Method for estimating signal system capacity based on sparse gaussian process regression

Abstract

The application provides a signal system passing capacity evaluation method based on a sparse Gaussian process regression, and belongs to the field of intelligent traffic signal control. Specifically, the green signal ratio variable is included in the input feature and is simultaneously modeled to capture the mutual influence relationship between the signal configuration and the traffic state variable, so that a data-driven traffic flow model is developed by using the GP regression to reflect the complex nonlinear mapping between the high-dimensional variables, reduce the complexity of the calculation, obtain the uncertainty of the quantitative model, and accurately and dynamically evaluate the passing capacity of the intersection. The modified Gaussian kernel is used for modeling to capture the mutual influence relationship between the signal configuration and the traffic state variable, the data sparsification calculation is used to develop a data-driven traffic flow model by using the GP regression, the relationship that the signal timing (g / C) influences the traffic flow fluctuation with the change of the traffic flow is embodied, and the passing capacity of the intersection is dynamically evaluated.

Description

Technical Field

[0001] This application belongs to the field of intelligent traffic signal control, and specifically proposes a method for evaluating the traffic capacity of a signal system based on sparse Gaussian process regression. Background Technology

[0002] With the rapid growth of urban traffic flow, existing fixed-duration traffic signal control systems are unable to effectively cope with complex traffic conditions. Currently, artificial intelligence-based adaptive traffic signal control technology has been applied, which can adjust signals according to real-time traffic data and significantly improve traffic efficiency.

[0003] However, most studies on intersection capacity do not consider the impact of road supply on traffic. For example, external environmental factors, including traffic signals and weather conditions, are not taken into account. Furthermore, traffic flow under adaptive signaling systems exhibits instantaneous fluctuations due to flexible signal timing adjustments. Classical models (such as the FD model and many kinematic wave models), which assume a balanced state where all vehicles operate at the same speed and spacing, cannot be applied to this scenario.

[0004] Lin et al. [1] (L. Lin, J. Li, F. Chen, J. Ye, and J. Huai, “Road trafficspeed prediction: A probabilistic model fusing multi-source data,” IEEE Trans. Knowl. Data Eng., vol. 30, no. 7, pp. 1310–1323, Jul. 2017, doi:10.1109 / TKDE.2017.2718525.) solved the problem of traffic speed estimation on unobserved links using trajectory sensor and social media data on some links, where GP was used to reconstruct traffic speeds on all links. However, how to model macroscopic traffic flow using data-driven methods remains an open question. In recent years, some researchers have managed to solve the problem of traffic state estimation with the help of GP. Yuan et al. [2](Y. Yuan, Z. Zhang, XT Yang, and S. Zhe, “Macroscopic traffic flow modeling with physics regularized Gaussian process: Anew insight into machine learning applications in transportation,” Transp. Res. B, Methodol., vol. 146, pp. 88–110, Apr. 2021, doi:10.1016 / j.trb.2021.02.007.) A recent study combined Gaussian processes with classical macroscopic traffic flow models for traffic state estimation, but did not consider the effects of interactions among multiple factors. Li et al. [3] (J. Li, J. Boonaert, A. Doniec, and G. Lozenguez, “Multi-models machine learning methods for traffic flow estimation from floating car data,” Transp. Res. C, Emerg.Technol., vol. 132, Nov. 2021, Art. no. 103389, doi: 10.1016 / j.trc.2021.103389.) focuses on traffic flow measurement based on floating car data, and GP is used to estimate traffic flow from driving profiles. Sederlin et al. [4] (M. Sederlin, X. Ma, and J. Jin, “A hybrid modelling approach for traffic state estimation at signaled intersections,” in Proc.IEEE Int. Intell. Transp. Syst. Conf. (ITSC), Indianapolis, IN, USA, Sep. 2021, pp. 3604–3609, doi: 10.1109 / ITSC48978.2021.9564540) They developed a traffic state estimation model based on a Bayesian filtering framework, where the generalized approach (GP) is used to model the state-space transitions of traffic states. However, these studies are not related to modeling the relationships between traffic state variables.

[0005] Existing GP models not only have high computational complexity due to the inverse operation of multiple covariance matrices, but also require dynamic road capacity definitions and new road capacity estimation methods to accurately assess the capacity of intersections due to the uncertainty of traffic flow under adaptive signaling systems. This is clearly still a challenging problem.

[0006] In view of the above, this application is hereby submitted. Summary of the Invention

[0007] The signal system capacity assessment method based on sparse Gaussian process regression described in this application aims to address the problems of the existing technology by incorporating the green ratio variable into the input features and simultaneously modeling it to capture the interaction between signal configuration and traffic state variables. In this way, by using GP regression to develop a data-driven traffic flow model, it reflects the complex nonlinear mapping between high-dimensional variables, while reducing computational complexity, quantifying the uncertainty of the model, and accurately and dynamically assessing the capacity of intersections.

[0008] The signal system capacity assessment method based on sparse Gaussian process regression incorporates the green ratio variable into the input features, uses a modified Gaussian kernel for modeling to capture the interaction between signal configuration and traffic state variables, and performs data sparsification calculation to develop a data-driven traffic flow model using GP regression. This model reflects the relationship between signal timing and traffic flow fluctuations, and dynamically assesses the capacity of intersections.

[0009] Furthermore, the method includes the following steps:

[0010] Step (1): Select the target;

[0011] Select the city where the adaptive signal system operates and the target intersection, and obtain the basic information of the target intersection;

[0012] Step (2): Obtain traffic flow data;

[0013] The number of vehicles passing by per minute q is calculated by the sensing devices under the adaptive signal system, the speed v of each vehicle is measured, and the signal cycle at the corresponding time point, i.e., the green signal ratio g / c, is recorded and the data is sent back to the central system platform.

[0014] Step (3): Determine input features:

[0015] The flow rate q, speed v, corresponding periodic green ratio g / c and occupancy rate o are input as features into the Gaussian process GP. The Gaussian process GP will dynamically map the transition between the vehicle flow rate qk,t-1 and the vehicle flow rate qk,t at control time t in lane k.

[0016] Step (4): Input the Gaussian process and model it;

[0017] The Gaussian process (GP) dynamically maps the system transition between the vehicle flow rate qk,t-1 and the vehicle flow rate qk,t at control time t. The mapping expression is as follows:

[0018] ;

[0019] Step (5): Modify the kernel function;

[0020] Modify the standard Gaussian kernel as follows:

[0021] ;

[0022] ;

[0023] in, It is a diagonal matrix that defines the length proportion of each dimension of the input features, where m represents the dimension of the feature. This allows GP regression to automatically determine the importance of each feature and reduce the influence of irrelevant features.

[0024] Step (6): Add noise;

[0025] The randomness of traffic flow is represented by including a noise term ε, i.e., y = f(x) + ε; where ε is a normal distribution N(0, 0, ..., 0). The noise term;

[0026] Step (7), data sparsification;

[0027] Induced points are created in the samples to reduce the computational complexity of the model; the sparsified set of induced points U is: ;

[0028] Step 8) Hyperparameter optimization;

[0029] When training the model, the hyperparameters of the kernel function are inferred from the data to determine the mapping between the input and output, and the marginal likelihood function is maximized as follows:

[0030] ;

[0031] Where θ is the hyperparameter vector of the kernel function. It is a noise parameter;

[0032] Step (9): Assess traffic capacity;

[0033] The training model is complete and outputs the predicted traffic capacity value. The traffic capacity expression is as follows:

[0034] ;

[0035] Step (10): Evaluate model performance;

[0036] The dataset was randomly divided into two subsets, with 80% used as the training set and the other 20% as the test set. Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were used as performance metrics for the GP regression model; the expressions are as follows:

[0037] ;

[0038] .

[0039] Furthermore, step (6) allows noise to be included in the GP regression model by adding a constant to the diagonal of the original kernel matrix K; the kernel matrix is... ;

[0040] Assuming the mean function is 0, the prior distribution of the observations can be expressed as:

[0041] ;

[0042] Where I represents the identity matrix, Let K denote the noise constant, and K be an N-dimensional covariance matrix, where the element in the i-th row and j-th column is represented as k(x). i ,x j );

[0043] Combine the zero-mean GP's y with the predicted value The joint prior distribution is written as follows:

[0044] ;

[0045] in, It is the covariance matrix of the observed values ​​and the new observation. It is the new observation and its covariance matrix;

[0046] For new observations and the corresponding predicted value The posterior of this GP regression can be written as:

[0047] ;

[0048] in, , In the formula, μ is the posterior mean; Σ is the posterior variance; I is the N-dimensional identity matrix; and the 95% confidence interval can be expressed as [μ+1.96Σ, μ-1.96Σ].

[0049] Furthermore, in step (7), the locations of the induced points are distributed within the sample set X. For a given U, let f(x) and f(x) be denoted as f(x). ) for y, , and thus y The probability distributions of U are:

[0050] ;

[0051] in, , ;

[0052] According to the inverse theorem and Bayes' theorem, we know The approximate distribution is:

[0053] ;

[0054] in, , , , .

[0055] In summary, the proposed method for evaluating the traffic capacity of signal systems based on sparse Gaussian process regression has the following advantages and beneficial effects:

[0056] 1. This application modifies the Gaussian kernel by adding a diagonal matrix that defines the specific length ratio of each dimension of the input elements, thereby enabling the Gaussian distribution to better interpret the physical relationships between traffic flows.

[0057] 2. Existing technology GPR requires processing an N×N covariance matrix. Due to the short intervals and high frequency of data collection in adaptive systems, the data scale is relatively large, and the computation time will increase significantly. This application reduces the computational complexity of the model by sparsifying the data and creating appropriate induction points in the samples.

[0058] 3. This application develops a data-driven traffic flow model using GP regression, which can bridge the gap in existing technologies in capturing the interaction between signal configuration and traffic state variables, and demonstrate the relationship between signal timing g / C and traffic flow fluctuations, thus significantly improving the accuracy of assessing intersection capacity. Attached Figure Description

[0059] This application will now be further illustrated with reference to the following figures:

[0060] Figure 1 This is a schematic diagram of a sparse Gaussian regression process; where (a) is a schematic diagram of the learning process; and (b) is a schematic diagram of the evaluation process.

[0061] Figure 2This is a flowchart for assessing the traffic capacity of an adaptive signaling system. Detailed Implementation

[0062] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0063] Example 1, such as Figure 1 and Figure 2 As shown, this application proposes a novel signal system capacity assessment method based on sparse Gaussian process regression. This method targets the dynamic assessment of road capacity by expanding road capacity from a stable value to a variable term to adapt to the dynamic changes in roadside factors, i.e., signal timing, in existing adaptive signal systems. Instead of fixing capacity assessment to traditional calculation formulas, this method explores the capacity fluctuations within the current adaptive signal system.

[0064] Current analyses of road capacity generally rely on static definitions, which are driven by road design. These definitions assume road capacity remains constant over a relatively long period. However, supply-side factors affecting traffic capacity, such as traffic signals, typically change over time. Gaussian process regression (GP) is a type of nonparametric probability based on Bayesian theory. The output of GP is modeled as a random variable for each input vector, and the learning function (i.e., the output corresponding to all input vectors) becomes a stochastic process. The distribution of each random variable (upon which GP places a Gaussian prior, making the stochastic process tractable) quantifies the uncertainty of the output.

[0065] This application addresses the dynamic nature of road capacity, which varies over time, by introducing higher-dimensional data to better fit the empirical relationships between traffic variables. That is, it simulates these relationships in a data-driven manner, rather than starting from predefined assumptions in the functional form of basic traffic state variables. Therefore, the data-driven traffic flow model proposed in this application is more suitable for analyzing complex and unstable traffic flows, and can effectively address the uncertainties such as randomness and instantaneous fluctuations in traffic flow under adaptive systems.

[0066] The method for evaluating the traffic capacity of a signal system based on sparse Gaussian process regression comprises the following steps:

[0067] Step (1): Select the target;

[0068] Select the city where the adaptive signal system operates and the target intersection, and obtain the basic information of the target intersection;

[0069] Understanding the basic structure and operating principle of adaptive signal systems reveals that the most basic system structure of an adaptive control system consists of three parts: sensing devices (supporting integrated traffic detection cameras and radar-visual integrated machines, etc.), traffic adaptive control units (adaptive edge computing timing optimization devices), and background traffic optimization storage servers.

[0070] The sensing devices continuously process video images of the monitored area every second to obtain first-hand data on the road surface and vehicles. By analyzing vehicle passage characteristics, traffic flow, vehicle motion characteristics, and driver behavior patterns, the traffic adaptive controller summarizes the parameters from the intersection sensing devices and comprehensively considers the traffic optimization adjustment parameters sent by the traffic optimization server to make real-time decisions on the current phase operation and periodic timing scheme adjustments at the intersection.

[0071] Step (2): Obtain traffic flow data;

[0072] The number of vehicles passing by per minute, q, is calculated by the sensing devices under the adaptive signal system, the speed v of each vehicle is measured, and the signal cycle at the corresponding time point, i.e., the green signal ratio g / c, is recorded. The data is then sent back to the central system platform.

[0073] Step (3): Determine input features:

[0074] Traffic flow q, speed v, corresponding periodic green light ratio g / c, and occupancy rate o are input as features into the Gaussian process GP. The Gaussian process GP dynamically maps the system transition between the vehicle traffic flow qk,t-1 and the vehicle traffic flow qk,t at control time t. Besides Nk,t-1, the speed measurement value from the loop detector, signal controller information, and occupancy rate serve as control inputs; the single input vector connected to these features is denoted as the input feature:

[0075] ;

[0076] Where, q k,t-1:t In this context, q describes the flow rate entering the studied lane k, measured at the intersection entrance; v k,t-1:t It is the vehicle speed measured at the intersection; g k,t-1:t It is the green ratio of the signal controlling that lane during the estimated interval. k,t-1:t It is the vehicle time occupancy rate measured by the detector at time t-1;

[0077] Step (4): Input the Gaussian process and model it;

[0078] The GPR principle assumes a set of observed data X = {x1, x2, ..., x...} N}, The corresponding target value is Y={y1,y2…yN The objective function f(x) is modeled using a Gaussian process, and its prior distribution is:

[0079] ;

[0080] In the formula, m(x) is the mean function; k(x) i ,x j (x) is the covariance function; i ,x j () represents the element in the i-th row and j-th column; It follows a Gaussian distribution;

[0081] The Gaussian process (GP) dynamically maps the system transition between the vehicle flow rate qk,t-1 and the vehicle flow rate qk,t at control time t. The mapping expression is as follows:

[0082] ;

[0083] Step (5): Modify the kernel function;

[0084] The kernel function plays a crucial role in Gaussian traffic flow modeling, essentially acting as a similarity measure between vectors in the input space. For traffic flow modeling, this application aims to ensure that the input variables of the model are related to the traffic volume on the roads, employing the following Gaussian kernel formula:

[0085] ;

[0086] in, It is the length scale of the kernel, and it is a hyperparameter of the model;

[0087] Since the posterior mean of GP regression does not have a physically meaningful form like existing models, this application modifies it to allow GP regression to interpret the physical elements of traffic flow. To allow the model to adapt to features of various dimensions, the standard Gaussian kernel is modified as follows:

[0088] ;

[0089] ;

[0090] in, It is a diagonal matrix that defines the specific length proportion of each dimension of the input features, where m represents the dimension of the feature, enabling GP regression to automatically determine the importance of each feature and reduce the influence of irrelevant features;

[0091] Step (6): Add noise;

[0092] The existing GP regression model assumes that the observations are noise-free, i.e., y=f(x).

[0093] This application uses a noise term ε to represent the randomness of traffic flow for aggregated traffic variables, which is more reasonable and makes the prediction results more consistent with the capacity assessment of real road data.

[0094] That is, y = f(x) + ε. Where ε is a normal distribution N(0, ..., ... The noise term;

[0095] Noise is allowed to be included in the GP regression model by adding a constant to the diagonal of the original kernel matrix K; the kernel matrix is... ;

[0096] Assuming the mean function is 0, the prior distribution of the observations can be expressed as:

[0097] ;

[0098] Where I represents the identity matrix, Let K denote the noise constant, and K be an N-dimensional covariance matrix, where the element in the i-th row and j-th column is represented as k(x). i ,x j );

[0099] The above formula allows the kernel to incorporate the inherent noise in each sample of the dataset; otherwise, the posterior variance at the observation point would be zero; in this case, the zero-mean GP's y and the predicted value would be... The joint prior distribution is written as follows:

[0100] ;

[0101] in, It is the covariance matrix of the observed values ​​and the new observation. It is the new observation and its covariance matrix.

[0102] For new observations and the corresponding predicted value The posterior of this GP regression can be written as:

[0103] ;

[0104] in, , In the formula, μ is the posterior mean; Σ is the posterior variance; and I is the N-dimensional identity matrix. The 95% confidence interval can be expressed as [μ+1.96Σ, μ-1.96Σ].

[0105] Step (7), data sparsification;

[0106] The existing GPR needs to process an N×N covariance matrix. Since the adaptive system collects data at short intervals and at high frequencies, the data size is relatively large, and the computation time will increase significantly.

[0107] To address this, this application employs data sparsification, specifically by creating suitable induction points in the samples to reduce the computational complexity of the model; the sparsified induction point set U is:

[0108] ;

[0109] The locations of the induction points can be uniformly distributed within the sample set X. For a given U, let f(x) and f(x) be denoted as f(x). ) for y, , and thus y The probability distributions of U are:

[0110] ;

[0111] in, , ;

[0112] According to the inverse theorem and Bayes' theorem, we know The approximate distribution is:

[0113]

[0114] in, , , , ;

[0115] Therefore, sparse Gaussian process regression transforms the covariance matrix inversion calculation of the existing GPR into diagonal matrix inversion, reducing the computational complexity by approximately N. 2 ;

[0116] Step (8), hyperparameter optimization;

[0117] During model training, the hyperparameters of the kernel function are inferred from the data, such as... l θ To determine the mapping between input and output, we need to find the marginal likelihood. This can be achieved by maximizing the marginal likelihood. The marginal likelihood function is as follows:

[0118] ;

[0119] Where θ is the hyperparameter vector of the kernel function. It is a noise parameter;

[0120] Step (9): Assess traffic capacity;

[0121] The training model ends and outputs the traffic capacity prediction value. The traffic capacity expression is as follows (12). Based on the results, the influence relationship between input feature factors and traffic capacity is analyzed, as well as the fluctuation of traffic capacity caused by the green ratio g / c of ​​the specific environment adaptive signal system parameter selected in this application.

[0122] ;

[0123] Step (10): Evaluate model performance;

[0124] The dataset was randomly divided into two subsets, with 80% used as the training set and the other 20% as the test set. Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were used as performance metrics for the GP regression model; the expressions are as follows:

[0125] ;

[0126] ;

[0127] In summary, the embodiments shown in the accompanying drawings are merely preferred solutions for achieving the objectives of this invention. Those skilled in the art can draw inspiration from these embodiments and directly derive other alternative structures that conform to the design concept of this invention. Other structural features derived therefrom should also fall within the scope of the solutions described in this invention.

Claims

1. A method for evaluating the traffic capacity of a signal system based on sparse Gaussian process regression, characterized in that: The green ratio variable is incorporated into the input features, and a modified Gaussian kernel is used for modeling to capture the interaction between signal configuration and traffic state variables. Data sparsification calculation is used to develop a data-driven traffic flow model using GP regression, which reflects the relationship between signal timing and traffic flow fluctuations, and dynamically evaluates the capacity of intersections. It has the following steps, Step (1): Select the target; Select the city where the adaptive signal system operates and the target intersection, and obtain the basic information of the target intersection; Step (2): Obtain traffic flow data; The number of vehicles passing by per minute q is calculated by the sensing devices under the adaptive signal system, the speed v of each vehicle is measured, and the signal cycle at the corresponding time point, i.e., the green signal ratio g / c, is recorded and the data is sent back to the central system platform. Step (3): Determine input features: The traffic flow q, speed v, corresponding periodic green light ratio g / c, and occupancy rate o are input as features into the Gaussian process GP, which controls the vehicle flow q in lane k at time t. k,t-1 Traffic flow q k,t Dynamic mapping of the system between transitions; Step (4): Input the Gaussian process and model it; The Gaussian process GP will control the vehicle flow q in lane k at time t. k,t-1 Traffic flow q k,t The system dynamic mapping between the transitions is expressed as follows: Step (5): Modify the kernel function; Modify the standard Gaussian kernel as follows: in, It is a diagonal matrix that defines the length proportion of each dimension of the input features, where m represents the dimension of the feature. This allows GP regression to automatically determine the importance of each feature and reduce the influence of irrelevant features. Step (6): Add noise; The randomness of traffic flow is represented by including a noise term ε, i.e., y = f(x) + ε; where ε is a normal distribution N(0, 0, ..., 0). The noise term; Step (6) allows noise to be included in the GP regression model by adding a constant to the diagonal of the original kernel matrix K; the kernel matrix is... ; Assuming the mean function is 0, the prior distribution of the observations can be expressed as: Where I represents the N-dimensional identity matrix, Let K denote the noise constant, and K be an N-dimensional covariance matrix, where the element in the i-th row and j-th column is represented as k(x). i ,x j ); Combine the zero-mean GP's y with the predicted value y The joint prior distribution is written as follows: ） in, It is the covariance matrix of the observed values ​​and the new observation. It is the new observation and its covariance matrix; For a new observation x* and the corresponding new predicted value y*, the posterior of the GP regression can be written as: in, , In the formula, μ is the posterior mean; Σ is the posterior variance; I is the N-dimensional identity matrix; the 95% confidence interval can be expressed as [μ+1.96Σ, μ-1.96Σ]; Step (7), data sparsification; Induced points are created in the samples to reduce the computational complexity of the model; the sparsified set of induced points U is: Step (8), hyperparameter optimization; When training the model, the hyperparameters of the kernel function are inferred from the data to determine the mapping between the input and output, and the marginal likelihood function is maximized as follows: Where θ is the hyperparameter vector of the kernel function. It is a noise parameter; Step (9): Assess traffic capacity; The training model is complete and outputs the predicted traffic capacity value. The traffic capacity expression is as follows: Step (10): Evaluate model performance; The dataset was randomly divided into two subsets, with 80% used as the training set and the other 20% as the test set. Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were used as performance metrics for the GP regression model; the expressions are as follows:

2. The signal system traffic capacity assessment method based on sparse Gaussian process regression according to claim 1, characterized in that: In step (7), the locations of the induced points are distributed within the sample set X. For a given U, let f(x) and f(x*) be y and y*, respectively. Thus, the probability distributions of y, y*, and U are: in, , ; By using the inverse theorem and Bayes' theorem, the approximate distribution of y* is: in, , , ， 。

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