Calibration method for estimating parameters of a stochastic microscopic traffic simulation model

Abstract

The present invention discloses a calibration method for estimating parameters of a stochastic microscopic traffic simulation model. First, the number of repetitions N is determined for different models and data sets; the calibration range of the parameters is determined, and the calibration range of the parameters is consistent with the physical meaning of the parameters; parameters are extracted and iterated within the calibration range of the parameters, and the speed and spacing information of the simulation output by the model is used; multiple rounds of simulations are repeated, and the total error is calculated for the speed and spacing information output by each simulation and the actual experimental data, and the minimum value of the total error of N simulations is taken as the objective function; the speed and spacing are respectively selected as performance metric indicators, and an optimization algorithm is used to solve for the optimal parameters; the performance of the two sets of parameters is verified, the error on the data set is calculated, and the smaller one is selected as the calibration result. The present invention realizes the calibration of parameters by establishing an optimization framework capable of calibrating the parameters of the stochastic model.

Description

Technical Field

[0001] The present invention relates to the technical field of road traffic management, and particularly to a calibration method for estimating parameters of a stochastic microscopic traffic simulation model. Background Art

[0002] Traffic simulation technology, which integrates interdisciplinary fields such as traffic engineering, computer science, software engineering, and systems science, is very important in the construction of intelligent transportation systems and the process of transportation planning and decision-making. Traffic simulation models are the cornerstone of traffic simulation technology. Only by establishing a traffic simulation model that correctly depicts the generation and evolution of traffic congestion can traffic conditions be analyzed through traffic simulation of actual roads and road networks, and traffic management measures that can effectively guide traffic management departments be proposed.

[0003] Before applying a traffic simulation model to urban traffic flow simulation, it is necessary to calibrate the parameters of the model, that is, to find one or several sets of parameters that best match the actual traffic conditions, and finally use the calibrated parameters to simulate and predict the evolution process of urban traffic flow. Therefore, the calibration work is the bridge connecting the simulation model and traffic simulation applications.

[0004] Traffic simulation models are further divided into microscopic models, mesoscopic models, and macroscopic models. Among them, microscopic models have been widely used in traffic simulation because they consider refined driving behaviors. Specifically, a microscopic model refers to modeling the individual driving behaviors (car-following and lane-changing) of drivers, that is, based on the description of driving behaviors, driven by individual rules, to explore the complex emergence laws of group behaviors, namely traffic flow. The most widely used microscopic car-following model is the IDM model, which has five parameters with clear physical meanings. It has a simple structure but can reproduce some relatively complex traffic phenomena. This model is a deterministic model, that is, given parameters and environmental inputs, its output is determined. A series of existing studies have shown that the simulation results of such deterministic models do not match some actual traffic flow phenomena. For example, they cannot correctly simulate traffic oscillations, that is, stop-and-go waves. In recent years, research has proven that introducing randomness is the key factor in reproducing traffic oscillation laws. Based on this, many stochastic models have been proposed, but the uncertainty between the input and output of stochastic models has brought new difficulties to the parameter calibration work.

[0005] Specifically, the model parameter estimation part is to find a set of parameters that best match the macro and micro phenomena in reality by solving an optimization problem. Based on this set of parameters, the prediction performance of the model is evaluated, and at the same time, the calibrated parameters are applied to specific traffic planning or traffic control problems to provide model outputs. Therefore, unreasonable calibration parameters and calibration methods not only cannot correctly use the model to describe the actual characteristics of traffic flow, but also have a negative impact on traffic planning or traffic control.

[0006] In the existing research on the calibration of traffic simulation models, most are focused on the calibration methods for deterministic models. There is no random term in deterministic models, which leads to the situation that their calibration methods may no longer be applicable to the calibration of stochastic models. In recent years, in the practice of calibrating stochastic models, two types of calibration methods have emerged. The first one is to change the original objective function from the total error of a single simulation to the mean of the total errors of multiple simulations. However, the idea of this calibration method does not correctly consider the epistemic uncertainty error and the stochastic uncertainty error and their relationship. Another type of calibration method is to continue with the maximum likelihood estimation method for calibrating deterministic models, but it is unable to evaluate the reliability of the obtained parameter set.

[0007] In summary, the parameter calibration methods and frameworks in the existing technologies are all for deterministic models and cannot effectively handle the uncertainty of the output of stochastic traffic simulation models, which will hinder the popularization and engineering application of stochastic traffic simulation models. Summary of the Invention

[0008] The present invention aims to provide a calibration method for estimating the parameters of a stochastic microscopic traffic simulation model based on the error division of epistemic uncertainty and stochastic uncertainty, and to establish an effective calibration method for stochastic traffic simulation models based on the error division of epistemic uncertainty and stochastic uncertainty.

[0009] The technical solution adopted to achieve the object of the present invention is as follows:

[0010] A calibration method for estimating the parameters of a stochastic microscopic traffic simulation model, comprising the following steps:

[0011] S1. Determine the number of repetitions N for different models and data sets;

[0012] S2. Determine the calibration range of the parameters, and the calibration range of the parameters is consistent with the physical meaning of the parameters;

[0013] S3. Extract parameters within the calibration range of the parameters and iterate, and use the speed and spacing information output by the model for simulation;

[0014] S4. Repeat multiple rounds of simulations, calculate the total error for the speed and spacing information output by each simulation and the actual experimental data, and take the minimum value of the total errors of N simulations as the objective function;

[0015] S5. Select speed and spacing as performance measurement indicators respectively, and use an optimization algorithm to solve with the goal of minimizing the nested optimization calibration model to obtain the optimal parameters; this nested optimization calibration model is based on the minimum error of multiple rounds of simulations as the optimization goal, and uses model parameters and random seeds as decision variables; the specific mathematical representation of the nested optimization calibration model is as follows:

[0016] minz

[0017]

[0018]

[0019] subject to: β min ≤β≤β max

[0020] wherein, GoF is the error function, MoP i obs , MoP i sim are the performance metric indicators in the actual data and the simulation data respectively, selected as the spacing or the speed, F(β) is the traffic simulation model, β is the parameter, β min and β max are the upper and lower bounds of the parameter, N is the number of experiments;

[0021] S6. Verify the performance of the two sets of parameters calibrated using the speed and the spacing, calculate the error of the two sets of parameters on the data set, and select the smaller set of parameters as the calibration result.

[0022] Based on the error theory and optimization technology, for the calibration of the stochastic model, considering two types of uncertainties, this invention constructs an objective function that can effectively identify the optimal parameters, and establishes an optimization framework that can calibrate the parameters of the stochastic model, thereby realizing the calibration of the parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is a flowchart of the calibration method for estimating the parameters of the stochastic microscopic traffic simulation model of this invention.

[0024] Figure 2 is a schematic diagram of the frequency distribution of MRMin and the result of fitting it with the extreme value distribution.

[0025] Figure 3 is a schematic diagram of the relationship between the number of repetitions and the stability (standard deviation) of the objective function.

[0026] Figure 4 is a diagram of the relationship of the vehicle spacing of the experimental trajectory.

[0027] Figure 5 is a schematic diagram of the vehicle speed of the experimental trajectory.

[0028] Figure 6 is a box plot of 9 sets of parameters calibrated by three calibration methods using 9 experimental trajectories (from left to right are the results calibrated by the MRMEean, MLE, and MRMin methods respectively).

[0029] Figure 7It is a box plot of the random parameter distribution among the nine sets of parameters calibrated by nine synthetic trajectories using three calibration methods (from left to right are the results calibrated by the MRMEean, MLE, and MRMin methods).

[0030] Figure 8a1 、 Figure 8a2 、 Figure 8b1 、 Figure 8b2 、 Figure 8c1 、 Figure 8c2 They are respectively the contour plots of the objective function at different parameter values (Global Optimum is the optimal solution in the current contour plot, and Preset Values are the preset parameters of the synthetic trajectory).

[0031] Figure 9a 、 Figure 9b 、 Figure 9c They are respectively the schematic diagrams of the trajectory prediction intervals simulated by the parameters calibrated by the three methods of MRMEean, MLE, and MRMin (where the solid line is the experimental trajectory and the gray band is the simulation prediction interval). Specific implementation manners

[0032] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0033] The present invention aims to construct an objective function that can effectively identify the optimal parameters and establish an optimization framework that can calibrate the parameters of the stochastic model for the calibration of the stochastic model based on the error theory and optimization technology, considering two types of uncertainties.

[0034] As Figure 1 shown, the calibration method for estimating the parameters of the stochastic microscopic traffic simulation model in the embodiment of the present invention includes the steps:[[]]

[0035] Step S1. Determine the number of repetitions N for different models and data sets.

[0036] Since the number of repetitions will affect the stability of the objective function, theoretically speaking, the larger the number of repetitions, the more stable the objective function. The minimum error is essentially a type of extreme value. For the simulation model and data set applied in the present invention, through simulation tests, it is obtained that the objective function follows an extreme value distribution, as Figure 3 shown. And by calculating the standard deviation of the objective function at different numbers of repetitions, it can be seen that when the number of repetitions N rises from 0 to about 300, the stability of the objective function is greatly improved. When N is greater than 300, the improvement in stability is very limited and the calculation efficiency will be significantly reduced.

[0037] Step S2. Determine the calibration range of the parameters so that the calibration range of the parameters is consistent with the physical meaning of the parameters, and avoid the parameter solutions obtained due to overly large or small solution spaces not conforming to reality;

[0038] Step S3. Extract parameters within the calibration range of the parameters and iterate, and use a predetermined model to output simulated speed and spacing information;

[0039] Step S4. Repeat the simulation for multiple rounds, calculate the total error between the speed and spacing output by each simulation and the actual experimental data, and take the minimum value of the total error of N simulations as the objective function;

[0040] Step S5. Select the speed and spacing as performance metric indicators respectively, aim at minimizing the nested optimization calibration model, and use an optimization algorithm to solve to obtain the optimal parameters; the nested optimization calibration model is based on the minimum error of multiple rounds of simulations as the optimization objective, with the model parameters and random seeds as decision variables. The specific mathematical representation of the nested optimization calibration model is as follows:

[0041] min z

[0042]

[0043]

[0044] subject to:β min ≤β≤β max (1)

[0045] where GoF is the error function, MoP is the performance metric indicator, generally the vehicle spacing or speed, and β is the parameter.

[0046] Step S6. Verify the performance of the two sets of parameters calibrated using the speed and spacing, calculate the error of the two sets of parameters on the dataset, and select the smaller set of parameters as the calibration result.

[0047] Figure 3 and Figure 4 are the experimental datasets used in the present invention to test the calibration method.

[0048] The experiment was conducted on a straight road approximately 1.5 kilometers long at a highway traffic test site, involving an autonomous vehicle (AV) and a human-driven vehicle (HV). The experiment was carried out 9 times under the same conditions. Before the experiment started, in each run, the AV moved as the leading vehicle, using the same control parameters and following the same designed trajectory. The human-driven vehicle (HV) was driven by the same driver following the autonomous vehicle (AV), so the driving environment of the human-driven vehicle (HV) was almost the same. The trajectories of both vehicles were collected by high-precision GPS. Therefore, the dataset used in this application is the time and spatial position data of nine trajectories. The calibration method proposed in the present invention is not specific to the dataset, and this dataset is only used to test the effects of different calibration methods.

[0049] In step S3, the present invention selects the stochastic simulation model 2D-IDM for testing the calibration method. 2D-IDM inherits the excellent characteristics of IDM, and each parameter has a clear physical meaning. The random term of this stochastic simulation model has a simple form. By adopting the method of time-varying time headway, it can capture the randomness of driving behavior and describe the dynamic relationship between speed and spacing. Existing research has proved that 2D-IDM can simulate traffic oscillations consistent with the actual situation. Its formula is as follows:

[0050]

[0051]

[0052]

[0053] In the formula, a n (t) is the acceleration of vehicle n at time t, n is the vehicle number, a is the maximum acceleration, b is the maximum deceleration, v n (t) is the speed of vehicle n at time t, v max is the maximum vehicle speed, s * (t) is the ideal spacing, Δx n (t) is the actual spacing between vehicle n and the vehicle in front at time t, s 0 is the minimum vehicle spacing, T(t) is the time headway at time t, Δv n (t) is the speed difference between the front and rear vehicles at time t, Δt is the time interval, T 1 and T 2 are the minimum and maximum time intervals respectively, r(t) and r 1 (t) are two random numbers uniformly distributed between [0,1], and p is the random probability.

[0054] The algorithm used in the present invention is the genetic algorithm, which is a commonly used heuristic algorithm for solving unconstrained and constrained nonlinear optimization problems based on imitating the natural selection process of biological evolution. This algorithm repeatedly modifies the population composed of individual solutions. At each step, individuals are randomly selected from the current population and used as parents to generate the next generation of offspring. The GA function in Matlab is directly used to solve the calibration problem.

[0055] The error function form used in the present invention is RMSE, that is, the root mean square error. Compared with the root mean square error of the percentage, RMSE can well handle the situation where the data points are close to 0. That is, if the speed of the actual experimental trajectory is close to, the denominator of the root mean square error of the percentage will be close to 0, which leads to an overly large weight of the error at this data point, resulting in inaccurate results during overall optimization. The form of RMSE is as follows:

[0056]

[0057] where is the simulation spacing at the k-th time step in the i-th repeated simulation, is the actual spacing data at the k-th time step in the experimental dataset.

[0058] To prove the effectiveness of the present invention, it is tested through two types of trajectories, namely the experimental trajectory and the synthetic trajectory. The calibration range of the set parameters is shown in Table 1. The number of simulation repetitions is 300 times.

[0059] Table 1. Calibration range of parameters

[0060]

[0061] First, the experimental trajectory is used for testing. The comparison between the two calibration methods and the new calibration method is as Figure 6 shown. It can be seen that the MRMean method indeed causes the stochastic model to degenerate into a deterministic model because the calibrated stochastic parameter ΔT approaches 0, that is, it is no longer random. The parameter p calibrated by the MLE method has a wide spread. The data in this application are obtained from the experiments of the same driver in the same driving environment. Ideally, the values of the nine sets of calibrated parameters should be relatively concentrated. Therefore, there are doubts about the calibration results of the parameters by the MLE method.

[0062] Table 2. Preset values and calibration ranges of synthetic trajectory parameters

[0063]

[0064] Compared with the other two types of previous calibration methods, the present application can effectively calibrate the random parameters, which will be illustrated by the calibration of synthetic trajectories. Thirty virtual trajectories were generated using a set of parameters in Table 2 and 2D-IDM. These virtual trajectories were generated by the model rather than collected in reality. Therefore, by using these virtual trajectories for calibration, the difference between the values of the calibrated parameters and the preset set of parameter values can be evaluated. If the calibration method is effective, the calibrated parameters should be close to the preset parameters. For the convenience of solution, the present application only calibrates the random parameters and focuses on the effects of the three methods in calibrating the random-related parameters.

[0065] Figure 7 The calibration results of the synthetic trajectories are shown. The calibration of 3 random parameters by MRMean led to the degradation of the random CF model, similar to the results of Figure 6 For MLE, the calibration effect of the random parameter p is very good. However, there are still two unstable outliers. The ΔT calibrated by MLE has a large deviation from the true value, indicating that MLE is inaccurate. In contrast, MRMin has a relatively good calibration effect on all three parameters.

[0066] To further illustrate the nature and effectiveness of the objective function, the contour plots of the objective function during the calibration process with different parameter values are drawn. For MRMin, it is found that there is a global minimum in this heat map, and the parameters that take this value are almost equal to the preset parameters, as shown in Figure 8a1 and Figure 8a2 For MRMean, no matter how many times the contour plot is resampled, it always reaches the global optimum when p takes the upper boundary, so the optimal solution it solves deviates significantly from the preset value. For MLE, its objective function is very unstable and the shape of the contour plot is irregular. Therefore, a stable global optimum cannot be found near the preset value, as shown in Figure 8c1 and Figure 8c2 These all indicate that only by using the objective function of MRMin can the global optimal solution be identified near the preset parameters.

[0067] Figure 9a 、 Figure 9b 、 Figure 9c respectively show the trajectory prediction intervals simulated by the parameters calibrated by the three methods. Figure 9a is the MRMean method, Figure 9b is the MLE method, Figure 9c is the MRMin method. The random parameters calibrated by the calibration method of the present application can effectively predict 9 experimental trajectories, such as Figure 9a 、 Figure 9b 、 Figure 9cAs shown, the simulation prediction interval of the parameters calibrated by MRMean is very narrow, indicating that the randomness of the parameters calibrated by it is very small, resulting in the degradation of the randomness model into a deterministic model and poor prediction effect. The prediction interval simulated by the parameters calibrated by MRMin can almost cover 9 trajectories, while MLE cannot, which demonstrates the superiority of the MRMin method.

[0068] The foregoing has shown and described the basic principles, main features and advantages of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above-described exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms.

[0069] Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced by the present invention.

[0070] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. Calibration methods for estimating parameters of stochastic microscopic traffic simulation models, It is characterized in that The following steps are involved: S1. Determine the number of repetitions N for different models and data sets; S2. Determine the calibration range of the parameter, which is consistent with the physical meaning of the parameter; S3. extracting parameters within the calibration range of the parameters and iterating, and outputting the simulated speed and spacing information using the preselected model; S4. Repeat multiple rounds of simulation, calculate the total error between the speed and spacing information output by each simulation and the actual experimental data, and take the minimum value of the total error of N simulations as the objective function; S5. Select speed and spacing as performance metrics respectively, take minimizing the nested optimization calibration model as the goal, use the optimization algorithm to solve and obtain the optimal parameters; the nested optimization calibration model is based on the minimum error of multiple rounds of simulation as the optimization goal, and takes model parameters and random seeds as decision variables, which is expressed as follows: min z MoP i obs = F(β) subject to: β min ≤ β ≤ β max where GoF is the error function, MoP i obs , MoP i sim are the performance metrics in the actual data and the simulation data, respectively, selected as the spacing or the speed, F(β) is the traffic simulation model, β is a parameter, β min and β max are the upper and lower bounds of the parameter, and N is the number of experiments; S6. Verify the performance of the two sets of parameters calibrated by speed and spacing, calculate the errors of the two sets of parameters on the data set, and select the smaller set of parameters as the calibration result.

2. The calibration method for estimating parameters of a stochastic microscopic traffic simulation model according to claim 1, It is characterized in that In step S3, the random simulation model 2D-IDM is used to output simulated speed and spacing information.

3. The calibration method for estimating parameters of a stochastic microscopic traffic simulation model according to claim 1, It is characterized in that In step S5, the optimization algorithm is a genetic algorithm, and the GA function in matlab is directly used to solve the calibration problem.

4. The calibration method for estimating parameters of a stochastic microscopic traffic simulation model according to claim 1, It is characterized in that In step S5, the GoF error function uses the root mean square error RMSE.

5. The calibration method for estimating parameters of a stochastic microscopic traffic simulation model according to claim 4, It is characterized in that The root mean square error RMSE is in the following form: wherein, is the simulation spacing at the k-th time step in the i-th repeated simulation, is the actual spacing data at the k-th time step in the experimental dataset, and K represents the number of time steps.

6. The calibration method for estimating parameters of a stochastic microscopic traffic simulation model according to claim 2, It is characterized in that In step S3, the random simulation model 2D-IDM is used to simulate the traffic oscillation consistent with the actual situation, and the formula is as follows: where a n (t) is the acceleration of vehicle n at time t, n is the vehicle number, a is the maximum acceleration, b is the maximum deceleration, v n (t) is the speed of vehicle n at time t, v max is the maximum vehicle speed, s * (t) is the ideal spacing, Δx n (t) is the actual spacing between vehicle n and the preceding vehicle at time t, s 0 is the minimum vehicle spacing, T(t) is the time headway at time t, Δv n (t) is the speed difference between the front and rear vehicles at time t, Δt is the time interval, T 1 and T 2 are the minimum and maximum time intervals respectively, r(t) and r 1 (t) are two random numbers uniformly distributed in the interval [0, 1], and p is the random probability.

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