Traffic simulation robust calibration method and system considering heterovariance noise

Abstract

The invention provides a traffic simulation robust calibration method and system considering heterovariance noise, which considers heterovariance of traffic simulation, constructs a Gaussian process agent model, adopts a Bayesian optimization algorithm for processing, determines a sampling point of a next simulation parameter, and determines simulation repetition times of the sampling point under the next simulation parameter. According to the method, the optimal sampling point is determined through iterative calculation according to the collection function improved according to the expectation and the expectation and variance distribution under the target function of the next simulation parameter, and experimental results show that the robust Bayesian optimization algorithm considering the heterovariance can well recognize the robust solution under the low calculation cost.

Description

Technical Field

[0001] The present invention belongs to the technical field related to simulation optimization, and in particular relates to a robust calibration method and system for traffic simulation considering heteroscedastic noise. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] The increasing complexity of traffic systems, including the high dimensionality of traffic networks, the diversity of traffic control schemes, and the complexity of traffic flow patterns, requires high-precision traffic simulation to simulate dynamic systems. Therefore, microscopic traffic simulation has become an important tool over the years. In order to make the simulation results closer to reality, it is necessary to determine appropriate simulation parameters based on actual data. This process is the calibration of simulation model parameters. For simplicity, this problem is called parameter calibration problem. In essence, this problem is a simulation-based optimization problem, which attempts to adjust simulation parameters to match simulation outputs and corresponding field measurements as closely as possible.

[0004] For the calibration problem of traffic simulation, traditional methods usually assume that the simulation random level is constant everywhere, and rarely consider its variance when calibrating the simulation, which makes the calibrated simulation less robust in practical applications. Summary of the invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a robust calibration method and system for traffic simulation considering heteroscedastic noise, which takes into account the heteroscedasticity of traffic simulation, constructs a Gaussian process proxy model, and uses a Bayesian optimization algorithm for processing, which can well identify robust solutions.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a robust calibration method for traffic simulation considering heteroscedastic noise, comprising:

[0008] Determine the traffic simulation model to be used and the number of times the simulation of the sample points is repeated under the simulation parameters;

[0009] The robust calibration problem of traffic simulation is expressed as a simulation-based robust optimization problem. A Gaussian process proxy model considering heteroscedastic noise is constructed. The sampling points of the next simulation parameters are determined based on the Bayesian optimization algorithm. The number of simulation repetitions of the sample points under the next simulation parameters, as well as the expectation and variance distribution under the objective function of the next simulation parameters are determined. The sampling points of the optimal simulation parameters are determined by iterative calculation based on the expected improved acquisition function.

[0010] In a second aspect, the present invention provides a robust calibration system for traffic simulation considering heteroscedastic noise, comprising:

[0011] A determination module is configured to: determine the traffic simulation model to be adopted and the number of times the simulation of the sample point is repeated under the simulation parameters;

[0012] The optimization module is configured to: express the traffic simulation robust calibration problem as a simulation-based robust optimization problem, construct a Gaussian process proxy model considering heteroscedastic noise, determine the sampling point of the next simulation parameter based on the Bayesian optimization algorithm, and determine the number of simulation repetitions of the sample point under the next simulation parameter, as well as the expectation and variance distribution under the objective function of the next simulation parameter, and iteratively calculate the sampling point of the optimal simulation parameter according to the expected improved acquisition function.

[0013] In a third aspect, the present invention provides an electronic device comprising a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in the first aspect is performed.

[0014] In a fourth aspect, the present invention provides a computer-readable storage medium for storing computer instructions, wherein when the computer instructions are executed by a processor, the method described in the first aspect is performed.

[0015] One or more of the above technical solutions have the following beneficial effects:

[0016] In the present invention, the heteroscedasticity of traffic simulation is taken into consideration, a Gaussian process proxy model is constructed, and a Bayesian optimization algorithm is used for processing to determine the sampling point of the next simulation parameter, the number of simulation repetitions of the sample point under the next simulation parameter, and the expectation and variance distribution under the objective function of the next simulation parameter. The optimal sampling point is determined by iterative calculation based on the expected improved acquisition function. Experimental results show that at a lower computational cost, the robust Bayesian optimization algorithm of the present invention that takes heteroscedasticity into consideration can well identify robust solutions.

[0017] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0019] Figure 1 A schematic flow chart of a robust calibration method for traffic simulation considering heteroscedastic noise is provided for the first embodiment of the present invention;

[0020] FIG2( a ) is a main road selected as a research area in the first embodiment of the present invention;

[0021] FIG2( b ) is a simulation model of a research area constructed using the open source microscopic road traffic simulation software package Simulation of Urban Mobility (SUMO) in Example 1 of the present invention;

[0022] Figure 3 This is a performance comparison chart of different strategies in Example 1 of the present invention. DETAILED DESCRIPTION

[0023] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0024] It should be noted that the terms used herein are for describing specific embodiments only and are not intended to be limiting of exemplary embodiments according to the present invention.

[0025] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0026] Embodiment 1

[0027] This embodiment discloses a robust calibration method for traffic simulation considering heteroscedastic noise, including:

[0028] Determine the traffic simulation model to be used and the number of times the simulation of the sample points is repeated under the simulation parameters;

[0029] The robust calibration problem of traffic simulation is expressed as a simulation-based robust optimization problem. A Gaussian process proxy model considering heteroscedastic noise is constructed. The sampling points of the next simulation parameters are determined based on the Bayesian optimization algorithm. The number of simulation repetitions of the sample points under the next simulation parameters, as well as the expectation and variance distribution under the objective function of the next simulation parameters are determined. The sampling points of the optimal simulation parameters are determined by iterative calculation based on the expected improved acquisition function.

[0030] This embodiment first considers the heteroscedasticity of traffic simulation and formulates the parameter calibration problem as a robust optimization problem based on simulation. In order to solve this robust optimization problem, a robust Bayesian optimization method considering heteroscedasticity is proposed. The algorithm is based on Bayesian optimization, can handle heteroscedastic noise, and has robust identification capabilities. Specifically, considering the existence of heteroscedastic noise, the formulation of the proxy model, the sampling strategy of new points, and the evaluation of samples are systematically designed.

[0031] This embodiment uses real-world vehicle trajectories as actual measurements to calibrate traffic simulation. The trajectory data comes from an open source dataset called pNEUMA. pNEUMA contains traffic flow data collected by drones over multiple consecutive days in the central business district of Athens. A main road with a length of 450m and three intersections was selected as the study area, as shown in Figure 2(a). There is mixed traffic flow on the road, with a total of 6 types of vehicles, including: cars, buses, taxis, motorcycles, heavy vehicles and medium-sized vehicles. A simulation model of the study area was constructed using the open source microscopic road traffic simulation software package Simulation of Urban Mobility (SUMO), as shown in Figure 2(b).

[0032] Combine the following Figure 1 A traffic simulation robust calibration method considering heteroscedastic noise proposed in this embodiment is described in detail, specifically including:

[0033] Step 1: Calculate the number of simulation repetitions of the sample point under each simulation parameter;

[0034] Solving the robust calibration problem of traffic simulation considering heteroscedasticity can be mathematically expressed as a simulation-based robust optimization problem:

[0035]

[0036] Constrained by:

[0037]

[0038] θ l ≤θ≤θ m (1)

[0040] Where θ represents the simulation parameter, f(θ) represents the difference between the simulation output and the actual measured value, E[·] represents the expectation, Var[·] represents the variance, represents the threshold of simulation variance; θ l With θ m They represent the lower and upper bounds of the simulation parameter values ​​respectively.

[0041] The goal of the optimization problem is to minimize the expectation of the difference between the simulation output and the actual measurement. The constraints define the constraints on the randomness of the simulation, as well as an interval constraint. Solving the robust calibration problem of traffic simulation considering heteroscedasticity is to solve this optimization problem. Due to the randomness of traffic simulation, multiple simulation repetitions are generally performed for each sample point to obtain the effective expectation E[f(θ)] and variance Var[f(θ)]. Since simulation computing resources are usually limited, it is necessary to calculate the number of simulation repetitions for each simulation parameter sample point.

[0042] Step 11: Perform initial simulation when setting simulation parameters θ.

[0043] When the simulation parameter of the sampling point is set to θ, first m init The simulation is repeated.

[0044] Step 12: Based on the current number of simulations, estimate the distribution of the expected E[f(θ)] and variance Var[f(θ)] corresponding to the set simulation parameter θ. For specific methods, see step 2.

[0045] Check if the conditions are met That is, whether one of the constraints in formula (1) is satisfied. If satisfied, proceed to the next step. If not satisfied, no longer simulate the simulation parameter, obtain the expected E[f(θ)] and variance Var[f(θ)] corresponding to the simulation parameter, and complete the sampling of the sampling point.

[0046] Step 13: Check if the following conditions are met:

[0047]

[0048] Among them, f * represents the best result obtained in the previous sampling, is the predefined significance level. If none of the above conditions are met, proceed to the next step. If any of the above conditions are met, the simulation parameter is no longer simulated, and the expected E[f(θ)] and variance Var[f(θ)] corresponding to the simulation parameter are obtained, completing the sampling of the sampling point.

[0049] This step indicates that if the probability that the current sampling point is better than the previous best sampling point is greater than the threshold, the simulation of the sampling point is stopped; if the probability that the current sampling point is worse than the previous best sampling point is greater than the threshold, the simulation of the sampling point is also stopped; if neither is the case, it means that it is impossible to determine which is better between the current sampling point and the previous best sampling point, and the simulation of the sampling point is repeated.

[0050] Step 14: Execute m for the sampling point with simulation parameter θ add The simulation is repeated. Then, step 13 is executed to check whether the conditions are met and the loop is iterated.

[0051] Step 2: Based on the simulation results of the simulation parameter sample points, estimate the expected and variance distribution of the objective function under the simulation parameters.

[0052] The specific steps include:

[0053] Step 21: When calculating the expectation E[f(θ)], use Bayesian inference to estimate E[f(θ)]:

[0054] p(E[f(θ)]|f (1) ,…,f (m) )∝p(E[f(θ)]p(f (1) ,…,f (m) |E[f(θ)]) (4)

[0056] Among them, f (1) ,……,f (m) represents the evaluation of f(θ) after m simulation repetitions.

[0057] Without losing generality, this embodiment assumes that f(θ)~N(E[f(θ)],Vat[f(θ)], then the posterior distribution of the expected E[f(θ)] is:

[0058]

[0059] in, represents the mean of f;

[0060] Step 22: The formula for estimating the variance Var[f(θ)] is:

[0061]

[0062] Wherein, m is the number of simulations of the simulation parameter θ.

[0063] The following table shows the adaptive simulation repetition scheme obtained by combining step 1 with step 2. The adaptive number of repeated simulations is performed on a single sampling point, and the expected E[f(θ)] and variance Var[f(θ)] corresponding to the simulation parameter θ are obtained.

[0064] Table 1 Adaptive simulation repetition scheme

[0065]

[0066] Step 3: Determine the next simulation parameter sampling point based on the Bayesian optimization method, repeat the above steps for the sampling point, and iterate to find the optimal simulation parameters.

[0067] Since f(·) is non-convex, non-differentiable and has heteroscedastic noise, it is necessary to be able to search effectively in a random manner. Bayesian optimization is a widely used method to solve expensive black box optimization problems. Bayesian optimization can effectively search for solutions with limited computing resources, obtain better optimization results within a small number of steps, and does not require derivative information of the function to be optimized, so it is very suitable for expensive black box parameter tuning problems.

[0068] Bayesian optimization consists of two iterative steps. First, a proxy model is constructed using data from sampling points, that is, an analytical function that estimates the distribution of the original objective function is obtained. Secondly, new points of model improvement are searched and evaluated. Usually, the first step is performed using a Gaussian process. Gauss does not take the functional form of the mapping from input to output. Instead, it places a prior distribution on each possible function and updates the distribution using training data (i.e., sampling points). Therefore, Gauss is able to capture complex and highly nonlinear relationships. The second step is performed by optimizing the acquisition function, which is usually expressed as a trade-off between high expectations and high uncertainty. Bayesian optimization has been widely developed and applied in solving deterministic and random problems with homogeneous noise. In this embodiment, BO is modified for the case of heteroscedasticity. Therefore, for the case of heteroscedasticity, this embodiment makes some modifications to traditional Bayesian optimization and proposes an algorithm for processing heteroscedastic noise and identifying robust solutions.

[0069] Step 31: Construct a Gaussian process surrogate model considering heteroscedastic noise.

[0070] Define (θ, y, r) as the sampling point of Bayesian optimization, where θ is the simulation parameter of the sampling point of Bayesian optimization, and y and r are the estimated values ​​of E[f(θ)] and Var[f(θ)], respectively, which can be obtained from step 2.

[0071] Assuming that n sampling points have been used, let D = {(θ 1 ,y 1 ,r 1 ),…,(θ n ,y n ,r n )}. The Gaussian process assumes that any finite set of points has a joint multivariate Gaussian distribution, namely:

[0072] Y n ~N(μ n ,K n +R) (7)

[0074] Among them, Y n =(y 1 ,…,y n ) T .μ n is the expectation of a multivariate Gaussian distribution, starting with μ n Set to 0. K n is the covariance matrix, And in the Gaussian process, y i and j The covariance of is measured by a kernel function. This embodiment uses the radial basis function kernel function, one of the most widely used kernel functions:

[0075]

[0076] Among them, l is the hyperparameter of the kernel function and can be determined by the user.

[0077] R is a diagonal matrix, and the elements on the main diagonal of R are Among them, m i represents the simulation parameter θ i The number of simulation evaluations, i=1,…,n.

[0078] According to the definition of Gaussian process, the objective function for the unsampled point (θ′, y′) follows the following distribution:

[0079]

[0080] Among them, K * =(Cov(y 1 ,y′),Cov(y 2 ,y′),…,Cov(y n ,y′)) T , K ** = Cov(y′,y′), F n =(y 1 ,…,y n ),μ * represents the mean of the prior distribution of y′, which is generally set to 0. For a given θ′, the posterior distribution of y′ is:

[0081]

[0082] Then the approximation of Var[f(θ)] is introduced. Another Gaussian process is defined as the log function of Var[f(θ)], that is, log(Var[f(θ)])~GP(·,·). Similar to formula (10), given θ', the posterior distribution of log(r′) is:

[0083]

[0084] Among them, R n =(log(r 1 ),...,log(r n )) T .

[0085] Step 32: Given the approximate values ​​of E[f(θ)] and Var[f(θ)], it is necessary to identify the optimal sampling point.

[0086] The acquisition function used in this embodiment is developed based on the expectation to improve the acquisition function, and there are two strategies in total.

[0087] Let y* represents the minimum objective function value so far. The basic idea of ​​​​expected improvement is to sample a new point so that y * -The expected value of y(θ) reaches its maximum value, that is:

[0088] max θ E[y * -y(θ)] (12)

[0089] Where y represents the objective function E[f(θ)] corresponding to the simulation parameters.

[0090] Formula (12) is equivalent to solving the following problem:

[0091]

[0092] Where Φ and φ are the cumulative distribution function and probability density function of the Gaussian distribution, respectively. μ(θ) is the expectation of y(θ)|θ, and σ(θ) is the variance of y(θ)|θ.

[0093] Strategy 1: Strategy 1 takes the expected improvement of the acquisition function as the objective function and uses the surrogate model of log(Var[f(θ)]) as the variance constraint.

[0094] New points are sampled by solving the following optimization problem:

[0095]

[0096] Constrained by:

[0097] τ(θ)≤log(σ c )

[0098] θ l ≤θ≤θ m (15)

[0099] Where τ(θ) is the expectation of the distribution in formula (11).

[0100] Strategy 2: In the parameter calibration problem, the selection of new points is also restricted by the noise level. Therefore, a probability of point stratification based on variance constraint is introduced, using p c (θ) to represent:

[0101]

[0102] Among them, γ(θ) is the variance of the distribution of formula (11). This embodiment adopts p c (θ) is used to modify the objective function of the acquisition function. The formula of the modified acquisition function is:

[0103]

[0104] Constrained by:

[0105] θ l ≤ θ ≤ θ m (17)

[0106] The algorithm performance proposed in this embodiment is as Figure 3 shown. For the two strategies proposed in step 32, when the computational cost is relatively low, the estimated value of the objective function can be reduced by about 35%. In terms of the accuracy of the solution, Strategy 2 is better than Strategy 1. In 6 experiments, the performance of the initial points varies greatly, and the robust Bayesian optimization algorithm considering heteroscedasticity shows robustness to the quality of the initial points.

[0107] To verify the robustness of this solution, the calibrated simulation model was used to reproduce the traffic conditions of another day. Specifically, the 6 simulation models calibrated in the above experiments were adopted. Each simulation model was repeated 5 times, and then the simulation output was compared with the actual measurement results. The experimental results are shown in Table 2. Table 2 shows the robustness of the calibrated simulation model under different scenarios.

[0108] Table 2 Robustness of the solution

[0109]

[0110] The simulation was calibrated using the algorithm of this embodiment. The two strategies in step 32 were tested. 5 initial samples were randomly selected for each method, and the algorithm was terminated after 300 simulation repetitions. The performance of these methods as a function of the simulation repetitions is as Figure 3 shown, where the x-axis shows the total number of simulation repetitions, and the y-axis shows the estimated value of the objective function for the current iteration (i.e., the best point determined by the method so far).

[0111] Embodiment 2

[0112] The purpose of this embodiment is to provide a traffic simulation robust calibration system considering heteroscedastic noise, including:

[0113] A determination module configured to: determine the adopted traffic simulation model and the number of simulation repetitions of the sample points under the simulation parameters;

[0114] An optimization module configured to: construct a Gaussian process surrogate model considering heteroscedastic noise, determine the sampling point of the next simulation parameter based on the Bayesian optimization algorithm, determine the number of simulation repetitions of the sample points under the next simulation parameter, and the expectation and variance distribution under the objective function of the next simulation parameter, and iteratively calculate and determine the best sampling point according to the acquisition function of the expected improvement.

[0115] In more embodiments, there is also provided:

[0116] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in Embodiment 1 is performed. For the sake of brevity, no further description is given here.

[0117] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0118] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0119] A computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the method described in embodiment 1 is completed.

[0120] The method in the first embodiment can be directly embodied as a hardware processor, or a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0121] A computer program product includes a computer program, and when the computer program is executed by a processor, the method described in the first embodiment is implemented.

[0122] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer executable instructions, such as instructions included in a program module, which are executed in a device on a real or virtual processor of the target to perform the process / method as described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In various embodiments, the functions of program modules can be combined or divided between program modules as needed. Machine executable instructions for program modules can be executed in local or distributed devices. In distributed devices, program modules can be located in local and remote storage media.

[0123] The computer program code for implementing the method of the present invention can be written in one or more programming languages. These computer program codes can be provided to the processor of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program code, when executed by the computer or other programmable data processing device, causes the function / operation specified in the flow chart and / or block diagram to be implemented. The program code can be executed completely on a computer, partially on a computer, as an independent software package, partially on a computer and partially on a remote computer or completely on a remote computer or server.

[0124] In the context of the present invention, computer program codes or related data may be carried by any appropriate carrier to enable a device, apparatus or processor to perform the various processes and operations described above. Examples of carriers include signals, computer readable media, etc. Examples of signals may include electrical, optical, radio, acoustic or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0125] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0126] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A robust calibration method for traffic simulation considering heteroscedastic noise, characterized in that: include: Determine the traffic simulation model to be used and the number of times the simulation of the sample points is repeated under the simulation parameters; A Gaussian process proxy model considering heteroscedastic noise is constructed, and the sampling points of the next simulation parameters are determined based on the Bayesian optimization algorithm. The number of simulation repetitions of the sample points under the next simulation parameters, as well as the expectation and variance distribution under the objective function of the next simulation parameters are determined. The sampling points of the optimal simulation parameters are determined by iterative calculation based on the expected improved acquisition function.

2. A robust calibration method for traffic simulation considering heteroscedastic noise as claimed in claim 1, characterized in that: Determine the number of times the sample point simulation is repeated under the simulation parameters, specifically: The sampling points are m init times simulation repetition; Based on the current number of simulations, estimate the distribution of the expectation and variance corresponding to the set simulation parameters; It is determined whether the variance corresponding to the set simulation parameter satisfies the first constraint condition. If so, it is determined whether the expectation corresponding to the set simulation parameter satisfies the second constraint condition. If so, the sampling of the sampling point is completed.

3. A robust calibration method for traffic simulation considering heteroscedastic noise as described in claim 2, characterized in that: Determine whether the expectation corresponding to the set simulation parameter satisfies the second constraint condition. If not, execute m on the sampling point of the set simulation parameter. add The simulation is repeated, and the execution time is determined by m add After the second simulation, it is determined whether the expectation corresponding to the simulation parameter satisfies the second constraint condition. If so, the sampling of the sampling point is completed.

4. A robust calibration method for traffic simulation considering heteroscedastic noise as described in claim 2 or 3, characterized in that: The first constraint condition is to satisfy one of the following constraints: i l ≤θ≤θ m Where f(θ) represents the difference between the simulated output and the actual measured value, E[·] represents the expectation, Var[·] represents the variance, represents the threshold of simulation variance; The second constraint condition is to satisfy one of the following constraints: Among them, f * represents the best result obtained in the previous sampling, is the predefined significance level, f(θ) represents the difference between the simulated output and the actual measured value, and E[·] represents the expectation.

5. A robust calibration method for traffic simulation considering heteroscedastic noise as claimed in claim 1, characterized in that: A Gaussian process proxy model considering heteroscedastic noise is constructed. The sampling point of the next simulation parameter is determined based on the Bayesian optimization algorithm. The number of simulation repetitions of the sample point under the next simulation parameter is determined, as well as the expectation and variance distribution under the objective function of the next simulation parameter. The optimal sampling point is determined by iterative calculation based on the expected improved acquisition function. Specifically: A joint multivariate Gaussian distribution is constructed based on the sampling points; wherein the covariance in the multivariate Gaussian distribution is measured by a kernel function; According to the definition of Gaussian process, the distribution conditions satisfied by the objective function of the unsampled points and the posterior distribution of the unsampled points are determined; The optimal sampling point is determined by iterative calculation based on the desired improved acquisition function.

6. A robust calibration method for traffic simulation considering heteroscedastic noise as claimed in claim 5, characterized in that: The optimal sampling point is determined by iterative calculation based on the desired improved acquisition function, specifically: Taking the expected improvement acquisition function as the objective function and using the proxy model of log(Var[f(θ)]) as the variance constraint, solve the following optimization problem to sample new points: Constrained by: τ(θ)≤log(σ c ) i l ≤θ≤θ m where τ(θ) is the expectation of the posterior distribution of log(r′).

7. A robust calibration method for traffic simulation considering heteroscedastic noise as claimed in claim 5, characterized in that: The optimal sampling point is determined by iterative calculation based on the expected improved acquisition function. Specifically, a probability of point stratification based on variance constraint is introduced, and p is used c (θ) is used to represent the c (θ) is used to modify the objective function of the acquisition function, solve the following optimization problem, and sample new points: Constrained by: i l ≤θ≤θ m Where θ represents the simulation parameter, f(θ) represents the difference between the simulation output and the actual measured value, E[·] represents the expectation, Var[·] represents the variance, represents the threshold of simulation variance; θ l With θ m They represent the lower and upper bounds of the simulation parameter values ​​respectively.

8. A robust calibration system for traffic simulation considering heteroscedastic noise, characterized in that: include: A determination module is configured to: determine the traffic simulation model to be adopted and the number of times the simulation of the sample point is repeated under the simulation parameters; The optimization module is configured to: construct a Gaussian process proxy model considering heteroscedastic noise, determine the sampling point of the next simulation parameter based on the Bayesian optimization algorithm, and determine the number of simulation repetitions of the sample point under the next simulation parameter, as well as the expectation and variance distribution under the objective function of the next simulation parameter, and iteratively calculate the sampling point of the optimal simulation parameter based on the expected improved acquisition function.

9. An electronic device, characterized in that: The method comprises a memory and a processor and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method according to any one of claims 1 to 7 is completed.

10. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the method described in any one of claims 1 to 7.

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