A highway tunnel segmentation method based on trajectory data

Abstract

The application provides a highway tunnel segmentation method based on trajectory data. The driving behaviors of vehicles at different longitudinal positions of a highway tunnel are quite different. Existing tunnel segmentation methods mainly consider the physiological changes of drivers and driving comfort, and cannot be completely applied to precise control of tunnels. Based on the vehicle position, speed and acceleration micro-information calculated by extracting the continuous trajectory data of the vehicle, the differences in group driving behaviors at different longitudinal positions of the tunnel can be analyzed. The application extracts and calculates parameters from vehicle trajectory data, explores the change law of driving risk in the tunnel, divides the tunnel road section according to the risk characteristics by combining an unsupervised learning algorithm, and finally considers the brightness difference inside and outside the tunnel and the change of traffic space to correct the length of the road section near the tunnel entrance and exit. The research results can provide decision support for tunnel operation management and help to realize precise traffic control of different road sections of the tunnel.

Description

Technical Field

[0001] This invention belongs to the field of traffic safety technology, specifically relating to the segmentation of highway tunnels based on trajectory data, including data extraction and calculation, data processing, and data application. By extracting and calculating parameters using vehicle trajectory data, and considering driving characteristics, principal component analysis and k-means clustering algorithms are combined to achieve refined segmentation of highway tunnels. Background Technology

[0002] Due to significant differences in brightness between the interior and exterior of highway tunnels and limited traffic space, drivers' perception of tunnel environment information varies, leading to substantial differences in driving behavior at different longitudinal positions within the tunnel and constantly changing vehicle safety. With the development of computer vision technology, large-scale, high-precision vehicle trajectory data has been applied. Trajectory data provides microscopic information about vehicle position and speed, supporting precise calculation and analysis of vehicle risks. Through massive amounts of real-world, continuous trajectory data, detailed analysis of differences in driving behavior among drivers at different longitudinal positions within the tunnel is possible. Existing tunnel segmentation methods primarily consider driver psychophysiological changes and driving comfort, and are not entirely suitable for precise tunnel management. This invention combines multi-source data from brightness detectors, millimeter-wave radar, and integrated radar-visual systems. It explores changes in vehicle driving risks within tunnels using continuous vehicle trajectory data, and divides tunnel segments based on risk characteristics using unsupervised learning algorithms. This method has high applicability. Summary of the Invention

[0003] To address the aforementioned problems, this invention proposes a method for segmenting highway tunnels based on trajectory data. The research results can effectively divide tunnels into segments, providing decision support for tunnel operation and management, facilitating precise control of tunnel segments, improving driving safety, and ensuring the safe and orderly operation of tunnels. To achieve the above objectives, this invention adopts the following technical solution:

[0004] Step 1: Parameter extraction based on trajectory data

[0005] The original vehicle trajectory data records the trajectories of all vehicles on the road, including time, vehicle number, vehicle's horizontal and vertical coordinates, and horizontal and vertical velocity features. The original trajectory data is preprocessed, and vehicle positions are correlated to extract and calculate relevant parameters, specifically including: vehicle's horizontal and vertical coordinates, velocity, acceleration, the horizontal and vertical coordinates of the vehicle ahead, and the speed of the vehicle ahead.

[0006] Step 2: Calculation of vehicle driving characteristics based on trajectory data

[0007] Determine the minimum road unit length for analysis, and divide the analysis segment into p road units based on the minimum road unit length. Select six tunnel segment characteristic indicators B1, B2, B3, B4, B5, and B6. The characteristic indicators for each road unit are calculated as follows:

[0008] (1) Average speed

[0009]

[0010] In the formula: v x v is the vehicle's speed within the road unit; v is the vehicle's instantaneous speed at each data collection point during the statistical period; i is the data collection number of the vehicle during the statistical period, i = 1, 2, ... t; t is the total number of data collections of the vehicle during the statistical period.

[0011]

[0012] In the formula: The average speed of all vehicles within the road unit; i is the vehicle number, i = 1, 2, ..., n; n is the number of vehicles; v xi Let be the speed of vehicle i within the road unit.

[0013] (2) Velocity standard deviation

[0014]

[0015] In the formula: σ is the standard deviation of vehicle speed within the road unit; i is the vehicle number, i = 1, 2, ..., n; n is the number of vehicles counted within the road unit; v xi Let i be the speed of vehicle i within the road unit; This represents the average speed of all statistical vehicles within the road unit.

[0016] (3) Average headway

[0017]

[0018] In the formula: TH i x is the headway between vehicle i and the vehicle in front within the road unit; F,t x L,t Let v be the longitudinal position of the vehicle in front and the vehicle behind at time t; L,t Let be the instantaneous velocity of car i after time t.

[0019]

[0020] In the formula: ATH is the average headway of vehicles within a road unit; i is the vehicle number, i = 1, 2, ..., n; n is the number of vehicles counted within the road unit; TH iThe headway between vehicle i and the vehicle in front within the road unit.

[0021] (4) Average speed difference

[0022] Δv i =v L,t -v F,t

[0023] In the formula: Δv is the speed difference between the following vehicle i and the preceding vehicle within the road unit; v F,t v L,t Let t be the instantaneous speeds of the vehicle in front and the vehicle behind.

[0024]

[0025] In the formula: Δv represents the average speed difference within a road unit; i is the vehicle number, i = 1, 2, ..., n; n is the number of vehicles counted within the road unit; Δv i Let i be the speed difference between the following vehicle i and the preceding vehicle within the road unit.

[0026] (5) Average Time to Collision

[0027]

[0028] Where: TTC i x represents the collision time between the following vehicle i and the preceding vehicle within the road unit; F,t x L,t Let v be the position of the vehicle in front and the vehicle behind at time t; F,t v L,t Let l be the instantaneous speed of the vehicle in front and the vehicle behind at time t; i The length of the vehicle in front.

[0029]

[0030] Where: ATTC is the average collision time of all vehicles within the road unit; i is the vehicle number, i = 1, 2, ..., n; n is the number of vehicles within the road unit; TTC i The collision time between the following vehicle i and the preceding vehicle within the road unit.

[0031] (6) Average Deceleration Rate to Avoid a Crash

[0032]

[0033] Where: DRAC i v is the deceleration of the following vehicle i within the road unit to avoid a collision with the preceding vehicle; F,t vL,t Let x be the speed of the vehicle in front and the vehicle behind at time t; F,t x L,t Let l represent the positions of the preceding and following vehicles at time t; i The length of the vehicle in front.

[0034]

[0035] Where: ADRAC is the average collision avoidance deceleration within the road unit; i is the vehicle number, i = 1, 2, ..., n; n is the number of vehicles counted within the road unit; DRAC i The deceleration of the following vehicle i within the road unit to avoid a collision with the vehicle in front.

[0036] Based on the above parameters, the original data analysis matrix B, composed of the characteristic indicators of p road units, is obtained:

[0037]

[0038] In the formula: B is the original data analysis matrix; B j j = 1, 2, ..., 6 is the set of attribute j for each road unit; b ij Let j be the value of feature j for the i-th road unit, i = 1, 2, ..., p, j = 1, 2, ..., 6.

[0039] Step 3: Processing of segmented characteristic indicators for highway tunnels based on principal component analysis

[0040] (1) Data noise reduction

[0041] The Lowes local weighted scatter smoothing method is used to denoise the feature indices B1, B2, B3, B4, B5, and B6 of p road units. The window size is 0.1, and the resulting data matrix after smoothing... as follows:

[0042]

[0043] In the formula: This is the original data matrix after smoothing; p is the number of road units; Let x be the set of the j-th eigenvalues ​​of each road unit after smoothing, where j = 1, 2, ..., 6; ij , i = 1, 2, ..., p, j = 1, 2, ..., 6 are the j-th feature values ​​of the i-th road unit after smoothing.

[0044] The specific calculation process for smoothing is as follows:

[0045] S1: Determine an interval centered at the center coordinate x0 of the road unit. The formula for calculating the width of the interval window is as follows:

[0046] span = g × p

[0047] Where: x0 is the center coordinate of the road unit; span is the width of the sliding window; g is the window ratio, that is, the proportion of the number of scatter points participating in the local regression to the total number of scatter points; p is the number of scatter points, that is, the number of road units.

[0048] S2: Calculate the weight values ​​of all points within the window width:

[0049]

[0050] Where: ω i (x) represents the weight values ​​of all points within the window; i is the window number; x represents the adjacent points within the span associated with the current center point; x i d is the x-coordinate of the center of window i; i It is the x-coordinate i The distance to the farthest adjacent point within the span.

[0051] S3: Use weighted linear regression to fit a straight line to the scatter points within the window. Obtain the predicted values.

[0052] S4: Move to the next point x i+1 Then perform the above steps to obtain the predicted value. The calculation stops once all points have been calculated.

[0053] (2) Processing of segmented characteristic indicators of highway tunnels

[0054] For the original data matrix Perform Z-Score normalization transformation:

[0055]

[0056] in

[0057] In the formula: i is the road unit number; j is the characteristic index number; x ij Let j be the value of the characteristic index j of road unit i; S is the arithmetic mean of characteristic index j. j The standard deviation of characteristic index j; The value of the characteristic index j of road unit i after standardization transformation.

[0058] After standardization, we obtain the standardized matrix X. * :

[0059]

[0060] When applying principal component analysis, its applicability must be statistically tested. The KMO value is used for this test.

[0061]

[0062] In the formula: i,j are index numbers, i,j=1,2,…,6; r ij Let a represent the simple correlation coefficient between the i-th index and the j-th index; ij This represents the partial correlation coefficient between the i-th and j-th indicators. A KMO value above 0.5 indicates that the data is suitable for principal component analysis.

[0063] Based on the correlation coefficient r ij X is obtained * The sample correlation matrix R:

[0064]

[0065] E is the identity matrix, λ i Let i = 1, 2, 3, 4, 5, 6 be the eigenvalues, and construct the characteristic polynomial |R - λ|. i E|。 Let |R-λ i E|=0, calculate the eigenvalues ​​of R and sort them from largest to smallest: λ1≥λ2≥λ3≥λ4≥λ5≥λ6.

[0066]

[0067] Based on the cumulative contribution rate of the principal components, determine the few principal components that can basically reflect all the feature information. For example, the ratio of the sum of the variances of the current k (k<6) principal components to the total variance. When the value is greater than or equal to 0.85, the first k principal components are selected.

[0068] For data matrix X * Dimensionality reduction is performed to obtain the analysis matrix Z. p×k .

[0069] Z p×k =X * (L1L2L3L4L5L6)

[0070] In the formula: Z p×k X is the dimensionality-reduced analysis matrix; * The normalized matrix; L1, L2, ..., L k These are the eigenvectors corresponding to the first k eigenvalues.

[0071] Step 4: Highway Tunnel Segmentation Based on k-means Clustering

[0072] K-means clustering is used to cluster the dimensionality-reduced vehicle driving feature data of p road units, grouping road units with similar characteristics into the same road segment set. The specific calculation process is as follows:

[0073] S1: Select initial centroids. Specify the number of classes m, and select m samples as cluster centers u1, u2, u3, ..., u4. m .

[0074] S2: Data Assignment. Calculate the distance from each feature data point to its centroid using Euclidean distance, and assign each data point to the centroid closest to it.

[0075] S3: Centroid Update and Iteration. Calculate the mean of all data points and update the centroid. After calculating the new centroid, continuously iterate through step S2 until no data points change the cluster and the sum of the distances from each data point in the cluster to the centroid is minimized.

[0076] S4: Clustering classification results. Based on the number of tunnel segments, p road units are clustered into m classes. The total length D of the road units contained in the i-th class is... i This is the basic length of the road section.

[0077] Step 5: Adjustment of the length of the road section adjacent to the highway tunnel entrance and exit

[0078] After determining the basic length of each tunnel section, considering the variations and limitations of tunnel brightness inside and outside, vehicle speed, and tunnel clearance height, a tunnel brightness correction coefficient f is used. l Speed ​​correction factor f v Tunnel clearance height correction factor f h The lengths of the tunnel entrance and exit sections are adjusted. The calculation methods for each coefficient are as follows:

[0079] (1) Brightness correction factor f for tunnel entrance and exit sections l

[0080]

[0081] In the formula: f l L is the tunnel brightness correction factor; D The external brightness refers to the actual measured brightness at a distance of 200m from the tunnel entrance, 1.5m above the ground, facing the tunnel entrance at a 20° field of view, expressed in cd / m². 2 The data source is the data transmitted back from the luminance monitoring instrument; L is the external luminance value used in the tunnel design, cd / m. 2 .

[0082] (2) Speed ​​correction factor f v

[0083] Calculate the speed correction factor by combining the average vehicle speed and the maximum speed limit of the road section.

[0084]

[0085] In the formula: To correct for the average vehicle speed on the road segment, in km / h; is the average speed of all vehicles passing through road unit j, in km / h; w is the number of road units contained in the modified road segment.

[0086]

[0087] In the formula: f v This is a correction factor for driving speed; To correct the average vehicle speed on the road segment; V max The maximum speed limit for the road is [km / h].

[0088] (3) Tunnel clearance height correction factor f h

[0089] f h = 1 + 0.05(7 - h)

[0090] In the formula: f h is the correction factor for tunnel clearance height; h is the tunnel clearance height, in meters.

[0091] Based on the above information regarding the brightness correction factor f l Speed ​​correction factor f v Tunnel clearance height correction factor f h The final calculation formula for the length D of the road section adjacent to the tunnel entrance / exit is as follows:

[0092] D = D i ×f l ×f v ×f h

[0093] Where D is the corrected length of the road section adjacent to the tunnel entrance / exit; D i f is the initial length of road segment i adjacent to the tunnel entrance / exit; l f is the tunnel brightness correction factor; v f is the speed correction factor; h This is the correction factor for tunnel clearance height. Attached Figure Description

[0094] Figure 1 Invention Flowchart

[0095] Figure 2 Parameter extraction and calculation flowchart

[0096] Figure 3 Example of a tunnel segmentation scenario Detailed Implementation

[0097] The technical solution of this disclosure will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit this disclosure.

[0098] The flowchart of this invention is as follows Figure 1 As shown, this method mainly consists of three parts: parameter extraction and calculation based on trajectory data, selection of segmented feature indicators for highway tunnels, and calculation and correction of the length of each tunnel segment based on clustering. The specific execution steps are as follows:

[0099] Step 1: Parameter extraction based on trajectory data

[0100] The raw vehicle trajectory data includes time, vehicle number, vehicle coordinates, and lateral and longitudinal velocity features. The raw trajectory data is preprocessed and vehicle positions are correlated. Parameter extraction and calculation are performed, specifically including vehicle speed, vehicle acceleration, and multi-vehicle interaction features, such as the speed and position relationships between vehicles ahead and behind. Examples of trajectory data fields and required trajectory fields are shown in Tables 1 and 2.

[0101] Table 1 Example of trajectory data fields

[0102]

[0103]

[0104] Table 2 Demand Trajectory Fields

[0105]

[0106] Step 2: Calculation of vehicle driving characteristics based on trajectory data

[0107] The analysis segment was selected as a 500m section outside the highway tunnel and its entrances / exits. The minimum analysis unit length was determined, and the analysis segment was divided into p road units. Based on the parameters extracted from the trajectory data, the characteristic indices B1, B2, B3, B4, B5, and B6 of each road unit in the tunnel were calculated.

[0108] Case Study: The tunnel is 1500m long, and the total length of the analyzed road segment is 2500m. The minimum analysis unit length is 10m, meaning the analyzed road segment is divided into 250 road units. Six analytical characteristic indicators are used: B1, B2, B3, B4, B5, and B6 represent average speed, speed standard deviation, average headway, average speed difference, average collision time, and average collision avoidance deceleration, respectively. The calculation methods are detailed in the invention description.

[0109] Step 3: Processing of segmented characteristic indicators for highway tunnels based on principal component analysis

[0110] (1) Data noise reduction

[0111] The LOWESS (Locally Weighted Scatterplots) method was used to smooth the feature indices B1, B2, B3, B4, B5, and B6. LOWESS uses a single point as the center, extracts data before and after it, and performs a weighted linear regression using a weighted function. The specific calculation process is as follows:

[0112] Step 31: Define an interval centered at x0. The formula for calculating the width of the interval window is as follows:

[0113] span = g*p

[0114] Where: x0 is the center coordinate of the road unit; span is the width of the sliding window; g is the window ratio, that is, the proportion of the number of scatter points participating in the local regression to the total number of scatter points, which is 0.1; p is the number of scatter points, that is, the number of road units, which is 250.

[0115] Step 32: Calculate the weight values ​​of all points within the window width:

[0116]

[0117] Where: p is the window number; ω i (x) represents the weight values ​​of all points within the window; x represents the adjacent points within the span associated with the current center point; x i d is the x-coordinate of the window center; i It is the x-coordinate i The distance to the farthest adjacent point within the span.

[0118] Step 33: Use weighted linear regression to fit a straight line to the scatter points within the window. Obtain the predicted values.

[0119] Step 34: Move to the next point x i+1 Then perform the above steps to obtain the predicted value. The calculation stops once all points have been calculated.

[0120] Finally, the original data matrix was formed after smoothing the six indicators of the 250 road units. as follows:

[0121]

[0122] In the formula: The original data matrix after smoothing; Let i be the value of the i-th feature after smoothing, where i = 1, 2, 3, 4, 5, 6.

[0123] (2) Processing of segmented characteristic indicators of highway tunnels

[0124] For the original data matrix Perform Z-Score normalization transformation:

[0125]

[0126] in

[0127] In the formula: i is the road unit number; j is the indicator number; x ij Let j be the value of index j for road unit i; S is the arithmetic mean of index j. j Let j be the standard deviation of index j; The value of index j for road unit i after standardization transformation.

[0128] After standardization, we obtain the standardized matrix X. * :

[0129]

[0130] When applying principal component analysis, the suitability of the data must be statistically tested. The KMO value is used for this test.

[0131]

[0132] In the formula: i is the road unit number, i = 1, 2, ..., 250; j is the indicator number, j = 1, 2, ..., 6; r ij This represents the simple correlation coefficient; a ij This represents the partial correlation coefficient. A KMO value above 0.5 indicates that the data is suitable for principal component analysis.

[0133] Principal component analysis (PCA) is used to reduce the dimensionality of variables and enhance the correlation between indicators. Based on the correlation coefficient r... ij X is obtained * The sample correlation matrix R:

[0134]

[0135] E is the identity matrix, λ i Let i = 1, 2, 3, 4, 5, 6 be the eigenvalues, and construct the characteristic polynomial |R - λ|. i E|。 Let |R-λ iE|=0, calculate the eigenvalues ​​of R and sort them from largest to smallest: λ1≥λ2≥λ3≥λ4≥λ5≥λ6.

[0136]

[0137] Based on the cumulative contribution rate of the principal components, determine the few principal components that can basically reflect all the feature information. For example, the ratio of the sum of the variances of the current k (k<6) principal components to the total variance. When the value is greater than or equal to 0.85, the first k principal components are selected.

[0138] Calculate the analysis matrix Z after dimensionality reduction. 250×k This serves as an indicator for the refined division of tunnel sections.

[0139] Z p×k =X * (L1L2L3L4L5L6)

[0140] In the formula: Z p×k X is the dimensionality-reduced analysis matrix; * The normalized matrix; L1, L2, ..., L k These are the eigenvectors corresponding to the first k eigenvalues.

[0141] Case Study: Principal component analysis (PCA) yielded the following variance percentages for six indicators: average speed, speed standard deviation, average headway, average speed difference, average collision time, and average collision avoidance deceleration: 45.29%, 37.40%, 7.42%, 5.84%, 3.32%, and 0.74%, respectively. The cumulative variance percentage for the first three principal components reached 90.12%. Combined with the eigenvector coefficients, the data matrix X... * Dimensionality reduction is performed to obtain the analysis matrix Z. 250×3 .

[0142] Step 4: Highway Tunnel Segmentation Based on k-means Clustering

[0143] k-means clustering was used to group road units with similar characteristics into the same road segment set. The clustering steps are as follows:

[0144] S1: Select initial centroids. Specify the number of classes m, divide the tunnel segment into m segments, and randomly select the initial m samples as class centers, u1, u2, u3, ..., u m .

[0145] S2: Data Assignment. For each data sample in the analysis matrix Z, the distance between the sample and the center of each class is calculated using Euclidean distance, and each data point is assigned to the class closest to it:

[0146]

[0147] In the formula: Label i For category labels; z i To analyze the data sample values ​​in matrix Z; u j Let j be the value of the m-th sample center, where j = 1, 2, ..., m.

[0148] S3: Centroid Update and Iteration. For each data class, recalculate the mean of the data points in that class and use it as the new centroid for that data class.

[0149]

[0150] Where: u j For the new center of mass; c j z represents the number of samples contained in each category, i.e., the number of road units in the road segment set of that category. i For each category, there are samples.

[0151] After calculating the new centroid, step S2 is iterated continuously until no data points change the cluster and the sum of the distances from each data point in the cluster to the centroid is minimized.

[0152] S4: Clustering classification results. Based on the number of tunnel segments, the p road units are finally clustered into m classes.

[0153] Example: The number of categories is specified as m=8, that is, 250 road units are clustered into 8 categories. The length of each road segment is the number of road units contained in the category × the length of the road unit, where the length of the road unit is 10m. The lengths of each tunnel segment after clustering are shown in Table 3.

[0154] Table 3. Tunnel Section Division

[0155]

[0156] Step 5: Adjustment of the length of the road section adjacent to the highway tunnel entrance and exit

[0157] After determining the length of each tunnel segment, the lengths of road sections adjacent to tunnel entrances and exits are adjusted considering factors such as brightness inside and outside the tunnel, vehicle speed, and tunnel clearance. The calculation methods for each adjustment factor are as follows:

[0158] (1) Brightness correction factor f for tunnel entrance and exit sections l

[0159]

[0160] In the formula: L DThe external brightness refers to the actual measured brightness at a distance of 200m from the tunnel entrance, 1.5m above the ground, facing the tunnel entrance at a 20° field of view, expressed in cd / m². 2 The data source is the data transmitted back from the luminance monitoring instrument; L is the external luminance used in the tunnel design, cd / m². 2 ;f l This is the tunnel brightness correction factor.

[0161] (2) Speed ​​correction factor f v

[0162] Calculate the speed correction factor by combining the average vehicle speed and the maximum speed limit of the road section.

[0163]

[0164] In the formula: To correct for the average vehicle speed on the road segment, in km / h; is the average speed of all vehicles passing through road unit j, in km / h; w is the number of road units contained in the modified road segment.

[0165]

[0166] In the formula: f v This is a correction factor for driving speed; To correct for the average vehicle speed on the road segment, in km / h; V max The maximum speed limit for the road is [km / h].

[0167] (3) Tunnel clearance height correction factor f h

[0168] f h = 1 + 0.05(7 - h)

[0169] In the formula: f h is the correction factor for tunnel clearance height; h is the tunnel clearance height, in meters.

[0170] Based on the above information regarding the brightness correction factor f l Speed ​​correction factor f v Tunnel clearance height correction factor f h The final calculation formula for the length D of the road section adjacent to the tunnel entrance / exit is as follows:

[0171] D = D i ×f l ×f v ×f h

[0172] Where D is the corrected length of the road section adjacent to the tunnel entrance / exit; D if is the initial length of road segment i adjacent to the tunnel entrance / exit; l f is the tunnel brightness correction factor; v f is the speed correction factor; h This is the correction factor for tunnel clearance height.

[0173] Case Study: In Step 4, the tunnel is divided into 8 segments, and the length of each segment is calculated. Considering that the farther segments have a smaller impact on the driving characteristics inside the tunnel, the tunnel is ultimately divided into 6 segments: approach segment, entrance segment, transition segment, middle segment, exit segment, and departure segment. An example of tunnel segmentation is shown below. Figure 3 As shown in Table 4, the correction coefficients and correction lengths of the road sections adjacent to the tunnel entrances and exits are calculated based on the correction coefficient formula.

[0174] Table 4. Road Section Length Correction

[0175]

[0176] Note: The initial length of the entrance section is 60m outside the tunnel and 100m inside the tunnel; the initial length of the exit section is 80m inside the tunnel and 60m outside the tunnel.

[0177] The corrected length of the entrance section is 80m outside the tunnel and 130m inside the tunnel. The corrected length of the exit section is 100m inside the tunnel and 80m outside the tunnel.

Claims

1. A method for segmenting highway tunnels based on trajectory data, characterized in that, Specifically, the following steps are included: Step 1: Parameter extraction based on trajectory data The original vehicle trajectory data records the trajectory of all vehicles on the road, including time, vehicle number, vehicle horizontal and vertical coordinates, and horizontal and vertical speed characteristics. The original trajectory data is preprocessed and the positions of the vehicles in front and behind are correlated. Extract and further calculate the required parameters, including: time, vehicle's horizontal and vertical coordinates, speed, acceleration, preceding vehicle number, preceding vehicle's horizontal and vertical coordinates, and preceding vehicle speed; Step 2: Calculation of vehicle driving characteristics based on trajectory data Determine the minimum analysis unit length of the road, and divide the analysis segment into p road units based on the minimum unit length; select 6 tunnel segment characteristic indicators B1, B2, B3, ..., B6, which are respectively represented as average speed, speed standard deviation, average headway, average speed difference, average collision time, and average collision avoidance deceleration. Step 3: Processing of segmented characteristic indicators for highway tunnels based on principal component analysis (1) Data noise reduction The Lowes local weighted scatter smoothing method is used to denoise the feature indices B1, B2, B3, ..., B6 respectively, with a window size of 0.

1. After smoothing, a p×6 original data matrix is ​​formed. In the formula: This is the original data matrix after smoothing; p is the number of road units; Let x be the set of the j-th eigenvalues ​​of each road unit after smoothing, where j = 1, 2, ..., 6; ij , i = 1, 2, ..., p, j = 1, 2, ..., 6 are the j-th feature values ​​of the i-th road unit after smoothing; (2) Processing of segmented characteristic indicators of highway tunnels For the original data matrix After performing the Z-Score normalization transformation, the normalized matrix X is obtained. * : In the formula: X * For the normalized matrix; x ij Let j be the standardized value of feature j for road unit i, where i = 1, 2, ..., p; j = 1, 2, ..., 6; and p is the number of road units calculated based on the minimum unit length. The applicability of principal component analysis was tested using the KMO value: In the formula: i is the road unit number, i = 1, 2, ..., p; j is the indicator number, j = 1, 2, ..., 6; r ij This represents the simple correlation coefficient; a ij This represents the partial correlation coefficient; a KMO value above 0.5 indicates that the data is suitable for principal component analysis. Based on the correlation coefficient r ij Find X * The sample correlation matrix R: E is the identity matrix, λ i Let i = 1, 2, 3, 4, 5, 6 be the eigenvalues, and construct the characteristic polynomial |R - λ|. i E|;Let |R-λ i E|=0, calculate the eigenvalues ​​of R and sort them in descending order: λ1≥λ2≥λ3≥λ4≥λ5≥λ6; Based on the cumulative contribution rate of the principal components, determine the few principal components that can basically reflect all the feature information; for example, the ratio of the sum of the variances of the current k principal components to the total variance. When k is greater than or equal to 0.85, select the first k principal components; k < 6. Calculate the analysis matrix Z after dimensionality reduction. 250×k This serves as an indicator for the refined division of tunnel sections; Z p×k =X * (L1L2L3L4L5L6) In the formula: Z p×k This is the dimensionality-reduced analysis matrix; X * The normalized matrix; L1, L2, ..., L k These are the eigenvectors corresponding to the first k eigenvalues; Step 4: Highway Tunnel Segmentation Based on k-means Clustering Given m classes, select m samples as the centers u1, u2, u3, ..., u4 of each class. m The k-means method is used to cluster the features of each road unit after dimensionality reduction, and road units with similar features are grouped into the same road segment set; finally, p road units are clustered into m classes, and the sum of the lengths of the road units contained in each class is the initial length of the road segment. Step 5: Adjustment of the length of the road section adjacent to the highway tunnel entrance and exit After determining the initial length of each tunnel segment, the lengths of the road segments adjacent to the tunnel entrances and exits are corrected, taking into account factors such as the brightness inside and outside the tunnel, vehicle speed, and tunnel clearance height. The calculation methods for each correction factor are as follows: (1) Brightness correction factor f for tunnel entrance and exit sections l In the formula: L D The external brightness refers to the actual measured brightness at a distance of 200m from the tunnel entrance, 1.5m above the ground, facing the tunnel entrance at a 20° field of view, expressed in cd / m². 2 The data source is the data transmitted back from the luminance monitoring instrument; L is the external luminance used in the tunnel design, in cd / m². 2 ; f l This is the tunnel brightness correction factor; (2) Speed ​​correction factor f v Calculate the speed correction factor by combining the average vehicle speed and the maximum speed limit of the road section; In the formula: To correct for the average vehicle speed on the road segment, in km / h; The average speed of all vehicles passing through road unit j is given in km / h; w is the number of road units contained in the modified road segment. In the formula: f v This is a correction factor for driving speed; To correct for the average vehicle speed on the road segment, in km / h; V max The maximum speed limit for the road is [km / h]. (3) Tunnel clearance height correction factor f h f h =1+0.05(7-h) In the formula: f h The tunnel clearance height correction factor is given by h, where h is the tunnel clearance height in meters. Based on the above information regarding the brightness correction factor f l Speed ​​correction factor f v Tunnel clearance height correction factor f h The final calculation formula for the length D of the road section adjacent to the tunnel entrance / exit is as follows: D=D i ×f l ×f v ×f h Where D is the corrected length of the road section adjacent to the tunnel entrance / exit; D i f is the initial length of road segment i adjacent to the tunnel entrance / exit; l f is the tunnel brightness correction factor; v f is the speed correction factor; h This is the correction factor for tunnel clearance height.

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