A Copula-based lane-changing interaction behavior feature analysis method

Abstract

The present application belongs to the technical field of intelligent transportation systems and discloses a lane change interaction behavior feature analysis method based on Copula. By accurately extracting micro-interaction features and clustering the change interaction behaviors using three clustering algorithms, the present application can effectively and automatically identify potential change interaction patterns from a large amount of raw data and classify different change interaction behaviors. At the same time, the Copula theory is introduced to model the dependency relationship between vehicles. By using functions such as Clayton Copula, Normal Copula and Student-T Copula, the complex nonlinear dependency structure between vehicles in the change interaction behavior, especially the relationship between key indicators such as headway, can be effectively captured. Through the parameter estimation method, the fitting effect of the Copula model is optimized, thereby improving the prediction ability.

Description

Technical Field

[0001] The present application belongs to the technical field of intelligent transportation systems, and specifically relates to a Copula-based lane change interaction behavior feature analysis method, which can be used to analyze the lane change interaction pattern of vehicles in weaving areas and provide support for autonomous driving decisions. Background Art

[0002] In modern transportation systems, weaving areas are critical nodes in traffic flow. Weaving areas are typically where highways, urban roads, and other important roads intersect. Vehicles frequently change lanes here, leading to road resource constraints and unstable traffic flow. Due to the large number of lanes and high traffic volume in weaving areas, vehicles' lane-changing behavior in these areas is not only influenced by other vehicles but also closely related to the overall state of traffic flow. For example, during periods of high traffic volume, drivers may frequently change lanes due to increased traffic pressure, further exacerbating traffic congestion and the risk of accidents. Therefore, effectively capturing and analyzing traffic flow patterns in weaving areas has become an important research topic in transportation engineering and autonomous driving systems.

[0003] Traditional lane-changing behavior research has focused on analyzing individual vehicle behavior. Existing studies primarily use discrete choice models or rule-based approaches based on individual driver decisions to model lane-changing behavior. Rule-based models typically rely on pre-set 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 struggle to fully and accurately describe lane-changing behavior in real traffic environments. Discrete-choice models: These models, based on utility maximization theory, establish a probabilistic model of a driver's lane-changing choices under different scenarios. For example, Ahmed et al. developed a vehicle lane-changing probability model, while Toledo et al. constructed an integrated model that considers both forced and free lane-changing processes. However, these models have limitations in handling the correlation between multiple choices, which can lead to estimation bias and inaccurate predictions. Cellular automaton-based models divide the road into discrete cells and simulate traffic flow by specifying rules for vehicle movement between cells. However, traditional cellular automaton models typically use a fixed sequence for updating vehicle states and use identical transition rules. This fails to fully account for the behavioral differences and diversity of different drivers, resulting in limitations in simulating lane-changing behavior in real traffic scenarios. These studies generally ignore the interactions between interacting vehicles before and after a lane change. For example, Qu Dayi et al. proposed a classification method for lane-changing behavior: free lane change, forced lane change, and cooperative lane change, and established corresponding minimum safe distance models. However, this study primarily focused on the interaction between the lane-changing vehicle and the following vehicle in the target lane, failing to fully consider the influence of all relevant vehicles. Furthermore, Ji Wenchao proposed a lane-changing model for urban roads based on driving behavior analysis. This model considers the driver's lane-changing intention and the decisions of the following vehicle in the adjacent lane, but it still has limitations in handling multi-vehicle interactions in complex traffic environments. These methods often ignore the mutual influence between vehicles. For example, when changing lanes, a vehicle may be affected by the behavior of the preceding and following vehicles, as well as the vehicles in the target lane and ahead. These influences are multi-layered and dynamic. Existing models lack the ability to accurately model these complex interactions, often resulting in low prediction accuracy. Furthermore, most existing studies rely on small-scale experimental data, which fails to capture the complexity of real-world traffic environments. Traditional traffic data collection often focuses on specific road sections or time periods and fails to reflect dynamically changing traffic flow behavior. Therefore, how to use large-scale real-time traffic data to analyze and predict traffic behavior in weaving areas becomes 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 become a research hotspot. Methods such as deep learning and graph neural networks can model complex interactions between vehicles to a certain extent. However, these methods typically rely on large amounts of labeled data and lack the ability to clearly model statistical dependencies. Therefore, how to automatically identify lane-changing patterns from data using unsupervised learning methods and accurately model these interactions using statistical models remains a key challenge in optimizing decision-making in intelligent transportation and autonomous driving.

[0005] In general, traffic flow analysis in weaving areas requires more sophisticated and comprehensive models to describe the complex vehicle interactions. Combining real-time traffic data with advanced computing technology can effectively improve traffic management 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 lane change interaction behavior feature analysis method.

[0007] In order to solve the technical problem, the technical solution of this application is: a lane change interaction behavior feature analysis method based on Copula, comprising the following steps:

[0008] Step 1: Data collection: Use drones to capture video of the weaving area and identify the trajectory data of vehicles that change lanes.

[0009] Step 2: Data preprocessing;

[0010] 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 headway.

[0011] Step 2-2: Data cleaning and normalization of micro-interaction features;

[0012] Step 3: Cluster analysis;

[0013] Step 3-1: Input the preprocessed micro-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;

[0014] Step 3-2: Construct feature space. Use the extracted micro-interaction features to construct a multi-dimensional feature space as the input for cluster analysis.

[0015] Step 3-3: Run the clustering algorithm selected in step 3-1 in the cluster execution phase of the cluster analysis to divide the lane change interaction behaviors into multiple cluster categories, each cluster category representing a specific lane change mode;

[0016] Step 3-4: Then use the silhouette coefficient or CH index to evaluate the cluster categories and determine the optimal number of cluster categories;

[0017] Step 4: Copula modeling, using the Copula model to model and predict the statistical dependencies of different transformation interaction behaviors;

[0018] Step 4-1: First, perform marginal distribution fitting. Perform marginal distribution analysis on the headway of each cluster category and select the distribution type that best describes the headway.

[0019] Step 4-2: According to the distribution type, select the corresponding Copula function to establish a Copula model to capture the nonlinear dependency structure between variables;

[0020] Step 4-3: Use the maximum likelihood estimation method to estimate the parameters of the selected Copula model;

[0021] Step 4-4: Evaluate the fitting effects of different Copula models and select the optimal Copula model;

[0022] Step 5: Behavior interpretation, interpret the optimal Copula model and output the transformation interaction behavior classification.

[0023] Preferably, step 1 specifically includes: using drone aerial photography technology to shoot real-time traffic flow video in the weaving area, and combining YOLOv5 and DeepSort to extract vehicle trajectories, and identifying the trajectory data of vehicles that change lanes, wherein the vehicle trajectory data includes vehicle position, speed, acceleration and lane changing behavior.

[0024] Preferably, the absolute speed in step 2-1 is the speed of the target vehicle itself, which is expressed as:

[0025] ;

[0026] in:

[0027] For vehicles i In time t Absolute speed, km / h;

[0028] is the position change of the vehicle;

[0029] is the lane-changing vehicle moment, s;

[0030] The relative speed is the relative speed between adjacent vehicles, which is expressed as:

[0031] ;

[0032] in:

[0033] For vehicles i With vehicle j Relative speed between them, km / h;

[0034] For vehicles j In time t Absolute speed, km / h;

[0035] The relative distance is the relative distance between vehicles, which is expressed as:

[0036] ;

[0037] in:

[0038] For vehicles i With vehicle j In time t Relative distance at time, m;

[0039] and Vehicles i With vehicle j In time t Position at time, m;

[0040] The headway is the headway between vehicles, expressed as:

[0041] ;

[0042] When the relative speed is zero, the headway is defined as a maximum value or supplemented by interpolation.

[0043] Preferably, the data cleaning and normalization processing of the micro-interaction features in step 2-2 is specifically as follows: detecting the micro-interaction features and removing outliers, and then using the minimum-maximum normalization method to convert the micro-interaction features of different dimensions into a unified [0,1] scale range.

[0044] Preferably, the objective function of the K-means algorithm in step 3-1 is:

[0045] ;

[0046] Where:

[0047] For the n samples, i∈{1,2,...,N} , N is the total number of samples;

[0048] For clusters Optimize;

[0049] is the centroid of the cluster;

[0050] A is the number of clusters.

[0051] Preferably, the step 4-1 specifically comprises: converting the headway of each cluster category to obtain a corresponding marginal distribution function;

[0052] ;

[0053] Where:

[0054] is any given headway value;

[0055] is a probability operator, indicating that the headway time ≤ The probability of this event occurring;

[0056] The step 4-2 is specifically as follows: according to the distribution type, the corresponding Copula function is selected to establish the Copula model, which is expressed as:

[0057] ;

[0058] Where:

[0059] are the parameters of the Copula model;

[0060] and are two real number thresholds, which are used to calculate the probability that the headway does not exceed them;

[0061] and These are the marginal distributions of the headway time for the two lane change modes.

[0062] Preferably, the Copula function in step 4-2 includes Normal Copula, Student-T Copula, Clayton Copula, Gumbel Copula and Frank Copula;

[0063] The basic formula of the Copula function is:

[0064] ;

[0065] The Normal Copula is:

[0066] ;

[0067] The Student-T Copula is:

[0068] ;

[0069] The functional forms of the Clayton Copula, Gumbel Copula, and Frank Copula shown are constructed using the following formulas:

[0070] ;

[0071] in:

[0072] is the cumulative distribution function of the standard bivariate normal distribution;

[0073] is the inverse of the cumulative distribution function of the standard bivariate normal distribution;

[0074] is the correlation coefficient matrix between variables;

[0075] is the inverse matrix of the correlation coefficient matrix;

[0076] is one of the random variables in the case of a binary variable, the marginal distribution function of the random variable, = ;

[0077] For the 1,2,...,N The marginal distribution function of a random variable is i∈{1,2,...,N} , For the i The marginal distribution function of a random variable;

[0078] is another random variable in the case of a binary variable;

[0079] is a vector whose elements are the quantiles of the standard normal distribution;

[0080] is a vector The transpose of

[0081] is the identity matrix;

[0082] is the degree of freedom parameter, which is used to define the shape of the distribution;

[0083] is a matrix with correlation coefficients ρ and degrees of freedom k Univariate cumulative distribution function of the distribution;

[0084] To have degrees of freedom k Univariate The inverse cumulative distribution function of the distribution;

[0085] is a generating function that satisfies strictly monotonically decreasing and convexity, and ;

[0086] is the inverse function of the generating function.

[0087] condition and In the generated function The strict monotonically decreasing and convex definitions of are compatible. The former is the normalization condition of the generating function, and the latter is the definition condition that ensures that the copula is within the valid range. Together, they define the reasonable behavior of the copula.

[0088] Preferably, the Normal Copula is suitable for describing the linear dependency in lane change interaction behavior and is used when the traffic flow is smooth; the Clayton Copula is suitable for capturing left tail dependency and is suitable for describing interdependent behavior under low speed or congestion conditions; the Student-T Copula is used to capture tail dependency and is used to describe extreme behavior.

[0089] Preferably, step 5 is specifically as follows: behavior interpretation, interpreting the optimal Copula model, providing an understanding of different transformation interaction behaviors from the aspects of speed, acceleration, and trajectory characteristics, and interpreting and labeling different types of transformation interaction behaviors by analyzing the characteristic distribution patterns of each clustering category and combining the dependency relationships revealed by the Copula model. Finally, outputting a transformation interaction behavior classification result with clear physical meaning to provide support for autonomous driving decision-making and traffic management.

[0090] Preferably, a lane change interaction behavior feature analysis method based on Copula includes a lane change interaction behavior feature analysis system based on Copula, and the lane change interaction behavior feature analysis system based on Copula includes a data acquisition module, a data processing module, a clustering analysis module, a dependency modeling module and a behavior interpretation module; the data acquisition module is used to collect weaving area videos and identify vehicle trajectory data of lane changes therefrom; the data processing module is used to extract microscopic interaction features of vehicle trajectory data; the clustering analysis module uses K-means, hierarchical clustering or self-organizing feature mapping to perform cluster analysis on transformation interaction behaviors; the dependency modeling module uses the Copula model to model and predict the statistical dependency relationship of different transformation interaction behaviors; the behavior interpretation module understands and interprets different transformation interaction behaviors by analyzing speed, acceleration and trajectory characteristics.

[0091] Compared with the prior art, the advantages of this application are:

[0092] (1) This application is based on drone aerial photography data. By accurately extracting micro-interaction features, it uses unsupervised learning methods such as K-means, hierarchical clustering, or self-organizing feature mapping to cluster transformation interaction behaviors. These methods can effectively and automatically identify potential transformation interaction patterns from a large amount of raw data and classify different transformation interaction behaviors, providing data support for subsequent behavior analysis and modeling.

[0093] (2) For different transformation interaction modes, this application introduces Copula theory to model the dependency between vehicles. By using functions such as Clayton Copula, Normal Copula and Student-T Copula, the application can effectively capture the complex nonlinear dependency structure between vehicles in the transformation interaction behavior, especially the relationship between key indicators such as headway. By using parameter estimation methods, the fitting effect of the Copula model is optimized, thereby improving the prediction ability. Compared with traditional methods, Copula theory can more accurately describe the statistical dependency between various transformation interaction modes, thereby improving the understanding and prediction ability of transformation interaction behavior.

[0094] (3) This application adopts a statistically based modeling method with low computational complexity, can quickly process large-scale traffic data, and is suitable for real-time traffic analysis and prediction. By optimizing the algorithm and model structure, this application can operate efficiently in actual traffic environments, provide instantaneous analysis results of transformation and interactive behavior, and provide real-time support for traffic mobility management and safety warnings;

[0095] (4) This application is not only applicable to the analysis of traditional traffic flow data, but can also 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 and coordinated lane-changing behavior between vehicles are the key to improving driving safety and smoothness. The lane-changing interaction behavior clustering analysis method based on Copula theory is efficient, accurate, and real-time. It can deeply analyze the interaction mode during the lane-changing process of vehicles, and provide strong support for the optimization of intelligent transportation systems, the improvement of the safety of autonomous driving systems, and traffic flow management.

[0096] (5) This application can comprehensively consider multiple factors, such as vehicle speed, headway, relative lane position, etc., to conduct multi-dimensional transformation interaction behavior analysis, help identify lane change risks in different scenarios, and provide a scientific basis for optimizing traffic flow management in weaving areas;

[0097] (6) By analyzing the interactive behavior of the transition in the weaving area in real time, this application can provide accurate traffic flow predictions, help traffic management departments monitor traffic conditions in real time, identify potential traffic congestion and accident risks, and provide decision support for intelligent transportation systems and autonomous vehicles; at the same time, based on the identification of the interactive behavior pattern, it can provide early warning of possible safety hazards and improve road safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 This is a flow chart of a lane-changing interaction behavior feature analysis method based on Copula;

[0099] Figure 2 Extracting schematic diagrams of vehicle trajectories for UAV aerial photography;

[0100] Figure 3 Schematic diagram for micro-interaction feature extraction;

[0101] Figure 4 Schematic diagram of the Kendall rank correlation coefficient distribution of each cluster category result. DETAILED DESCRIPTION

[0102] The present application is described in detail below with reference to the accompanying drawings and specific examples, but the present application is not limited to these examples. This application covers any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this application. To provide a thorough understanding of this application, specific details are described in detail in the following examples of this application, but those skilled in the art can fully understand this application without these detailed descriptions.

[0103] like Figure 1 As shown, the present application discloses a lane change interaction behavior feature analysis method based on Copula, comprising the following steps:

[0104] Step 1: Data collection: Use drones to capture video of the weaving area and identify the trajectory data of vehicles that change lanes.

[0105] Step 2: Data preprocessing;

[0106] 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 headway.

[0107] Step 2-2: Data cleaning and normalization of micro-interaction features;

[0108] Step 3: Cluster analysis;

[0109] Step 3-1: Input the preprocessed micro-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;

[0110] Step 3-2: Construct feature space. Use the extracted micro-interaction features to construct a multi-dimensional feature space as the input for cluster analysis.

[0111] Step 3-3: Run the clustering algorithm selected in step 3-1 in the cluster execution phase of the cluster analysis to divide the lane change interaction behaviors into multiple cluster categories, each cluster category representing a specific lane change mode;

[0112] Step 3-4: Then use the silhouette coefficient or CH index to evaluate the cluster categories and determine the optimal number of cluster categories;

[0113] Step 4: Copula modeling, using the Copula model to model and predict the statistical dependencies of different transformation interaction behaviors;

[0114] Step 4-1: First, perform marginal distribution fitting. Perform marginal distribution analysis on the headway of each cluster category and select the distribution type that best describes the headway.

[0115] Step 4-2: According to the distribution type, select the corresponding Copula function to establish a Copula model to capture the nonlinear dependency structure between variables;

[0116] Step 4-3: Use the maximum likelihood estimation method to estimate the parameters of the selected Copula model;

[0117] Step 4-4: Evaluate the fitting effects of different Copula models and select the optimal Copula model;

[0118] Step 5: Behavior interpretation, interpret the optimal Copula model and output the transformation interaction behavior classification.

[0119] Preferably, step 1 specifically includes: using drone aerial photography technology to shoot real-time traffic flow video in the weaving area, and combining YOLOv5 and DeepSort to extract vehicle trajectories, and identifying the trajectory data of vehicles that change lanes, wherein the vehicle trajectory data includes vehicle position, speed, acceleration and lane changing behavior.

[0120] Preferably, the absolute speed in step 2-1 is the speed of the target vehicle itself, which is expressed as:

[0121] ;

[0122] in:

[0123] For vehicles i In time t Absolute speed, km / h;

[0124] is the position change of the vehicle;

[0125] is the lane-changing vehicle moment, s;

[0126] The relative speed is the relative speed between adjacent vehicles, which is expressed as:

[0127] ;

[0128] in:

[0129] For vehicles i With vehicle j Relative speed between them, km / h;

[0130] For vehicles j In time t Absolute speed, km / h;

[0131] The relative distance is the relative distance between vehicles, which is expressed as:

[0132] ;

[0133] in:

[0134] For vehicles i With vehicle j In time t Relative distance at time, m;

[0135] and Vehicles i With vehicle j In time t Position at time, m;

[0136] The headway is the headway between vehicles, expressed as:

[0137] ;

[0138] When the relative speed is zero, the headway is defined as a maximum value or supplemented by interpolation.

[0139] Preferably, the data cleaning and normalization processing of the micro-interaction features in step 2-2 is specifically as follows: detecting the micro-interaction features and removing outliers, and then using the minimum-maximum normalization method to convert the micro-interaction features of different dimensions into a unified [0,1] scale range.

[0140] Preferably, the objective function of the K-means algorithm in step 3-1 is:

[0141] ;

[0142] Where:

[0143] For the n samples, i∈{1,2,...,N} , N is the total number of samples;

[0144] For clusters Optimize;

[0145] For the clusters;

[0146] is the centroid of the cluster;

[0147] A is the number of clusters, determined by the silhouette coefficient or CH index.

[0148] Preferably, the step 4-1 specifically comprises: converting the headway of each cluster category to obtain a corresponding marginal distribution function;

[0149] ;

[0150] Where:

[0151] is any given headway value;

[0152] is a probability operator, indicating that the headway time ≤ The probability of this event occurring;

[0153] The step 4-2 is specifically as follows: according to the distribution type, the corresponding Copula function is selected to establish the Copula model, which is expressed as:

[0154] ;

[0155] Where:

[0156] are the parameters of the Copula model;

[0157] and are two real number thresholds, which are used to calculate the probability that the headway does not exceed them;

[0158] and These are the marginal distributions of the headway time for the two lane change modes.

[0159] Preferably, the Copula function in step 4-2 includes Normal Copula, Student-T Copula, Clayton Copula, Gumbel Copula and Frank Copula;

[0160] The basic formula of the Copula function is:

[0161] ;

[0162] The Normal Copula is:

[0163] ;

[0164] The Student-T Copula is:

[0165] ;

[0166] The functional forms of the Clayton Copula, Gumbel Copula, and Frank Copula shown are constructed using the following formulas:

[0167] ;

[0168] in:

[0169] is the cumulative distribution function of the standard bivariate normal distribution;

[0170] is the inverse of the cumulative distribution function of the standard bivariate normal distribution;

[0171] is the correlation coefficient matrix between variables;

[0172] is the inverse matrix of the correlation coefficient matrix;

[0173] is one of the random variables in the case of a binary variable, the marginal distribution function of the random variable, = ;

[0174] For the 1,2,...,N The marginal distribution function of a random variable is i∈{1,2,...,N} , For the i The marginal distribution function of a random variable;

[0175] is another random variable in the case of a binary variable;

[0176] is a vector whose elements are the quantiles of the standard normal distribution;

[0177] is a vector The transpose of

[0178] is the identity matrix;

[0179] is the degree of freedom parameter, which is used to define the shape of the distribution;

[0180] is a matrix with correlation coefficients ρ and degrees of freedom k Univariate cumulative distribution function of the distribution;

[0181] To have degrees of freedom k Univariate The inverse cumulative distribution function of the distribution;

[0182] is a generating function that satisfies strictly monotonically decreasing and convexity, and ;

[0183] is the inverse function of the generating function.

[0184] Preferably, the Normal Copula is suitable for describing the linear dependency in lane change interaction behavior and is used when the traffic flow is smooth; the Clayton Copula is suitable for capturing left tail dependency and is suitable for describing interdependent behavior under low speed or congestion conditions; the Student-T Copula is used to capture tail dependency and is used to describe extreme behavior.

[0185] Preferably, step 5 is specifically as follows: behavior interpretation, interpreting the optimal Copula model, providing an understanding of different transformation interaction behaviors from the aspects of speed, acceleration, and trajectory characteristics, and interpreting and labeling different types of transformation interaction behaviors by analyzing the characteristic distribution patterns of each clustering category and combining the dependency relationships revealed by the Copula model. Finally, outputting a transformation interaction behavior classification result with clear physical meaning to provide support for autonomous driving decision-making and traffic management.

[0186] Preferably, a lane change interaction behavior feature analysis method based on Copula includes a lane change interaction behavior feature analysis system based on Copula, and the lane change interaction behavior feature analysis system based on Copula includes a data acquisition module, a data processing module, a clustering analysis module, a dependency modeling module and a behavior interpretation module; the data acquisition module is used to collect weaving area videos and identify vehicle trajectory data of lane changes therefrom; the data processing module is used to extract microscopic interaction features of vehicle trajectory data; the clustering analysis module uses K-means, hierarchical clustering or self-organizing feature mapping to perform cluster analysis on transformation interaction behaviors; the dependency modeling module uses the Copula model to model and predict the statistical dependency relationship of different transformation interaction behaviors; the behavior interpretation module understands and interprets different transformation interaction behaviors by analyzing speed, acceleration and trajectory characteristics.

[0187] Example 1

[0188] like Figure 1 As shown, the lane change interaction behavior feature analysis method based on Copula in this embodiment includes the following steps:

[0189] Step 1: Data collection;

[0190] Aerial video of the weaving area is captured using a drone. Vehicle trajectories are extracted using YOLOv5 and DeepSort to determine if the vehicle trajectory intersects the lane equation. If yes, the trajectory of the vehicle that changed lanes is obtained and the moment of the lane change is extracted. If no, the trajectory of the vehicle that did not change lanes is extracted.

[0191] Step 2: Data preprocessing;

[0192] Extract the trajectories of adjacent vehicles before and after the lane-changing vehicle changes lanes, extract microscopic interaction features, perform data cleaning, and perform normalization processing.

[0193] Step 3: Cluster analysis;

[0194] The best clustering algorithm is selected from the clustering algorithm set using the silhouette coefficient or CH index, the feature space is constructed, clustering is performed, and cluster categories are evaluated.

[0195] Step 4: Copula modeling;

[0196] Marginal distribution fitting, Copula function selection, Copula parameter estimation, Copula model evaluation, and optimal Copula model.

[0197] Step 5: Behavior interpretation, interpret the optimal Copula model and output the transformation interaction behavior classification.

[0198] Example 2

[0199] In this embodiment, a lane change interaction behavior feature analysis method based on Copula includes the following steps:

[0200] Step 1: Data collection;

[0201] like Figure 2 The figure shows a schematic diagram of vehicle trajectory extraction from drone aerial photography. UAV aerial photography technology is used to obtain high-precision vehicle trajectory data in the weaving area. In specific implementation, drones are deployed above the weaving area to capture traffic flow videos in real time and capture the driving trajectories of vehicles. YOLOv5 and DeepSort technologies are combined to extract all vehicle trajectories and identify the trajectory data of vehicles that have changed lanes.

[0202] The data acquisition module is responsible for collecting real-time vehicle trajectory data in the weaving area through high-precision GPS equipment or other sensors. The collected vehicle trajectory data includes information such as vehicle position, speed, acceleration, lane-changing behavior, etc. The data recording time interval is Δt, which is usually 0.1 second or shorter.

[0203] Step 2: Data preprocessing;

[0204] This step preprocesses the collected data and extracts microscopic interaction features. First, absolute speed, relative speed, relative distance, and headway are selected as microscopic interaction features. Then, during the data cleaning phase, outliers, such as those caused by sensor errors, are detected and removed to ensure data accuracy. Finally, the data is normalized using a minimum-maximum normalization method to convert feature values of different dimensions to a unified scale of [0, 1] to improve the stability and convergence speed of model training.

[0205] The extracted vehicle trajectory data is transmitted to the data processing module via wireless communication technology for subsequent analysis.

[0206] Absolute speed: The vehicle's own speed, expressed as:

[0207] ;

[0208] Where:

[0209] For vehicles i In time t Absolute speed, km / h;

[0210] is the position change of the vehicle;

[0211] is the lane-changing vehicle moment, s;

[0212] Relative speed: The relative speed between adjacent vehicles, defined as:

[0213] ;

[0214] For vehicles i With vehicle j Relative speed between them, km / h;

[0215] For vehicles j In time t Absolute speed, km / h;

[0216] Relative distance: The relative distance between vehicles, defined as:

[0217] ;

[0218] Where:

[0219] For vehicles i With vehicle j In time t Relative distance at time, m;

[0220] and Vehicles i With vehicle j In time t Position at time, m;

[0221] Time Headway (THW): The time headway between vehicles, defined as:

[0222] ;

[0223] When the relative speed is zero, the headway is defined as a maximum value or supplemented by interpolation.

[0224] like Figure 3 As shown in the figure, it is a schematic diagram of micro-interaction feature extraction. The parameters in the figure represent the following:

[0225] A vehicle changing lanes in the current lane i Speed, km / h;

[0226] is the speed of the vehicle behind the lane-changing vehicle in the current lane, km / h;

[0227] is the speed of the vehicle in front of the lane-changing vehicle in the current lane, km / h;

[0228] is the speed of the vehicle following the lane-changing vehicle in the target lane, km / h;

[0229] is the speed of the vehicle ahead of the lane-changing vehicle in the target lane, km / h;

[0230] A vehicle changing lanes in the original lane i With following vehicles r The relative distance between them, m;

[0231] A vehicle changing lanes in the original lane i With the car in front f The relative distance between them, m;

[0232] For vehicles changing lanes in the target lane i With following vehicles r The relative distance between them, m;

[0233] For vehicles changing lanes in the target lane i With the car in front f The relative distance between them, m;

[0234] H c,i,f 、 H c,i,r 、 H t,i,f 、 H t,i,r There are four types of headway.

[0235] Step 3: Cluster analysis;

[0236] This step performs unsupervised cluster analysis on the preprocessed data. First, the preprocessed micro-interaction features are fed into one of three clustering algorithms: K-means, hierarchical clustering, or self-organizing feature mapping. The silhouette coefficient or CH index is used to select the optimal clustering algorithm. Next, a feature space is constructed, using the extracted micro-interaction features to construct a multidimensional feature space as input for the cluster analysis. The selected clustering algorithm is then run during the cluster execution phase of the cluster analysis, dividing the lane-changing interactions into multiple cluster categories, each representing a specific lane-changing pattern. Finally, the silhouette coefficient or CH index is used to evaluate the cluster categories and determine the optimal number of cluster categories.

[0237] The K-means clustering algorithm is used to classify the behavior patterns. The goal is to classify the lane-changing behaviors into K clusters, where each cluster represents a specific interaction pattern. The objective function of the K-means algorithm is:

[0238] ;

[0239] Where:

[0240] For the n samples, i∈{1,2,...,N} , N is the total number of samples;

[0241] For clusters Optimize;

[0242] For the clusters;

[0243] is the centroid of the cluster;

[0244] A is the number of clusters.

[0245] like Figure 4 As shown, cluster category 0, cluster category 1, cluster category 2, cluster category 3 and cluster category 4 are obtained.

[0246] Step 4: Copula modeling;

[0247] This step uses the Copula model to model and predict the statistical dependencies of different transformation interaction modes. First, marginal distribution fitting is performed, and marginal distribution analysis is performed on the headway data of each cluster category to select the distribution type that best describes the data characteristics. Secondly, based on the characteristics of the marginal distribution, an appropriate Copula function is selected to capture the nonlinear dependency structure between variables. Then, the parameters of the selected Copula model are estimated using methods such as maximum likelihood estimation. Finally, indicators such as AIC and BIC are used to evaluate the fitting effects of different Copula models and select the optimal model.

[0248] The Copula model is constructed by the following steps:

[0249] Step 4-1: Data transformation: By transforming the headway data under each cluster category, the corresponding marginal distribution function is obtained:

[0250] ;

[0251] Where:

[0252] is any given headway value;

[0253] is a probability operator, indicating that the headway time ≤ The probability of this event occurring;

[0254] Step 4-2: Construct a Copula model and fit the joint distribution based on the dependency structure of the data:

[0255] ;

[0256] Where:

[0257] are the parameters of the Copula model;

[0258] and are two real number thresholds, which are used to calculate the probability that the headway does not exceed them;

[0259] and These are the marginal distributions of the headway time for the two lane change modes.

[0260] As shown in Table 1, these are the results of modeling different copulas. In the table, the optimal copula for cluster category 0 is ClaytonCopula, the optimal copula for cluster category 1 is Normal Copula, the optimal copula for cluster category 2 is ClaytonCopula, the optimal copula for cluster category 3 is Normal Copula, and the optimal copula for cluster category 4 is ClaytonCopula.

[0261] Table 1 Modeling results of different copulas

[0262]

[0263] Step 5: Behavior explanation;

[0264] This step primarily interprets the modeling results, providing an understanding of different lane-changing behavior patterns based on speed, trajectory, and acceleration characteristics. By analyzing the characteristic distribution patterns of each cluster category and combining them with the dependencies revealed by the Copula model, different types of lane-changing interactions are explained and labeled. Ultimately, a lane-changing behavior classification result with clear physical meaning is output, providing support for autonomous driving decision-making and traffic management.

[0265] like Figure 4 The figure below shows the distribution of the Kendall rank correlation coefficient for each cluster category, and the Kendall rank correlation coefficient matrix for the four headway types in the five cluster categories. The Kendall rank correlation coefficient is a nonparametric statistical method used to measure the correlation between two variables. Its value ranges from -1 to 1; 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

[0266] The above five steps constitute a complete lane-changing interaction behavior clustering analysis method. Each step is closely connected through data flow, and the output of the previous step serves as the input of the next step, forming a complete technical closed loop.

[0267] This application works as follows:

[0268] This application proposes a lane change interaction behavior feature analysis method based on Copula, which includes a data acquisition module, a data processing module, a clustering analysis module, a dependency modeling module and a behavior interpretation module; the data acquisition module is responsible for using drone aerial video to obtain the trajectory data of vehicles in the weaving area through vehicle trajectory technology; the data processing module mainly preprocesses and extracts features of the collected data; the clustering analysis module performs cluster analysis on the processed data, and uses K-Means, hierarchical clustering and self-organizing feature mapping (SOM) to identify different lane change interaction behavior patterns; the dependency modeling prediction module uses the Copula model to model and predict the statistical dependency relationship of different lane change interaction behaviors; finally, the behavior interpretation module interprets the modeling results and provides an understanding of different lane change behavior patterns in terms of speed, acceleration and trajectory characteristics.

[0269] The preferred embodiments of the present application have been described in detail above, but the present application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the purpose of the present application.

[0270] 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 the specific embodiments, and the scope of the present application is defined by the appended claims.

Claims

1. A lane-changing interaction behavior feature analysis method based on Copula, characterized in that: The following steps are involved: Step 1: Data collection: Use drones to capture video of the weaving area and identify the trajectory data of vehicles that change lanes. 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 headway. Step 2-2: Data cleaning and normalization of micro-interaction features; Step 3: Cluster analysis; Step 3-1: Input the preprocessed micro-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 feature space. Use the extracted micro-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 in the cluster execution phase of the cluster analysis to divide the lane change interaction behaviors into multiple cluster categories, each cluster category representing a specific lane change mode; Step 3-4: Then use the silhouette coefficient or CH index to evaluate the cluster categories and determine the optimal number of cluster categories; Step 4: Copula modeling, using the Copula model to model and predict the statistical dependencies of different transformation interaction behaviors; Step 4-1: First, perform marginal distribution fitting. Perform marginal distribution analysis on the headway of each cluster category and select the distribution type that best describes the headway. Specifically, transform the headway of each cluster category to obtain the corresponding marginal distribution function. ； Where: is any given headway value; is a probability operator, indicating that the headway time ≤ The probability of this event occurring; THW is the headway; Step 4-2: According to the distribution type, select the corresponding Copula function to establish a Copula model to capture the nonlinear dependency structure between variables. The Copula model is expressed as: ； Where: are the parameters of the Copula model; and are two real number thresholds, which are used to calculate the probability that the headway does not exceed them; and These are the marginal distributions of headway times for the two lane change modes; 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 transformation interaction behavior classification.

2. The lane change interaction behavior feature analysis method based on Copula according to claim 1, characterized in that: Specifically, step 1 includes: using drone aerial photography technology to capture real-time traffic flow video in the weaving area, and extracting vehicle trajectories in combination with YOLOv5 and DeepSort to identify the trajectory data of vehicles that have changed lanes. The vehicle trajectory data includes vehicle position, speed, acceleration, and lane-changing behavior.

3. The lane change interaction behavior feature analysis method based on Copula according to claim 1, characterized in that: The absolute speed in step 2-1 is the speed of the target vehicle itself, which is expressed as: ； in: For vehicles i In time t Absolute speed, km / h; is the position change of the vehicle; is the lane-changing vehicle moment, s; The relative speed is the relative speed between adjacent vehicles, which is expressed as: ； in: For vehicles i With vehicle j Relative speed between them, km / h; For vehicles j In time t Absolute speed, km / h; The relative distance is the relative distance between vehicles, which is expressed as: ； in: For vehicles i With vehicle j In time t Relative distance at time, m; and Vehicles i With vehicle j In time t Position at time, 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.

4. The lane change interaction behavior feature analysis method based on Copula according to claim 1, characterized in that: The data cleaning and normalization processing of the micro-interaction features in step 2-2 is specifically as follows: detecting the micro-interaction features and removing outliers, and then using the minimum-maximum normalization method to convert the micro-interaction features of different dimensions into a unified scale range of [0,1].

5. The lane change interaction behavior feature analysis method based on Copula according to claim 1, characterized in that: The objective function of the K-means algorithm in step 3-1 is: ； Where: For the n samples, i∈{1,2,...,N} , N is the total number of samples; For clusters Optimize; For the clusters; is the centroid of the cluster; A is the number of clusters.

6. The lane change interaction behavior feature analysis method based on Copula according to claim 1, 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 functional forms of the Clayton Copula, Gumbel Copula, and Frank Copula shown are constructed using the following formulas: ； in: is the cumulative distribution function of the standard bivariate normal distribution; is the inverse 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, = ; For the 1,2,...,N The marginal distribution function of a random variable is i∈{1,2,...,N} , For the i The marginal distribution function of a random variable; is another random variable in the case of a binary variable; is a vector whose elements are the quantiles of the standard normal distribution; is a vector The transpose of is the identity matrix; is the degree of freedom parameter, which is used to define the shape of the distribution; is a matrix with correlation coefficients ρ and degrees of freedom k Univariate cumulative distribution function of the distribution; To have degrees of freedom k Univariate The inverse cumulative distribution function of the distribution; is a generating function that satisfies strictly monotonically decreasing and convexity, and ; is the inverse function of the generating function.

7. The lane change interaction behavior feature analysis method based on Copula according to claim 6, characterized in that: The Normal Copula is suitable for describing linear dependencies in lane-changing interactions and is used when traffic flow is smooth. The Clayton Copula is suitable for capturing left-tail dependencies and is suitable for describing interdependent behaviors under low-speed or congested conditions. The Student-T Copula is used to capture tail dependencies and is used to describe extreme behaviors.

8. The lane change interaction behavior feature analysis method based on Copula according to claim 1, characterized in that: Step 5 specifically includes: behavioral interpretation, interpreting the optimal Copula model to provide an understanding of different transformation interaction behaviors from the perspective of speed, acceleration, and trajectory characteristics. By analyzing the characteristic distribution patterns of each cluster category and combining the dependencies revealed by the Copula model, different types of transformation interaction behaviors are interpreted and labeled. Ultimately, a transformation interaction behavior classification result with clear physical meaning is output to provide support for autonomous driving decision-making and traffic management.

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