 1 Results of Different Copula Modeling Step 5: Behavior Interpretation; This step mainly interprets the modeling results and provides an understanding of different lane-changing behavior patterns in terms of speed, trajectory, and acceleration characteristics. By analyzing the characteristic distribution laws of each cluster category and combining with the dependence relationship revealed by the Copula model, different types of transformation interaction behaviors are interpreted and labeled, and finally, a lane-changing behavior classification result with clear physical meaning is output to support autonomous driving decision-making and traffic management.

[0048] As Figure 4 shown, it is a schematic diagram of the distribution of Kendall rank correlation coefficients for the results of each cluster category. Among the five cluster categories, the Kendall rank correlation coefficient matrix for the four headways. The Kendall rank correlation coefficient is a non-parametric statistical method used to measure the correlation between two variables, and its value ranges from -1 to 1; 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

[0049] The above five steps constitute a complete lane-changing interaction behavior clustering analysis method. Each step is closely connected through data flow. The output of the previous step serves as the input of the next step, forming a complete technical closed-loop.

[0050] The working principle of this application is as follows: The present application proposes a method for analyzing the characteristics of lane-changing interaction behavior based on Copula, including a data acquisition module, a data processing module, a clustering analysis module, a dependence modeling module, and a behavior interpretation module; the data acquisition module is responsible for using the aerial video of an unmanned aerial vehicle to obtain the trajectory data of vehicles in the weaving area through vehicle trajectory technology; the data processing module mainly preprocesses and extracts features from the collected data; the clustering analysis module performs clustering analysis on the processed data and uses K-Means, hierarchical clustering, and self-organizing feature mapping (SOM) to identify different transformation interaction behavior patterns; the dependence modeling and prediction module uses the Copula model to model and predict the statistical dependence relationships of different transformation interaction behaviors; finally, the behavior interpretation module interprets the modeling results and provides an understanding of different lane-changing behavior patterns from aspects such as speed, acceleration, and trajectory characteristics.

[0051] The above has made a detailed description of the preferred implementation mode of the present application. However, the present application is not limited to the above implementation mode, and various changes can be made without departing from the purpose of the present application within the scope of knowledge possessed by those of ordinary skill in the art.

[0052] Many other changes and modifications can be made without departing from the concept and scope of the present application. It should be understood that the present application is not limited to a specific implementation mode, and the scope of the present application is defined by the appended claims.

Claims

1. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula, characterized in that, It includes the following steps: Step 1: Data collection; Obtain the video of the weaving area through UAV aerial photography, and identify the vehicle trajectory data of lane-changing vehicles from it; Step 2: Data preprocessing; Step 2-1: Extract microscopic interaction features from the vehicle trajectory data identified in Step 1. The microscopic interaction features include absolute speed, relative speed, relative distance, and time headway; Step 2-2: Perform data cleaning and normalization on the microscopic interaction features; Step 3: Cluster analysis; Step 3-1: Input the preprocessed microscopic interaction features into three clustering algorithms, namely K-means, hierarchical clustering, or self-organizing feature mapping, and use the silhouette coefficient or CH index to select the best clustering algorithm; Step 3-2: Construct a feature space, and use the extracted microscopic interaction features to construct a multi-dimensional feature space as the input for cluster analysis; Step 3-3: Run the clustering algorithm selected in Step 3-1 during the clustering execution stage of cluster analysis, and divide the transform interaction behaviors into multiple clustering categories, where each clustering category represents a specific lane-changing pattern; Step 3-4: Then use the silhouette coefficient or CH index to evaluate the clustering categories and determine the optimal number of clustering categories; Step 4: Copula modeling, use the Copula model to model and predict the statistical dependence relationship of different transform interaction behaviors; Step 4-1: First, perform marginal distribution fitting, conduct marginal distribution analysis on the time headway of each clustering category, and select the distribution type that best describes the time headway; Step 4-2: According to the distribution type, select the corresponding Copula function to establish a Copula model for capturing the non-linear dependence structure between variables; Step 4-3: Use the maximum likelihood estimation method to estimate the parameters of the selected Copula model; Step 4-4: Evaluate the fitting effects of different Copula models and select the optimal Copula model; Step 5: Behavior interpretation, interpret the optimal Copula model and output the classification of transform interaction behaviors.

2. The method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 1, characterized in that, Specifically, Step 1 is: Use UAV aerial photography technology to capture the traffic flow video of the weaving area in real time, and combine YOLOv5 and DeepSort to extract vehicle trajectories, and identify the vehicle trajectory data of lane-changing vehicles from them. The vehicle trajectory data includes vehicle position, speed, acceleration, and lane-changing behavior.

3. The method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 2, characterized in that, In Step 2-1, the absolute speed is the speed of the target vehicle itself, expressed as: ； Where: For a vehicle i at a time t absolute speed, km / h; The position change amount of the vehicle; Time for lane-changing vehicle, s; The relative speed is the relative speed between adjacent vehicles, expressed as: ； Where: for a vehicle i and the vehicle j relative speed therebetween, km / h; For a vehicle j at time t the absolute speed, km / h; The relative distance is the relative distance between vehicles, expressed as: ； Where: for a vehicle i with the vehicle j at time t the relative distance, m; and are the positions of the vehicle i and the vehicle j at time t , m; The time headway is the time headway between vehicles, expressed as: ； When the relative speed is zero, the time headway is defined as a maximum value or supplemented by interpolation.

4. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 3, characterized in that In Step 2-2, the specific operation of performing data cleaning and normalization on the microscopic interaction features is: Detect the microscopic interaction features and remove outliers, and then use the min-max normalization method to convert the microscopic interaction features with different dimensions to a unified [0,1] scale range.

5. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 1, characterized in that The objective function of the K-means algorithm in Step 3-1 is: ； In the formula: For the n th sample, i ∈ {1, 2,..., N} , N being the total number of samples; To optimize the cluster ; is the th cluster; is the centroid of the cluster; A is the number of clusters.

6. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 3, characterized in that Step 4-1 is specifically as follows: By transforming the headway of each clustering category, the corresponding marginal distribution function is obtained. ； In the formula: is a value of the headway for any given vehicle headway; is the probability operator, indicating the probability that the headway ≤ of this event occurring; Step 4-2 is specifically as follows: According to the distribution type, the corresponding Copula function is selected to establish a Copula model, expressed as: ； In the formula: are the parameters of the Copula model; and are two real - number thresholds, which are respectively used to calculate the probabilities that the headway does not exceed them; and are the marginal distributions of the time headways of the two lane-changing patterns, respectively.

7. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 6, characterized in that The Copula functions in Step 4-2 include Normal Copula, Student-T Copula, Clayton Copula, Gumbel Copula, and Frank Copula. The basic formula of the Copula function is: ； The Normal Copula is: ； The Student-T Copula is: ； The function forms of the shown Clayton Copula, Gumbel Copula, and Frank Copula are constructed using the following formula: ； Where: is the cumulative distribution function of the standard bivariate normal distribution; is the inverse function of the cumulative distribution function of the standard bivariate normal distribution; is the correlation coefficient matrix between variables; is the inverse matrix of the correlation coefficient matrix; For one of the random variables in the case of binary variables, the marginal distribution function of the random variable, = ; is the marginal distribution function of the 1,2,...,N th random variable, i ∈ {1, 2,..., N} , is the marginal distribution function of the i th random variable; is another random variable in the case of a binary variable; is a vector whose elements are quantiles of the standard normal distribution; is the transpose of the vector ; is the identity matrix; is a degree-of-freedom parameter used to define the shape of the distribution; for a univariate ρ cumulative distribution function of a k distribution with a correlation coefficient matrix and degrees of freedom; for the inverse cumulative distribution function of a univariate k distribution with degrees of freedom; is a generating function that satisfies strict monotonic decrease, convexity, and ; Is the inverse function of the generating function.

8. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 7, characterized in that, The Normal Copula is applicable to describing the linear dependence relationship in lane-changing interaction behaviors and is used when the traffic flow is stable; the Clayton Copula is applicable to capturing left-tail dependence and is used to describe the interdependent behaviors under low vehicle speeds or congestion conditions; the Student-T Copula is used to capture tail dependence and is used to describe extreme behaviors.

9. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula according to claim 1, characterized in that, Step 5 is specifically as follows: Behavior interpretation. Interpret the optimal Copula model, provide an understanding of different transformation interaction behaviors from aspects such as speed, acceleration, and trajectory characteristics. By analyzing the characteristic distribution laws of each clustering category and combining with the dependence relationship revealed by the Copula model, interpret and label different types of transformation interaction behaviors, and finally output the classification results of transformation interaction behaviors with clear physical meanings to provide support for autonomous driving decision-making and traffic management.

10. A method for analyzing the characteristics of lane-changing interaction behavior based on Copula, characterized in that, It includes a Copula-based lane-changing interaction behavior feature analysis system. The Copula-based lane-changing interaction behavior feature analysis system includes a data acquisition module, a data processing module, a clustering analysis module, a dependence modeling module, and a behavior interpretation module; the data acquisition module is used to collect videos in the weaving area and identify the vehicle trajectory data of lane changes from them; the data processing module is used to extract the microscopic interaction characteristics of the vehicle trajectory data; the clustering analysis module uses K-means, hierarchical clustering, or self-organizing feature mapping to perform clustering analysis on the transformation interaction behaviors; the dependence modeling module uses the Copula model to model and predict the statistical dependence relationships of different transformation interaction behaviors; The behavior interpretation module understands and interprets different transformation interaction behaviors by analyzing speed, acceleration, and trajectory characteristics.

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