A method for estimating traffic capacity based on traffic basic map parameter calibration

Abstract

The application relates to a traffic capacity estimation method based on traffic basic graph parameter calibration, belongs to the technical field of intelligent traffic systems and traffic flow modeling, and particularly relates to a traffic capacity estimation method based on traffic basic graph parameter calibration. The application aims to solve the problem that the existing method cannot obtain accurate traffic basic graph parameters, resulting in low traffic capacity estimation precision. The process is as follows: step one, obtaining historical traffic flow single vehicle data samples of a road section; processing the obtained single vehicle data samples to obtain a final aggregated data set; step two, obtaining adaptive weights based on kernel density estimation based on the obtained final aggregated data set; step three, obtaining an optimal parameter set of a traffic basic graph model by adopting a particle swarm optimization algorithm based on the adaptive weights; and step four, obtaining traffic capacity based on the optimal parameter set of the traffic basic graph model.

Description

Technical Field

[0001] This invention belongs to the field of intelligent transportation systems and traffic flow modeling technology, specifically involving a capacity estimation method based on traffic basic map parameter calibration. Background Technology

[0002] Traffic fundamental maps are core theoretical models describing the relationships between macroscopic characteristics of traffic flow (volume, speed, and density). Existing traffic fundamental map models typically face three main problems in practical applications: First, uneven sample distribution. Most actual traffic observation data on highways is collected in free-flow conditions, resulting in free-flow data dominating the dataset, while congested data is relatively sparse. Second, significant fitting bias. The uneven sample distribution causes the traffic fundamental map model to favor free-flow data during fitting, overfitting the densely populated low-density regions while neglecting the relatively sparse medium-to-high-density regions. Third, inaccurate key parameters. Parameter fitting bias further leads to inaccurate capacity estimation, making it difficult to accurately reflect the true carrying capacity of roads, thus affecting the scientific nature of traffic management decisions. Currently, a systematic solution is still lacking.

[0003] Therefore, there is an urgent need in this field for a methodology that can systematically solve the fitting bias caused by uneven sample distribution and improve the accuracy of capacity estimation methods based on traffic map parameter calibration. Summary of the Invention

[0004] The purpose of this invention is to solve the problem that existing methods cannot obtain accurate traffic base map parameters, resulting in low accuracy of capacity estimation. Therefore, this invention proposes a capacity estimation method based on traffic base map parameter calibration.

[0005] The specific process of a capacity estimation method based on traffic fundamental map parameter calibration is as follows:

[0006] Step 1: Obtain historical traffic flow data samples of individual vehicles at road cross-sections; perform time aggregation processing on the obtained individual vehicle data samples to generate an aggregated dataset with 2-minute intervals; clean each data sample in the aggregated dataset to obtain cleaned data samples; perform time scale conversion on the total 2-minute traffic flow in each cleaned data sample using the adjacent time period accumulation method to obtain the hourly total traffic flow; obtain the final aggregated dataset.

[0007] Step 2: Based on the final aggregated dataset obtained in Step 1, obtain adaptive weights based on kernel density estimation;

[0008] Step 3: Based on adaptive weights, the particle swarm optimization algorithm is used to obtain the optimal parameter set of the basic traffic map model;

[0009] Step 4: Obtain traffic capacity based on the optimal parameter set of the basic traffic map model.

[0010] The beneficial effects of this invention are as follows:

[0011] The present invention provides a capacity estimation method based on traffic map parameter calibration, which can effectively solve the fitting bias problem caused by uneven data distribution. The key point is to improve the estimation accuracy of the key parameter of capacity and improve the accuracy of capacity estimation.

[0012] This invention improves model fitting performance: It reduces the root mean square error (RMSE) and mean absolute error (MAE) of most basic traffic map models in medium-to-high density regions. Although the error increases slightly in low-density regions (by about 5%, which is within an acceptable range), through strategic trade-offs, it achieves a systematic improvement in fitting performance for key traffic feature areas, making the model predictions more closely reflect actual traffic conditions.

[0013] This invention improves the accuracy of capacity estimation: It effectively alleviates the capacity estimation bias caused by uneven sample distribution in traffic fundamental map models. In actual observation data, free-flow samples dominate while congestion data are sparse. By using kernel density estimation for weighting, the capacity estimates of each traffic fundamental map model are closer to the high-value regions in the actual observation data, significantly improving the accuracy of road capacity representation and providing a more reliable basis for traffic planning and management decisions.

[0014] Advantages of the calibration method in this invention: This invention proposes a data-driven adaptive weight setting strategy. Based on kernel density estimation, it automatically identifies sparse and dense regions of data distribution and adaptively calculates weights according to the density of data distribution, enabling the traffic fundamental map model to better characterize key traffic flow features. At the cost of a slight decrease in local accuracy, it significantly improves the model's prediction accuracy in medium- and high-density areas and the accuracy of capacity estimation, enhancing the model's engineering practical value.

[0015] This invention relates to a capacity estimation method based on traffic fundamental map parameter calibration, belonging to the field of intelligent transportation systems and traffic flow modeling technology. The method comprises four main steps: data preparation and preprocessing, adaptive weight calculation based on kernel density estimation, parameter estimation based on particle swarm optimization, and model evaluation. This invention utilizes kernel density estimation to automatically identify sparse regions in the data distribution and adaptively calculates weights according to the density of the data distribution. Then, a weighted optimization method is used to fit the parameters of the classic traffic fundamental map model. This method effectively overcomes the fitting bias problem caused by uneven sample distribution, significantly improves the estimation accuracy of the key parameter of capacity, and thus enhances the application value and reliability of traffic fundamental map models in practical engineering. Attached Figure Description

[0016] Figure 1 This is a flowchart of the capacity estimation method based on traffic map parameter calibration of the present invention;

[0017] Figure 2 A comparison chart showing the fitting effect of the Greenberg model on data for a regular road segment with and without KDE weighting;

[0018] Figure 3 A comparison chart showing the data fitting effect of the Drake model with and without KDE weighting on a typical road segment;

[0019] Figure 4 A comparison chart showing the data fitting effect of the METANET model with and without KDE weighting for a regular road segment;

[0020] Figure 5 A comparison of the data fitting effects of the Cellular Transport Model (CTM) with and without KDE weighting on conventional road segments;

[0021] Figure 6 A comparison chart showing the data fitting effect of the 3PL model with and without KDE weighting on a regular road segment;

[0022] Figure 7 A comparison chart showing the data fitting effect of the Cheng model with and without KDE weighting on a regular road segment;

[0023] Figure 8 A comparison of the data fitting effects of the Greenberg model with and without KDE weighting for hard shoulder closed road sections;

[0024] Figure 9 A comparison of the data fitting effects of the Drake model with and without KDE weighting for hard shoulder closed road sections;

[0025] Figure 10 A comparison of the data fitting effects of the METANET model with and without KDE weighting for closed hard shoulder road sections;

[0026] Figure 11 A comparison of the data fitting effects of the Cellular Transport Model (CTM) with and without KDE weighting on closed hard shoulder road sections;

[0027] Figure 12 A comparison of the data fitting effects of the 3PL model with and without KDE weighting for closed hard shoulder road sections;

[0028] Figure 13 A comparison of the data fitting effects of the Cheng model with and without KDE weighting for closed hard shoulder road sections;

[0029] Figure 14This is a schematic diagram of the distribution of standard road segment data and KDE fitting curves for the detection points used in the example.

[0030] Figure 15 This is a schematic diagram of the data distribution and KDE fitting curve of the hard shoulder closed road section used in the example;

[0031] Figure 16 This paper presents a comparison of evaluation indices for fitting various density intervals of a conventional road segment using six models with and without KDE weighting in an application example of this invention. Specifically, subfigures (a), (c), and (e) show the RMSE values ​​of the six models after fitting the low, medium, and high density intervals under the two processing methods, respectively; subfigures (b), (d), and (f) show the MAE values ​​of the fitting low, medium, and high density intervals under the corresponding conditions.

[0032] Figure 17 This document compares the evaluation metrics of the fitting effects of six models on different density ranges of hard shoulder closed road sections with and without KDE weighting in an application example of this invention. Specifically, subfigures (a), (c), and (e) correspond to the RMSE index values ​​of the six models for low, medium, and high density ranges of hard shoulder closed road sections under two processing methods, respectively; subfigures (b), (d), and (f) show the MAE index values ​​after fitting the low, medium, and high density ranges under the corresponding conditions. Detailed Implementation

[0033] Specific implementation method one: Combining Figure 1 This embodiment describes a capacity estimation method based on traffic map parameter calibration. The specific process is as follows:

[0034] Step 1: Obtain historical traffic flow data samples of individual vehicles at road cross-sections; perform time aggregation processing on the obtained individual vehicle data samples to generate an aggregated dataset with 2-minute intervals; clean each data sample in the aggregated dataset to obtain cleaned data samples; perform time scale conversion on the total 2-minute traffic flow in each cleaned data sample using the adjacent time period accumulation method to obtain the hourly total traffic flow; obtain the final aggregated dataset.

[0035] Step 2: Based on the final aggregated dataset obtained in Step 1, obtain adaptive weights based on kernel density estimation;

[0036] Step 3: Based on adaptive weights, the particle swarm optimization algorithm is used to obtain the optimal parameter set of the basic traffic map model;

[0037] Step 4: Obtain traffic capacity based on the optimal parameter set of the basic traffic map model.

[0038] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: in step one, historical traffic flow single-vehicle data samples of road cross-sections are obtained; the obtained single-vehicle data samples are time-aggregated to generate aggregated datasets with 2-minute intervals; each data sample in the aggregated dataset is cleaned to obtain cleaned data samples; the total flow in each cleaned data sample over 2 minutes is converted to an hourly total flow using the adjacent time period accumulation method; the final aggregated dataset is obtained, and each data sample (one sample every 2 minutes) in the final aggregated dataset includes the hourly total flow, speed, and density;

[0039] The specific process is as follows:

[0040] Step 1: Obtain historical traffic flow data samples for individual vehicles at the road cross-section. These samples include time, lane number, speed, vehicle type, and headway to the vehicle in front. The specific process is as follows:

[0041] Traffic flow data from the regular road section and the closed hard shoulder section of the G85 Yinkun Expressway (Gongshan to Xiaopu section, hereinafter referred to as "Gongxiao Expressway") were selected as the research object. The data samples came from microwave radar detectors set at kilometer markers k2013+400 and k2017+280 of the Gongxiao Expressway. The data samples were single-vehicle traffic flow data, and each record corresponded to the passage information of a single vehicle, including time, lane number, speed, vehicle type, and headway to the vehicle in front. The data collection period was from May 1, 2025 to May 31, 2025.

[0042] Step 1 and Step 2: Perform time aggregation processing on the bicycle data samples obtained in Step 1 to generate an aggregated dataset with 2-minute intervals.

[0043] Each data sample in the aggregated dataset (one sample every 2 minutes, taking 10 vehicles passing through in 2 minutes as an example; total flow is the total number of vehicles passing through in 2 minutes (converted to equivalent); small vehicle flow is the total number of small vehicles passing through in 2 minutes, for example, 4 vehicles; large vehicle flow is the total number of large vehicles passing through in 2 minutes, for example, 6 vehicles; speed is the average speed of 10 vehicles; density is the density calculated based on the headway between 10 vehicles and the vehicle in front; small vehicle ratio is the proportion of small vehicles among 10 vehicles, for example, 0.6) includes total flow, small vehicle flow, large vehicle flow, speed, density, and small vehicle ratio;

[0044] Step 13: Clean each data sample in the aggregated dataset to obtain cleaned data samples (the number of data samples is reduced), and remove abnormal records that obviously do not conform to physical laws.

[0045] The specific process is as follows:

[0046] The effective speed range is set to [0, 140] km / h, and the effective headway range is... The effective density range is [0, 120] pcu / km / ln;

[0047] If the first If a data sample does not simultaneously satisfy the above constraints, then delete the first one. Data sample;

[0048] Step 14: To convert minute-level traffic flow data into hour-level traffic flow data, the total traffic flow in each cleaned data sample for 2 minutes is converted to an hourly total flow using the method of accumulating adjacent time periods. This method, which accumulates the traffic flow of two adjacent 2-minute periods and converts it into hourly flow, helps to smooth short-term fluctuations and more accurately reflect the dynamic characteristics of traffic flow.

[0049] The specific calculation formula is as follows:

[0050]

[0051] In the formula, For the first The total hourly flow rate of each data sample, in units of pcu / h / ln;

[0052] For the first The total flow rate of each data sample over 2 minutes, in units of pcu / 2min / ln;

[0053] For the first The total flow rate of each data sample over 2 minutes is expressed in pcu / 2min / ln.

[0054] Each sample consists of one row, and each row records one data point within a 2-minute period (8:00-8:02), including traffic flow, small vehicle traffic flow, large vehicle traffic flow, speed, density, and the proportion of small vehicles.

[0055] Step 1, part 5: Obtain the final aggregated dataset. Each data sample in the final aggregated dataset (one sample every 2 minutes) includes the total hourly traffic, speed, and density.

[0056] The other steps and parameters are the same as in Specific Implementation Method 1.

[0057] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that: in steps 1 and 2, the single-vehicle data samples obtained in step 1 are subjected to time aggregation processing to generate an aggregated dataset with 2-minute intervals. Each data sample in the aggregated dataset includes total traffic flow, small vehicle traffic flow, large vehicle traffic flow, speed, density, and small vehicle ratio.

[0058] The specific process is as follows:

[0059] Step 121: The process of obtaining the total traffic in each data sample in the aggregated dataset is as follows:

[0060] Within a 2-minute time window, the total traffic flow has been uniformly converted to standard vehicle equivalent based on vehicle type, with the flow unit being pcu / 2min / ln; for example: if there are 2 lanes, 20 vehicles pass through the 2 lanes, and 10 vehicles pass through the 1 lane, the total traffic flow through a single lane is 10.

[0061] The calculation formula is:

[0062]

[0063] In the formula, For the first The total flow rate of each data sample over 2 minutes, in units of pcu / 2min / ln;

[0064] For the first The data sample includes small vehicle traffic flow, in veh / 2min. For the first Large vehicle traffic flow in the data sample, in veh / 2min; This represents the number of lanes; in this example, we take 2. The vehicle conversion factor for large vehicles is 2.5, based on the "Technical Standards for Highway Engineering" (JTG B01—2014).

[0065] Step 1, Step 2, Step 3: Aggregate the traffic flow of small vehicles in each data sample in the dataset. The acquisition process is as follows:

[0066] The number of small vehicles passing through the detection section within a 2-minute time window; the small vehicle flow rate is measured in veh / 2min.

[0067] Steps 1-3: Aggregate the large vehicle traffic flow data in each data sample of the dataset. The acquisition process is as follows:

[0068] The number of large vehicles passing through the detection section within a 2-minute time window; the large vehicle flow rate is measured in veh / 2min.

[0069] Steps one through four: The process of obtaining the speed from each data sample in the aggregated dataset is as follows:

[0070] Within a 2-minute time window, the average speed of all vehicles at the cross section is detected; the speed unit is km / h; for example, if 10 vehicles pass by, the average speed of each vehicle is calculated, and then the average speeds of the 10 vehicles are added together and divided by 10 to obtain the final speed.

[0071] Steps one through five, obtaining the proportion of small cars (e.g., 0.6) in each data sample of the aggregated dataset, are as follows:

[0072] Within a 2-minute time window, the proportion of small vehicles to the total number of natural vehicles at the detection section is used for density calculation.

[0073] Steps 1-6: The process of obtaining the density of each data sample in the aggregated dataset is as follows:

[0074] The density within a 2-minute time window is calculated based on the headway; the density unit is pcu / km / ln; the density calculation formula is:

[0075]

[0076] In the formula, For the first Density in each data sample, in units of pcu / km / ln; The total number of vehicles passing through the detection section within a 2-minute time window; The first cross-section to pass through within a 2-minute time window The instantaneous speed of a vehicle, measured in km / h; The first cross-section to pass through within a 2-minute time window The time distance between the front of one vehicle and the vehicle in front, expressed in seconds per veh. The proportion of small cars passing through the detection section within a 2-minute time window;

[0077] Other steps and parameters are the same as in specific implementation method one or two.

[0078] Specific Implementation Method Four: This implementation method differs from one of the specific implementation methods one to three in that: in step two, adaptive weights based on kernel density estimation are obtained based on the final aggregated dataset obtained in step one.

[0079] The specific process is as follows:

[0080] To address the fitting bias problem caused by uneven sample distribution in traditional parameter calibration methods, this invention introduces kernel density estimation (KDE) technology and proposes an adaptive sample weight calculation method. The core idea of ​​this method is to automatically identify sparse samples and assign them higher weights based on the distribution characteristics of traffic data. Simultaneously, a density square root transformation strategy is introduced to effectively alleviate the fitting bias caused by uneven sample distribution by gently compressing the distribution range of the original probability density. This ensures that sparse samples are given sufficient attention while avoiding the excessive neglect of common samples.

[0081] Step 21: Select bandwidth using the Silverman rule. The bandwidth calculation formula is as follows:

[0082]

[0083] In the formula,

[0084] The bandwidth is estimated for kernel density, in units of pcu / h / ln; This represents the total number of data samples in the final aggregated dataset obtained in step one.

[0085] For all of the final aggregated dataset obtained in step one The standard deviation of all hourly traffic data in a data sample; for example, 100 samples, 100 rows of data, each row containing one traffic data point, for a total of 100 traffic data points, take the standard deviation corresponding to the 100 traffic data points;

[0086] For all of the final aggregated dataset obtained in step one The interquartile range of all hourly flow data in the data sample, that is, the difference between the 75th percentile and the 25th percentile;

[0087] To construct a kernel density estimation model, the bandwidth parameter of the Gaussian kernel function must first be determined. Bandwidth determines the smoothness of density estimation and directly affects the sensitivity of weight allocation. This invention employs the classic Silverman rule for adaptive bandwidth selection, which provides robust and computationally efficient bandwidth estimation when the data distribution is unknown.

[0088] Step 22: Construct a probability density estimation model based on the Gaussian kernel function; the specific process is as follows:

[0089] Based on the optimal bandwidth determined in step S21 The Gaussian kernel function is used to perform nonparametric probability density estimation of the flow data distribution. Kernel density estimation is performed by placing a kernel function at each sample point and summing and averaging the contributions of all kernel functions to smoothly fit the probability density distribution of the flow over the entire range of values.

[0090] Step 221: The general form of kernel density estimation is:

[0091]

[0092] In the formula, Indicates flow rate The estimated probability density at; The Gaussian kernel function;

[0093] Represents any flow rate value to be estimated for the probability density, in units of pcu / h / ln;

[0094] Step 222, Order , As an intermediate variable;

[0095] The Gaussian kernel function is defined as:

[0096]

[0097] Step 223: Substitute the Gaussian kernel function into the general form of kernel density estimation to obtain the probability density estimation model of the Gaussian kernel function for flow data; the expression is:

[0098]

[0099] The probability density estimation model based on the Gaussian kernel function is applied to each sample point. Place a point centered at that point with a bandwidth of By controlling the broadened Gaussian probability density "kernel", and through the superposition and averaging of all kernel functions, a smooth fit of the probability density distribution of the entire flow range is achieved.

[0100] Steps two and three: Calculate the sample probability density and normalize it; the specific process is as follows:

[0101] The final aggregated dataset will be the first... Total hourly flow of data samples Substituting the probability density estimation model of the Gaussian kernel function for traffic data obtained in steps two, two, and three, we can calculate the probability density of the first Gaussian kernel function in the final aggregated dataset. Total hourly flow of data samples The corresponding original probability density estimate The expression is:

[0102]

[0103] In the formula, For the final aggregated dataset, the first Total hourly flow of data samples The original probability density estimate;

[0104] For the final aggregated dataset, the first The total hourly flow of each data sample. ;

[0105] probability density Intuitively represents the sample points Frequency of occurrence in the overall traffic distribution: a higher probability density indicates that samples near that traffic value are more common; a lower probability density indicates that samples near that traffic value are sparser. To eliminate the influence of the absolute value of the probability density on the dimensions and preserve the relative sparsity among samples, the original probability density estimate of the total hourly traffic for each data sample in the final aggregated dataset is normalized to obtain the normalized probability density:

[0106]

[0107] In the formula, For the final aggregated dataset, the first Total hourly flow of data samples The normalized probability density;

[0108] The normalization process is a linear scaling process that does not change the relative density relationship between samples, and therefore does not affect the weight allocation logic built based on the relative density values.

[0109] Step 24: To prevent excessive differentiation of sample weights during subsequent optimization, a density square root transformation strategy is adopted to perform nonlinear compression on the normalized probability density, resulting in the transformed probability density; the specific process is as follows:

[0110] The formula for the square root transformation of density is:

[0111]

[0112] In the formula, For the final aggregated dataset, the first Hourly flow of data samples The transformed probability density;

[0113] This transformation maintains the monotonicity of the probability density while moderately compressing the density range, effectively mitigating extreme differences between weights and thus significantly improving the numerical stability of parameter calibration.

[0114] Step 25: Based on the transformed probability density, calculate the nth probability density value in the final aggregated dataset. Initial weights of data samples ;

[0115] The initial weights are standardized to obtain standardized adaptive weights;

[0116] The specific process is as follows:

[0117] Step 2.51: Based on the transformed probability density, calculate the first probability density value in the final aggregated dataset. Initial weights of data samples ; indicates as:

[0118]

[0119] In the formula, For the final aggregated dataset, the first The initial weights of each data sample;

[0120] The weights are designed to be inversely proportional to the probability density, meaning that samples with lower probability density (sparser samples) are assigned higher weights.

[0121] Step 252: To eliminate the influence of the absolute values ​​of the initial weights and ensure the relativity and numerical stability of the weight system, the initial weights are standardized to obtain the final aggregated dataset. The standardized adaptive weights of each data sample are represented as:

[0122]

[0123] In the formula, For the final aggregated dataset, the first Adaptive weights after standardization of data samples; For all in the final aggregated dataset Initial weights of data samples The arithmetic mean, ;

[0124] Standardized adaptive weight sequence satisfy .

[0125] Weight sequence This will be used as the core input for the subsequent step S32 to construct the weighted objective function.

[0126] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0127] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that: in step three, the optimal parameter set of the traffic basic map model is obtained based on adaptive weights using a particle swarm optimization algorithm; the specific process is as follows:

[0128] To calibrate key parameters of fundamental traffic map models and address fitting bias caused by uneven sample distribution, this invention proposes a parameter estimation method based on Particle Swarm Optimization (PSO) using kernel density estimation weighting. First, six classic fundamental traffic map models and their parameters to be estimated are identified. Second, a weighted objective function incorporating KDE weights is constructed. Then, physical constraints are applied based on traffic flow theory and actual data. Finally, PSO is used to solve the constrained weighted optimization problem.

[0129] Step 3: Select 6 basic traffic map models and their corresponding parameters to be estimated;

[0130] Traffic fundamental maps are basic theoretical models that describe the macroscopic relationship between flow rate, speed, and density;

[0131] The six basic traffic graph models cover the development of models from early logarithmic and exponential types to recent complex forms, and have important theoretical and practical value.

[0132] Step 3.2: Construct an objective function and an optimization objective for each basic traffic map model;

[0133] Step 33: Construct physical constraints for each basic traffic graph model;

[0134] Steps 3 and 4: Solve for the optimal parameter set of the six basic traffic map models based on the particle swarm optimization algorithm.

[0135] The other steps and parameters are the same as in any of the specific implementation methods one to four.

[0136] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that: Step 31, selecting six basic traffic map models and their corresponding parameters to be estimated; the specific process is as follows:

[0137] The six basic traffic graph models include the Greenberg model (1959), the Drake model (1967), the METANET model (1989), the Cell Transmission Model (CTM) (1994), the 3PL model (2011), and the Cheng model (2021);

[0138] The mathematical form of the Greenberg model is The parameter to be estimated is , ;

[0139] The mathematical form of the Drake model is: The parameter to be estimated is , ;

[0140] The mathematical form of the METANET model is The parameter to be estimated is , , ;

[0141] The mathematical form of the Cellular Transport Model (CTM) is: The parameter to be estimated is , , ;

[0142] The mathematical form of the 3PL model is: The parameter to be estimated is , , ;

[0143] The mathematical form of the Cheng model is: The parameter to be estimated is , , ;

[0144] in, For density, It is a velocity-density function;

[0145] This is the critical speed, measured in km / h. Congestion density, expressed in pcu / km / ln;

[0146] Free-flow velocity, in km / h; This is the critical density, expressed in pcu / km / ln.

[0147] The reverse wave speed is expressed in km / h.

[0148] For shape parameters; For shape parameters; For shape parameters;

[0149] Limitations of traditional calibration methods

[0150] Although the above models have significant value in both theoretical development and engineering practice, their parameters often face the following problems when calibrated using traditional fitting methods:

[0151] Uneven sample distribution: Most highway traffic flow data are collected in free flow conditions, resulting in free flow samples dominating the dataset and congested flow samples being sparse.

[0152] Fitting bias: Uneven sample distribution causes the basic traffic map model to be overly biased towards the free flow region during the fitting process, resulting in a decrease in the fitting accuracy of congestion flow data.

[0153] Capacity estimation bias: In traffic flow theory, flow rate... ,density With speed There exists a basic relationship between them, represented as: Typically, traffic capacity can be estimated by finding the point corresponding to the maximum flow rate on the flow-density curve. However, in cases of uneven sample distribution, the traffic capacity obtained by traditional methods is often lower than the actual observed value.

[0154] Currently, there is still a lack of systematic solutions to the fitting bias problem caused by unbalanced sample distribution. Therefore, this invention proposes a density-weighted calibration method based on KDE, and selects the aforementioned six representative models to conduct a comparative analysis of KDE-weighted and unweighted methods to verify the effectiveness of the weighting strategy.

[0155] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0156] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: in step three-two, an objective function is constructed for each basic traffic map model, along with the optimization objective of the objective function; the specific process is as follows:

[0157] To overcome parameter estimation bias caused by uneven sample distribution, this invention introduces an adaptive weighting mechanism. This is based on the KDE sample weights obtained in step two. We construct an objective function with weighted root mean square error (WRMSE) as the core, assign different fitting importance to different samples, thereby improving the fitting accuracy of key area data;

[0158] The objective function is the same for all six basic traffic map models, and its expression is as follows:

[0159]

[0160] In the formula, This is the weighted root mean square error, in units of pcu / h / ln;

[0161] For the first The predicted hourly traffic flow values ​​for each data sample, in units of pcu / h / ln; traffic flow predicted by the basic traffic graph model.

[0162] The acquisition process is as follows:

[0163] Based on the parameters of the basic traffic map model and the first Density of data samples The basic traffic graph model outputs the first... speed of data samples The first output based on the basic graph model speed of data samples and the Density of data samples The first one obtained The predicted hourly flow rate of each data sample. ;

[0164] Model calibration aims to optimize parameters To minimize WRMSE, the objective function of the six basic traffic graph models is the same, and the objective function is expressed as:

[0165]

[0166] In the formula, This is the set of model parameters to be calibrated; specifically:

[0167] When the model to be calibrated is a Greenberg model, the model parameter set for and ;

[0168] When the model to be calibrated is the Drake model, the model parameter set for and ;

[0169] When the model to be calibrated is a METANET model, the model parameter set for , and ;

[0170] When the model to be calibrated is a Cellular Transport Model (CTM), the model parameter set is... for , and ;

[0171] When the model to be calibrated is a 3PL model, the model parameter set for , and ;

[0172] When the model to be calibrated is the Cheng model, the model parameter set for , and .

[0173] The other steps and parameters are the same as those in any of the specific implementation methods one to six.

[0174] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that: in step three, physical constraints are constructed for each basic traffic map model; the specific process is as follows:

[0175] To ensure that the calibration parameters of each model have physical interpretability and practical rationality, this invention introduces the following constraints based on traffic flow theory and existing experience to ensure that the parameter values ​​conform to the basic laws of traffic.

[0176] Step 331: Construct parameter boundary constraints for each basic traffic map model; the specific process is as follows:

[0177] Based on traffic flow theory and actual observation data, search boundaries were set for the parameters to be calibrated for each model;

[0178] For the Greenberg model, The range of values ​​is , The range of values ​​is ;

[0179] For the Drake model, The range of values ​​is , The range of values ​​is ;

[0180] For the METANET model, The range of values ​​is , The range of values ​​is , The range of values ​​is ;

[0181] For the Cellular Transport Model (CTM), The range of values ​​is , The range of values ​​is and The range of values ​​is ;

[0182] For the 3PL model, The range of values ​​is , The range of values ​​is and The range of values ​​is ;

[0183] For the Cheng model, The range of values ​​is , The range of values ​​is and The range of values ​​is ;

[0184] Step 332: Construct capacity constraints for each basic traffic map model. The capacity constraints are the same for each basic traffic map model.

[0185] capacity Defined as the maximum predicted flow rate of the model to be calibrated within the effective density range;

[0186] The specific calculation method for traffic capacity is as follows:

[0187]

[0188] In the formula, For model parameter set The corresponding maximum throughput capacity is expressed in pcu / h / ln.

[0189] This is the upper limit of the density search determined based on the actual samples; for example, 100 samples, 100 rows of data, each row of data has one density, a total of 100 densities, and the maximum value among the 100 densities is used as the upper limit;

[0190] Based on the requirements for traffic capacity of expressways under different design speeds in the "Technical Standards for Highway Engineering" (JTG B01—2014), and to ensure that the calibration results do not exceed the actual traffic capacity of the road section, the upper limit of traffic capacity is set at 2200 pcu / h / ln, i.e. .

[0191] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0192] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that: in steps three and four, the optimal parameter sets of the six basic traffic map models are solved based on the particle swarm optimization algorithm.

[0193] Particle Swarm Optimization (PSO) is a stochastic optimization algorithm based on swarm intelligence, inspired by the cooperative behaviors of groups in nature, such as flocks of birds foraging and schools of fish swimming. PSO achieves efficient solutions to complex optimization problems by simulating information sharing and collaborative search among individuals. This invention uses PSO to calibrate key parameters of six basic traffic graph models.

[0194] The specific process is as follows:

[0195] Step 3-41: Initialize the particle swarm;

[0196] The specific process is as follows:

[0197] For the Greenberg model: each particle is composed of and Two parameters constitute the initial population of the Greenberg model; all particles constitute the initial population of the Greenberg model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; the initial velocity of each particle is randomly generated.

[0198] For the Drake model: each particle is composed of and Two parameters constitute the initial population of the Drake model; all particles constitute the initial population; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; the initial velocity of each particle is randomly generated.

[0199] For the Cellular Transport Model (CTM): Each particle is composed of... , and The system consists of three parameters; all particles constitute the initial population of the Cellular Transport Model (CTM); the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated.

[0200] For the METANET model: each particle is composed of , and The model consists of three parameters; all particles constitute the initial population of the METANET model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated.

[0201] For the 3PL model: each particle is composed of , and The model consists of three parameters; all particles constitute the initial population of the 3PL model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated.

[0202] For the Cheng model: each particle is composed of , and The system consists of three parameters; all particles constitute the initial population of the Cheng model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated.

[0203] In particle swarm optimization (PSO) algorithms, the "population" refers to a collection of particles, each representing a candidate solution in the solution space. The search dimension is determined based on the parameter structure of the model to be calibrated, and each particle represents a set of parameters to be optimized. To avoid confusion, the key concepts in PSO algorithms are explained below:

[0204] Particle: A point in the solution space, representing a set of model parameters to be calibrated (the set of model parameters to be calibrated). For the Greenberg model, for and For the Drake model, for and For the METANET model, for , and For the Cellular Transport Model (CTM), for , and For the 3PL model, for , and For the Cheng model, for , and );

[0205] Position: The coordinates of the particle in the solution space, i.e., the values ​​of a set of model parameters to be calibrated in the current iteration step;

[0206] Velocity: The direction and step size of a particle's movement in the solution space, which determines how the parameters are adjusted in the next iteration, and is independent of the speed of vehicles in the traffic flow;

[0207] Population: The set of all particles, i.e., a group of multiple sets of candidate parameters, which is 50 in this example;

[0208] The initial position of each particle is randomly generated within the parameter boundaries set in step 331.

[0209] Step 3.4.2: Construct the fitness functions for 6 basic traffic map models. The fitness functions for the 6 basic traffic map models are the same. The specific process is as follows:

[0210] The fitness function is used to evaluate the fit of each parameter combination; this invention uses the first... Predicted hourly flow values ​​for each data sample Compared with actual traffic Minimizing the weighted root mean square error between them is the optimization objective. ;

[0211] The objective function WRMSE from step 3.2 is used as the fitness function;

[0212] Step 3-43: Let the number of iterations be... ;

[0213] Steps 3 and 4

[0214] 1) Calculate the fitness value of the Greenberg model and update the individual optimum and global optimum; the specific process is as follows:

[0215] For each particle, calculate the fitness value. ;

[0216] If the fitness value is less than the particle's historical best value, then update the individual's optimal solution; if the fitness value is also less than the historical best value of the entire population, then update the global optimal solution.

[0217] If the fitness value is greater than or equal to the particle's historical best value, the individual optimal solution is not updated; if the fitness value is greater than or equal to the historical best value of the entire population, the global optimal solution is not updated.

[0218] 2) Calculate the fitness value of the Drake model and update the individual optimum and global optimum;

[0219] 3) Calculate the fitness value of the Cellular Transfer Model (CTM) and update the individual optimum and global optimum;

[0220] 4) Calculate the fitness value of the METANET model and update the individual optimum and global optimum;

[0221] 5) Calculate the fitness value of the 3PL model and update the individual optimum and global optimum;

[0222] 6) Calculate the fitness value of the Cheng model and update the individual optimum and global optimum;

[0223] Steps three, four, and five: Update particle velocity and position; the specific process is as follows:

[0224] The calculation is performed using the GlobalBest Particle Swarm Optimizer (GlobalBestPSO) from the pyswarms library, and the speed update formula is as follows:

[0225]

[0226]

[0227] In the formula, For the first Particles in the next iteration In dimensions The speed on; For the first Particles in the next iteration In dimensions The speed on; For the first Particles in the next iteration In dimensions The position (i.e., parameter value) on the top; For the first Particles in the next iteration In dimensions The position (i.e., parameter value) on the top; For particles In dimensions The best historical position; For the entire population in dimension The historical global optimal position; The inertial weight controls the particle's ability to explore in the search space; in this invention, it is set to 0.9. These are the cognitive learning factor and the social learning factor, respectively, which are set to 2.0 in this study; for Random numbers within the range are used to increase the randomness of the search;

[0228] To prevent particles from going out of bounds, the positions of particles that exceed the parameter range set in step 331 are corrected for boundaries.

[0229] For the Greenberg model, dimensions For the Drake model, dimensions For the Cellular Transport Model (CTM), the dimension For the METANET model, dimensions For the 3PL model, dimensions For the Cheng model, dimensions ;

[0230] Steps three through six: Iteration termination judgment and parameter output; the specific process is as follows:

[0231] Convergence condition: When the improvement of the global optimal fitness value in 50 consecutive iterations is less than... When the algorithm has converged, the iteration is stopped.

[0232] Let the number of iterations Repeat steps 3, 4, and 5 until the global optimal fitness value of the Greenberg model satisfies the convergence condition, and find the parameter set that makes the Greenberg model fit best.

[0233] Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the Drake model satisfies the convergence condition, and find the parameter set that makes the Drake model fit best.

[0234] Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the cell transport model (CTM) satisfies the convergence condition, and find the parameter set that makes the CTM fit best.

[0235] Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the METANET model satisfies the convergence condition, and find the parameter set that makes the METANET model fit best.

[0236] Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the fitness value of the 3PL model meets the convergence condition, and find the parameter set that makes the 3PL model fit best.

[0237] Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the Cheng model satisfies the convergence condition, and find the parameter set that makes the Cheng model fit best.

[0238] This method is versatile and can be applied to parameter calibration problems of various traffic flow models, such as the Greenberg model, Drake model, METANET model, Cellular Transport Model (CTM), 3PL model, and Cheng model.

[0239] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0240] Specific Implementation Method 10: This implementation method differs from one of the specific implementation methods one to nine in that: in step four, the traffic capacity is obtained based on the optimal parameter set of the basic traffic map model;

[0241] The specific process is as follows:

[0242] 1) For the Greenberg model:

[0243] Based on the optimal parameter set , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ;

[0244] In the formula, For model parameter set The corresponding maximum throughput capacity is expressed in pcu / h / ln.

[0245] This is the upper limit of the density search determined based on the actual samples;

[0246] like Figure 2 middle, The model is based on Calculated according to Different for the sake of being different. The range of values ​​is , and The maximum value obtained by multiplication is ;

[0247] 2) For the Drake model:

[0248] Based on the optimal parameter set , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ;

[0249] 3) For the METANET model:

[0250] Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ;

[0251] 4) For the Cellular Transport Model (CTM):

[0252] Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ;

[0253] 5) For the 3PL model:

[0254] Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ;

[0255] 6) For the Cheng model:

[0256] Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity .

[0257] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0258] Example:

[0259] The model parameter calibration and solution process is primarily implemented using Python. Specifically, the pyswarms library is used for the particle swarm optimization algorithm, and the KernelDensity module from the scikit-learn library is used for kernel density estimation. The model successfully estimated the core parameters of different basic graph models. All parameters satisfy the physical constraints, and the traversability does not exceed the agreed upper limit, indicating that the parameter solution process effectively excludes non-physical solutions and ensures the rationality of the parameter estimates.

[0260] Figure 2-7 and Figure 8-13 The fitted curves of six basic traffic map models with and without KDE weighting are shown respectively. The velocity-density relationship of each model when weighted by KDE. This shows the velocity-density relationship for each model without weighting. Table 1 summarizes the impact of each model on traffic capacity. The estimation results.

[0261] Table 1. Pairing of 6 basic traffic graph models with and without KDE weighting estimation results

[0262]

[0263] By comparing the parameter estimation results with and without KDE weighting, the following conclusions can be drawn:

[0264] (1) Weighted estimation of traffic capacity generally improves: The weighting strategy significantly improves the model's fit to data on conventional road sections and closed hard shoulder sections, and the obtained traffic capacity is closer to the high value area of ​​the original observation data. Especially in closed hard shoulder sections, the improvement is more obvious, indicating that the weighting has a stronger corrective effect on the parameters of this type of road section. At the same time, the METANET model, the Cellular Transfer Model (CTM), and the Cheng model all improved the traffic capacity of closed hard shoulder sections by more than 50%, indicating that these three models are highly sensitive to the weighting strategy.

[0265] (2) Weighted free flow velocity increases overall: The free flow velocity of all models increases after weighting, indicating that the unweighted model may underestimate the actual free flow velocity due to overfitting low-density samples.

[0266] S5. Model Evaluation:

[0267] To systematically evaluate the fitting performance and applicability of the KDE weighted model, this invention adopts a segmented density interval evaluation strategy, combining the root mean square error (RMSE) and mean absolute error (MAE) to comprehensively evaluate the model's fitting ability under different traffic flow conditions.

[0268] Specifically, it includes the following sub-steps:

[0269] S51. Construction of the evaluation indicator system:

[0270] RMSE and MAE were selected as evaluation metrics to verify the model's fit performance. RMSE represents the standard deviation of the model's prediction error, measuring the average deviation between predicted and actual values; MAE represents the average absolute value of the prediction error, measuring the average magnitude of the prediction deviation for each sample. The specific calculation formulas are as follows:

[0271]

[0272]

[0273] S52. Segmented Interval Evaluation Strategy:

[0274] Considering the heterogeneity of traffic flow across different density ranges, the density is divided into [0,10), [10,20), and [10,20). The fitting performance was evaluated using three interval segments:

[0275] Low-density interval [0,10) pcu / km / ln: corresponds to free flow state, where traffic flow is not significantly disturbed and the flow rate increases approximately linearly with increasing density;

[0276] Medium density range [10,20) pcu / km / ln: corresponds to the transitional flow state, where traffic flow begins to be slightly disturbed and the flow rate growth slows down;

[0277] High-density area pcu / km / ln: corresponds to the congested flow state, where traffic flow is severely disrupted and the flow rate decreases as density increases.

[0278] By conducting segmented evaluations, the differences in the model's fitting performance under different traffic flow conditions can be identified, thereby ensuring the applicability of the proposed model in various scenarios.

[0279] To systematically analyze the improvement effect of the KDE weighted strategy, conventional road sections and hard shoulder closed road sections were selected as research objects. The evaluation indicators of weighted and unweighted models in each density interval were compared, and the actual data distribution of each detection point (e.g., Figure 14 , Figure 15 The analysis was performed as shown in the figure, and the evaluation index results for each detection point are as follows. Figure 16 and Figure 17 As shown.

[0280] (1) For regular road sections: In the low-density range, the RMSE and MAE of each model generally increased slightly after KDE weighting (the increase was about 5%, which is within the acceptable range); in the medium-density range, the RMSE and MAE of each model generally decreased after weighting, and the model performance was improved. Among them, the MAE of the METANET model decreased by 12.38%; in the high-density range, the RMSE and MAE of the Greenberg model and the Cellular Transfer Model (CTM) decreased after weighting. Among them, the RMSE and MAE of the Greenberg model decreased by 12.62% and 16.56% respectively, while the indicators of the other four models increased slightly (the increase was <5%, which is within the acceptable range).

[0281] (2) For hard shoulder closed sections: In the low-density range, the RMSE and MAE of each model generally increased after weighting, and the performance decreased; In the medium-density range, except for a slight increase in the RMSE of a few models, the RMSE and MAE of each model generally decreased after weighting, and the performance improved significantly. Among them, the MAE of the METANET model decreased by 11.52%; In the high-density range, except for a slight increase in the MAE of a few models, the RMSE and MAE of each model generally decreased after weighting. Among them, the RMSE and MAE of the Drake model decreased by 18.94% and 24.45% respectively, and the 3PL model decreased by 16.28% and 20.38% respectively.

[0282] (3) Combination Figure 14 , Figure 15It can be seen that free-flow data dominates, while congested flow data is sparse, exhibiting a significant imbalance. Due to the extremely high proportion of samples in low-density areas, the unweighted model overfits to this region, resulting in smaller errors in this area, while the fitting deviation is larger in medium- and high-density areas. Furthermore, because traditional methods tend to fit the free-flow state with the larger sample size, their estimation of traffic capacity is also prone to significant bias.

[0283] (4) Based on the adaptive weights assigned by KDE, higher weight compensation is given to samples in medium- and high-density regions. This method effectively balances the impact of uneven sample distribution, enabling the model to better capture the changing characteristics of medium- and high-density regions during fitting. Although the error in the low-density region increases slightly, the fitting quality in the medium- and high-density region is improved. Thus, while maintaining overall performance, the estimation accuracy of the key parameter of traffic capacity is significantly improved.

[0284] The results show that the KDE weighting method can automatically identify and compensate for sparse data regions. By dynamically allocating sample weights, it shifts the traffic fundamental map model from "simple fitting of most low-density samples" to "more accurately characterizing key traffic flow features." Although the weighting method slightly sacrifices fitting accuracy in low-density regions (within an acceptable range), it significantly improves the fitting effect in medium- and high-density regions, especially enhancing the estimation of capacity. This improvement effectively enhances the model's engineering applicability.

[0285] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

[0286] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A capacity estimation method based on traffic map parameter calibration, characterized in that: The specific process of the method is as follows: Step 1: Obtain historical traffic flow data samples of individual vehicles at road cross-sections; perform time aggregation processing on the obtained individual vehicle data samples to generate an aggregated dataset with 2-minute intervals; clean each data sample in the aggregated dataset to obtain cleaned data samples; perform time scale conversion on the total 2-minute traffic flow in each cleaned data sample using the adjacent time period accumulation method to obtain the hourly total traffic flow; obtain the final aggregated dataset. Step 2: Based on the final aggregated dataset obtained in Step 1, obtain adaptive weights based on kernel density estimation; Step 3: Based on adaptive weights, the particle swarm optimization algorithm is used to obtain the optimal parameter set of the basic traffic map model; Step 4: Obtain traffic capacity based on the optimal parameter set of the basic traffic map model.

2. The capacity estimation method based on traffic map parameter calibration according to claim 1, characterized in that: In step one, historical traffic flow data samples of individual vehicles at road cross-sections are obtained; the obtained individual vehicle data samples are time-aggregated to generate aggregated datasets with 2-minute intervals; each data sample in the aggregated dataset is cleaned to obtain cleaned data samples; the total flow in each cleaned data sample over 2 minutes is converted to an hourly total flow using the adjacent time period accumulation method; the final aggregated dataset is obtained, and each data sample in the final aggregated dataset includes the hourly total flow, speed, and density. The specific process is as follows: Step 1: Obtain historical traffic flow data samples for individual vehicles on the road cross-section. The individual vehicle data samples include time, lane number, speed, vehicle type, and headway to the vehicle in front. Step 1 and Step 2: Perform time aggregation processing on the bicycle data samples obtained in Step 1 to generate an aggregated dataset with 2-minute intervals. Each data sample in the aggregated dataset includes total traffic flow, small vehicle traffic flow, large vehicle traffic flow, speed, density, and the proportion of small vehicles. Step 13: Clean each data sample in the aggregated dataset to obtain the cleaned data sample; The specific process is as follows: The effective speed range is set to [0, 140] km / h, and the effective headway range is... The effective density range is [0, 120] pcu / km / ln; If the first If a data sample does not simultaneously satisfy the above constraints, then delete the first one. Data sample; Step 14: For each data sample after cleaning, the total flow rate over 2 minutes is converted to a time scale using the method of accumulating adjacent time periods to obtain the total flow rate per hour; The specific calculation formula is as follows: In the formula, For the first The total hourly flow rate of each data sample, in units of pcu / h / ln; For the first The total flow rate of each data sample over 2 minutes, in units of pcu / 2min / ln; For the first The total flow rate of each data sample over 2 minutes, in units of pcu / 2min / ln; Step 15: Obtain the final aggregated dataset. Each data sample in the final aggregated dataset includes the total hourly traffic, speed, and density.

3. The capacity estimation method based on traffic map parameter calibration according to claim 2, characterized in that: In steps one and two, the single-vehicle data samples obtained in step one are subjected to time aggregation processing to generate an aggregated dataset with a 2-minute interval. Each data sample in the aggregated dataset includes total traffic, small vehicle traffic, large vehicle traffic, speed, density, and small vehicle ratio. The specific process is as follows: Step 121: The process of obtaining the total traffic in each data sample in the aggregated dataset is as follows: The total flow rate passing through within a 2-minute time window, with the flow rate unit being pcu / 2min / ln; The calculation formula is: In the formula, For the first The total flow rate of each data sample over 2 minutes, in units of pcu / 2min / ln; For the first The data sample includes small vehicle traffic flow, in veh / 2min. For the first Large vehicle traffic flow in the data sample, in veh / 2min; Number of lanes; For large vehicles, the vehicle conversion factor is used. Step 1, Step 2, Step 3: Aggregate the traffic flow of small vehicles in each data sample in the dataset. The acquisition process is as follows: The number of small vehicles passing through the detection section within a 2-minute time window; the small vehicle flow rate is measured in veh / 2min. Steps 1-3: Aggregate the large vehicle traffic flow data in each data sample of the dataset. The acquisition process is as follows: The number of large vehicles passing through the detection section within a 2-minute time window; the large vehicle flow rate is measured in veh / 2min. Steps one through four: The process of obtaining the speed from each data sample in the aggregated dataset is as follows: Within a 2-minute time window, the average speed of all vehicles at the cross section is measured; the speed unit is km / h. Steps 1-5, the process of obtaining the proportion of small cars in each data sample in the aggregated dataset is as follows: Within a 2-minute time window, the proportion of small vehicles passing through the detection section to the total number of natural vehicles; Steps 1-6: The process of obtaining the density of each data sample in the aggregated dataset is as follows: The density within a 2-minute time window is calculated based on the headway; the density unit is pcu / km / ln; the density calculation formula is: In the formula, For the first Density in each data sample, in units of pcu / km / ln; The total number of vehicles passing through the detection section within a 2-minute time window; The first cross-section to pass through within a 2-minute time window The instantaneous speed of a vehicle, measured in km / h; The first cross-section to pass through within a 2-minute time window The time distance between the front of one vehicle and the vehicle in front, expressed in seconds per veh. This represents the proportion of small cars that pass through the detection section within a 2-minute time window.

4. The capacity estimation method based on traffic map parameter calibration according to claim 3, characterized in that: In step two, adaptive weights based on kernel density estimation are obtained from the final aggregated dataset obtained in step one. The specific process is as follows: Step 21: Select bandwidth using the Silverman rule. The bandwidth calculation formula is as follows: In the formula, The bandwidth is estimated for kernel density, in units of pcu / h / ln; This represents the total number of data samples in the final aggregated dataset obtained in step one. For all of the final aggregated dataset obtained in step one The standard deviation of all hourly flow data in the data sample; For all of the final aggregated dataset obtained in step one The interquartile range of all hourly flow data in the data sample, that is, the difference between the 75th percentile and the 25th percentile; Step 22: Construct a probability density estimation model based on the Gaussian kernel function; the specific process is as follows: Step 221: The general form of kernel density estimation is: In the formula, Indicates flow rate The estimated probability density at; The Gaussian kernel function; Represents any flow rate value to be estimated for the probability density, in units of pcu / h / ln; Step 222, Order , As an intermediate variable; The Gaussian kernel function is defined as: Step 223: Substitute the Gaussian kernel function into the general form of kernel density estimation to obtain the probability density estimation model of the Gaussian kernel function for flow data; the expression is: Steps two and three: Calculate the sample probability density and normalize it; The specific process is as follows: The final aggregated dataset will be the first... Total hourly flow of data samples Substituting the probability density estimation model of the Gaussian kernel function for traffic data obtained in steps two, two, and three, we can calculate the probability density of the first Gaussian kernel function in the final aggregated dataset. Total hourly flow of data samples The corresponding original probability density estimate The expression is: In the formula, For the final aggregated dataset, the first Total hourly flow of data samples The original probability density estimate; For the final aggregated dataset, the first The total hourly flow of each data sample. ; The original probability density estimate of the total hourly traffic for each data sample in the final aggregated dataset is normalized to obtain the normalized probability density: In the formula, For the final aggregated dataset, the first Total hourly flow of data samples The normalized probability density; Step 24: Employ a density square root transformation strategy to perform nonlinear compression on the normalized probability density, obtaining the transformed probability density; the specific process is as follows: The formula for the square root transformation of density is: In the formula, For the final aggregated dataset, the first Hourly flow of data samples The transformed probability density; Step 25: Based on the transformed probability density, calculate the nth probability density value in the final aggregated dataset. Initial weights of data samples ; The initial weights are standardized to obtain standardized adaptive weights; The specific process is as follows: Step 2.51: Based on the transformed probability density, calculate the first probability density value in the final aggregated dataset. Initial weights of data samples ; indicates as: In the formula, For the final aggregated dataset, the first The initial weights of each data sample; Step 252: Standardize the initial weights to obtain the final aggregated dataset. The standardized adaptive weights of each data sample are represented as: In the formula, For the final aggregated dataset, the first Adaptive weights after standardization of data samples; For all in the final aggregated dataset Initial weights of data samples The arithmetic mean, ; Standardized adaptive weight sequence satisfy .

5. The capacity estimation method based on traffic map parameter calibration according to claim 4, characterized in that: In step three, the optimal parameter set of the traffic basic map model is obtained based on adaptive weights using a particle swarm optimization algorithm; the specific process is as follows: Step 3: Select 6 basic traffic map models and their corresponding parameters to be estimated; Step 3.2: Construct an objective function and an optimization objective for each basic traffic map model; Step 33: Construct physical constraints for each basic traffic graph model; Steps 3 and 4: Solve for the optimal parameter set of the six basic traffic map models based on the particle swarm optimization algorithm.

6. The capacity estimation method based on traffic map parameter calibration according to claim 5, characterized in that: In step three, six basic traffic map models and their corresponding parameters to be estimated are selected; the specific process is as follows: The six basic traffic graph models include the Greenberg model, the Drake model, the METANET model, the Cellular Transport Model (CTM), the 3PL model, and the Cheng model. The mathematical form of the Greenberg model is The parameter to be estimated is , ; The mathematical form of the Drake model is: The parameter to be estimated is , ; The mathematical form of the METANET model is The parameter to be estimated is , , ; The mathematical form of the Cellular Transport Model (CTM) is: The parameter to be estimated is , , ; The mathematical form of the 3PL model is: The parameter to be estimated is , , ; The mathematical form of the Cheng model is: The parameter to be estimated is , , ; in, For density, It is a velocity-density function; This is the critical speed, measured in km / h. Congestion density, expressed in pcu / km / ln; Free-flow velocity, in km / h; This is the critical density, expressed in pcu / km / ln. The reverse wave speed is expressed in km / h. For shape parameters; For shape parameters; For shape parameters; 7. The capacity estimation method based on traffic map parameter calibration according to claim 6, characterized in that: In step three, step two involves constructing an objective function and an optimization objective for each basic traffic map model; the specific process is as follows: The objective function is the same for all six basic traffic map models, and its expression is as follows: In the formula, This is the weighted root mean square error, in units of pcu / h / ln; For the first The predicted hourly traffic flow values ​​for each data sample, in units of pcu / h / ln; traffic flow predicted by the basic traffic graph model. The acquisition process is as follows: Based on the parameters of the basic traffic map model and the first Density of data samples The basic traffic graph model outputs the first... speed of data samples ; The first output based on the basic graphical model speed of data samples and the Density of data samples The first one obtained The predicted hourly flow rate of each data sample. ; The objective functions of the six basic traffic graph models share the same optimization objective, which is expressed as follows: In the formula, This is the set of model parameters to be calibrated; specifically: When the model to be calibrated is a Greenberg model, the model parameter set for and ; When the model to be calibrated is the Drake model, the model parameter set for and ; When the model to be calibrated is a METANET model, the model parameter set for , and ; When the model to be calibrated is a Cellular Transport Model (CTM), the model parameter set is... for , and ; When the model to be calibrated is a 3PL model, the model parameter set for , and ; When the model to be calibrated is the Cheng model, the model parameter set for , and .

8. The capacity estimation method based on traffic map parameter calibration according to claim 7, characterized in that: In step three, physical constraints are constructed for each basic traffic map model; the specific process is as follows: Step 331: Construct parameter boundary constraints for each basic traffic map model; the specific process is as follows: For the Greenberg model, The range of values ​​is , The range of values ​​is ; For the Drake model, The range of values ​​is , The range of values ​​is ; For the METANET model, The range of values ​​is , The range of values ​​is , The range of values ​​is ; For the Cellular Transport Model (CTM), The range of values ​​is , The range of values ​​is and The range of values ​​is ; For the 3PL model, The range of values ​​is , The range of values ​​is and The range of values ​​is ; For the Cheng model, The range of values ​​is , The range of values ​​is and The range of values ​​is ; Step 332: Construct capacity constraints for each basic traffic map model. The capacity constraints are the same for each basic traffic map model. The specific calculation method for traffic capacity is as follows: In the formula, For model parameter set The corresponding maximum throughput capacity is expressed in pcu / h / ln. This represents the upper limit of the density search.

9. The capacity estimation method based on traffic map parameter calibration according to claim 8, characterized in that: In steps three and four, the optimal parameter sets for the six basic traffic map models are solved using the particle swarm optimization algorithm. The specific process is as follows: Step 3-41: Initialize the particle swarm; The specific process is as follows: For the Greenberg model: each particle is composed of and Two parameters constitute the initial population of the Greenberg model; all particles constitute the initial population of the Greenberg model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; the initial velocity of each particle is randomly generated. For the Drake model: each particle is composed of and Two parameters constitute the initial population of the Drake model; all particles constitute the initial population; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; the initial velocity of each particle is randomly generated. For the Cellular Transport Model (CTM): Each particle is composed of... , and The system consists of three parameters; all particles constitute the initial population of the Cellular Transport Model (CTM); the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated. For the METANET model: each particle is composed of , and The model consists of three parameters; all particles constitute the initial population of the METANET model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated. For the 3PL model: each particle is composed of , and The model consists of three parameters; all particles constitute the initial population of the 3PL model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated. For the Cheng model: each particle is composed of , and The system consists of three parameters; all particles constitute the initial population of the Cheng model; the initial position of each particle is randomly generated within the parameter boundaries set in step 331; and the initial velocity of each particle is randomly generated. Step 3.4.2: Construct the fitness functions for 6 basic traffic map models. The fitness functions for the 6 basic traffic map models are the same. The specific process is as follows: With the first Predicted hourly flow values ​​for each data sample Compared with actual traffic Minimizing the weighted root mean square error between them is the optimization objective. ; The objective function WRMSE from step 3.2 is used as the fitness function; Step 3-43: Let the number of iterations be... ; Steps 3 and 4 1) Calculate the fitness value of the Greenberg model and update the individual optimum and global optimum; the specific process is as follows: For each particle, calculate the fitness value. ; If the fitness value is less than the particle's historical best value, then update the individual's optimal solution; if the fitness value is also less than the historical best value of the entire population, then update the global optimal solution. If the fitness value is greater than or equal to the particle's historical best value, then the individual's optimal solution is not updated; If the fitness value is greater than or equal to the historical best value of the entire population, the global optimal solution is not updated; 2) Calculate the fitness value of the Drake model and update the individual optimum and global optimum; 3) Calculate the fitness value of the Cellular Transfer Model (CTM) and update the individual optimum and global optimum; 4) Calculate the fitness value of the METANET model and update the individual optimum and global optimum; 5) Calculate the fitness value of the 3PL model and update the individual optimum and global optimum; 6) Calculate the fitness value of the Cheng model and update the individual optimum and global optimum; Steps three, four, and five: Update particle velocity and position; the specific process is as follows: The calculation is performed using the globally optimal particle swarm optimizer from the pyswarms library, and the speed update formula is as follows: In the formula, For the first Particles in the next iteration In dimensions The speed on; For the first Particles in the next iteration In dimensions The speed on; For the first Particles in the next iteration In dimensions The position above; For the first Particles in the next iteration In dimensions The position above; For particles In dimensions The best historical position; For the entire population in dimension The historical global optimal position; Inertial weight; These are cognitive learning factors and social learning factors, respectively. for Random numbers within the interval; For the Greenberg model, dimensions For the Drake model, dimensions For the Cellular Transport Model (CTM), the dimension For the METANET model, dimensions For the 3PL model, dimensions ; For the Cheng model, dimensions ; Steps three through six: Iteration termination judgment and parameter output; the specific process is as follows: Convergence condition: When the improvement of the global optimal fitness value in 50 consecutive iterations is less than... When the algorithm has converged, the iteration is stopped. Let the number of iterations Repeat steps 3, 4, and 5 until the global optimal fitness value of the Greenberg model satisfies the convergence condition, and find the parameter set that makes the Greenberg model fit best. Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the Drake model satisfies the convergence condition, and find the parameter set that makes the Drake model fit best. Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the cell transport model (CTM) satisfies the convergence condition, and find the parameter set that makes the CTM fit best. Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the METANET model satisfies the convergence condition, and find the parameter set that makes the METANET model fit best. Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the fitness value of the 3PL model meets the convergence condition, and find the parameter set that makes the 3PL model fit best. Let the number of iterations Repeat steps 3-4-3 and 3-4-4 until the global optimal fitness value of the Cheng model satisfies the convergence condition, and find the parameter set that makes the Cheng model fit best.

10. The capacity estimation method based on traffic map parameter calibration according to claim 9, characterized in that: In step four, the traffic capacity is obtained based on the optimal parameter set of the basic traffic map model. The specific process is as follows: 1) For the Greenberg model: Based on the optimal parameter set , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ; In the formula, For model parameter set The corresponding maximum throughput capacity is expressed in pcu / h / ln. This represents the upper limit of the density search. 2) For the Drake model: Based on the optimal parameter set , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ; 3) For the METANET model: Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ; 4) For the Cellular Transport Model (CTM): Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ; 5) For the 3PL model: Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity ; 6) For the Cheng model: Based on the optimal parameter set , , Calculation speed , medium density The range of values ​​is Based on speed and density Calculate traffic capacity .

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