Intersection signal control multi-period division method based on k-shape

Abstract

The application discloses a kind of k-shape-based intersection signal control multi-period division methods, by using k-shape algorithm in traffic control period division is carried out shape similarity matching and adapts to different length time series, and by Calinski-Harabasz (CH) index and profile coefficient method determines cluster number, using k-shape cluster calculates the distance between each time series and new cluster center, according to minimum distance reassign time series to nearest cluster, again update cluster center to invariant or reach predetermined iteration number;After output, the visual clustering result is compared with the trend of data, and each group of data is divided into the cluster it belongs to.The application solves the defect that k value needs to be determined manually in the traditional way, provides a new idea for multi-period division of intersection signal timing, and relieves the congestion degree of road intersection in different periods, improves the operation efficiency of intersection.

Description

Technical Field

[0001] This invention relates to a method for dividing traffic control at road intersections into multiple time periods, and more particularly to a method for dividing traffic signal control at intersections into multiple time periods based on k-shape. Background Technology

[0002] Time-based control remains the primary method for intersection signal control. However, actual traffic conditions are complex and variable, resulting in poor timeliness and necessitating periodic adjustments to existing signal control schemes. Therefore, improving the efficiency of time-segmented control within time-based signal control is a key issue that urban traffic signal control must address.

[0003] Multi-period signal timing optimization at single-point intersections is an important means to alleviate road traffic congestion, improve traffic capacity, and reduce traffic delays. Its core idea is to divide the day into several control periods with the same traffic flow state based on the daily traffic flow variation patterns during the signal timing optimization process. The main methods for this division include coarse methods, heuristic search algorithms, and cluster analysis algorithms. Regarding heuristic algorithms, Park introduced a greedy search algorithm to divide control periods, considering the losses caused by the transition period of the control timing scheme, optimizing the timing parameters for each unit of time, and initially dividing the periods using the periodicity of each unit of time as the input variable for hierarchical clustering. Finally, a greedy algorithm is used to search for some possible division points near the initial division point. This method is quite sensitive to the initial division point, and the optimal number of clusters cannot be determined. Most domestic and international research on multi-period division methods for intersections focuses on cluster analysis algorithms. Wang et al. used the k-means clustering method to divide intersection periods based on traffic flow data, identifying time transition points through traffic flow data from each approach lane. Many subsequent period division methods are derived from the k-means algorithm. However, clustering algorithms like k-means are general-purpose clustering algorithms, and their clustering effect on time series data may not be ideal because they do not consider the specific characteristics of time series data. Furthermore, they assume that clusters are convex, but multi-period data from intersections may contain non-convex patterns. Additionally, when k-means clustering divides intersections into multiple time periods, some time periods are too short. To ensure the division results function correctly in practice, time periods with short durations are merged into their adjacent time periods, introducing a degree of subjectivity. Summary of the Invention

[0004] Purpose of the invention: To address the shortcomings of existing technologies and considering that traffic flow data is time-series data, exhibiting different trends and certain regularities over time, this invention proposes a k-shape-based method for multi-period segmentation of intersection signal control. By employing the k-shape algorithm to perform shape similarity matching and adapt to time series of different lengths during traffic control period segmentation, and determining the number of clusters using the Calinski-Harabasz (CH) exponent and silhouette coefficient method, this invention overcomes the shortcomings of traditional methods that require manual determination of the k-value. It provides a new approach to multi-period segmentation of intersection signal timing, alleviates congestion at road intersections at different times, and improves the operational efficiency of intersections.

[0005] Technical solution: The k-shape-based multi-time period segmentation method for intersection signal control of this invention includes the following steps:

[0006] (1) Data Preparation and Collection: Time-series traffic flow data for each approach lane at the intersection is obtained. To accurately reflect the traffic flow trends at different times, the time-series data needs to be split. If the data for each approach lane is segmented, the time period division after clustering will be chaotic. Therefore, the data for the approach lanes are merged to form 24-hour traffic flow data for the intersection.

[0007] (2) Data preprocessing: z-standardization is used to standardize the total traffic flow of each approach lane at the intersection over 24 hours. The steps of z-standardization are as follows:

[0008] First, calculate the mean μ and standard deviation σ for each time series:

[0009]

[0010]

[0011] Where n is the length of the time series, q ti It represents the traffic flow at the i-th time point.

[0012] Then z-normalize each time series in It is the traffic flow at the i-th time point after z-standardization; thus ensuring that each dimension contributes equally to the distance calculation, avoiding the impact of different numerical ranges on the distance metric.

[0013] (3) Determining the k-value: Before using the k-shape clustering algorithm, the number of clusters, i.e., the k-value, is determined in advance. First, based on the changes in traffic flow at the intersection, the range of k-values ​​is initially determined according to human experience. For a given range of k-values, the Calinski-Harabasz (CH) index and silhouette coefficient method are used to further determine the k-value. The CH index focuses on the ratio of intra-cluster similarity to inter-cluster difference, while the silhouette coefficient comprehensively considers intra-cluster similarity and inter-cluster difference. Therefore, when selecting the number of clusters k, the optimal k-value is determined by maximizing the CH index and silhouette coefficient. The process is as follows:

[0014] (3.1) The CH index includes intra-cluster dispersion and inter-cluster dispersion. Intra-cluster dispersion It measures the density between data points within a cluster, where W k C is the intra-cluster scatter of the k-th cluster. i It is the i-th cluster, μ i It is cluster C i The closer the data points are to the center of the cluster, the better; this is usually represented by the trace of the intra-cluster covariance matrix. Inter-cluster dispersion. The separation between different clusters was measured, where B k It is the inter-cluster scatter of the k-th cluster, n i It is cluster C i The number of data points in the dataset, μ, represents the global data center; ideally, data points should be as dispersed as possible across different clusters, typically represented by the trace of the global covariance matrix. For a given range of k values, calculate the CH exponent for each k value and select the k that maximizes the CH exponent. a The value is used as the optimal number of clusters, and the calculation formula is as follows:

[0015]

[0016] Here, CH(k) represents the CH index corresponding to each k value within the range of k values.

[0017] (3.2) Use the profile coefficient to verify the k determined in step (3.1). a The silhouette coefficient is set to a value between -1 and 1. A silhouette coefficient close to 1 indicates high cluster density and high inter-cluster separation, resulting in good clustering. A silhouette coefficient close to 0 indicates similar cluster density and inter-cluster separation, resulting in moderate clustering. A silhouette coefficient close to -1 indicates low cluster density and low inter-cluster separation, resulting in poor clustering. The optimal number of clusters is determined by comparing the silhouette coefficients within the selected k-value range. The calculation formula is as follows:

[0018]

[0019] Where S(i) is the contour coefficient of the i-th data point; a(i) is the average distance from data point i to other points in the same cluster; b(i) is the average distance from data point i to the nearest point in a different cluster.

[0020] Plot the k value and the corresponding profile coefficients graphically, and find the k value corresponding to the point with the largest profile coefficient. b The value is the optimal k value. Finally, check k. b =k a If the two values ​​are consistent, meaning the same k value performs well in both methods, then choose that k value.

[0021] (4) The k-shape algorithm is used to compare and analyze different time periods: the traffic flow trend is divided into an upward trend, a downward trend, and no obvious trend. In an upward trend, the traffic flow moves from low peak to flat peak or from flat peak to high peak. If the flat peak duration is short when moving from low peak to high peak, it will show a large upward trend. A downward trend moves from high peak to flat peak or from flat peak to low peak. No obvious trend refers to the flat peak period, where the traffic flow fluctuates more. Different time periods are selected for comparison and analysis based on the above trends. The appropriate time period length can well reflect the above trend shape. The specific length selection should be judged based on the traffic flow survey of the intersection. If the selected time period length is too long, some details in the traffic flow change trend will be obscured; if it is too short, it is difficult to reflect the traffic flow change trend. In order to avoid discontinuous time periods of the same category, there are many segments, which makes the control scheme switch more frequently in actual application. The length of each time period is set to be more than 2 hours, and the categories are closely related to the morning and evening peaks and conform to the actual situation. This invention first uses a cross-correlation metric to measure the shape similarity of time series, and then uses Shape-Based Distance (SBD) calculation to transform the shape similarity into a distance metric. The steps of k-shape clustering using cross-correlation and SBD distance are as follows:

[0022] (4.1) Select a time period length m to segment the data and form a time series input dataset. in Therefore A set of time series, This represents the traffic volume at time m, and the other groups follow the same pattern. The number of groups after data segmentation is... T represents the total number of data points.

[0023] (4.2) Selecting initial cluster centers, i.e., initial cluster centers. For each segment, randomly select some index sequences from within the segment as initial cluster centers, ensuring that the selected initial cluster centers represent different shapes and patterns within the segment. Therefore, this covers different time series patterns within the segment and avoids selecting similar time series within the same segment.

[0024] (4.3) Calculating Cross-Correlation Metrics: The cross-correlation metric for each pair of time series and cluster centers (index sequences) at different time lags is calculated. This involves sliding the two sequences along the time axis and comparing their overlap. In cross-correlation calculations, one sequence is slid to a different position on the other sequence, and a new sequence is generated by comparing their similarity. The value of this new sequence reflects the degree of matching between the two sequences at different time points, with larger values ​​indicating a better match. Zero-padding is used to address length differences during similarity comparisons, ensuring that the cluster centers and time series are of equal length. If the cluster center length is shorter than the time series length, zeros are added to the end of the cluster center to make its length equal to the time series length. Zero-padding ensures overlap when performing cross-correlation calculations between cluster centers and time series of different lengths. Assume there is a time series... and index sequence Given sequences of length m, to achieve translation invariance, let the sliding window be s, keeping y constant, and calculate the inner product between two sequences by sliding x step by step:

[0025]

[0026] The range of values ​​for s in the formula is [-m, m].

[0027] Define a cross-correlation sequence of length 2m-1 w represents the total number of moves. The formula for calculating the cross-correlation sequence is:

[0028]

[0029] in, The calculations are performed sequentially according to the following formula:

[0030]

[0031] s=k=wm

[0032] The similarity between x and y at each step is calculated using R. Ultimately, R is the sum of the dot products of the effective regions (summing over small blocks in each pair). A larger R indicates greater similarity between the two sequences. The goal of this calculation is to find the position of w such that the cross-correlated sequences... Maximum. Thus, Compared to Optimal offset The position w is then determined. Normalization is then performed to eliminate inherent distortion, as calculated below:

[0033]

[0034] This indicates the normalization of cross-correlation sequences.

[0035] (4.4) Calculate SBD distance: using the selected In the calculation, the shape similarity between the time series and the cluster centers is compared, and the most similar one is selected. Then use The SBD (Shortest Difference Between Shapes) is obtained; the more similar the shapes, the smaller the SBD. The normalized NCC (Negative Controlled Coefficient) value is between -1 and 1; therefore, the SBD value is between 0 and 2. The shape information is converted into a distance value using the following formula:

[0036]

[0037] Distance values ​​represent the similarity between two time series.

[0038] (4.5) For each time series, find the minimum distance value, which indicates that the time series is closest to the cluster center. Find all time series with the closest cluster centers and assign the time series to the cluster with the minimum distance.

[0039] (4.6) Calculate the average shape of all members in each cluster. For each cluster that has been assigned to a cluster, first determine the time series of all members within that cluster and align the time series to ensure they have corresponding data at the same time points. Calculate the average of the values ​​of all cluster members at each time point to obtain a time series with an average shape, and so on. Use the calculated average shape as the updated cluster center for all time series in that cluster. This ensures that the cluster center reflects the overall shape of the time series in the cluster. That is, for a time series with k clusters, each with a length of m, calculate the value J of the average shape for each time point t. t as follows:

[0040]

[0041] Among them, a i,t This represents the value of the i-th cluster member at time t.

[0042] (4.7) Repeat steps (4.3), (4.4), (4.5), and (4.6), recalculating the distance between each time series and the new cluster center for k-shape clustering, and reallocating the time series to the nearest cluster based on the minimum distance; then, update the cluster centers again. This process is repeated iteratively until the convergence condition is met, i.e., the cluster centers no longer change or the predetermined number of iterations is reached.

[0043] (5) Visualize the clustering results: Compare the trends of each group of data in the output clusters, and assign each group of data to its respective cluster to form a cluster visualization. At this point, the basic time period division has been completed. Then, combine the actual traffic volume to make fine adjustments to the combination of time periods, thus achieving the goal of multi-time period division of the intersection.

[0044] In step (1), the collected traffic flow data is formed into time series data Q, where Q has T data points. Therefore, for one-dimensional sample data... This represents the traffic volume at time i. For example, dividing a 24-hour day into 15-minute intervals based on phase, we get T = 96.

[0045] In step (2), when z-standardization is used, the data is converted into a standard normal distribution with a mean of 0 and a standard deviation of 1 by subtracting the mean and dividing by the standard deviation, thereby standardizing the total traffic flow of each approach lane at the intersection over 24 hours.

[0046] In step (4), the time period is set to be longer than 2 hours.

[0047] In step (4.2), the selected initial cluster center represents different shapes and patterns within the segment.

[0048] In step (4.3), when calculating the cross-correlation measure of each pair of time series and cluster centers at different time lags, the two series are slid along the time axis and the degree of overlap is compared.

[0049] In step (4.5), the time series of all the closest cluster centers are found and the time series are assigned to the clusters with the smallest distance.

[0050] In step (4.6), for each cluster that has been assigned a cluster, the time series of all members within the cluster are first determined and the time series are aligned.

[0051] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0052] (1) The clustering algorithm used in the k-shape-based multi-period segmentation method for intersection signal control in this invention focuses on processing the shape similarity of time series data, rather than just considering the numerical values. This has advantages in processing non-convex data, allowing for more flexible adaptation to different traffic patterns and making it more suitable for intersection data in different time periods. This makes it more robust and accurate in traffic control period segmentation, providing a powerful and effective method for intelligent traffic management.

[0053] (2) The k-shape clustering algorithm used in this invention can identify traffic flow patterns with similar shapes, thereby dividing different time periods. This helps to understand the traffic characteristics of different time periods more precisely, and it has a certain robustness to outliers, avoiding interference from outliers, enhancing the robustness of time period division, making time period division more accurate, and providing personalized strategies for signal control and traffic management at intersections. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the multi-time period segmentation method of the present invention;

[0055] Figure 2 This is a schematic diagram illustrating the process of determining the number of clusters in this invention;

[0056] Figure 3 This is a flowchart illustrating the execution of the k-shape clustering algorithm in this invention.

[0057] Figure 4 This is a line graph showing the number of clusters in this invention;

[0058] Figure 5 This is a visualization of k-shape clustering of time-series data according to the present invention. Detailed Implementation

[0059] This embodiment uses the standard intersection of Mingyuan Road, an east-west secondary arterial road, and Chengde South Road, a north-south main arterial road, in Qingjiangpu District, Huai'an City, Jiangsu Province, as an example to verify the effectiveness of the proposed method. Chengde South Road has a four-lane cross-section with four lanes for both directions. Mingyuan Road also has a four-lane cross-section with six lanes for both directions. This intersection uses timed four-phase signal control, and the study will use 15-minute traffic flow data as the data object. 24-hour traffic data from the intersection will be used as sample data to form a time series sample. Let represent the traffic volume at time i, and T = 96. After the statistical survey was completed, the traffic flow was converted, and the results are shown in Table 1.

[0060] Table 1. Traffic flow at each approach lane of the intersection

[0061]

[0062] 1. Standardize the time series data. Perform z-standardization on each data point, which involves subtracting the mean from each data point and then dividing by the standard deviation. This results in a standardized dataset with a standard normal distribution of 0 mean and 1 standard deviation. Save the standardized time series data for further analysis. The specific formula is as follows:

[0063]

[0064] It is the standardized value of z for the i-th data point.

[0065] It is the original value of the i-th data point.

[0066] μ is the mean of the data.

[0067] σ is the standard deviation of the data.

[0068] 2. Based on manual experience, the range of values ​​for k is initially determined, and k is set to [3, 7]. For a given range of k values, the CH exponent is used for calculation, let C... i It is the i-th cluster, n i It is cluster C i The number of data points in x ij It is cluster C i The feature vector of the j-th data point, μ i It is cluster C i The mean of all data points in the cluster C. i Calculate its covariance matrix S i The calculation formula is:

[0069]

[0070] Using the trace of the covariance matrix, calculate the intra-cluster scatter of all clusters. Among them, trace(S) i ) represents the covariance matrix S i The trace is the sum of the elements on the diagonal of the covariance matrix. Similarly, the inter-cluster divergence B is calculated in the manner described above. k Finally, the CH exponent is calculated to obtain its maximum value, k. a =4; Simultaneously, the silhouette coefficient method is used to calculate the k value, that is, for each k value within the range, its corresponding silhouette coefficient is calculated, and the k value with the highest silhouette coefficient is selected. b The value is high, and the silhouette coefficient is close to 1. Considering both the CH index and the silhouette coefficient, a relatively better k value is selected. If the results are consistent, meaning the same k value performs well in both methods, then there is more confidence in choosing that k value. Finally, the number of clusters is as follows: Figure 4 As shown.

[0071] 3. To illustrate the trend changes in traffic flow, an appropriate time series length is selected. In this embodiment, a 3-hour time series is used. The 24-hour traffic flow at the intersection is divided into 8 groups of 3-hour datasets as input data for k-shape. Cluster analysis is performed with a cluster count of 4 obtained in the previous step, as follows: Figure 5 As shown.

[0072] 4. From Figure 5The k-shape algorithm divides the eight time-series data sets into four clusters. Cluster 1 has two data sets with an upward trend and relatively gentle fluctuations, indicating a transition from off-peak to peak periods. Cluster 2 has three data sets with a downward trend, generally indicating a transition from peak to off-peak or from off-peak to low-peak periods. Cluster 3 has only one data set with significant fluctuations, preliminarily identified as a transition from nighttime low to morning peak. Cluster 4 has two data sets with high volatility and no clear trend, indicating a off-peak period. The classified results are then matched with eight 3-hour datasets to determine the clustering of the eight data sets. The results are as follows:

[0073] Table 1. Data set partitioning results

[0074]

[0075] Comparing the graphs and tables reveals that the k-shape approach is relatively accurate in judging and classifying the trends of traffic flow time-series data, and segmenting the data into 3-hour time-series segments is also reasonable. Based on the segmentation results, and considering the traffic volume within each time period, further combinations of signal timing periods are made, ultimately dividing the 24 hours of a day into 6 time periods for signal timing optimization. The segmentation results are as follows:

[0076] Table 2 Time Period Division Results

[0077]

[0078]

[0079] The results show that the k-shape algorithm-based traffic control time period segmentation method of this invention can easily and effectively characterize the time period characteristics of intersections by utilizing the changing trends of time series data. Moreover, this scheme can greatly improve the traffic problems at intersections and increase the operational efficiency of intersections.

Claims

1. A method for k-shape based intersection signal control multi-phase division, characterized in that: Comprise the following steps: (1) Data preparation and collection: obtain the traffic time series data of each approach at the intersection, merge the data of the approaches to form the traffic flow data of the intersection for 24 hours; (2) Data preprocessing: adopt z standardization to standardize the total traffic flow of each approach of the intersection for 24 hours, and the steps of z standardization are as follows: First, calculate the mean μ and standard deviation σ of each time series: wherein m is the length of the time series, is the traffic flow at the i-th time point; Then each time series is z-standardized where is the z-standardized traffic flow at the i-th time point. (3) k value determination: firstly, determine the value range of the value, and then determine the optimal k value by maximizing the Calinski-Harabasz (CH) index and the silhouette coefficient, the process is: (3.1) Calculate the CH index corresponding to each k value, and select the k value that makes the CH index maximum as the optimal cluster number, and the calculation formula is: a ​ where CH(k) represents the CH index corresponding to each k value in the k value range; B k is the inter-cluster dispersion of the kth cluster; W k is the intra-cluster dispersion of the kth cluster, and n is the number of data points; (3.2) Determine the optimal cluster number by comparing the silhouette coefficient in the k value range, and the calculation formula is as follows: Wherein, S(i) is the silhouette coefficient of the ith data point; a(i) is the average distance from the data point i to other points in the same cluster; b(i) is the average distance from the data point i to the nearest point in the different cluster; Plot the k values against the corresponding profile coefficients, find the k corresponding to the maximum profile coefficient b value is the optimal k value, finally check k b = k a ; (4) Adopt k-shape algorithm to compare and analyze different time period lengths: (4.1) Selecting time series length m to segment data, forming a time series input data set wherein is a set of time series composed of represents t m traffic volume value at time t; the number of data segments is T is the total number of data;​ (4.2) Select the initial cluster center, and randomly select the index sequence in the segment as the initial cluster center; (4.3) Calculate the cross-correlation measure, calculate the cross-correlation measure of each pair of time series and index sequence under different time lags, and compare the overlap degree; Assume time series and index sequence The time series length is m, and the sliding window is s. Keep y unchanged, and slide x step by step to calculate the inner product between the two sequences: s is in the range [-m, m]; define the cross-correlation sequence with length 2m-1 w is the number of all movements; the formula for calculating the cross-correlation sequence is: wherein The calculation of the following formula is used: s=k=w-m The similarity of x and y at each step is calculated using R, and the position of w is found such that the cross-correlation sequence is maximized; then the best offset of is determined relative to At the w position, normalization is performed to eliminate inherent distortion, and the calculation formula is as follows: denotes the cross-correlation sequence normalization; (4.4) Calculate Shape-Based Distance (SBD) distance: Using the selected In the calculation, the shape similarity between the time series and the cluster center is compared, and the most similar one is taken Then use Get SBD, the normalized NCC value is between [-1, 1], and the SBD value is between [0, 2]. The shape information is converted into a distance value, and the formula is as follows: distance value representing similarity between two time series; (4.5) For each time series, find the minimum value in the distance value, find the time series closest to the cluster center, and assign the time series to the cluster corresponding to the minimum distance; (4.6) Calculate the average shape of all members of each cluster, calculate the average of the values of all cluster members at each time point, get a time series of average shapes, take the calculated average shape as the updated cluster center of all time series in the cluster; time series with k clusters, each sequence length m, for each time point t, calculate the value of the average shape J t As follows: where a i,t denotes the value of the ith cluster member at time t; (4.7) Repeat steps (4.3) to (4.6), recalculate the distance between each time series and the new cluster center, and reassign the time series to the nearest cluster according to the minimum distance; update the cluster center again; iterate until the convergence condition is met, that is, the cluster center no longer changes or reaches the predetermined number of iterations; (5) Compare the trend of the output visual clustering result with each group of data, divide each group of data into the corresponding cluster, and then combine the traffic to adjust the time period. 2.The k-shape based intersection signal control multi-phase division method according to claim 1, wherein: In step (1), the collected traffic flow data is formed into time series data Q, Q including T data, for one-dimensional sample data i = 1, 2, 3, …, T; denotes the traffic volume value at time i. 3.The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (1), T is obtained by setting the time interval as T according to the phase for 24 hours. 4.The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (2), when z standardization is adopted, the data is converted into a standard normal distribution with a mean of 0 and a standard deviation of 1 by subtracting the mean and dividing by the standard deviation, so as to standardize the total traffic flow of each approach of the intersection for 24 hours.

5. The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (4), the trend of traffic flow is divided into rising trend, falling trend and no obvious trend. 6.The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (4), the length of the time period is set to be greater than 2 hours.

7. The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (4.2), the selected initial cluster center represents different shapes and patterns in the segment.

8. The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (4.3), when calculating the cross-correlation measure of each pair of time series and cluster center under different time lags, slide the two sequences on the time axis, and compare the overlap degree.

9. The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (4.5), find all the time series closest to the cluster center, and assign the time series to the cluster corresponding to the minimum distance.

10. The k-shape based intersection signal control multi-phase division method of claim 1, wherein: In step (4.6), for each cluster that has already been assigned, first determine all the time series of the members in the cluster, and align the time series.

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