Vehicle trajectory curvature fitting degree multi-modal analysis method based on spatial configuration coupling and suggested speed generation method

Abstract

The application discloses a vehicle trajectory curvature fitting degree multi-modal analysis method and a recommended speed generation method based on spatial configuration coupling, and belongs to the technical field of intelligent traffic and road safety. In order to solve the problem that the vehicle trajectory deviates from the risk caused by the disconnection between the static design speed and the actual running speed on the highway curve-slope combined section, the application collects the curvature data of the road center line and the vehicle driving trajectory and draws a curvature space distribution diagram; multi-dimensional indexes are determined based on the curvature, and then a trajectory-line shape cooperation index is obtained according to the multi-dimensional indexes, and multi-modal analysis is realized based on the trajectory-line shape cooperation index; the multi-dimensional indexes include overall trend matching degree, robust fault tolerance capability, local deviation sensitivity and comprehensive fluctuation degree. Then, a gradual speed difference sliding method is adopted to screen a high cooperation degree speed interval based on the analyzed TLCI, and a final recommended speed interval is determined based on a statistical significance threshold value, a road design standard and an actual vehicle running condition.

Description

Technical Field

[0001] This invention belongs to the field of intelligent transportation and road safety technology, and specifically relates to a method for generating vehicle suggested speed. Background Technology

[0002] Currently, most highways in operation in my country use static speed limit management strategies based on design speed. This fails to fully consider the varying impacts of different curve-slope combinations and actual road conditions on vehicle operating speeds. This results in mismatches between design and actual operating speeds on some curve-slope sections, affecting driving safety and traffic efficiency. Furthermore, existing methods are mostly based on analysis of single vehicle types or fixed speed ranges, lacking refined consideration of the dynamic characteristics of different vehicle types and differences in actual operating speeds, making it difficult to achieve precise speed guidance under dynamic vehicle-road coordination.

[0003] To address the aforementioned issues, this invention takes a specific highway as the research object, combining its actual operational characteristics and relevant operational indicators. Starting with vehicle trajectory data extracted from drone aerial video, it analyzes vehicle driving states and their correlation with road alignment by calculating the trajectory curvature fitting degree, and further studies the vehicle speed distribution patterns on curve-slope combination road sections under different alignment conditions. Based on this, a recommended speed range for specific curve-slope combination road sections and vehicle types is proposed, providing data support and methodological reference for improving road alignment design and operational safety. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of vehicle trajectory deviation risk caused by the disconnect between static design speed and actual operating speed in combined curve and slope sections of highways.

[0005] A multimodal analysis method for vehicle trajectory curvature fitting degree based on spatial configuration coupling includes:

[0006] Curvature data of the road centerline and vehicle trajectory are collected and a curvature spatial distribution map is drawn. Based on the curvature, multi-dimensional indicators are determined, and then the trajectory-linearity coordination index is obtained based on the multi-dimensional indicators. Multimodal analysis is realized based on the trajectory-linearity coordination index. The multi-dimensional indicators include: overall trend matching degree, robust fault tolerance, local deviation sensitivity, and comprehensive fluctuation degree.

[0007] Furthermore, the process of collecting curvature data of the road centerline and vehicle trajectory and drawing a curvature spatial distribution map includes the following steps:

[0008] S101. Digitize the road centerline map, establish a coordinate system with the lower left corner of the first frame of the video as the origin, and collect the road centerline coordinate data.

[0009] S102. Perform curve fitting on the road centerline coordinate data to generate a curvature space distribution map of the road centerline.

[0010] S103. Extract the horizontal and vertical coordinates and instantaneous speed data of all vehicles in each frame under the combined curve and slope road section. Calculate the curvature of the trajectory points based on the vehicle trajectory coordinates and draw the curvature spatial distribution map of all vehicle trajectories.

[0011] Furthermore, the multi-dimensional indicators include: overall trend matching degree, robustness and fault tolerance, local deviation sensitivity, and comprehensive volatility degree, as follows:

[0012] The curvature data of the vehicle's trajectory is denoted as The curvature data of the road centerline is denoted as The coefficient of determination R between the two 2 Mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE) are respectively used to represent the overall trend matching degree, robust fault tolerance, local deviation sensitivity, and comprehensive fluctuation degree.

[0013] Furthermore, in the process of obtaining the trajectory-linear coordination index based on multi-dimensional indicators, the R-value of all vehicles is first calculated. 2 The average values ​​of MAE, MSE, and RMSE are used to calculate the trajectory-linear coherence index TLCI = K1 × R. 2 +K2× (1-MAE) +K3× (1-MSE) +K4× (1-RMSE), where K1-K4 are index coefficients.

[0014] Furthermore, the index coefficients K1-K4 are set to 0.50, 0.20, 0.15, and 0.15, respectively.

[0015] A proposed speed generation method includes:

[0016] The number of vehicles in each preset speed range is statistically analyzed, and the trajectory-linearity coordination index TLCI is obtained based on the multimodal analysis method of vehicle trajectory curvature fitting degree based on spatial configuration coupling as described in any one of claims 1 to 5.

[0017] Based on TLCI, the progressive speed difference sliding method is used to screen the high coherence speed range, that is, to determine the core speed range corresponding to the TLCI peak value of different vehicle types.

[0018] The final recommended speed range is determined based on statistical significance thresholds, road design standards, and actual vehicle operating conditions.

[0019] Furthermore, the process of using the progressive speed difference sliding method to screen for high-cooperation speed ranges includes:

[0020] (201) Based on the road design speed and the actual vehicle operating speed, the vehicles are classified and processed, and the basic speed sliding range is set for each. The first fixed window width is used, and the sliding calculation is performed in the entire basic speed range with a fixed step size. The peak distribution area of ​​the trajectory-linear coordination index TLCI is initially identified, and the peak speed range of TLCI is determined.

[0021] (202) Based on the peak speed range of TLCI identified by the basic speed range sliding analysis, the sliding window width is reduced to the second fixed window width, and the second round of sliding analysis is performed with a fixed step size to determine the core speed range corresponding to the peak TLCI of different vehicle types.

[0022] Furthermore, the process of determining the final recommended speed range based on statistical significance thresholds, road design standards, and actual vehicle operating conditions includes:

[0023] A threshold is set based on the quantile values ​​of the vehicle sample number distribution across all speed ranges. Only speed ranges with a vehicle sample number not lower than this threshold are retained as valid analysis objects. On this basis, the ranges with TLCI values ​​in the top K% of all samples are further screened and identified as candidate suggested speed ranges.

[0024] Furthermore, K% is taken as 2%.

[0025] Furthermore, the process of determining the final recommended speed range based on statistical significance thresholds, road design standards, and actual vehicle operating conditions also includes a step of collaborative optimization of the recommended speed range. The specific process includes:

[0026] The candidate suggested speed range is coordinated and matched with the road design speed. When the upper limit of the candidate suggested speed range exceeds both the road design speed and the statutory maximum speed limit, its upper limit is constrained to the statutory maximum speed limit. For the part of the candidate suggested speed range that is lower than the minimum speed limit standard, it is uniformly adjusted to the minimum speed limit standard, and finally the suggested speed range is obtained.

[0027] The beneficial effects of this invention are as follows:

[0028] This invention realizes a method for generating speed ranges for curved and sloping road sections driven by vehicle trajectory data, enabling the final generated suggested speed ranges to simultaneously conform to road geometry and actual vehicle operating patterns. First, by organically combining spatial configuration coupling analysis and the speed difference sliding method, a dynamic correlation model of "road alignment-vehicle trajectory-operating speed" is established, overcoming the limitations of traditional static design speeds. This makes the generated suggested speeds more consistent with actual vehicle operating characteristics, achieving dynamic collaborative adaptation between vehicles and the road. Second, it improves the accuracy of driving risk identification and the targeted nature of control. Through the construction of a multi-dimensional trajectory-alignment synergy index (TLCI) evaluation system, the synergy between trajectory and alignment is comprehensively evaluated from multiple perspectives, significantly improving the accuracy of driving risk identification for curved and sloping road sections and providing a scientific basis for implementing differentiated speed control for different vehicle types. Simultaneously, it ensures the scientific nature of the speed optimization method and the reliability of the results. Directly using the TLCI index as the core criterion for speed optimization is scientifically sound; the speed difference sliding method can precisely and progressively capture the optimal speed range; and the introduction of a statistical significance threshold verification ensures the universality of the suggested speeds. Then, precise speed guidance customized for different vehicle types was implemented. Different speed slip analysis ranges were set to address the differences in dynamic characteristics between small passenger cars and large trucks. The final recommended speed was determined based on different distribution patterns, such as continuous high-fit intervals or single high-fit peaks, effectively improving the targeting and practicality of speed guidance, and significantly reducing accident rates and improving traffic efficiency. Finally, a practically applicable closed-loop optimization mechanism was constructed. By establishing a "road alignment-vehicle type-recommended speed" mapping database and integrating it into variable message signs and vehicle-road cooperative systems, a closed-loop optimization mechanism of "perception-decision-execution-evaluation" was built. This ensures that the system can adapt to dynamic changes in traffic flow, providing a complete technical solution for traffic management departments to formulate scientific and compliant speed limit schemes. Attached Figure Description

[0029] Figure 1 A flowchart of a proposed speed generation method for curved and sloping road sections based on trajectory curvature fitting degree.

[0030] Figure 2 This is a road reference map for section 1 (from K2+400 to K2+819 of a certain expressway).

[0031] Figure 3 This is a road reference map for section 2 (from K6+672 to K7+053 of a certain expressway).

[0032] Figure 4 This is a road reference map for section 3 (from K7+045 to K7+416 of a certain expressway).

[0033] Figure 5 This is a spatial distribution diagram of the curvature of the centerline of the curved slope section (section 1).

[0034] Figure 6 This is a spatial distribution diagram of the curvature of the centerline of the curved slope section (section 2).

[0035] Figure 7 This is a spatial distribution diagram of the curvature of the centerline of the curved slope section (section 3).

[0036] Figure 8 A curvature space comparison diagram of road alignment and vehicle trajectory for each combination of curves and slopes (segment 1-car).

[0037] Figure 9 A curvature space comparison diagram of the road alignment and vehicle trajectory for each combination of curves and slopes (section 1-truck).

[0038] Figure 10 A curvature space comparison diagram of road alignment and vehicle trajectory for each combination of curves and slopes (segment 2-car).

[0039] Figure 11 A curvature space comparison diagram of road alignment and vehicle trajectory for each combination of curves and slopes (section 2-truck).

[0040] Figure 12 A curvature space comparison diagram of road alignment and vehicle trajectory for each combination of curves and slopes (segment 3-car).

[0041] Figure 13 A curvature space comparison diagram of road alignment and vehicle trajectory for each combination of curves and slopes (section 3-truck).

[0042] Figure 14 This is a speed coordination distribution map of segment 1-car TLCI-interval after the first round of sliding analysis.

[0043] Figure 15 This is a speed coordination distribution map of the TLCI section of road segment 1 after the first round of sliding analysis.

[0044] Figure 16 This is a speed coordination distribution map of the 2-car TLCI section of the road segment after the first round of sliding analysis.

[0045] Figure 17 This is a speed coordination distribution map of the TLCI section of road segment 2-truck after the first round of sliding analysis.

[0046] Figure 18 This is a speed coordination distribution map of the 3-car TLCI section after the first round of sliding analysis.

[0047] Figure 19This is a speed coordination distribution map of section 3-truck TLCI after the first round of sliding analysis.

[0048] Figure 20 This is the speed coordination distribution map of segment 1-car TLCI-interval after the second round of sliding analysis.

[0049] Figure 21 This is the speed coordination distribution map of segment 1-truck TLCI-section after the second round of sliding analysis.

[0050] Figure 22 This is the speed coordination distribution map of the 2-car TLCI section of the road segment after the second round of sliding analysis and verification.

[0051] Figure 23 This is a speed coordination distribution map of the 2-truck TLCI section after the second round of sliding analysis.

[0052] Figure 24 This is the speed coordination distribution map of the 3-car TLCI section of the road segment after the second round of sliding analysis and verification.

[0053] Figure 25 This is a speed coordination distribution map of the 3-truck TLCI section after the second round of sliding analysis. Detailed Implementation

[0054] This invention mainly comprises four stages: The first stage involves constructing a curvature coupling relationship map of roads and vehicle trajectories through multi-source data acquisition and processing; the second stage uses a multimodal analysis model to quantitatively evaluate the synergy between trajectory and alignment, generating a trajectory-alignment synergy index; the third stage employs a progressive speed difference sliding method to precisely screen high-synergy speed ranges from macro to micro levels; and the fourth stage, based on statistical significance verification and traffic regulations, determines and publishes the final recommended speed customized for each vehicle model, forming a closed loop of perception, decision-making, and execution. Specific implementation methods are described below. Specific implementation method one:

[0056] A multimodal analysis method for vehicle trajectory curvature fitting degree based on spatial configuration coupling includes:

[0057] Collect curvature data of the road centerline and vehicle trajectory and plot the curvature spatial distribution map;

[0058] By visually comparing curvature change trends, the spatial coordination between vehicle trajectory and road alignment is qualitatively assessed.

[0059] A multi-dimensional fitting and quantitative model was established, and key fitting indices were selected based on the characteristics of curved and sloping road sections. The geometric compatibility of the driving trajectories of different vehicle types with the road alignment in variable curvature road sections was quantitatively analyzed. More specifically,

[0060] The process of collecting curvature data of the road centerline and vehicle trajectory and drawing a curvature spatial distribution map includes the following steps:

[0061] S101. Digitize the road centerline map using Engauge Digitizer software, establish a coordinate system with the bottom left corner of the first frame of the video as the origin, and collect the road centerline coordinate data.

[0062] S102. Use Python to perform curve fitting on the road centerline coordinate data to generate a curvature space distribution map of the road centerline.

[0063] S103. Using Tracker software, extract the horizontal and vertical coordinates, instantaneous speed, and other data of all vehicles in each frame of the curved and sloping road section. Based on the vehicle trajectory coordinates, calculate the curvature of the trajectory points using the NumPy library, and plot the curvature space distribution map of all vehicle trajectories using Matplotlib.

[0064] By visually comparing curvature change trends, the spatial coordination between vehicle trajectories and road alignments is qualitatively assessed, including trend consistency, amplitude similarity, and smoothness of change. This provides an intuitive and physically meaningful explanation and verification for quantitative indicators such as the Trajectory-Alignment Coordination Index (TLCI). Specifically, its applications are reflected in the following three aspects:

[0065] 1. Verify quantitative results: When TLCI calculation shows high synergy in a certain interval, visualization can be used to confirm whether the trajectory and linear curvature trend of that interval are truly consistent, thus eliminating calculation artifacts.

[0066] 2. Analyze the causes of deviations: When TLCI shows poor coordination, visualization can directly reveal the problem, namely: whether the trajectory has insufficient curvature at the curve (steering too early / too late), or whether the trajectory curvature fluctuates too much (unstable driving behavior), thus providing direction for subsequent speed suggestion optimization.

[0067] 3. Enhance the reliability of conclusions: By combining quantitative calculations with qualitative assessments, a closed loop of evidence is formed, significantly improving the credibility and persuasiveness of the final recommended speed range.

[0068] The process of qualitatively assessing the spatial coordination between vehicle trajectory and road alignment through visual comparison of curvature change trends includes:

[0069] S201. Overlay the curvature space distribution map of the road centerline with the curvature space distribution map of the actual driving trajectories of a large number of vehicles in the same rectangular coordinate system to generate a curvature space comparison map.

[0070] S202. Through systematic analysis of the curvature space comparison diagram, the trajectory and line shape can be identified as having the following three key regions:

[0071] (A) Trajectory Concentration Zone: On a specific road segment, the curvature of the driving trajectories of the vast majority of vehicles exhibits high consistency and stability, forming a narrow trajectory curvature band that closely matches the road's design curvature line. This zone must simultaneously meet the following two statistical conditions:

[0072] 1. Consistency condition: Within a specific road segment, the standard deviation of the curvature of all vehicle trajectories is less than or equal to 0.0015 m. -1 This threshold ensures that the dispersion of the trajectory curvature values ​​is extremely low.

[0073] 2. Compatibility condition: The average absolute deviation between the vehicle trajectory curvature and the road design curvature of this road section is less than or equal to 0.002 m. -1 This threshold ensures that the vehicle trajectory cluster, as a whole, is highly consistent with the road design intent.

[0074] (B) Trajectory Discrete Region: On a specific road segment, the curvature of the vehicle's trajectory shows significant differentiation, forming a wide trajectory curvature band, indicating a region with greater uncertainty and inconsistency in driver behavior.

[0075] The determination of this region is based on the dispersion of the trajectory group: within a specific road segment, the standard deviation of the curvature of all vehicle trajectories is greater than 0.004 m. -1 This threshold indicates that the trajectory curvature value is dispersed, reflecting disagreements among drivers regarding route selection or speed control on this road segment, indicating high behavioral uncertainty and representing a potential safety risk point or a section with poor alignment guidance.

[0076] (C) Trajectory Deviation Zone: The area where the curvature of the vehicle's trajectory deviates systematically and holistically from the road design curvature (such as turning too early, returning to center too late, or cutting off the curve).

[0077] The determination of this area is based on the systematic deviation between the trajectory group and the design alignment: within a specific road segment, the average absolute deviation between the vehicle trajectory curvature and the road design curvature is consistently greater than 0.005 m. -1This indicates that the trajectory cluster as a whole has undergone a statistically significant and non-accidental systematic deviation relative to the design alignment. This systematic deviation is specifically manifested in typical patterns such as "early steering" (the deviation peak appears before the design curvature peak), "delayed correction" or "curve cutting" (the trajectory curvature value is consistently lower than the design curvature value throughout the entire curve section).

[0078] By comparing the curvature of vehicle trajectories with that of road alignments, the degree of fit between vehicle trajectories and road alignments in this combination of curves and slopes can be qualitatively identified, providing visual evidence for subsequent quantitative analysis.

[0079] The process of selecting key fitting indicators based on the characteristics of curved and sloping road sections, and quantitatively analyzing the geometric compatibility of the driving trajectory of different vehicle types with the road alignment in variable curvature road sections, includes the following steps:

[0080] S301. For curvature, select and construct a multi-dimensional indicator evaluation system: overall trend matching degree (coefficient of determination R). 2 ), robustness (mean absolute error MAE), local bias sensitivity (mean square error MSE), and overall volatility (root mean square error RMSE).

[0081] S302, using SPSS to fit four curvature fitting indices R for three curved and sloping road sections and two vehicle types. 2 Statistical analysis was performed on MAE, MSE, and RMSE.

[0082] S303. To comprehensively quantify the geometric compatibility of trajectory and alignment, a summary table of the statistical distribution characteristics of fitting indices for each vehicle type on each road segment is output, and the Trajectory-Alignment Compatibility Index (TLCI) is used for characterization. This index integrates the above four key fitting indices and calculates the average value of the key fitting indices. Then, the result is expressed as TLCI = 0.50 × R. 2 The trajectory-linear compatibility index is obtained by adding 0.20 × (1-MAE) + 0.15 × (1-MSE) + 0.15 × (1-RMSE). The TLCI is used as a geometric compatibility index to achieve multimodal analysis of vehicle trajectory curvature fitting based on spatial configuration coupling. Specific Implementation Method Two:

[0084] This embodiment is a method for generating customized suggested speeds for vehicle types on curved and slope-combined road sections based on the progressive speed difference sliding method, including:

[0085] (1) Multi-dimensional trajectory data statistics and synergy index calculation;

[0086] (2) The progressive speed difference sliding method is used to screen the speed range with high coordination.

[0087] (3) Based on the TLCI distribution pattern, suggested speed ranges are determined, and a statistical significance threshold is introduced to verify the effectiveness of high-cooperation ranges; finally, precise suggested speed ranges that dynamically match specific road alignments and vehicle types are generated and published in real time through the vehicle-road cooperative system to achieve vehicle-road speed cooperative guidance and active safety improvement. More specifically,

[0088] The process of performing multi-dimensional trajectory data statistics and calculating the synergy index includes the following steps:

[0089] (101) Statistical analysis of the number of vehicles in each preset speed range;

[0090] (102) Calculate R for all vehicle trajectories within this interval. 2 The average value of four curvature fitting indices: MAE, MSE, and RMSE;

[0091] (103) Calculate the comprehensive trajectory-linear coordination index TLCI for this interval. In this embodiment, TLCI = 0.50 × R 2 + 0.20 × (1-MAE) + 0.15 × (1-MSE) + 0.15 × (1-RMSE).

[0092] The process of using the progressive speed difference sliding method to screen for high-cooperation speed ranges includes the following steps:

[0093] (201) Basic velocity range sliding analysis:

[0094] Based on road design speed and actual vehicle operating speed, small passenger and freight vehicles and large passenger vehicles are classified and processed separately, with [70, 120] and [50, 100] (unit: km / h) set as the basic speed sliding ranges, respectively. A fixed window width of 20 km / h is used, with a fixed step size of 1 km / h, to perform sliding calculations within the entire basic speed range, initially identifying the peak distribution area of ​​the Trajectory-Linear Coherence Index (TLCI) and determining the TLCI peak speed range. The window width of 20 km / h is set to balance data smoothness and local feature preservation, avoiding noise interference caused by an excessively narrow window and preventing blurring of the peak area caused by an excessively wide window, thus effectively covering the TLCI peak speed range in the initial exploration stage.

[0095] (202) Precise positioning of core speed range: Based on the peak speed range of TLCI identified by the basic speed range sliding analysis, the sliding window width is reduced to 10 km / h, and a fixed step size of 1 km / h is maintained to perform the second round of sliding analysis. The window width is set to 10 km / h, which is based on the distribution width characteristics of TLCI peaks in the preliminary analysis results. By reducing the window width, the ability to distinguish local peaks is improved, thereby more accurately capturing the core speed range corresponding to the TLCI peaks of small passenger and freight vehicles and large passenger and freight vehicles, ensuring that the positioning accuracy meets the requirements of subsequent optimization.

[0096] The process of generating a precise recommended speed range that dynamically matches a specific road alignment and vehicle type determines the final recommended speed range based on a statistical significance threshold, road design standards, and actual vehicle operating conditions. The specific process includes the following steps:

[0097] (301) Setting the statistical significance threshold and screening candidate intervals: To ensure the statistical reliability of the recommended speed intervals, an effective threshold based on the sample distribution is set. Specifically, based on (202), the 70th percentile of the vehicle sample number distribution of all speed intervals is used as the threshold, and only speed intervals with a vehicle sample number not lower than this threshold are retained as valid analysis objects; on this basis, the intervals with TLCI values ​​in the top 2% of all samples are further screened and identified as candidate recommended speed intervals.

[0098] (302) Collaborative optimization of recommended speed ranges: Based on the road design speed, candidate recommended speed ranges identified by the progressive speed difference sliding method, and the statutory speed limit, collaborative optimization is performed on the candidate recommended speed ranges. The specific optimization process includes:

[0099] First, the candidate suggested speed range is coordinated and matched with the road design speed and the statutory maximum speed limit: if the upper limit of the candidate suggested speed range does not exceed the statutory maximum speed limit, it is considered that the range reflects the safe operating pattern of vehicles under actual alignment conditions, and its validity is directly confirmed; only when the upper limit of the candidate suggested speed range exceeds both the road design speed and the statutory maximum speed limit, its upper limit is constrained to the statutory maximum speed limit to eliminate the impact of extreme behaviors and ensure safety and compliance.

[0100] Secondly, the speed limits for the portion of the candidate recommended speed range below 60 km / h will be uniformly increased to 60 km / h to meet the statutory minimum speed limit requirements, ensuring both safety and basic traffic efficiency.

[0101] The final recommended speed range is generated to match the alignment conditions of the curved and sloping road section and to balance safety and efficiency.

[0102] Example 1:

[0103] Combination Figure 1 This embodiment describes a multimodal analysis method for vehicle trajectory curvature fitting degree based on spatial configuration coupling, which includes the following steps:

[0104] Step 1: Based on the highway's design specifications, historical traffic accident data, and road alignment conditions, a section of the highway with frequent traffic accidents and failing to meet road alignment design requirements was selected as the research object. This invention selected three sections with combined curves and slopes, namely:

[0105] (1) Section 1-K2+400 to K2+819, basic circular curve combined with convex vertical curve;

[0106] (2) Section 2-K6+672 to K7+053, the first half of the S-shaped curve is combined with a concave vertical curve;

[0107] (3) Section 3-K7+045 to K7+416, the latter half of the S-shaped curve is combined with a convex vertical curve;

[0108] The sections from K6+672 to K7+053 and from K7+045 to K7+416 are continuous S-shaped curves. The design standards and detailed parameters for each section are shown in Table 1.

[0109] Table 1 Design Standards and Detailed Parameters for Each Road Section

[0110]

[0111] Step 2: Using AutoCAD software, draw road reference lines from the captured drone aerial photos. See the road reference line diagrams for the three curved and sloping sections. Figures 2-4 , Figures 2-4 The reference lines are for section 1 (from K2+400 to K2+819 of the expressway), section 2 (from K6+672 to K7+053 of the expressway), and section 3 (from K7+045 to K7+416 of the expressway).

[0112] Step 3: Import the drawn road reference line map into Engauge Digitizer software. Establish a rectangular coordinate system with the bottom left corner of the first frame's rectangular video frame as the origin and the 69 line as the scale. Collect coordinate points on the center lines of the two roads. Based on the series of coordinate data of the road center lines, use Python's NumPy library to calculate the curvature of the road center lines. The curvature calculation formula is:

[0113]

[0114] in, , It is a function of the horizontal and vertical position of the road centerline in a rectangular coordinate system. It is the first derivative. It is the second derivative.

[0115] Step 4: Based on the calculated curvature data, use the matplotlib library in Python to plot the curvature spatial distribution map of the road centerline for the three curved-slope combination road sections. See [link / reference]. Figures 5-7 , Figures 5-7 This is a spatial distribution map of the curvature of the road centerline in the curved and sloping sections, divided into sections 1 to 3. The horizontal axis in the map represents the distance from each point to the origin in the x-direction in the drone aerial photograph, determined according to the scale conversion.

[0116] Step 5: Extract basic vehicle operation data from the Tracker software, including frame number, vehicle code (track_id), vehicle type (type), X coordinate (center_x), Y coordinate (center_y), and speed value (v_values). Some data is shown in Table 2.

[0117] Table 2 Raw data on vehicle operation on curved and sloping road sections

[0118]

[0119] Step 6: Based on the extracted vehicle trajectory coordinates, calculate the tangent change rate between adjacent trajectory points using the method in Step 3, thereby obtaining the curvature spatial distribution map of each vehicle type on the three curve-slope combination road sections.

[0120] Step 7: Overlay the curvature diagram of the designed road alignment with the curvature diagrams of the actual driving trajectories of a large number of vehicles in the same Cartesian coordinate system, and perform a qualitative analysis of the synergy between vehicle trajectories and road alignment. See the curvature space comparison diagram of road alignment and vehicle trajectories. Figures 8-13 . Figures 8-13 These are curvature space comparison diagrams of the road alignment (sections 1-3) and the trajectories of different vehicles (cars, trucks) for different combinations of curves and slopes.

[0121] Step 8: To accurately quantify the degree of coordination between vehicle trajectory and road design alignment, a multi-dimensional evaluation system is constructed, which includes four core indicators and one comprehensive evaluation indicator. The trajectory-alignment relationship is comprehensively evaluated from multiple perspectives, such as error magnitude, stability, and goodness of fit, providing accurate data support for subsequent screening of high-coordination speed ranges.

[0122] Assuming the design curvature is Design curvature refers to the curvature of the road centerline; trajectory curvature is... n is the number of points in the "x-coordinate" of the rectangular coordinate system.

[0123] (1) Overall trend matching degree (coefficient of determination R) 2 This indicator measures the overall consistency between the trend of vehicle trajectory curvature and the trend of road centerline curvature. Its calculation formula is:

[0124]

[0125] (2) Robustness tolerance (Mean Absolute Error, MAE): This index measures the absolute level of fitting deviation, is insensitive to outliers, and reliably reflects the average fitting error. Its calculation formula is:

[0126]

[0127] (3) Local bias sensitivity (mean square error): This index is the mean of the sum of squares of the errors between the predicted data and the corresponding points in the original data. It is highly sensitive to outliers (such as sudden and drastic fluctuations in the trajectory) and can effectively amplify and capture significant fitting biases. Its calculation formula is:

[0128]

[0129] (4) Overall volatility (Root Mean Square Error RMSE): This indicator is the square root of the MSE, has the same dimensions as the original data, and can more intuitively reflect the average volatility of the fitted points. Its calculation formula is:

[0130]

[0131] (5) Based on the practical engineering significance of vehicle trajectory fitting and the characteristics of each index, a comprehensive evaluation index, "Track-Linear Coordination Index (TLCI)," is designed, with the following formula:

[0132] TLCI = 0.50 × R 2 + 0.20 × (1-MAE) + 0.15 × (1-MSE) + 0.15 × (1-RMSE)

[0133] Step 9: Calculate and summarize the average values ​​of the curvature fitting index of the driving speed and trajectory of all vehicles under each curve and slope combination section, including R. 2 MAE, MSE, and RMSE are used as partial example data, which are shown in Table 3. The complete dataset shows that there are certain differences in the curvature fit of different vehicles at different speeds (the first four indicators in Table 2), laying the foundation for subsequent synergy analysis in speed ranges.

[0134] Table 3. Fitting Indices for Vehicle Speed ​​and Trajectory Curvature

[0135]

[0136] Example 2:

[0137] Combination Figure 1 This embodiment describes a method for generating customized vehicle-specific suggested speeds for curved and sloping road sections based on a progressive speed difference sliding method. This method is a speed analysis technique based on the fit between vehicle trajectory and road curvature. It involves sliding window analysis of trajectory speed data, i.e., continuously comparing and calculating vehicle speeds within a certain time or spatial range. The method includes the following steps:

[0138] Step 1: Determine the speed range to be studied based on the road design speed, the speed limits for different vehicle types, and the actual speeds of all vehicles collected from the Tracker software.

[0139] Based on the project feasibility study, preliminary design approval, and the "Technical Standards for Highway Engineering" (JTG B01-2014), the design speed for this road section is determined to be 100 km / h, with maximum speed limits of 110 km / h for small and 90 km / h for large passenger and freight vehicles, and a minimum speed limit of 60 km / h. However, data collected from Tracker software shows that a certain proportion of large passenger and freight vehicles travel at speeds below 50 km / h. Therefore, this invention sets differentiated base speed ranges for small passenger and freight vehicles and large passenger vehicles, namely [70, 120] and [50, 100] (unit: km / h).

[0140] Step 2: Based on the balance and optimization principle of vehicle speed distribution characteristics and engineering analysis, the progressive speed difference sliding method is used to conduct full-domain sliding analysis of the basic speed range, and to preliminarily explore the speed range with high fitting degree.

[0141] 201) To achieve efficient and stable scanning of the global speed distribution, a relatively wide sliding window (20 km / h) was used for preliminary analysis. This width is sufficient to smooth out random speed fluctuations of individual vehicles, avoid instability in TLCI calculation due to an excessively small window, and effectively capture the macroscopic trend of the coordination degree changing with speed. Simultaneously, global sliding calculations were performed with a fixed step size of 1 km / h to count the number of vehicles in each speed interval, and to preliminarily explore high-value distribution areas of the Trajectory-Linear Coordination Index (TLCI).

[0142] 202), and simultaneously, calculate the average of four key fitting metrics for each trajectory segment, namely: coefficient of determination (R²). 2 The mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE) are also known as error.

[0143] 203) Subsequently, using the average of the four fitting indices obtained in the previous step, the comprehensive trajectory-linearity compatibility index (TLCI) for each speed range is calculated through a weighted comprehensive evaluation model. TLCI is a scalar value between 0 and 1. The higher the value, the higher the overall fitting level between the vehicle's trajectory and the road geometry within that speed range, and the better the compatibility.

[0144] 204) Based on the results of the global sliding analysis, and using the trajectory-linear coordination index (TLCI) data corresponding to each velocity interval, draw the TLCI-interval velocity coordination distribution map after the first round of sliding analysis, see... Figures 14-19 This figure displays the TLCI value distribution across different speed ranges using a bar chart, and connects the TLCI values ​​of each range with a trend line, visually presenting the overall trend of TLCI changes with speed. The high-cooperation speed range with TLCI values ​​in the top 2% is highlighted in the figure. This visualization method clearly identifies the speed distribution segments with optimal trajectory-road alignment coordination, providing an accurate input range for the subsequent fine-tuning stage of the progressive speed difference sliding method. Table 4 summarizes the speed ranges where TLCI reaches its peak for each vehicle type.

[0145] Table 4. Speed ​​ranges for each vehicle type to reach peak TLCI on various curve-slope combination road sections.

[0146]

[0147] Step 3: To make the local features of TLCI clearer, the sliding range is narrowed, and a progressive velocity difference sliding method is used for high-resolution sliding analysis to accurately locate the core velocity range.

[0148] 301) Based on the high-coordination speed range identified in the first round of coarse screening, the sliding window ranges of small and large passenger and freight vehicles are reduced to [70, 115] and [50, 85] respectively (unit: km / h).

[0149] 302) Within the contracted range, using a sliding window of 10 km / h and a sliding step of 1 km / h, a second round of progressive sliding analysis is conducted from low speed to high speed. After each sliding step, the number of vehicles whose speed falls within each preset speed range on the target curve-slope combination section, and R... 2 The average values ​​of MAE, MSE, RMSE, and TLCI are used. The choice of this width aims to achieve the highest speed resolution while ensuring statistical significance. A narrower window can more sensitively reveal the peak characteristics of TLCI, thereby accurately identifying the optimal core speed range for small passenger and freight vehicles and large passenger vehicles within the macro trend area.

[0150] 303) Based on the obtained TLCI and speed interval data, draw the TLCI-interval speed coordination distribution map for the second round of sliding analysis. By highlighting the high coordination speed intervals with TLCI values ​​in the top 2%, the core high coordination speed intervals corresponding to small passenger and freight vehicles and large passenger and freight vehicles can be accurately identified.

[0151] Step 4: Determine the final recommended speed range based on statistical significance verification, road design standards, and actual vehicle operating conditions.

[0152] 401) To ensure the statistical reliability of the recommended speed ranges, based on actual statistical data, the 70th percentile of the vehicle sample size distribution across all speed ranges is used as the effective threshold. Each core speed range precisely located in step 3 is validated, and only speed ranges with a vehicle sample size not lower than this threshold are retained as valid analysis objects. Furthermore, only speed ranges with a TLCI value in the top 2% are considered as candidate recommended speed ranges. The validated TLCI-speed range distribution diagram is shown below. Figures 20-25 The summary table of the synergy index and its speed range is shown in Table 5. The complete data can be found in Tables 13-18 below.

[0153] Table 5. Speed ​​ranges for each vehicle type to reach peak TLCI on various curve-slope combination road sections.

[0154]

[0155] 402) Based on the design concept of operating speed, this invention comprehensively considers the road design speed, the candidate suggested speed ranges identified through the progressive speed difference sliding method, and the statutory minimum speed limit, and optimizes the suggested speed ranges accordingly. Specifically, firstly, the candidate suggested speed ranges for each vehicle type are determined according to the speed difference sliding method, and then they are compared and coordinated with the design speed and the statutory maximum speed limit, while ensuring that the suggested speed is not lower than the statutory minimum speed limit. For the portion of the identified candidate suggested speed range below 60 km / h, it is uniformly increased to 60 km / h, thus forming a final suggested speed range that matches the alignment conditions of the curved and sloping road section, meets both safety requirements and ensures traffic efficiency, as shown in Table 6.

[0156] Table 6 Recommended speed ranges for different vehicle types on road sections with three curves and slopes.

[0157]

[0158] Step 5: Issuance and Application of Suggested Speed ​​Information. The finalized, precisely recommended speed range, dynamically matched to the specific curve-slope combination road section alignment and vehicle type, is issued in real time to the corresponding vehicle type via a vehicle-to-infrastructure (V2X) communication system (such as RSU or cloud platform). Upon receiving the information, vehicles can display it on their in-vehicle displays or use it as an input reference for Advanced Driver Assistance Systems (ADAS), thereby achieving vehicle-to-infrastructure speed coordination guidance and effectively improving active driving safety on curve-slope combination road sections.

[0159] The dynamically suggested speeds generated by this invention are an important supplement to existing road design and control methods based on fixed design speeds. Their value lies in: providing personalized safety guidance based on actual vehicle trajectory data for drivers; offering empirical feedback for road designers to optimize alignment design and improve the coordination of alignment indicators; and providing core basis for traffic managers to formulate scientific and flexible speed control strategies. Ultimately, through a "data-driven decision-making" approach, it achieves end-to-end safety assurance and efficiency improvement from static design to dynamic operation.

[0160] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A multimodal analysis method for vehicle trajectory curvature fitting degree based on spatial configuration coupling, characterized in that, include: Collect curvature data of the road centerline and vehicle trajectory and draw a curvature spatial distribution map; Based on the determination of multi-dimensional indicators for curvature, a trajectory-linearity coordination index is obtained from the multi-dimensional indicators, and multimodal analysis is realized based on the trajectory-linearity coordination index; the multi-dimensional indicators include: overall trend matching degree, robustness tolerance, local deviation sensitivity, and comprehensive fluctuation degree. The curvature data of the vehicle's trajectory is denoted as The curvature data of the road centerline is denoted as The coefficient of determination R between the two 2 Mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE) are respectively used as the overall trend matching degree, robust fault tolerance, local bias sensitivity, and comprehensive fluctuation degree. In the process of obtaining the trajectory-linear coordination index based on multi-dimensional indicators, the R-value of all vehicles is first calculated. 2 The average values ​​of MAE, MSE, and RMSE are used to calculate the trajectory-linear coherence index TLCI = K1 × R. 2 +K2× (1-MAE) +K3× (1-MSE) +K4× (1-RMSE), where K1-K4 are index coefficients.

2. The multimodal analysis method for vehicle trajectory curvature fitting degree based on spatial configuration coupling according to claim 1, characterized in that, The process of collecting curvature data of the road centerline and vehicle trajectory and drawing a curvature spatial distribution map includes the following steps: S101. Digitize the road centerline map, establish a coordinate system with the lower left corner of the first frame of the video as the origin, and collect the road centerline coordinate data. S102. Perform curve fitting on the road centerline coordinate data to generate a curvature spatial distribution map of the road centerline. S103. Extract the horizontal and vertical coordinates and instantaneous speed data of all vehicles in each frame on the curved and sloping road section. Calculate the curvature of the trajectory points based on the vehicle trajectory coordinates and draw the curvature spatial distribution map of all vehicle trajectories.

3. The multimodal analysis method for vehicle trajectory curvature fitting degree based on spatial configuration coupling according to claim 1, characterized in that, The index coefficients K1-K4 are set to 0.50, 0.20, 0.15, and 0.15, respectively.

4. A proposed speed generation method, characterized in that, include: The number of vehicles in each preset speed range is statistically analyzed, and the trajectory-linearity coordination index TLCI is obtained based on the multimodal analysis method of vehicle trajectory curvature fitting degree based on spatial configuration coupling as described in any one of claims 1 to 3. Based on TLCI, the progressive speed difference sliding method is used to screen the high coherence speed range, that is, to determine the core speed range corresponding to the TLCI peak value of different vehicle types. The final recommended speed range is determined based on statistical significance thresholds, road design standards, and actual vehicle operating conditions.

5. The proposed speed generation method according to claim 4, characterized in that, The process of using the progressive speed difference sliding method to screen for high-coordination speed ranges includes: (201) Based on the road design speed and the actual vehicle operating speed, the vehicles are classified and processed, and the basic speed sliding range is set for each. The first fixed window width is used, and the sliding calculation is performed in the entire basic speed range with a fixed step size. The peak distribution area of ​​the trajectory-linear coordination index TLCI is initially identified, and the peak speed range of TLCI is determined. (202) Based on the peak speed range of TLCI identified by the basic speed range sliding analysis, the sliding window width is reduced to the second fixed window width, and the second round of sliding analysis is performed with a fixed step size to determine the core speed range corresponding to the peak TLCI of different vehicle types.

6. A proposed speed generation method according to claim 4 or 5, characterized in that, The process of determining the final recommended speed range based on statistical significance thresholds, road design standards, and actual vehicle operating conditions includes: A threshold is set based on the quantile values ​​of the vehicle sample number distribution across all speed ranges. Only speed ranges with a vehicle sample number not lower than this threshold are retained as valid analysis objects. On this basis, the ranges with TLCI values ​​in the top K% of all samples are further screened and identified as candidate suggested speed ranges.

7. A proposed speed generation method according to claim 6, characterized in that, The K% value is 2%.

8. A proposed speed generation method according to claim 6, characterized in that, The process of determining the final recommended speed range based on statistical significance thresholds, road design standards, and actual vehicle operating conditions also includes a step of collaborative optimization of the recommended speed range, specifically including: The candidate suggested speed range is coordinated and matched with the road design speed. When the upper limit of the candidate suggested speed range exceeds both the road design speed and the statutory maximum speed limit, its upper limit is constrained to the statutory maximum speed limit. For the part of the candidate suggested speed range that is lower than the minimum speed limit standard, it is uniformly adjusted to the minimum speed limit standard, and finally the suggested speed range is obtained.

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