A network topology-based multi-period fault identification method for road network traffic detectors

Abstract

The application discloses a kind of network topology-based road network traffic detector multi-period fault identification method, belong to traffic detection technical field, specific steps include: first, obtain target road network topology structure, non-centroid node set, traffic detector layout position and continuous multi-period observation road section flow data;Non-centroid node-road section association matrix is constructed, and observation road section and unobserved road section set are divided;Solve the left null space base of unobserved road section association matrix to eliminate the influence of unobserved road section, and construct fault diagnosis matrix;Linear transformation is carried out to observed flow to obtain redundant error matrix, and joint sparse fault identification model is constructed by introducing row sparse constraint and is solved;Fault score is calculated by error matrix row norm, and suspected fault detector is obtained by screening.The application is adapted to detector non-full coverage road network scene, can effectively suppress random noise interference, improve the reliability and robustness of fault identification.

Description

Technical Field

[0001] This invention relates to the field of traffic detection technology, and specifically to a multi-period fault identification method for road network traffic detectors based on network topology. Background Technology

[0002] Existing technologies for fault identification and data quality control of road network traffic detectors mainly fall into two categories: single-detector data statistical discrimination and road network topology correlation analysis. The single-detector data statistical discrimination method identifies complete detector faults by setting empirical thresholds for traffic flow parameters such as flow rate, speed, and occupancy based on the statistical characteristics of individual detector data, combined with fault characteristic classification rules. The road network topology correlation analysis method relies on the flow conservation relationship, combining correlation verification of adjacent detector data, consistency checks of multi-source detection equipment, and regression-based data repair algorithms to identify and complete abnormal data. Some methods based on compressed sensing can infer sparsely distributed faulty detectors from single-time period observation data, providing fundamental support for traffic detector operation and maintenance and data quality control.

[0003] However, the aforementioned existing technologies still have unavoidable performance shortcomings in practical applications. On the one hand, fault identification methods based on topology conservation generally rely on the premise of deploying detectors across the entire road network, which cannot be directly adapted to urban road network scenarios where detectors only partially cover the area, thus limiting their application scenarios. On the other hand, existing methods mostly rely on observation data from a single set or a single time period for fault identification, making it difficult to effectively distinguish between persistent detector faults and data deviations caused by random measurement noise and short-term traffic fluctuations. They also lack the ability to identify faults in cases where the output data appears reasonable but actually has persistent deviations, and fail to fully utilize the inherent characteristic of stable fault locations over multiple consecutive time periods. Consequently, the anti-interference capability and reliability of fault identification results are generally low. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-period fault identification method for road network traffic detectors based on network topology, thereby solving the above-mentioned technical problems.

[0005] To achieve the above objectives, this invention provides a multi-period fault identification method for road network traffic detectors based on network topology, comprising the following steps: S1. Based on the topology of the target road network and the deployment scheme of traffic detectors, the traffic flow data of the observed road segments are collected in multiple consecutive time periods by extracting the set of non-centroid nodes of the road network, the connection relationship of road segments and the deployment location of each detector, so as to obtain the basic input data for fault identification. S2. Based on the road network topology in the basic input data, by constructing a non-centroid node-road segment association matrix, the entire road network is divided into a set of observed road segments and a set of unobserved road segments according to the detector deployment location, and the node-road segment association relationship after block division is obtained. S3. Based on the node-road segment association relationship after block division, the flow constraint term of the unobserved road segment is eliminated by solving the left null space basis of the association matrix of the unobserved road segment, and a fault diagnosis matrix including the observed road segment is constructed to obtain the linear consistency constraint relationship of the flow of the observed road segment. S4. Based on the fault diagnosis matrix and the observed road segment traffic data for each time period, the redundant error vector corresponding to each time period is obtained by performing a linear transformation on the observed traffic for each time period. The vectors of multiple time periods are stacked to form a redundant error matrix. S5. Based on the redundant error matrix and the fault diagnosis matrix, by introducing the row sparsity constraint of the detector error matrix, a joint sparse fault identification model based on multiple sets of observation data is constructed to obtain the optimized solution objective of fault identification. S6. Based on the joint sparse fault identification model, the error matrix estimation results of each detector in continuous multi-time periods are obtained by iteratively solving the problem using the near-end gradient descent algorithm. S7. Based on the error matrix estimation results of the detectors, the fault scores of each traffic detector are obtained by calculating the norm of each row vector. After screening according to the fault judgment rules, a set of suspected fault detectors is obtained.

[0006] Preferably, in S1, based on the requirements for collecting road traffic cross-section flow data, a traffic detector for collecting observation data is obtained by selecting a detection device that can directly acquire road section flow data; the traffic detector includes a loop detector, a video detector, a geomagnetic detector, an ultrasonic detector, a microwave detector, and an infrared detector.

[0007] Preferably, in S2, based on the node inflow and outflow rules of the directed traffic network, a non-centroid node-road segment association matrix is ​​constructed by numerically encoding the connection relationship between each non-centroid node and each road segment. , This represents the total number of non-centroid nodes in the road network. Given the total number of road segments in the road network, a matrix representation describing the traffic conservation relationship of the road network is obtained; Among them, the elements in the non-centroid node-road segment association matrix Satisfy: When the road segment Inflow to non-centroid nodes The value is 1 when the road segment is used. Outflow of non-centroid nodes The value is -1 in the ideal road segment and 0 in other cases; , For the first During the observation period, the flow conservation equation at non-centroidal nodes is: .

[0008] Preferably, step S3 specifically includes: S31. Based on the division results of the observed road segment set and the unobserved road segment set, the observed road segment association matrix is ​​obtained by dividing the non-centroid node-road segment association matrix into blocks according to the column dimension. Association matrix with unobserved road segments The corresponding block flow conservation equation is: ,in, The ideal flow vector for the observed road segment, The ideal flow vector for the unobserved road segment. To observe the number of road sections, This represents the total number of road segments in the road network. S32, Based on the Unobserved Road Segment Correlation Matrix The left null space basis matrix is ​​obtained by solving the left null space of the matrix. Satisfying the constraints This yields a linear transformation matrix that eliminates the unobserved traffic flow terms in the road segments; S33, Based on the left null space basis matrix Correlation matrix with observed road segments A fault diagnosis matrix is ​​constructed through matrix multiplication. This yields a fault diagnosis matrix that contains only the flow constraints of the observed road segments. ,in Let be the dimension of the left null space.

[0009] Preferably, the specific steps of S4 include: S41, based on the first The measured flow data of the observed road segment over a time period are used to determine the relationship between the ideal flow and the superposition of measurement errors, thus obtaining the detector error vector. Compared with the measured flow vector Ideal flow vector The correspondence satisfies ; S42, Based on Fault Diagnosis Matrix With the Measured flow vectors over a time period The first is obtained through linear transformation operation. Redundancy error vector for each time period Combined with ideal traffic to meet Constraints and derivation yield the following relationship between redundancy error and detector error: ; S43, Based on Continuity The redundant error vectors for each time period are concatenated by stacking them column-wise to obtain the redundant error matrix. The detector error matrix is ​​constructed by stacking the detector error vectors from each time period column by column. By combining the linear mapping relationship between single-time redundancy error and detector error, the relationship between the redundancy error matrix and the detector error matrix is ​​derived. .

[0010] Preferably, in S5, based on the characteristic that the fault detector position is relatively stable over multiple time periods, a joint sparse fault identification optimization model is constructed by applying sparse constraints to the detector error matrix, thereby obtaining the solution objective with the detector error matrix as the optimization variable; The expression for the joint sparse fault identification model is: ; in, The result is the estimation of the detector error matrix. Describing the Frobenius norm, For regularization parameters, For the detector error matrix, the first... The 2-norm of the row is used to characterize the first row. The degree of error aggregation across multiple time periods for each detector; For the detector error matrix The All elements in the row.

[0011] Preferably, the regularization parameters in the joint sparse fault identification model Based on the actual road network's measurement noise level and fault identification accuracy requirements, a preset value is set by adjusting the sparsity penalty to balance the row sparsity of the data fitting error and the detector error matrix.

[0012] Preferably, in S6, the joint sparse fault identification model is iteratively solved by alternately performing gradient descent and proximal soft thresholding operations based on the optimization framework to obtain the estimated result of the detector error matrix; The update expression for the gradient descent step is: ; in, For the first The detector error matrix of the next iteration This is the intermediate matrix after gradient descent. Let be the Lipschitz constant of the gradient; The expression for updating the soft threshold in the proximal row is: ; in, It is a positive truncation function. For the first The detector error matrix after the nth iteration OK; For the first In this iteration, the intermediate matrix calculated via the gradient descent step is... The Row vectors.

[0013] Preferably, in S7, based on the detector error matrix estimation results obtained by solving, the fault score of each traffic detector is obtained by calculating the 2 norm of each row vector of the matrix, and the fault probability quantification value of each detector is obtained. No. The formula for calculating the fault score of a traffic detector is as follows: ; in, For the first The fault score of a traffic detector indicates that the higher the score, the more consistently and significantly the detector contributes to redundancy error over multiple time periods, and the greater the likelihood of a fault.

[0014] Preferably, in S7, a preset fault determination threshold is used. By comparing the fault scores of each detector with the threshold, a set of suspected fault detectors is obtained, satisfying the following conditions: , This is the set of suspected fault detectors obtained through identification; If no fault determination threshold is set, the fault investigation priority sequence of traffic detectors is obtained by sorting the fault scores of each detector in descending order. The detector with the higher the fault score has a higher priority for investigation and maintenance.

[0015] Therefore, the present invention employs the above-mentioned multi-period fault identification method for road network traffic detectors based on network topology, which has the following beneficial effects: 1. By constructing a non-centroid node-road segment correlation matrix to characterize the traffic conservation relationship of the road network, a linear transformation is performed based on the left null space basis of the correlation matrix of unobserved road segments to eliminate the traffic constraint terms of unobserved road segments, and finally a fault diagnosis matrix containing only observed road segments is constructed. Consistency constraints between observation data can be established without relying on the deployment conditions of detectors across the entire road segment. It can be directly applied to the actual urban road network partially covered by detectors without the need for additional external calibration equipment and data, thus reducing the deployment cost and application threshold of fault identification.

[0016] 2. Based on the observation flow data of multiple consecutive time periods, a redundant error matrix is ​​constructed. Combining the characteristic that the position of the fault detector is relatively stable within consecutive time periods, the fault identification problem is transformed into a row sparse solution problem of the detector error matrix. A joint sparse fault identification model is established to fully explore the inherent correlation information of the observation data of multiple time periods. It can suppress the interference of random measurement noise in a single set of observation data on fault judgment, improve the identification accuracy and robustness of some faults and hidden fault detectors, and reduce the problems of misjudgment and missed judgment caused by data anomalies in a single time period.

[0017] 3. By employing the proximal gradient descent algorithm to solve the joint sparse fault identification model, and updating the detector error matrix row by row to achieve sparsity constraints, the algorithm has clear convergence logic, high computational efficiency, and can be adapted to road network detection scenarios of different scales. At the same time, the fault score of each detector is obtained by quantifying the row norm of the error matrix. It supports both directly outputting the set of suspected fault detectors with preset thresholds and generating a priority sequence for operation and maintenance investigation based on fault scores. The judgment method is flexible and configurable, and can provide a hierarchical and implementable decision-making basis for traffic detector operation and maintenance and traffic data quality control.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 A flowchart of a multi-period fault identification method for road network traffic detectors based on network topology provided by the present invention; Figure 2 A schematic diagram of the road network structure in an embodiment of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0021] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0022] The following is in conjunction with the appendix Figures 1-2 The embodiments of the present invention will be described in detail below.

[0023] Current road network traffic detector fault identification technologies are mainly divided into two categories: single detector data statistical discrimination and road network topology correlation analysis. Among them, the single detector data statistical discrimination method relies heavily on manually set empirical parameters, and can only identify complete faults with significantly abnormal data. It cannot capture partial faults that appear reasonable on the surface but actually have continuous deviations. Moreover, in large-scale road networks, it requires checking each one one by one, resulting in extremely low operation and maintenance efficiency. On the other hand, topology identification methods based on traffic conservation generally assume that detectors are deployed on the entire road network, which is difficult to adapt to the common scenario of partial detector coverage in actual urban road networks. Furthermore, they are mostly based on observation data from a single time period, which is prone to misjudgment and missed judgment. They fail to fully explore the inherent characteristics of the relatively stable location of fault detectors over continuous multiple time periods, and the accuracy and robustness of identifying hidden faults are difficult to meet the actual operation and maintenance requirements.

[0024] Based on the above analysis, specific embodiments of the present invention are given, including: This embodiment uses the Nguyen-Dupuis standard test network to verify the effectiveness of this method. The network topology is shown in [reference needed]. Figure 2 As shown, the road network consists of 13 nodes and 19 directed road segments. Nodes 1 and 4 are the origin and destination of traffic demand (centroid nodes), while nodes 5, 6, 7, 8, 9, 10, 11, 12, and 13 are ordinary connection nodes (non-centroid nodes). Ideally, the non-centroid nodes satisfy the conservation constraint that the inflow flow equals the outflow flow.

[0025] The detector deployment scheme in this embodiment is as follows: traffic detectors are deployed on road segments 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, and 19, totaling 16 observation road segments; road segments 4, 9, and 14 have no detectors deployed and are therefore unobserved road segments. This embodiment simulates a persistent partial failure of the traffic detectors corresponding to road segments 7 and 17, while the remaining detectors only contain random measurement noise, to verify the fault identification capability of the method.

[0026] This embodiment is performed according to the following steps: S1. Collect basic input data for fault identification: Based on the topology of the target road network and the traffic detector deployment scheme, extract the set of non-centroid nodes of the road network, the road segment connection relationships, and the deployment locations of each detector. Collect traffic flow data of the observed road segments for eight consecutive time periods (t1~t8) as the basic input data for fault identification. The time-segmented traffic flow data of each observed road segment are shown in Table 1.

[0027] Table 1. Traffic flow data for the observed road sections over eight consecutive time periods:

[0028] The traffic detector used in this embodiment is a loop detector that can directly obtain the traffic flow of the road cross section; in other implementation scenarios, it can also be replaced by any one or more combinations of video detectors, geomagnetic detectors, ultrasonic detectors, microwave detectors, and infrared detectors.

[0029] S2. Constructing the Non-Centric Node-Road Segment Association Matrix and Dividing the Road Segment Set: Based on the road network topology in the basic input data, according to the node inflow and outflow rules of the directed traffic network, the connection relationship between each non-centroid node and each road segment is numerically encoded to construct the non-centroid node-road segment association matrix. , This represents the total number of non-centroid nodes in the road network. Given the total number of road segments in the road network, we obtain a matrix representation describing the traffic conservation relationship in the road network.

[0030] The number of non-centroidal nodes in this embodiment Total number of road sections Therefore, the correlation matrix This is a 9x19 matrix. Matrix elements. The rule for determining the value is: when the road segment Inflow to non-centroid nodes hour, When the road section Outflow of non-centroid nodes hour, Other situations For the ideal road segment flow vector The flow conservation equation at non-centroid nodes satisfies The non-centroid node-road segment association matrix constructed in this embodiment as follows: ; Based on the location of traffic detectors, the entire road network is divided into observation segment sets. Set of unobserved road sections : Observation section set Number of observed road sections Unobserved road segment set Number of unobserved road sections .

[0031] S3. Construct a fault diagnosis matrix that only includes observed road segments: Based on the node-road segment association relationship after block division, eliminate the flow constraint term of the unobserved road segments by solving the left null space basis of the association matrix of the unobserved road segments, construct a fault diagnosis matrix that only includes observed road segments, and obtain the linear consistency constraint relationship of the flow of the observed road segments. Specifically, it consists of three sub-steps: S31, Correlation Matrix Blocking: Based on the partitioning results of the observed road segment set and the unobserved road segment set, the correlation matrix of non-centroid nodes-road segments is divided. Divide the data into blocks according to column dimensions to obtain the correlation matrix of observed road segments. Association matrix with unobserved road segments The corresponding block flow conservation equation is: ; In this embodiment, the association matrix of unobserved road segments as follows: ; Observation segment correlation matrix as follows: ; S32. Solving for the left null basis of the unobserved road segment correlation matrix: For the unobserved road segment correlation matrix Solve its left null space to obtain the left null space basis matrix. Satisfying the constraints This linear transformation matrix can eliminate the unknown, unobserved traffic flow terms in the conservation equations, retaining only the linear constraints of the observed traffic flow.

[0032] In this embodiment, the dimension of the left null space is obtained. Left null basis matrix as follows: ; S33. Constructing the fault diagnosis matrix: Based on the left null space basis matrix Correlation matrix with observed road segments A fault diagnosis matrix is ​​constructed through matrix multiplication. This yields a fault diagnosis matrix that contains only the flow constraints of the observed road segments. .

[0033] The fault diagnosis matrix in this embodiment as follows: ; Fault Diagnosis Matrix It describes the linear consistency constraint between the traffic flow of the observed road segments, formed by the road network topology and the traffic flow conservation relationship. Its value is determined only by the road network topology and the location of the detectors, and is independent of the specific traffic flow.

[0034] S4. Calculate the redundancy error matrix: Based on the fault diagnosis matrix and the observed road segment traffic data for each time period, the redundancy error vector corresponding to each time period is obtained by linearly transforming the observed traffic for each time period. The vectors of multiple time periods are stacked to form the redundancy error matrix.

[0035] Specifically, it consists of three sub-steps: S41. Decomposition of the error composition of measured flow rate: For the first... The measured flow vector of the observed road segment within a given time period. It is composed of the ideal flow rate and the detector measurement error, and satisfies: ; in, The ideal flow vector for the observed road segment, This represents the detector error vector for the corresponding time period.

[0036] S42. Calculation of Single-Time Redundancy Error Vector: Using the Fault Diagnosis Matrix For the Measured flow vectors over a time period Perform a linear transformation to obtain the redundancy error vector for that time period. .

[0037] Constraints satisfied by ideal flow The mapping relationship between redundancy error and detector error can be derived: ; This formula shows that the redundancy error is a linear mapping of the detector error; when the traffic detector is fault-free and the random measurement noise is small, the redundancy error should be close to the zero vector; when there is a faulty detector, the redundancy error will deviate significantly from zero.

[0038] S43. Multi-time-period redundant error matrix splicing: Select continuous... The observation data for each time period are used to stack and concatenate the redundant error vectors of each time period column-wise to obtain the redundant error matrix. .

[0039] The redundancy error matrix R calculated in this embodiment is as follows: ; S5. Construct a joint sparse fault identification model based on multiple sets of observation data: Based on the redundant error matrix and the fault diagnosis matrix, a joint sparse fault identification model is constructed by introducing row sparsity constraints on the detector error matrix, and the optimized solution objective for fault identification is obtained.

[0040] Based on the characteristic that the fault detector position is relatively stable over multiple consecutive time periods, the fault identification problem is transformed into a row sparse solution problem of the detector error matrix. The model expression is as follows: ; in, Here is the detector error matrix. The result is the estimation of the detector error matrix. Describing the Frobenius norm, For regularization parameters, For the detector error matrix, the first... The 2-norm of the row is used to characterize the first row. The degree of error aggregation across multiple time periods for each detector; For the detector error matrix The All elements in the row; In this embodiment, a regularization parameter is set based on the actual measured noise level of the road network and the required recognition accuracy. .

[0041] S6. Solve the joint sparse fault identification model: Based on the joint sparse fault identification model, iteratively solve the model using the near-end gradient descent algorithm to obtain the error matrix estimation results of each detector in multiple consecutive time periods.

[0042] This embodiment uses the proximal gradient descent algorithm to solve the problem. By alternately performing gradient descent and proximal soft thresholding operations, the optimal solution is gradually obtained through convergence. Algorithm iteration parameter settings: maximum number of iterations is 1000, and iteration convergence tolerance is [value missing]. The iteration stops prematurely when the relative change in the error matrix between two consecutive iterations is less than the tolerance. Gradient descent step update formula: ; in, For the first The detector error matrix of the next iteration This is the intermediate matrix after gradient descent. is the Lipschitz constant of the gradient, used to ensure that the step size of gradient descent satisfies the convergence condition of the algorithm.

[0043] Proximal row soft threshold update formula: ; in, The positive truncation function is defined as follows: When the calculated value within the parentheses is less than or equal to 0, the entire row output is 0, which indicates that the detector is fault-free, thus achieving a row sparsity effect. For the first The detector error matrix after the nth iteration OK; For the first In this iteration, the intermediate matrix calculated via the gradient descent step is... The Row vectors.

[0044] After the iteration is complete, the final estimate of the detector error matrix can be obtained. .

[0045] S7. Determine the set of suspected fault detectors: Based on the error matrix estimation results of the detectors, the fault score of each traffic detector is obtained by calculating the norm of each row vector. After filtering according to the fault determination rules, a set of suspected fault detectors is obtained. First, the fault score of each detector is calculated. The formula for calculating the fault score of each detector is as follows: ; in, For the first Fault score of each traffic detector; fault score The higher the value, the more consistently and significantly the detector contributes to redundancy error over multiple consecutive time periods, and the greater the likelihood of failure.

[0046] The calculation results of this embodiment show that the fault scores of the detectors corresponding to road segments 7 and 17 are significantly higher than those of the other 14 detectors, and are completely consistent with the preset actual fault locations, thus verifying the accuracy of this method.

[0047] Fault determination supports two rules, which can be selected according to actual application needs: Threshold determination mode: Preset fault determination threshold Filter to meet The detectors constitute a set of suspected fault detectors. , This is the set of suspected fault detectors obtained through identification; Priority sorting mode: If no threshold is set, all detectors are sorted in descending order of fault score to generate a fault investigation priority sequence. The higher the score of the detector, the higher the priority of on-site investigation and maintenance.

[0048] In summary, this invention achieves accurate fault identification in scenarios with incomplete detector coverage through road network topology modeling, elimination of unobserved road segments, and joint sparse solution across multiple time periods. Simultaneously, it enhances the robustness and reliability of fault identification by relying on the correlation constraints of continuous multi-time period data. Relying only on existing detector observation data and road network topology information, without the need for additional calibration equipment or manual troubleshooting, it provides efficient technical support for traffic detector operation and maintenance, road network data quality control, and intelligent transportation system operation management.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for multi-time-period fault identification of road network traffic detectors based on network topology, characterized in that, Includes the following steps: S1. Based on the topology of the target road network and the deployment scheme of traffic detectors, the traffic flow data of the observed road segments are collected in multiple consecutive time periods by extracting the set of non-centroid nodes of the road network, the connection relationship of road segments and the deployment location of each detector, so as to obtain the basic input data for fault identification. S2. Based on the road network topology in the basic input data, by constructing a non-centroid node-road segment association matrix, the entire road network is divided into a set of observed road segments and a set of unobserved road segments according to the detector deployment location, and the node-road segment association relationship after block division is obtained. S3. Based on the node-road segment association relationship after block division, the flow constraint term of the unobserved road segment is eliminated by solving the left null space basis of the association matrix of the unobserved road segment, and a fault diagnosis matrix including the observed road segment is constructed to obtain the linear consistency constraint relationship of the flow of the observed road segment. S4. Based on the fault diagnosis matrix and the observed road segment traffic data for each time period, the redundant error vector corresponding to each time period is obtained by performing a linear transformation on the observed traffic for each time period. The vectors of multiple time periods are stacked to form a redundant error matrix. S5. Based on the redundant error matrix and the fault diagnosis matrix, by introducing the row sparsity constraint of the detector error matrix, a joint sparse fault identification model based on multiple sets of observation data is constructed to obtain the optimized solution objective of fault identification. S6. Based on the joint sparse fault identification model, the error matrix estimation results of each detector in continuous multi-time periods are obtained by iteratively solving the problem through the near-end gradient descent algorithm. S7. Based on the error matrix estimation results of the detectors, the fault scores of each traffic detector are obtained by calculating the norm of each row vector. After screening according to the fault judgment rules, a set of suspected fault detectors is obtained.

2. The method for multi-time period fault identification of road network traffic detectors based on network topology according to claim 1, characterized in that: In S1, based on the requirements for collecting traffic flow at road cross-sections, a traffic detector for collecting observation data is obtained by selecting a detection device that can directly acquire road section traffic flow data; the traffic detector includes a loop detector, a video detector, a geomagnetic detector, an ultrasonic detector, a microwave detector, and an infrared detector.

3. The method for multi-time period fault identification of road network traffic detectors based on network topology according to claim 2, characterized in that: In S2, based on the inflow and outflow rules of the directed traffic network, a non-centroid node-road segment association matrix is ​​constructed by numerically encoding the connection relationship between each non-centroid node and each road segment. , This represents the total number of non-centroid nodes in the road network. Given the total number of road segments in the road network, we obtain a matrix representation describing the traffic conservation relationship in the road network. Among them, the elements in the non-centroid node-road segment association matrix Satisfy: When the road segment Inflow to non-centroid nodes The value is 1 when the road segment is used. Outflow of non-centroid nodes The value is -1 in the ideal road segment and 0 in other cases; , For the first During the observation period, the flow conservation equation at non-centroidal nodes is: .

4. The method for multi-time period fault identification of road network traffic detectors based on network topology according to claim 3, characterized in that: The specific steps of S3 include: S31. Based on the division results of the observed road segment set and the unobserved road segment set, the observed road segment association matrix is ​​obtained by dividing the non-centroid node-road segment association matrix into blocks according to the column dimension. Association matrix with unobserved road segments The corresponding block flow conservation equation is: ,in, The ideal flow vector for the observed road segment, The ideal flow vector for the unobserved road segment. To observe the number of road sections, This represents the total number of road segments in the road network. S32, Based on the Unobserved Road Segment Correlation Matrix The left null space basis matrix is ​​obtained by solving the left null space of the matrix. The constraints are satisfied. This yields a linear transformation matrix that eliminates the unobserved traffic flow terms in the road segments; S33, Based on the left null space basis matrix Correlation matrix with observed road segments A fault diagnosis matrix is ​​constructed through matrix multiplication. This yields a fault diagnosis matrix that contains only the flow constraints of the observed road segments. ,in Let be the dimension of the left null space.

5. The network topology based road network traffic detector multi-period fault identification method according to claim 4, characterized in that: The specific steps of S4 include: S41、based on the observation section measured flow data of the first time period, through the decomposition of the superposition of the ideal flow and the measurement error composition relationship, the detector error vector and the corresponding relationship of the measured flow vector , the ideal flow vector , satisfy ; S42、based on the fault diagnosis matrix the measured flow vector of the first time period , the redundant error vector of the first time period is obtained by linear transformation operation , combined with the constraints satisfied by the ideal flow , the relationship between the redundant error and the detector error is derived as ; S43, based on the continuity The redundant error vectors of the time periods are stacked in columns to form a redundant error matrix The detector error vectors of the time periods are stacked in columns to form a detector error matrix The linear mapping relationship between the single-period redundant error and the detector error is combined to derive the relationship between the redundant error matrix and the detector error matrix as .

6. The network topology based road network traffic detector multi-period fault identification method according to claim 5, characterized in that: In S5, based on the characteristic that the fault detector position is relatively stable over multiple time periods, a joint sparse fault identification optimization model is constructed by applying sparse constraints to the detector error matrix, and the solution objective with the detector error matrix as the optimization variable is obtained. The expression for the joint sparse fault identification model is: ； wherein, is an estimation result of the detector error matrix, denotes the Frobenius norm, is a regularization parameter, is the 2-norm of the first row of the detector error matrix, used to represent the degree of error aggregation of the first detector in consecutive time periods; is all elements of the first row of the detector error matrix, .

7. The method for multi-time period fault identification of road network traffic detectors based on network topology according to claim 6, characterized in that: Regularization parameter in joint sparse fault identification model Based on the measurement noise level of the actual road network and the fault identification accuracy requirement, the strength of the sparse penalty is adjusted to preset the value, which is used to balance the data fitting error and the row sparsity of the detector error matrix.

8. The network topology based road network traffic detector multi-period fault identification method of claim 6, wherein: In S6, based on the optimization framework of proximal gradient descent, the joint sparse fault identification model is iteratively solved by alternately performing gradient descent and proximal soft thresholding operations to obtain the estimated result of the detector error matrix. The update expression for the gradient descent step is: ； wherein, is the detector error matrix for the first iteration, is the intermediate matrix after gradient descent, is the Lipschitz constant of the gradient; The expression for updating the soft threshold in the proximal row is: ； wherein, is a positive valued truncation function, is the row of the detector error matrix after the th iteration; is the row vector of the intermediate matrix computed in the gradient descent step in the th iteration.

9. The network topology based road network traffic detector multi-period fault identification method of claim 8, wherein: In S7, based on the estimated results of the detector error matrix obtained by solving, the fault score of each traffic detector is obtained by calculating the 2 norm of each row vector of the matrix, and the fault probability quantification value of each detector is obtained. No. The formula for calculating the fault score of a traffic detector is as follows: ； in, For the first The fault score of a traffic detector indicates that the higher the score, the more consistently and significantly the detector contributes to redundancy error over multiple time periods, and the greater the likelihood of a fault.

10. A method for multi-time period fault identification of a road network traffic detector based on network topology as described in claim 9, characterized in that: In S7, based on a preset fault determination threshold By comparing the fault scores of each detector with the threshold, a set of suspected fault detectors is obtained, satisfying the following conditions: ; If no fault determination threshold is set, the fault investigation priority sequence of traffic detectors is obtained by sorting the fault scores of each detector in descending order. The detector with the higher the fault score has a higher priority for investigation and maintenance.

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