Steady state fundamental diagram estimation method based on traffic flow acceleration and deceleration characteristics

Abstract

The invention relates to the technical field of traffic safety management, and discloses a steady-state fundamental diagram estimation method based on traffic flow acceleration and deceleration characteristics, and the method comprises the following steps: S1, obtaining the trajectory data of a research region; s2, estimating a macroscopic traffic flow characteristic field according to the trajectory data; s3, constructing an NLKV sample according to the macroscopic traffic flow characteristic field; and S4, calibrating basic diagram model parameters through an NLKV sample. Compared with the prior art, the method has the advantages that the modeling accuracy and reliability of the traffic flow fundamental diagram are improved; the influence of a hysteresis effect is reduced; the model robustness is enhanced; gaussian hypothesis dependence on noise distribution is avoided; a frame reasonable in method is provided. By introducing an NLKV sample and ECE loss, the modeling accuracy of the traffic flow fundamental diagram is improved, the influence of a hysteresis effect is reduced, the model robustness is enhanced, Gaussian hypothesis dependence of noise distribution is avoided, and a frame reasonable in method is provided. The method has wide application prospects in the fields of intelligent traffic systems and the like due to the advantages.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic safety management, and particularly refers to a method for estimating a steady-state fundamental diagram based on the acceleration and deceleration characteristics of traffic flow. Background Art

[0002] The traffic flow fundamental diagram describes the functional relationship of macroscopic traffic flow parameters (flow rate, density, and speed) in a steady state. It is the basic input of a continuous traffic flow model and one of the basic information in application fields such as traffic capacity analysis, traffic state estimation and prediction, traffic management and control.

[0003] In existing research, when calibrating the parameters of the density-speed fundamental diagram model, local density-speed is used as an empirical sample, that is, the density and average speed in the same spatio-temporal domain are matched and regarded as a sample, and this kind of sample is called an LKV sample; the least squares method is used to calibrate the parameters of the fundamental diagram model on the LKV sample. This kind of method potentially assumes that the speed variable is independent of each other under different densities and follows a Gaussian distribution; the variance of the speed distribution between different densities is constant and does not change with density; at the same time, it is assumed that the mean of the Gaussian distribution corresponds to the steady-state speed at that density. Based on the above assumptions, the maximum likelihood estimation (MLE) is used to calibrate the model parameters.

[0004] However, LKV samples usually do not conform to the implicit assumptions of the above least squares method. First of all, traffic flow cannot instantaneously transition from one steady state to another, and the non-steady transition state is affected by drivers' expectations for the future. For example, if the density in downstream area B is greater than that in upstream area A, vehicles in A will decelerate in advance to adapt to the upcoming congestion state. At this time, the speed in A is affected by the density in B, which violates the independence assumption of the sample. Secondly, although the speed under the same density can be approximately modeled as a Gaussian distribution, there are differences in both the mean and variance of the speed distributions corresponding to different densities, which violates the assumption of the same distribution of the sample. Therefore, although calibrating model parameters by regression methods on LKV samples is a very common method, its theoretical basis is not solid.

[0005] In actual scenarios, it is difficult to observe steady-state traffic flow. In most cases, the traffic flow state is dynamically changing. When the state changes, drivers need a certain amount of time to adjust their driving behaviors, and the traffic flow also needs a certain amount of time to adjust to the new steady state. A typical manifestation is the hysteresis phenomenon of traffic flow. Therefore, LKV samples usually contain a large amount of non-steady-state data, which makes it difficult to model the steady-state fundamental diagram through LKV samples.

[0006] However, if we assume that the driver has a corresponding expected driving speed (expected speed) at different densities and adjusts the current speed through acceleration and deceleration behaviors to approach the expected speed, then the expected speed can be inferred from the current speed and acceleration and deceleration behaviors: when the expected speed is lower than the current speed, negative acceleration will appear in the traffic flow, and when the expected speed exceeds the current speed, positive acceleration will be observed. The acceleration and deceleration behaviors of the traffic flow only depend on the relationship between the current speed and the expected speed. Therefore, introducing acceleration can overcome the problem that the data samples are not independent of density. In addition, the steady-state and non-steady-state samples can be naturally distinguished at the macroscopic level through the acceleration and deceleration attributes, so as to fit the steady-state fundamental diagram that conforms to the physical meaning.

[0007] Defects of the existing sample construction methods are as follows:

[0008] Defect 1: The assumption of sample independence does not hold

[0009] The existing technology uses LKV samples (local density - speed samples) for parameter calibration. These samples are based on an assumption that the speed variables are independent of each other at different densities. However, in actual traffic flow, the speed of a vehicle is affected not only by the current density but also by the driver's expectations for the future (such as the congestion situation on the upcoming section of the road). This expectation causes the vehicle to adjust its speed in advance in the non-steady transition state, thus violating the assumption of sample independence.

[0010] Defect 2: The assumption of sample identical distribution does not hold

[0011] The existing technology assumes that the variance of the speed distribution between different densities is constant, does not change with density, and follows a Gaussian distribution. However, in actual traffic flow, there are differences in both the mean and variance of the speed distributions corresponding to different densities. This difference causes the LKV samples not to conform to the assumption of identical distribution, thus affecting the accuracy of parameter calibration.

[0012] Defect 3: It is difficult to distinguish between steady-state and non-steady-state samples

[0013] Due to the dynamic changes in the traffic flow state, the LKV samples usually contain a large amount of non-steady-state data. The existing technology lacks an effective method to distinguish between steady-state and non-steady-state samples, resulting in inaccurate calibration of model parameters. The existence of non-steady-state data makes the model unable to accurately reflect the characteristics of the traffic flow in the steady state.

[0014] Defect 4: The theoretical basis of the parameter calibration method is not solid

[0015] Since the LKV samples do not conform to the implicit assumptions of the least squares method (independence and identical distribution assumptions), the theoretical basis of the parameter calibration method based on LKV samples and the least squares method is not solid. This results in limitations in the performance and accuracy of the model in actual applications. Summary of the Invention

[0016] The technical problem to be solved by the present invention is to overcome the above technical difficulties and provide a steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow. Compared with the existing methods, the expected density is used to replace the current density, and the acceleration and deceleration labels are introduced. The samples constructed by the method in the present invention are called non-local velocity-density samples, abbreviated as NLKV samples. The present invention further proposes a method for calibrating the fundamental diagram model through NLKV samples, and realizes the parameter calibration of the velocity-density fundamental diagram through the classification process of acceleration and deceleration instead of the regression process of velocity. In addition, an improved cross-entropy loss function is proposed to accelerate convergence.

[0017] To solve the above technical problems, the technical solution provided by the present invention is as follows:

[0018] A steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow, comprising the following steps:

[0019] S1. Obtain the trajectory data of the research area;

[0020] S2. Estimate the macroscopic traffic flow characteristic field according to the trajectory data;

[0021] S3. Construct NLKV samples from the macroscopic traffic flow characteristic field;

[0022] S4. Calibrate the parameters of the fundamental diagram model through NLKV samples.

[0023] Further, the specific process of S1 is as follows:

[0024] The vehicle trajectory data of the research area can be obtained through means such as drone videos, lidar point clouds, and vehicle-mounted GPS; the trajectory data processed by corresponding technologies includes the position information x(n, t) of each observed vehicle n in the research area of a road section with a length of X at every 0.1-second time interval within the observation time T, satisfying 0 ≤ x ≤ X, 0 ≤ t ≤ T, t - (t - 1) = 0.1, n ∈ {1, 2,..., N}, where N is the total number of vehicles observed in the research area within T; a set of value cases is X = 2000m, T = 3600s.

[0025] Further, the specific process of S2 is as follows:

[0026] S21. Obtain the estimation interval corresponding to each group of characteristics in the macroscopic traffic flow characteristic field according to the step size of the spatio-temporal sliding window and the range of the spatio-temporal sub-domain

[0027] Assume that the time step of the spatio-temporal sliding window is t s , and the space step is x s , the time span of the spatio-temporal sub-domain is Δt, and the space span is Δx, t s < Δt, x s<Δx; The smaller the step size of the spatio-temporal sliding window, the finer the granularity of the macroscopic traffic flow characteristic field. However, more estimation operations are required simultaneously. The step size can be determined according to actual needs and computing power. To improve the accuracy of state estimation, the spatio-temporal subdomain needs to be large enough microscopically and small enough macroscopically. The recommended value range of the time span is from 20s to 60s, and the value range of the spatial span is from 100m to 300m. A set of value cases is t s = 2s, x s = 3m, Δt = 50s, Δx = 300m;

[0028] S211. Under the selected spatio-temporal sliding window, determine the spatio-temporal dimension N of the macroscopic traffic flow characteristic field in the research area x and N t ;

[0029] S2111. Determine the spatial dimension N of the macroscopic traffic flow characteristic field in the research area x

[0030] From the spatial range X of the research area, the spatial span Δx of the spatio-temporal subdomain, and the spatial step size x s of the spatio-temporal sliding window, the spatial dimension N x of the macroscopic traffic flow characteristic field can be calculated by Equation (1);

[0031]

[0032] where is the floor symbol; under the value settings of the case,

[0033] S2112. Determine the time dimension N of the macroscopic traffic flow characteristic field in the research area t

[0034] From the time range T of the research area, the time span Δt of the spatio-temporal subdomain, and the spatial step size t s of the spatio-temporal sliding window, the spatial dimension N t of the macroscopic traffic flow characteristic field can be calculated by Equation (2);

[0035]

[0036] where is the floor symbol; under the value settings of the case,

[0037] S212. Determine the spatio-temporal range of the trajectory corresponding to each group of characteristics in the macroscopic traffic flow characteristic field of the research area;

[0038] S2121. Determine the upper and lower limits of the trajectory time range corresponding to each time point

[0039] Let \(i\) represent each time point in the characteristic field, where \(0 < i\leq N\) t , \(i\) being an integer; for each \(i\), calculate the lower time limit \(t\) dw (i) and the upper time limit \(t\) up (i) according to equations (3) and (4);

[0040] t dw (i)=(i - 1)t s , #(3)

[0041] t up (i)=(i - 1)t s +Δt. #(4)

[0042] Under the value settings of the case, the minimum value of \(i\) is 1 and the maximum value is \(N\) t =1775, corresponding to \(t\) dw (1)=0, \(t\) up (1)=50, \(t\) dw (1775)=(1775 - 1)×2 = 3548, \(t\) up (1775)=(1775 - 1)×2+50 = 3598;

[0043] S2122. Determine the upper and lower limits of the trajectory space range corresponding to each spatial point

[0044] Let \(j\) represent each time point in the characteristic field, where \(0 < j\leq N\) x , \(j\) being an integer; for each \(j\), calculate the lower spatial limit \(x\) dw (j) and the upper spatial limit \(x\) up (j) according to equations (5) and (6);

[0045] x dw (j)=(j - 1)x s , #(5)

[0046] x up (j)=(j - 1)x s +Δx. #(6)

[0047] Under the value settings of the case, the minimum value of \(j\) is 1 and the maximum value is \(N\) x =566, corresponding to \(x\) dw (1)=0, \(x\) up (1)=3000, \(x\) dw (566)=(566 - 1)×3 = 1695, \(x\) up (566)=(566 - 1)×3+300 = 1995;

[0048] S22. Estimate the traffic flow characteristic parameters in the macroscopic traffic flow characteristic field;

[0049] S221. Estimate the macroscopic traffic flow characteristic parameters of a single spatio-temporal point;

[0050] S2211. Extract the trajectory data corresponding to the point

[0051] According to the lower time limit t corresponding to the spatio-temporal point (i, j) dw (i), the upper time limit t up (i), the lower space limit x dw (j) and the upper space limit x up (j), extract the trajectory data x within the corresponding spatio-temporal range i (n, t j ), satisfying t dw (i) ≤ t i ≤ t up (i), x dw (j) ≤ x j ≤ x up (j);

[0052] S2212. Count the total number of vehicles, total driving distance, and total driving time of the vehicle trajectories corresponding to the point;

[0053] The total number of vehicles N i，j is the number of non-repeating n in the trajectory data x i (n, t j );

[0054] For each vehicle n, use to represent the trajectory of this vehicle within the spatio-temporal range of the point. The driving distance and driving time of vehicle n are calculated by equations (7) and (8);

[0055]

[0056] The total driving distance is The total driving time is which is the sum of the driving distances and driving times corresponding to all vehicles;

[0057] S2213. Estimate the density, average speed, and acceleration corresponding to the point;

[0058] Estimate the density k(i, j), average speed v(i, j), and acceleration a(i, j) corresponding to the spatio-temporal point (i, j) by equations (9)-(11):

[0059]

[0060] Among them, Under the case value setting, ΔxΔt = 300×50 = 15000;

[0061] S222. Estimate the macroscopic traffic flow characteristic field;

[0062] Traverse each spatio-temporal point, estimate its corresponding density, average speed, and acceleration; sort the density, speed, and acceleration according to the spatio-temporal points to obtain the macroscopic traffic flow characteristic field, including the density field speed field and acceleration field Satisfy K(i, j) = k(i, j), V(i, j) = (i, j)A(i, j) = a(i, j).

[0063] Furthermore, the specific process of S3 is as follows:

[0064] S31. Construct the acceleration and deceleration labels of the samples from the acceleration field

[0065] According to the acceleration value corresponding to each spatio-temporal point, determine its acceleration and deceleration label y(i, j) by Equation (12):

[0066]

[0067] S32. Estimate the expected density of the samples from the traffic flow characteristic field

[0068] Estimate the expected density k a (i, j) of this point according to the current speed and downstream density of each spatio-temporal point by Equation (13):

[0069]

[0070] where t m is the operation reaction time of the driver. Under the value setting of the case, t m = 12s;

[0071] S33. Construct the NLKV samples

[0072] The NLKV sample of the spatio-temporal sub-domain (i, j) is {k a (i, j), V(i, j), y(i, j)}; traversing all spatio-temporal sub-domains can obtain all NLKV samples of the research area.

[0073] Furthermore, the specific process of S1 is as follows:

[0074] S41. Select the speed-density fundamental diagram model

[0075] According to the traffic characteristics and research requirements of the research scenario, select a suitable speed-density fundamental diagram model where θ is the parameter of the fundamental diagram model; one selection case is the Franklin-Newell model, and its expression is:

[0076]

[0077] Among them, v0, λ, and k jam are the parameters to be calibrated for the Franklin - Newell model;

[0078] S42. Calibrate the parameters of the basic diagram model

[0079] Construct an improved cross - entropy loss function as shown in Equation (15), taking the minimization of the loss value as the optimization objective, and solve the parameters θ of the basic diagram model through numerical iteration methods (such as the gradient descent algorithm, Adam algorithm);

[0080]

[0081] In the formula, m is the total number of NLKV samples. The expected density, speed, and acceleration - deceleration labels of the i - th sample are respectively represented by v i and y i ; ω is the proportion of acceleration samples, which is used to weight the loss function and satisfies:

[0082]

[0083] Among them, #{y i |y i = 0} represents the number of acceleration samples.

[0084] The objectives of the present invention:

[0085] 1. Propose a new sample construction method: Replace the current density with the expected density and introduce acceleration - deceleration labels to construct non - local velocity - density samples (NLKV samples). This method aims to overcome the problems that the sample independence assumption and the i.i.d. assumption in the prior art do not hold, and improve the accuracy and representativeness of the samples.

[0086] 2. Provide an effective method for distinguishing steady - state and non - steady - state samples: By introducing the acceleration - deceleration attribute, the present invention can effectively distinguish steady - state and non - steady - state samples at the macroscopic level. This helps to eliminate the influence of non - steady - state data on the calibration of model parameters and improve the accuracy and reliability of the model.

[0087] 3. Propose a new parameter calibration method: Based on NLKV samples, the present invention proposes to calibrate the parameters of the velocity - density fundamental diagram through the classification process of acceleration - deceleration rather than the regression process of speed. This method aims to overcome the problem that the theoretical basis of the parameter calibration method in the prior art is not solid, and improve the accuracy and practicality of parameter calibration.

[0088] In summary, the present invention aims to solve the problems existing in the prior art in calibrating the parameters of the traffic flow fundamental diagram model. By proposing a new sample construction method, a parameter calibration method, and an effective method for distinguishing steady-state and non-steady-state samples, the accuracy and reliability of the model are improved, providing more powerful support for fields such as traffic flow modeling, traffic state estimation and prediction, traffic management and control, etc.

[0089] The advantages of the present invention compared with the prior art are as follows:

[0090] 1. Improve the accuracy and reliability of traffic flow fundamental diagram modeling:

[0091] By introducing non-local density-velocity samples (NLKV), the present invention can more accurately estimate the basic characteristics of traffic flow. Compared with traditional local density-velocity samples (LKV), NLKV takes into account the expected density, thus more comprehensively reflecting the dynamic characteristics of traffic flow. NLKV samples can successfully separate the acceleration and deceleration regions and more accurately represent the real situation under physical steady state, which helps to improve the accuracy and reliability of the traffic flow model.

[0092] 2. Reduce the influence of hysteresis effect:

[0093] Traditional LKV samples are easily affected by the hysteresis effect, resulting in the fundamental diagram obtained by fitting not being able to reflect the steady-state characteristics. While NLKV samples reduce the influence of the hysteresis effect by considering traffic expectations, making the model more in line with the characteristics of actual traffic flow.

[0094] 3. Enhance the robustness of the model:

[0095] The present invention adopts the improved cross-entropy (ECE) loss as the loss function, which not only considers the cost of misclassification but also solves the problem of sample bias. This enhances the robustness of the model, enabling it to better cope with complex traffic flow environments.

[0096] 4. Avoid relying on the Gaussian assumption of noise distribution:

[0097] Traditional fitting processes usually adopt the least squares estimation method, which relies on the Gaussian assumption of noise distribution. However, the noise distribution in actual traffic flow may not exactly conform to the Gaussian distribution. The present invention bypasses this assumption by adopting the ECE loss, making the model more flexible and practical.

[0098] 5. Provide a methodologically reasonable framework:

[0099] NLKV samples include steady-state information through acceleration and deceleration characteristics, and the deceleration probability of the samples conforms to the independent and identically distributed assumption required by maximum likelihood estimation. This provides a methodologically reasonable framework for the estimation of fundamental diagram parameters, making the model more credible both theoretically and practically.

[0100] In summary, by introducing NLKV samples and ECE loss, the present invention improves the modeling accuracy of the fundamental diagram of traffic flow (FD), reduces the influence of hysteresis effect, enhances the model robustness, avoids the dependence on the Gaussian assumption of noise distribution, and provides a methodologically reasonable framework. These advantages enable the present invention to have broad application prospects in fields such as intelligent transportation systems. Specific Embodiments

[0101] In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more. Additionally, the term "comprising" and any of its variations are intended to cover non-exclusive inclusion.

[0102] The following further elaborates on the present invention in conjunction with the embodiments.

[0103] In the specific implementation of the embodiments of the present invention:

[0104] A steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow includes the following steps:

[0105] S1. Obtain the trajectory data of the research area:

[0106] The vehicle trajectory data of the research area can be obtained through means such as drone videos, lidar point clouds, and vehicle-mounted GPS; the trajectory data after corresponding technical processing includes the position information x(n, t) of each observed vehicle n at every 0.1-second time interval in a road section research area with a length of X within the observation time T, satisfying 0 ≤ x ≤ X, 0 ≤ t ≤ T, t - (t - 1) = 0.1, n ∈ {1, 2,..., N}, where N is the total number of vehicles observed in the research area within T; a set of value cases is X = 2000m, T = 3600s.

[0107] S2. Estimate the macroscopic traffic flow characteristic field based on the trajectory data:

[0108] S21. Obtain the estimation interval corresponding to each group of characteristics in the macroscopic traffic flow characteristic field according to the step size of the spatio-temporal sliding window and the range of the spatio-temporal subdomain

[0109] Assume that the time step of the spatio-temporal sliding window is t s , and the space step is x s , the time span of the spatio-temporal subdomain is Δt, the space span is Δx, t s < Δt, x s<Δx; The smaller the step size of the spatio-temporal sliding window, the finer the granularity of the macroscopic traffic flow characteristic field. However, more estimation operations are required simultaneously. The step size can be determined according to actual requirements and computing power. To improve the accuracy of state estimation, the spatio-temporal sub-domain needs to be large enough microscopically and small enough macroscopically. The recommended value range for the time span is from 20 s to 60 s, and the value range for the spatial span is from 100 m to 300 m. A set of value cases is t s = 2 s, x s = 3 m, Δt = 50 s, Δx = 300 m;

[0110] S211. Under the selected spatio-temporal sliding window, determine the spatio-temporal dimension N of the macroscopic traffic flow characteristic field of the research area x and N t ;

[0111] S2111. Determine the spatial dimension N of the macroscopic traffic flow characteristic field of the research area x

[0112] From the spatial range X of the research area, the spatial span Δx of the spatio-temporal sub-domain, and the spatial step size x s of the spatio-temporal sliding window, the spatial dimension N x of the macroscopic traffic flow characteristic field can be calculated by Equation (1);

[0113]

[0114] where, is the floor symbol; Under the value setting of the case,

[0115] S2112. Determine the time dimension N of the macroscopic traffic flow characteristic field of the research area t

[0116] From the time range T of the research area, the time span Δt of the spatio-temporal sub-domain, and the spatial step size t s of the spatio-temporal sliding window, the spatial dimension N t of the macroscopic traffic flow characteristic field can be calculated by Equation (2);

[0117]

[0118] where, is the floor symbol; Under the value setting of the case,

[0119] S212. Determine the spatio-temporal range corresponding to each group of characteristics in the macroscopic traffic flow characteristic field of the research area;

[0120] S2121. Determine the upper and lower limits of the trajectory time range corresponding to each time point

[0121] Let i represent each time point in the feature field, 0<i≤N t , i is an integer; for each i, the time lower limit t corresponding to the point is calculated by equations (3) and (4) dw (i) and the time limit t up (i);

[0122] t dw (i) = (i-1)t s ,#(3)

[0123] t up (i)=(i-1)t s +Δt.#(4)

[0124] In the case value setting, the minimum value of i is 1 and the maximum value is N. t =1775, corresponding to t dw (1) = 0, t up (1)=50,t dw (1775) = (1775-1) × 2 = 3548, t up (1775) = (1775-1) × 2 + 50 = 3598;

[0125] S2122: Determine the upper and lower limits of the trajectory space range corresponding to each spatial point

[0126] Use j to represent each time point in the feature field, 0<j≤N x , j is an integer; for each j, the spatial lower limit x corresponding to the point is calculated by equations (5) and (6): dw (j) and the space limit x up (j);

[0127] x dw (j) = (j-1)x s ,#(5)

[0128] x up (j) = (j-1)x s +Δx.#(6)

[0129] In the case value setting, the minimum value of j is 1 and the maximum value is N. x =566, corresponding to x dw (1) = 0, x up (1) = 300, x dw (566) = (566-1) × 3 = 1695, x up (566) = (566-1) × 3 + 300 = 1995;

[0130] S22, estimating traffic flow characteristic parameters in the macroscopic traffic flow characteristic field;

[0131] S221. Estimate the macroscopic traffic flow characteristic parameters of a single spatio-temporal point;

[0132] S2211. Extract the trajectory data corresponding to the point

[0133] According to the lower time limit t corresponding to the spatio-temporal point (i, j) dw (i), the upper time limit t up (i), the lower space limit x dw (j) and the upper space limit x up (j), extract the trajectory data x within the corresponding spatio-temporal range i (n, t j ), satisfying t dw (i) ≤ t i ≤ t up (i), x dw (j) ≤ x j ≤ x up (j);

[0134] S2212. Count the total number of vehicles, total driving distance, and total driving time of the vehicle trajectories corresponding to the point;

[0135] The total number of vehicles N i,j is the number of non-repeating n in the trajectory data x i (n, t j );

[0136] For each vehicle n, use to represent the trajectory of the vehicle within the spatio-temporal range of the point. The driving distance and driving time of vehicle n are calculated by equations (7) and (8);

[0137]

[0138] The total driving distance is The total driving time is which is the sum of the driving distances and driving times corresponding to all vehicles;

[0139] S2213. Estimate the density, average speed, and acceleration corresponding to the point;

[0140] Estimate the density k(i, j), average speed v(i, j), and acceleration a(i, j) corresponding to the spatio-temporal point (i, j) by equations (9)-(11):

[0141]

[0142] Among them, Under the case value setting, ΔxΔt = 300×50 = 15000;

[0143] S222. Estimate the macroscopic traffic flow characteristic field;

[0144] Traverse each spatio-temporal point, and estimate its corresponding density, average speed, and acceleration; sort the density, speed, and acceleration according to the spatio-temporal points, and the macroscopic traffic flow characteristic field can be obtained, including the density field speed field and acceleration field satisfying K(i, j) = k(i, j)V(i, j) = v(i, j), A(i, j) = a(i, j).

[0145] S3. Construct NLKV samples from the macroscopic traffic flow characteristic field:

[0146] S31. Construct the acceleration / deceleration labels of the samples from the acceleration field

[0147] According to the acceleration value corresponding to each spatio-temporal point, determine its acceleration / deceleration label y(i, j) by Equation (12):

[0148]

[0149] S32. Estimate the expected density of the samples from the traffic flow characteristic field

[0150] According to the current speed and downstream density of each spatio-temporal point, estimate the expected density k a (i, j):

[0151]

[0152] where t m is the operation reaction time of the driver. Under the value setting of the case, t m = 12s;

[0153] S33. Construct NLKV samples

[0154] The NLKV sample of the spatio-temporal sub-domain (i, j) is {k a (i, j), V(i, j), y(i, j)}; traversing all spatio-temporal sub-domains, all NLKV samples of the research area can be obtained.

[0155] S4. Calibrate the parameters of the fundamental diagram model through NLKV samples:

[0156] S41. Select the speed-density fundamental diagram model

[0157] According to the traffic characteristics and research requirements of the research scenario, select a suitable speed-density fundamental diagram model where θ is the parameter of the basic diagram model; one selected case is the Franklin - Newell model, and its expression is:

[0158]

[0159] where, v0, λ and k jam are the parameters to be calibrated for the Franklin - Newell model;

[0160] S42. Calibrate the parameters of the basic diagram model

[0161] Construct an improved cross - entropy loss function as shown in Equation (15), taking the minimization of the loss value as the optimization goal, and solve the parameter θ of the basic diagram model through numerical iteration methods (such as the gradient descent algorithm, Adam algorithm);

[0162]

[0163] In the formula, m is the total number of NLKV samples, and the expected density, speed, and acceleration - deceleration labels of the i - th sample are respectively represented by v i and y i ; ω is the proportion of accelerating samples, used to weight the loss function, and satisfies:

[0164]

[0165] where, #{y i |y i = 0} represents the number of accelerating samples.

[0166] The above describes the present invention and its implementation manners, and this description is not restrictive. If those of ordinary skill in the art are inspired by it and design similar embodiments to this technical solution without creative work without departing from the purpose of the present invention, they shall fall within the protection scope of the present invention.

Claims

1. A steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow, characterized in that: It includes the following steps: S1. Obtain the trajectory data of the research area; S2. Estimate the macroscopic traffic flow characteristic field according to the trajectory data; S3. Construct the NLKV samples from the macroscopic traffic flow characteristic field; S4. Calibrate the parameters of the fundamental diagram model through the NLKV samples.

2. The steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow according to claim 1, wherein The specific process of S1 is as follows: The vehicle trajectory data of the research area can be obtained through means such as drone videos, lidar point clouds, and in-vehicle GPS; the trajectory data after corresponding technical processing includes the position information x(n, t) of each observed vehicle n at every 0.1-second time interval on a road section of length X in the research area within the observation time T, satisfying 0 ≤ x ≤ X, 0 ≤ t ≤ T, t - (t - 1) = 0.1, n ∈ {1, 2,..., N}, where N is the total number of vehicles observed in the research area within T; a set of value cases is X = 2000m, T = 3600s.

3. The steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow according to claim 1, wherein The specific process of S2 is as follows: S21. Obtain the estimation interval corresponding to each group of characteristics in the macroscopic traffic flow characteristic field according to the step size of the spatio-temporal sliding window and the range of the spatio-temporal sub-domain Assume that the time step of the spatio-temporal sliding window is t s , and the space step is x s , the time span of the spatio-temporal subdomain is Δt, the space span is Δx, t s <Δt, x s <Δx; the smaller the step size of the spatio-temporal sliding window, the finer the granularity of the macroscopic traffic flow characteristic field, but at the same time more estimation operations need to be performed. The step size selection can be determined according to actual requirements and computing power; in order to improve the accuracy of state estimation, the spatio-temporal subdomain needs to be large enough microscopically and small enough macroscopically. The recommended value range of the time span is 20s to 60s, and the value range of the space span is 100m to 300m; a set of value cases is t s = 2s, x s = 3m, Δt = 50s, Δx = 300m; S211. Determine the spatio-temporal dimension N of the spatio-temporal feature field of the macroscopic traffic flow in the selected spatio-temporal sliding window x and N t ; S2111. Determine the spatial dimension N of the macroscopic traffic flow characteristic field in the research area x From the spatial range X of the research area, the spatial span Δx of the spatio-temporal subdomain, and the spatial step x of the spatio-temporal sliding window s , the spatial dimension N of the macroscopic traffic flow characteristic field x can be calculated by Equation (1); Among them, is the floor symbol; under the value setting of the case, S2112. Determine the time dimension N of the macroscopic traffic flow characteristic field in the research area t From the time range T of the research area, the time span Δt of the spatio-temporal sub-domain, and the spatial step t of the spatio-temporal sliding window s , the spatial dimension N of the macroscopic traffic flow characteristic field t can be calculated by Equation (2); Among them, is the floor function symbol; under the value setting of the case, S212. Determine the spatio-temporal range of the trajectories corresponding to each group of characteristics in the macroscopic traffic flow characteristic field of the research area; S2121. Determine the upper and lower limits of the trajectory time range corresponding to each time point Let \(i\) represent each time point in the characteristic field, where \(0 \lt i \leq N\), and \(i\) is an integer; for each \(i\), the lower time limit \(t_{(i)}\) and the upper time limit \(t^{(i)}\) corresponding to this point are calculated by equations (3) and (4). t , where \(i\) is an integer; for each \(i\), the lower time limit \(t_{(i)}\) corresponding to this point is calculated by equations (3) and (4). dw (i) and the upper time limit \(t^{(i)}\) up (i); t dw (i) = (i - 1)t s , #(3) t up (i) = (i - 1)t s + Δt, #(4) Under the value setting of the case, the minimum value of i is 1 and the maximum value is N t = 1775, corresponding to t dw (1) = 0, t up (1) = 50, t dw (1775) = (1775 - 1) × 20 = 3548, t up (1775) = (1775 - 1) × 2 + 50 = 3598; S2122. Determine the upper and lower limits of the trajectory space range corresponding to each space point Let \(j\) represent each time point in the characteristic field, where \(0 < j\leq N\), and \(j\) is an integer. For each \(j\), calculate the corresponding spatial lower limit \(x^{(j)}\) and spatial upper limit \(x^{(j)}\) according to equations (5) and (6). x , where \(j\) is an integer; for each \(j\), calculate the corresponding spatial lower limit \(x^{(j)}\) and spatial upper limit \(x^{(j)}\) according to equations (5) and (6). dw (j) and spatial upper limit \(x\) up (j); x dw (j) = (j - 1)x s , #(5) x up (j) = (j - 1)x s + Δx.#(6) Under the value setting of the case, the minimum value of j is 1 and the maximum value is N x = 566, corresponding to x dw (1) = 0, x up (1) = 300, x dw (566) = (566 - 1) × 3 = 1695, x up (566) = (566 - 1) × 3 + 300 = 1995; S22. Estimate the traffic flow characteristic parameters in the macroscopic traffic flow characteristic field; S221. Estimate the macroscopic traffic flow characteristic parameters at a single spatio-temporal point S2211. Extract the trajectory data corresponding to the point According to the lower time limit \(t\) corresponding to the spatio-temporal point \((i, j)\) dw (i), the upper time limit \(t\) up (i), the lower space limit \(x\) dw (j) and the upper space limit \(x\) up (j), extract the trajectory data \(x\) within the corresponding spatio-temporal range i (n, \(t\) j ), satisfying \(t\) dw (i) ≤ \(t\) i ≤ \(t\) up (i), \(x\) dw (j) ≤ \(x\) j ≤ \(x\) up (j); S2212. Count the total number of vehicles, total driving distance, and total driving time of the vehicle trajectories corresponding to the point; Total number of vehicles N i，j is the trajectory data x i (n, t j ) is the number of non-repeating n For each vehicle n, use to represent the trajectory of the vehicle within the point-time space range. The driving distance and driving time of vehicle n are calculated by equations (7) and (8); The total driving distance is The total driving time is It is the sum of the driving distances and driving times corresponding to all vehicles; S2213. Estimate the density, average speed, and acceleration corresponding to the point; Estimate the density k(i, j), average speed v(i, j), and acceleration a(i, j) corresponding to the spatio-temporal point (i, j) by formulas (9)-(11): Among them, Under the case value setting, ΔxΔt = 300 × 50 = 15000; S222. Estimate the macroscopic traffic flow characteristic field; Traverse each spatio-temporal point, estimate its corresponding density, average speed, and acceleration; sort the respective density, speed, and acceleration by spatio-temporal points to obtain the macroscopic traffic flow characteristic field, including the density field speed field and acceleration field satisfying K(i, j) = k(i, j), V(i, j) = v(i, j), A(i, j) = a(i, j).

4. A steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow according to claim 1, characterized in that The specific process of S3 is as follows: S31. Construct the acceleration / deceleration labels of the samples from the acceleration field Determine its acceleration / deceleration label y(i, j) by formula (12) according to the acceleration value corresponding to each spatio-temporal point: S32. Estimate the expected density of the samples from the traffic flow characteristic field Estimate the expected density k of each space-time point according to the current speed and downstream density of each space-time point by Equation (13). a (i, j): where t m is the driver's operation reaction time. Under the value setting of the case, t m = 12 s; S33. Construct the NLKV samples The NLKV samples of the spatio-temporal sub-domain (i, j) are {k a (i, j), V(i, j), y(i, j)}; By traversing all spatio-temporal sub-domains, all NLKV samples of the study area can be obtained.

5. A steady-state fundamental diagram estimation method based on the acceleration and deceleration characteristics of traffic flow according to claim 1, characterized in that, The specific process of S1 is as follows: S41. Select the speed-density fundamental diagram model Select an appropriate speed-density fundamental diagram model according to the traffic characteristics and research requirements of the research scenario where θ is the parameter of the fundamental diagram model; one selection case is the Franklin-Newell model, and its expression is: where \(v_0\), \(\lambda\) and \(k\) jam are the parameters to be calibrated for the Franklin - Newell model; S42. Calibrate the parameters of the fundamental diagram model Construct an improved cross-entropy loss function as in formula (15), take minimizing the loss value as the optimization objective, and solve the parameters θ of the fundamental diagram model through numerical iteration methods (such as gradient descent algorithm, Adam algorithm); Where m is the total number of NLKV samples, and the expected density, velocity, and acceleration / deceleration labels of the i-th sample are represented by v i and y i respectively; ω is the proportion of acceleration samples used to weight the loss function, satisfying: Among them, #{y i |y i = 0} represents the number of acceleration samples.

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