A road traffic anomaly detection method based on holomorphic embedding and global search

Abstract

The present invention provides a road traffic anomaly detection method based on holomorphic embedding and global search, including obtaining floating car data; defining specific road sections and calculating average speeds; constructing an urban road traffic network; constructing an average speed transfer matrix according to the probability distribution of speed conversion; constructing a tensor model according to the traffic data to be detected; using trust technology to perform global search to find a local optimal solution that meets error conditions; calculating the Kullback-Leibler divergence value of the speed transfer matrix and the average speed transfer matrix to detect anomalies in the urban road traffic network. The present invention can detect road traffic anomalies more accurately and efficiently, improve traffic management efficiency and traffic network effectiveness; and overcome the defects of the alternating least squares method, such as slow convergence, low computational efficiency, low precision, and inability to process CP decomposition of tensors containing many zero elements.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic anomaly detection, and in particular to a road traffic anomaly detection method based on holomorphic embedding and global search. Background Art

[0002] With the acceleration of urbanization, urban road traffic systems face increasingly severe challenges, including but not limited to traffic congestion, frequent traffic accidents, and delayed emergency response. Traditional traffic management methods often rely on manual observation and empirical judgment, which cannot meet the dynamic and complex needs of modern urban traffic.

[0003] With the development of the Internet of Things, big data, and artificial intelligence technologies, it has become possible to monitor traffic conditions using multiple sources of information, such as vehicle GPS, traffic cameras, and mobile communication data. Road traffic anomaly detection focuses on identifying situations that significantly deviate from normal traffic flow patterns. "Anomalies" here generally refer to behaviors or events where key indicators such as traffic flow, speed, and density deviate from historical statistical patterns or expected patterns within a given time period. These anomalies may be caused by traffic accidents, changing weather conditions, road construction, and emergencies. The results of road traffic anomaly detection can be applied in various ways to traffic management, optimizing traffic flow, improving safety, and enhancing the travel experience for citizens. While existing technologies can perform road traffic anomaly detection based on this data, they still face challenges such as the enormous data volume and difficulty extracting spatiotemporal features from the data.

[0004] In light of these challenges, tensor analysis techniques, particularly tensor CP decomposition (CP decomposition), have gradually attracted attention in the field of transportation research due to their ability to process multidimensional data. Tensor CP decomposition (CP decomposition) decomposes high-order tensors (i.e., multidimensional data structures) into a sum of several rank tensors, each representing a fundamental pattern or component in the data. This decomposition method demonstrates great potential in revealing the underlying structure of traffic behavior, pattern recognition, and anomaly detection, providing a new perspective and tool for anomaly detection in urban road traffic. The alternating least squares method (ALS) is a commonly used algorithm for solving CP decomposition. This method transforms the CP decomposition model into an unconstrained optimization problem. However, this method cannot guarantee convergence to a global optimum or a stationary point; it can only guarantee convergence until the objective function stops decreasing. Consequently, the CP decomposition of high-order tensors suffers from large errors, slow convergence, and low computational efficiency. Furthermore, it cannot handle CP decompositions of tensors containing many zero elements. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a road traffic anomaly detection method based on holomorphic embedding and global search. The present invention can detect road traffic anomalies more accurately and efficiently, thereby improving traffic management efficiency and traffic network performance; and the present invention overcomes the defect that the alternating least squares method cannot handle the CP decomposition of tensors containing a large number of zero elements.

[0006] The technical solution of the present invention is: a road traffic anomaly detection method based on holomorphic embedding and global search, comprising the following steps:

[0007] S1), obtain floating car data, and perform map matching and seasonal filtering on it;

[0008] S2), defining specific road segments and calculating the average speed of each road segment;

[0009] S3) Constructing an urban road traffic network based on the defined road segments;

[0010] S4), constructing an average speed transfer matrix based on the probability distribution of speed conversion;

[0011] S5), constructing a tensor decomposition model based on the traffic data to be detected and solving it;

[0012] S6) Using trust technology to perform global search to find a local optimal solution that meets the error condition; and reducing the local optimal solution to a speed transfer matrix, a factor matrix of adjacent road sections and time intervals in the urban road traffic network;

[0013] S7), calculating the Kullback-Leibler divergence value of the restored speed transfer matrix and the average speed transfer matrix in the road traffic network to detect abnormal conditions in the urban road traffic network.

[0014] Preferably, in step S1), seasonal components are removed from the original floating car data, and the nearest road or the most likely road is determined based on the three indicators of position, speed, and direction by calculating the distance between the GPS point and each road on the map and combining the speed and direction information of the vehicle. Specifically, the steps include:

[0015] S11), obtaining vehicle location data;

[0016] S12), loading road network data;

[0017] S13), cleaning the vehicle data;

[0018] S14), using a similarity matching algorithm to preliminarily match the GPS coordinates with roads in the road network;

[0019] S15), using the vehicle's speed and direction information to improve the matching results;

[0020] S16) Verify the results.

[0021] Preferably, in step S11), the vehicle location data includes GPS coordinates (longitude and latitude), timestamp, speed, and direction.

[0022] Preferably, in step S12), the road network data is geometric information, including the longitude and latitude of the road, the road type, and the speed limit.

[0023] Preferably, in step S15), the speed and direction information of the vehicle is used to improve the matching result, which specifically includes the following steps:

[0024] S151), checking whether the vehicle speed is within the expected speed range of the road;

[0025] S152), calculating the direction angle of the vehicle and comparing it with the direction of the road. If the direction of the vehicle is roughly the same as the direction of the road, the match is considered to be more reliable;

[0026] S153) comprehensively considers the degree of matching between the position, speed and direction of the vehicle and the road, and selects the road with the highest matching degree as the final result based on the comprehensive score.

[0027] Preferably, in step S16), a map visualization tool is used to check the matching results.

[0028] Preferably, in step S2), defining road sections and calculating the average speed of different road sections specifically includes the following steps:

[0029] S21), defining specific road sections based on map data, and road signs, intersections, or natural dividing points of the road;

[0030] S22), for each defined road section, extracting data of all vehicles passing through the road section;

[0031] S23), calculating the travel time of the vehicle through the road section based on the timestamps of the starting point and the end point of the road section passed by the vehicle;

[0032] S24), determining the length of each road section according to the map data;

[0033] S25) Calculate the average speed of each road section based on the length and travel time of each road section.

[0034] Preferably, in step S22), the extracted vehicle data includes vehicle ID, timestamp, location, and speed.

[0035] Preferably, in step S3), the urban road traffic network is constructed by using the defined road segments as edges and road intersections as nodes.

[0036] Preferably, in step S4), an average speed transfer matrix is ​​constructed according to the probability distribution of speed conversion; specifically, the steps include:

[0037] S41), defining Z speed intervals and collecting vehicle speed data on each road section; then traversing each vehicle speed data and counting it;

[0038] S42), constructing a speed probability distribution matrix according to the Z speed intervals;

[0039] S43), dividing the elements of each row of the speed probability distribution matrix by the sum of the elements of the row to obtain the average speed transfer matrix.

[0040] Preferably, in step S5), a tensor decomposition model is constructed and solved based on the traffic data to be detected, specifically including the following steps:

[0041] S51), the expression of the constructed tensor decomposition model is:

[0042]

[0043] Where, is a third-order tensor; represents the size of the velocity transfer matrix, represents the number of adjacent road segment pairs in the urban road traffic network, represents the number of time intervals; ; Indicates rank; They represent the speed transfer matrix, the factor matrix of adjacent road segments and time intervals in the urban road traffic network respectively;

[0044] S52), after the tensor is decomposed by CP, three factor matrices will be obtained 、 、 ; Establish the following unconstrained optimization problem to find a rank Tensor Make it and Close, that is:

[0045]

[0046] S53) The unconstrained optimization problem is transformed into a projected gradient system through trust technology, namely:

[0047]

[0048] Where, is the factor matrix Elements in for The Jacobian matrix of ; For time; is the number of time intervals; is a vector function where each element satisfy:

[0049]

[0050] in, ;

[0051] S54), fast and flexible holomorphic embedding method to solve the projected gradient system, and solve the function Perform a power series expansion:

[0052]

[0053] in, Is the solution function In the power series expansion of The coefficient of the term, As the starting point of the extension, substitute formula (5) into formula (3) and compare the two sides. The coefficients of the same-order terms are used to establish equations and equation groups, calculate the coefficients of the power series expansion, and then obtain the power series expansion of the solution function. Then, a rational approximation is constructed based on the existing power series coefficients to calculate the numerical solution that meets the error conditions.

[0054] The beneficial effects of the present invention are:

[0055] 1. The present invention solves differential equations by constructing a power series expansion of the solution function and adopts piecewise rational approximation. It only needs to divide the target interval into a small number of segments to approximate the extension path with high precision. It can effectively overcome the shortcomings of the alternating least squares method, such as slow convergence and low computational efficiency.

[0056] 2. The present invention uses global search technology to expand the search domain when solving optimization problems, and searches for multiple local optimal solutions through layer-by-layer search, thereby making it possible to find high-quality local optimal solutions, which can effectively overcome the low precision defect of the alternating least squares method;

[0057] 3. The present invention can detect abnormal road traffic conditions more accurately and efficiently, thereby improving traffic management efficiency and traffic network effectiveness; and the present invention overcomes the defect that the alternating least squares method cannot handle the CP decomposition of tensors containing a large number of zero elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of the process of the present invention;

[0059] Figure 2 A schematic diagram of the process of constructing and solving a tensor decomposition model for the present invention;

[0060] Figure 3 This is a schematic diagram of the process of calculating the projection gradient system of the present invention. DETAILED DESCRIPTION

[0061] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0062] like Figure 1 As shown, this embodiment provides a road traffic anomaly detection method based on holomorphic embedding and global search, comprising the following steps:

[0063] S1), obtain floating car data, and perform map matching and seasonal filtering on it;

[0064] This embodiment uses a Global Navigation Satellite System (GNSS) receiver installed on a vehicle to continuously track and record data received from satellites and transmit this data to a central server or cloud platform. It then removes seasonal components from the raw floating vehicle data and finds the nearest or most likely road by calculating the distance between the GPS point and each road on the map, combined with the vehicle's speed and direction information. Specifically, the steps are as follows:

[0065] S11), obtaining vehicle location data; including GPS coordinates (including longitude and latitude), timestamp, speed, and direction;

[0066] S12), loading road network data; road network data is mainly geometric information, usually including the latitude and longitude of the road, road type, and speed limit;

[0067] S13), performing data cleaning on the vehicle data, in this embodiment, removing outliers;

[0068] S14), using a similarity matching algorithm to preliminarily match the GPS coordinates with roads in the road network. This embodiment only considers location;

[0069] S15), using the vehicle's speed and direction information to improve the matching results;

[0070] S16) Verify the results. In this embodiment, a map visualization tool is used to check the matching results.

[0071] Preferably, in step S15), the speed and direction information of the vehicle is used to improve the matching result, which specifically includes the following steps:

[0072] S151), checking whether the vehicle speed is within the expected speed range of the road;

[0073] S152), calculating the direction angle of the vehicle and comparing it with the direction of the road. If the direction of the vehicle is roughly the same as the direction of the road, the match is considered to be more reliable;

[0074] S153) comprehensively considers the degree of matching between the position, speed and direction of the vehicle and the road, and selects the road with the highest matching degree as the final result based on the comprehensive score.

[0075] S2) defining specific road sections and calculating the average speed of each road section; specifically comprising the following steps:

[0076] S21), defining specific road sections based on map data, and road signs, intersections, or natural dividing points of the road;

[0077] S22), for each defined road section, extracting data of all vehicles passing through the road section, wherein the extracted vehicle data includes vehicle ID, timestamp, location, and speed;

[0078] S23), calculating the travel time of the vehicle through the road section based on the timestamps of the starting point and the end point of the road section passed by the vehicle;

[0079] S24), determining the length of each road section according to the map data;

[0080] S25), according to the length and travel time of each road section, calculate the average speed of the corresponding road section, and the calculation formula is expressed as:

[0081] ;

[0082] The calculated average speed is analyzed and checked for abnormal values ​​or extreme cases. If abnormal data is found, steps S23) - S25) are repeated.

[0083] S3) Constructing an urban road traffic network based on the defined road segments;

[0084] In this embodiment, the urban road traffic network is constructed by using defined road segments as edges and road intersections as nodes.

[0085] S4) Construct an average speed transfer matrix based on the probability distribution of speed conversion; specifically, the steps include:

[0086] S41), defining Z speed intervals and collecting vehicle speed data on each road section; then traversing each vehicle speed data and counting it;

[0087] S42) Construct a speed probability distribution matrix based on the Z speed intervals, where each row of the speed probability distribution matrix represents the current state and each column represents the next state; the elements in the matrix are Represents the vehicle speed from the interval Convert to interval The number of observations;

[0088] S43), dividing the elements of each row of the speed probability distribution matrix by the sum of the elements of the row to obtain the average speed transfer matrix.

[0089] S5) Construct a tensor decomposition model based on the traffic data to be detected and solve it; Figure 2 As shown, the specific steps include:

[0090] S51), the expression of the constructed tensor decomposition model is:

[0091]

[0092] Where, is a third-order tensor; represents the size of the velocity transfer matrix, represents the number of adjacent road segment pairs in the urban road traffic network, represents the number of time intervals; ; Indicates rank; They represent the speed transfer matrix, the factor matrix of adjacent road segments and time intervals in the urban road traffic network respectively;

[0093] S52), after the tensor is decomposed by CP, three factor matrices will be obtained 、 、 ; Establish the following unconstrained optimization problem to find a rank Tensor Make it and Close, that is:

[0094]

[0095] S53) The unconstrained optimization problem is transformed into a projected gradient system through trust technology, namely:

[0096]

[0097] Where, is the factor matrix Elements in for The Jacobian matrix of ; For time; is the number of time intervals; is a vector function where each element satisfy:

[0098]

[0099] in, ;

[0100] S54) Solve the projected gradient system using a fast and flexible holomorphic embedding method, and solve the function Perform a power series expansion:

[0101]

[0102] in, Is the solution function In the power series expansion of The coefficient of the term, As the starting point of the extension, substitute formula (5) into formula (3) and compare the two sides. The coefficients of the same-order terms are used to establish equations and equation groups, calculate the coefficients of the power series expansion, and then obtain the power series expansion of the solution function. Then, a rational approximation is constructed based on the existing power series coefficients to calculate the numerical solution that meets the error conditions.

[0103] As preferred in this embodiment, Figure 3 As shown, in step S54), the projected gradient system is solved using a fast and flexible holomorphic embedding method, which specifically includes the following steps:

[0104] S541), initialization, set the order of the power series expansion to , the allowable error threshold on both sides of the equation is , the maximum interval length of each extension is , the optional initial point is ;

[0105] S542) For a given ;by The power series with parameter is expressed as:

[0106]

[0107] in, yes In the power series expansion of The coefficient of the term;

[0108] S543), Substitute the power series into formula (3) to obtain the equation with the coefficients of the power series expansion as unknowns, namely:

[0109]

[0110] in, is an unknown vector In the power series expansion of The coefficient vector of the term; q is the degree of the power series expansion;

[0111] S544) Since the right side of formula (6) is a polynomial vector, formula (7) can be rewritten as:

[0112]

[0113] in, ; By deriving the power series expansion of the composite function, the vector function is calculated In the power series expansion of The coefficient vector of the term ;Compare The coefficients of the same-order terms are used to find the coefficients of the power series expansion;

[0114] From formula (8), we can get formula (9), and establish The equations that satisfy this are solved to obtain Value:

[0115]

[0116] S545) ,pass The power series information of Rational approximation of and its derivative;

[0117] S546) The rational approximation of the solution function and its derivative function are Substitute the value at into equation (3) and compare whether the difference between the left and right sides of the equation is less than the preset allowable error threshold. ;

[0118] If satisfied, record ;

[0119] If not satisfied, reduce , until it is satisfied, and finally recorded as ; then update ;

[0120] S547) Repeat steps S542) to S546) until the exist The value at is less than the given tolerance threshold ,but This is the numerical solution of the projected gradient system, denoted as ;

[0121] S548) Substitute into formula (1) and calculate whether the error condition is met. If so, proceed to step S7. If not, proceed to step S6.

[0122] S6) Use trust technology to perform global search to find the local optimal solution that meets the error condition and restore the velocity transfer matrix; specifically, the steps include:

[0123] S61), initialize the local optimal point set ;No. The set of local optimal points of the layer ; Escape point set ; Several search path sets , order layer ;

[0124] S62) Set the The set of local optimal points of the layer ;

[0125] S63) The local optimum in ,from Select a search path to find the escape point, denoted as , Subscript the search path and update the escape point set ;

[0126] S64), from the escape point Set out to find The local optimal point of the adjacent layer ;Substitute the local optimal point into formula (1) to calculate and determine whether the error condition is met;

[0127] If it satisfies, then save this local optimal point as , terminate the calculation;

[0128] If not satisfied, then judge whether If not, update , , then switch to another search path and repeat steps S63) and S64) for all local optimal points After completing the above steps, determine Is it equal to If yes, proceed to step S65), otherwise, update , proceed to step S62);

[0129] S65) and the local optimal solution It is reduced to the speed transfer matrix, the factor matrix of adjacent road sections and time intervals in the urban road traffic network.

[0130] S7), calculating the Kullback-Leibler divergence value of the restored speed transfer matrix and the average speed transfer matrix in the road traffic network to detect abnormal conditions in the urban road traffic network, specifically comprising the following steps:

[0131] S71) is the velocity transfer matrix restored in step S6), is the average velocity transfer matrix, the elements of each matrix and Respectively represent the speed range Transfer to speed zone The probability of ; calculate the Kullback-Leibler divergence value between the two matrices; specifically including the following steps:

[0132] S711), for each speed interval , calculate the Kullback-Leibler divergence value between the row vectors corresponding to the interval, for the The Kullback-Leibler divergence is defined as:

[0133]

[0134] Where, and Represents matrices respectively and No. OK;

[0135] S712) Take the average value of the Kullback-Leibler divergence of all rows according to the following formula to obtain the matrix and KL divergence of:

[0136]

[0137] Where Z is the number of speed intervals;

[0138] S72) A threshold is set based on historical data. If the Kullback-Leibler divergence value during the test period exceeds the preset threshold, it is considered that an abnormal situation exists.

[0139] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A road traffic anomaly detection method based on holomorphic embedding and global search, characterized in that: The following steps are involved: S1), obtain floating car data, and perform map matching and seasonal filtering on it; S2), defining specific road sections and calculating the average speed of each road section; S3), constructing an urban road traffic network based on the defined road sections; S4), constructing an average speed transfer matrix according to the probability distribution of speed conversion; specifically comprising the following steps: S41), defining Z speed intervals and collecting vehicle speed data on each road section; then traversing each vehicle speed data and counting it; S42), constructing a speed probability distribution matrix according to the Z speed intervals; S43), dividing the elements of each row of the speed probability distribution matrix by the sum of the elements of the row to obtain an average speed transfer matrix; S5), constructing a tensor decomposition model according to the traffic data to be detected, and solving it, the expression of the tensor decomposition model is: In the formula, is a third-order tensor; M represents the size of the speed transfer matrix, N represents the number of adjacent road segment pairs in the urban road traffic network, and T represents the number of time intervals; 1≤m≤M, 1≤n≤N, 1≤τ≤T; R represents the rank; They represent the speed transfer matrix, the factor matrix of adjacent road sections and time intervals in the urban road traffic network respectively; S6), using trust technology to perform global search to find a local optimal solution that meets the error condition; and reducing the local optimal solution to a speed transfer matrix, a factor matrix of adjacent sections and time intervals in the urban road traffic network; S7), calculating the Kullback-Leibler divergence value of the restored speed transfer matrix and the average speed transfer matrix in the road traffic network to detect abnormal conditions in the urban road traffic network.

2. The method for detecting road traffic anomalies based on holomorphic embedding and global search according to claim 1 is characterized in that: In step S1), the nearest road or the most likely road is found by calculating the distance between the GPS point and each road on the map and combining the speed and direction information of the vehicle.

3. The road traffic anomaly detection method based on holomorphic embedding and global search according to claim 1 is characterized in that: In step S2), road sections are defined and average speeds of different road sections are calculated, which specifically includes the following steps: S21), defining specific road sections according to map data, and road signs, intersections or natural dividing points of the road; S22), for each defined road section, extracting data of all vehicles passing through the road section; S23), calculating the travel time of the vehicle through the road section according to the timestamps of the starting point and the end point of the road section passed by the vehicle; S24), determining the length of each road section according to the map data; S25), according to the length and travel time of each road section, calculate the average speed of the corresponding road section.

4. The method for detecting road traffic anomalies based on holomorphic embedding and global search according to claim 3 is characterized in that: In step S22), the extracted vehicle data includes vehicle ID, timestamp, location, and speed.

5. The method for detecting road traffic anomalies based on holomorphic embedding and global search according to claim 1, characterized in that: In step S3), the urban road traffic network is constructed by using the defined road sections as edges and road intersections as nodes.

6. The method for detecting road traffic anomalies based on holomorphic embedding and global search according to claim 1, characterized in that: The tensor decomposition model described above is subjected to CP decomposition to obtain three factor matrices: Set up the following unconstrained optimization problem to find a tensor of rank R Make it Close, that is: And the unconstrained optimization problem is transformed into a projected gradient system through the trust technique, namely: In the formula, is the factor matrix The elements in ; DH is the Jacobian matrix of H; t is the time; T is the number of time intervals; is a vector function, where each element H h ,h=1,2,…,M×N×T satisfies: Among them, 1≤m≤M, 1≤n≤N, 1≤τ≤T.

7. The method for detecting road traffic anomalies based on holomorphic embedding and global search according to claim 6 is characterized in that: Using a fast and flexible holomorphic embedding method to solve the projected gradient system, the solution function x k Perform a power series expansion: in, is the solution function x k In the power series expansion of (t-t0) q The coefficient of the term, t0 is the starting point of the extension, and equation (5) is substituted into equation (3). By comparing the coefficients of the same-order terms on both sides (t-t0), equations and equation groups are established, and the coefficients of the power series expansion are calculated. Then, the power series expansion of the solution function is obtained, and then a rational approximation is constructed based on the existing power series coefficients to calculate the numerical solution that meets the error condition.

8. The method for detecting road traffic anomalies based on holomorphic embedding and global search according to claim 1 is characterized in that: In step S7), the Kullback-Leibler divergence value of the restored speed transfer matrix and the average speed transfer matrix in the road traffic network is calculated to detect abnormal conditions in the urban road traffic network, which specifically includes the following steps: S71), let P be the speed transfer matrix restored in step S6), Q be the average speed transfer matrix, and the element P of each matrix ij and Q ij They represent the probability of transferring from speed interval i to speed interval j respectively; the Kullback-Leibler divergence value between the two matrices is calculated; specifically, the steps are as follows: S711), for each speed interval i, calculate the Kullback-Leibler divergence value between the row vectors corresponding to the interval. For the i-th row, the Kullback-Leibler divergence is defined as: Where P i and Q i denote the i-th row of matrices P and Q respectively; S712), taking the average value of the Kullback-Leibler divergence of all rows according to the following formula to obtain the KL divergence of matrices P and Q: Where Z is the number of speed intervals; S72) A threshold is set based on historical data. If the Kullback-Leibler divergence value during the test period exceeds the preset threshold, it is considered that an abnormal situation exists.

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