Road network total flow robust estimation method under limited observation

Abstract

The invention discloses a road network total flow robust estimation method under limited observation, relates to the field of traffic flow estimation, and solves the technical problems that the existing sensor observation technology cannot realize full coverage of a road section and the number of sensors fluctuates to influence the observation effect. The method comprises the steps of deducing a theoretical relationship between the number of sensors and observation network accumulation; constructing a sensor subset sequence from actual observation data, and calculating the road network total flow of each sensor subset to obtain an empirical relationship between the number of sensors and observation network accumulation; searching an optimal parameter which enables a fitting effect of a theoretical relationship and an empirical relationship between the number of sensors and observation network accumulation to be optimal; obtaining an estimated value of the road network total flow from the optimal parameters; according to the method, stable and accurate estimation of the road network total flow can be realized under the limited and unstable observation condition of the limited sensor.

Description

Technical Field

[0001] The present invention relates to the field of traffic flow estimation, and in particular to a method for robustly estimating the full flow of a road network under limited observation. Background Art

[0002] The total flow of a road network is an important indicator in traffic, and accurate estimation of the total number of vehicles in the road network has important academic and engineering value. On the one hand, in the short term, the total flow of a road network can reflect the operating status of the road network (Daganzo, 2007), so that control measures can be taken to improve the overall mobility of the city (Xu and Li et al., 2024). On the other hand, in the long term, the total flow of a road network can be used to calculate traffic emissions (Barmpounakis and Montesinos-Ferrer et al., 2021, Halakoo and Yang et al., 2023), analyze the resilience of the network (Lu and Sun et al., 2024), and verify the effectiveness of various policies (Bilali and Fastenrath et al., 2022, Tassinari, 2024, Ahmed and Kamihigashi et al., 2023).

[0003] However, in reality, estimating the full flow of a road network faces two huge challenges. One is the huge cost of sensor installation, which makes it impossible to achieve full coverage of all road sections (Nie and Qin et al., 2023). For example, sensors for vehicle detection are usually installed only on some main roads. Another is that the number of sensors may fluctuate over time (due to short-term sensor failures and long-term newly installed sensors), resulting in inconsistent observations (Gentili and Mirchandani, 2018). This means that we cannot simply use the observed full flow of the road network to replace the true full flow. The former has received extensive attention and discussion, but it is always under idealized conditions ( and Osma-Pinto et al., 2024, Xu and Jing et al., 2022, Nie and Qin et al., 2023), for example, sensors do not fail and the number of sensors remains constant. The latter has received little attention. Summary of the invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the present invention provides a method for robustly estimating the full flow of a road network under limited observation, which solves the technical problems that the existing sensor observation technology cannot achieve full coverage of road sections and the number of sensors will fluctuate, affecting the observation effect.

[0005] A method for robustly estimating the full flow of a road network under limited observations includes:

[0006] Step 1: Derive the theoretical relationship between the number of sensors and the accumulation of observation networks;

[0007] Step 2: construct a sensor subset sequence from the actual observation data, calculate the full road network flow of each sensor subset, and obtain the empirical relationship between the number of sensors and the accumulation of the observation network;

[0008] Step 3: Search for the optimal parameters that best fit the theoretical and empirical relationships between the number of sensors and the accumulation of the observation network;

[0009] Step 4: Obtain an estimate of the total traffic volume of the road network from the optimal parameters.

[0010] Furthermore, the step 1 comprises:

[0011] Derive the theoretical relationship between the number of sensors m and the accumulation of observation networks V m =f(m;a j , n, V n )(1≤m≤n) is as follows:

[0012]

[0013] Where V m Represents a sensor set S consisting of m sensors m The observed total traffic volume of the road network; V n Represents the actual total traffic volume of the road network, which is composed of a sensor set S containing n sensors n Observed; a j represents the number of vehicles captured by j different sensors.

[0014] Furthermore, the step 2 comprises:

[0015] From S m Construct the following subset sequence in

[0016]

[0017] in is from Randomly select m i The value obtained by the sensor is K, which is a specific constant, and i, which is a general number that can take any value of K.

[0018] For each sensor set Calculate the total traffic volume of the road network observed The number of sensors m and the observed network accumulation V can be obtained m The empirical relationship between:

[0019]

[0020] Furthermore, the step 3 comprises:

[0021] Step 3.1: Define a binomial distribution to represent the possible values ​​of the total traffic volume of the road network corresponding to the i-th sensor subset;

[0022] Step 3.2: Determine the probability of the empirical relationship occurring under given parameters θ according to the binomial distribution defined in step 3.1;

[0023] Step 3.3: Determine the parameter that maximizes the probability of the empirical relationship appearing under the given parameter θ through grid search as the optimal parameter θ*.

[0024] Furthermore, the step 3.1 comprises:

[0025] Define the binomial distribution as follows to represent Possible values.

[0026]

[0027] in is a random variable whose distribution can be obtained by randomly selecting m from n sensors multiple times. i Sensors are used to calculate the road network flow to generate, is the probability that the car will pass by j different sensors (j≤n).

[0028] Furthermore, the step 3.2 includes:

[0029] Experience relationship The probability of occurrence under a given parameter θ is

[0030]

[0031] Furthermore, the step 3.3 includes:

[0032] Perform a grid search over the entire parameter space to find a set of parameters Make The highest probability of occurrence:

[0033]

[0034] In the formula, Represents the optimal total flow of the road network, consisting of n * Sensor collection of sensors Observed; represents the optimal number of vehicles captured by j different sensors.

[0035] Perform a grid search over the entire parameter space to find the optimal parameters θ *

[0036] Furthermore, with the optimal parameter θ * In As an estimate of the total traffic volume of the road network.

[0037] The beneficial effects of the present invention include:

[0038] 1. The mathematical principle of total volume perception of fixed multi-sensor road networks is used to estimate the true total volume, which is highly interpretable.

[0039] 2. It can achieve stable and accurate estimation of the total traffic volume of the road network under limited sensors and limited unstable observation conditions, and has good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of a method for robustly estimating the total flow of a road network under limited observations involved in an embodiment of the present application;

[0041] Figure 2 The operation dynamics of the Boston road network involved in the embodiments of the present application;

[0042] Figure 3 The operation dynamics of the Lisbon road network involved in the embodiments of the present application;

[0043] Figure 4 The operation dynamics of the Los Angeles road network involved in the embodiments of the present application;

[0044] Figure 5 The operation dynamics of the road network in Rio de Janeiro involved in the embodiments of the present application;

[0045] Figure 6 The operation dynamics of the San Francisco road network involved in the embodiment of the present application;

[0046] Figure 7 Sensor installation solutions for different simulated road networks and scenario 1 involved in the embodiments of the present application;

[0047] Figure 8 Sensor installation solutions for different simulated road networks and scenario 1 involved in the embodiments of the present application;

[0048] Fig. 9 Sensor installation solutions for different simulated road networks and scenario 1 involved in the embodiments of the present application;

[0049] Fig.10 They are the average experimental effects on scenario 1;

[0050] Fig.11 They are the average experimental effects on scenario 2;

[0051] Fig.12They are the average experimental results on scene 3. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0053] A robust estimation method for the total flow of a road network under limited observations, such as Figure 1 As shown, including:

[0054] Step 1: Derive the theoretical relationship between the number of sensors and the accumulation of observation networks;

[0055] Step 2: Construct a sensor subset sequence from the actual observation data, calculate the full road network flow of each sensor subset, and obtain the empirical relationship between the number of sensors and the accumulation of the observation network; specifically, when calculating the flow, the license plate numbers captured by multiple sensors will be deduplicated to obtain the total number of vehicles observed;

[0056] Step 3: Search for the optimal parameters that best fit the theoretical and empirical relationships between the number of sensors and the accumulation of the observation network;

[0057] Step 4: Obtain an estimate of the total traffic volume of the road network from the optimal parameters.

[0058] In order to ensure timeliness, this method uses processor i9-13900k and a single estimate is within ten minutes.

[0059] In another embodiment, the step 1 comprises:

[0060] Derive the theoretical relationship between the number of sensors m and the accumulation of observation networks V m =f(m;a j , n, V n )(1≤m≤n) is as follows:

[0061]

[0062] Where V m Represents a sensor set S consisting of m sensors m The observed total traffic volume of the road network; V nRepresents the actual total traffic volume of the road network, which is composed of a sensor set S containing n sensors n Observed; a j represents the number of vehicles captured by j different sensors.

[0063] In another embodiment, the step 2 comprises:

[0064] From S m Construct the following subset sequence in

[0065]

[0066] in is from Randomly select m i The value obtained by the sensor is K, which is a specific constant, and i, which is a general number that can take any value of K.

[0067] For each sensor set Calculate the total traffic volume of the road network observed The number of sensors m and the observed network accumulation V can be obtained m The empirical relationship between:

[0068]

[0069] In another embodiment, the step 3 comprises:

[0070] Step 3.1: Define a binomial distribution to represent the possible values ​​of the total traffic volume of the road network corresponding to the i-th sensor subset;

[0071] Step 3.2: Determine the probability of the empirical relationship occurring under given parameters θ according to the binomial distribution defined in step 3.1;

[0072] Step 3.3: Determine the optimal parameter by grid search, which parameter has the highest probability of occurrence of the empirical relationship under the given parameter θ.

[0073] In another embodiment, the step 3.1 comprises:

[0074] Define the binomial distribution as follows to represent Possible values.

[0075]

[0076] in is a random variable whose distribution can be obtained by randomly selecting m from n sensors multiple times. i Sensors are used to calculate the road network flow to generate, is the probability that the car will pass by j different sensors (out of n sensors).

[0077] In another embodiment, the step 3.2 comprises:

[0078] Experience relationship The probability of occurrence under a given parameter θ is

[0079]

[0080] In another embodiment, the step 3.3 comprises:

[0081] Perform a grid search over the entire parameter space to find a set of parameters Make The highest probability of occurrence:

[0082]

[0083] In the formula, represents different values ​​of θ, where the optimal value is θ * , Represents the optimal total flow of the road network, consisting of n * Sensor collection of sensors Observed; represents the optimal number of vehicles captured by j different sensors.

[0084] Perform a grid search over the entire parameter space to find the optimal parameters θ *

[0085] In another embodiment, the optimal parameter θ * In As an estimate of the total traffic volume of the road network.

[0086] The above-mentioned embodiments only express the specific implementation methods of the present application, and the description is relatively specific and detailed, but it cannot be understood as limiting the protection scope of the present application. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the technical solution concept of the present application, which all belong to the protection scope of the present application.

[0087] The simulation process of the method designed in this embodiment (hereinafter referred to as this method) is as follows:

[0088] SUMO-based simulation data from five selected road networks, Boston, Lisbon, Los Angeles, Rio de Janeiro, and San Francisco, are used as experimental scenarios. “Urban Traffic Simulation”, where SUMO is an open-source, highly portable, microscopic, and continuous traffic simulation software package designed to handle large networks.

[0089] Since the spatial scale of the original data is too large, some areas are selected for research. Under full observation conditions, the network dynamics of each road network observed by the license plate camera are as follows: Figure 2-6 shown.

[0090] The simulated data are aggregated at a time granularity of 600 seconds, and the number of vehicles with different license plate numbers appearing on the road network within 600 seconds is the actual network accumulation.

[0091] Specifically, in order to verify the effectiveness of this method, this embodiment sets three scenarios with different spatial distributions of sensors to verify the impact of this method under long-term changes in the number of sensors. At the same time, for each scenario, sensors are randomly selected from them to simulate the short-term impact of random failures.

[0092] Scenario 1: Sensors are randomly installed on road segments. In this case, they can be considered to be randomly selected from the entire road network, such as Figure 7 shown.

[0093] Scenario 2: Sensors are not randomly installed, but are intended to capture as many vehicles on the road network as possible. In this case, they cannot be considered to be randomly selected from the entire road network. In order to construct such a scenario, a greedy algorithm that prioritizes high-traffic sections is used to solve a sensor full observation set that contains as few sensors as possible and can cover all vehicles within the time period, such as Figure 8 As shown. Figure 8 In the figure, we show the number of road segments on each road network where sensors should be installed in order to achieve complete observation in a specific time period, namely S n .

[0094] Scenario 3: Sensors are installed only on high-traffic roads. We chose a sensor installation method that is most common in the real world, which is to install sensors on high-traffic roads first, sort the roads in descending order of traffic flow, and then select the top 20% of the roads to install sensors, such as Fig. 9 shown.

[0095] In summary, Scenario 1, Scenario 2, and Scenario 3 represent different sensor installation scenarios (i.e., different spatial distributions of sensors). In Scenario 1, sensors are installed randomly on road sections. In Scenario 3, sensors are installed only on sections with high traffic flow. Scenario 2 is between Scenario 1 and Scenario 3. The installation of sensors considers covering all vehicles with as few sensors as possible. Therefore, it is neither as random as Scenario 1 nor does it only include roads with high traffic flow like Scenario 3.

[0096] In addition, in each scenario, different proportions of sensors (randomly selected from the installed sensors) are set to evaluate the impact of the proposed method under random failures. At the same time, the network accumulation observed by the original sensors without correction is used as a baseline for comparison.

[0097] Figure 10-12 The results of the proposed method in different scenarios are shown. These figures show the average of the estimated effect of the proposed method in all time periods under different sensor ratios (using the mean absolute percentage error (MAPE) between the estimated and true values ​​as a metric). In scenarios 1 and 2, even with only 5% of the sensors online, our method is able to estimate the full flow of the road network within a MAPE error range of 20%. A MAPE error of 10% can be achieved with only 20% of the number of sensors. In the extreme sensor distribution scenario of scenario 3, a MAPE error of less than 30% can be achieved with 5% of the number of sensors. It can be seen that regardless of the road network, time and sensor distribution, compared with the baseline, the proposed method can effectively improve the accuracy of network accumulation estimation using fewer sensors. In addition, regardless of the scenario, the performance of the proposed method under different sensor ratios is stable, which shows that the proposed method can effectively handle the observation inconsistency problem caused by random sensor failures and has good robustness.

Claims

1. A method for robustly estimating the total flow of a road network under limited observation, characterized in that: include: Step 1: Derive the theoretical relationship between the number of sensors and the accumulation of observation networks; Step 2: construct a sensor subset sequence from the actual observation data, calculate the full road network flow of each sensor subset, and obtain the empirical relationship between the number of sensors and the accumulation of the observation network; Step 3: Search for the optimal parameters that best fit the theoretical and empirical relationships between the number of sensors and the accumulation of the observation network; Step 4: Obtain an estimate of the total traffic volume of the road network from the optimal parameters.

2. According to the method for robust estimation of the total flow of a road network under limited observations in claim 1, it is characterized in that: The step 1 comprises: Derive the theoretical relationship between the number of sensors m and the accumulation of observation networks V m =f(m;a j ,n,V n )(1≤m≤n) is as follows: Where V m Represents a sensor set S consisting of m sensors m The observed total traffic volume of the road network; V n Represents the actual total traffic volume of the road network, which is composed of a sensor set S containing n sensors n Observed; a j represents the number of vehicles captured by j different sensors.

3. According to the method for robust estimation of the total flow of a road network under limited observations in claim 1, it is characterized in that: The step 2 comprises: From S m Construct the following subset sequence in in is from Randomly select m i The sensor obtains For each sensor set Calculate the total traffic volume of the road network observed The number of sensors m and the observed network accumulation V can be obtained m The empirical relationship between:

4. The method for robustly estimating the total flow of a road network under limited observation according to claim 1 is characterized in that: The step 3 comprises: Step 3.1: Define a binomial distribution to represent the possible values ​​of the total traffic volume of the road network corresponding to the i-th sensor subset; Step 3.2: Determine the probability of the empirical relationship occurring under given parameters θ according to the binomial distribution defined in step 3.1; Step 3.3: Determine the parameter that maximizes the probability of the empirical relationship appearing under a given parameter θ through grid search as the optimal parameter θ * .

5. The method for robustly estimating the total flow of a road network under limited observation according to claim 4 is characterized in that: The step 3.1 comprises: Define the binomial distribution as follows to represent Possible values: in is a random variable whose distribution can be obtained by randomly selecting m from n sensors multiple times. i Sensors are used to calculate flow to generate, is the probability that the car will pass by j different sensors (j≤n).

6. The method for robustly estimating the total flow of a road network under limited observation according to claim 4 is characterized in that: The step 3.2 comprises: Experience relationship The probability of occurrence under a given parameter θ is 7. The method for robustly estimating the total flow of a road network under limited observation according to claim 4 is characterized in that: The step 3.3 includes: performing a grid search on the parameter space to find a set of parameters Make The highest probability of occurrence: In the formula, represents different values ​​of θ, where the optimal value is θ * , Represents the optimal total flow of the road network, consisting of n * Sensor collection of sensors Observed; represents the optimal number of vehicles captured by j different sensors.

8. The method for robustly estimating the total flow of a road network under limited observation according to claim 7, characterized in that: With the optimal parameter θ * In As an estimate of the total traffic volume of the road network.

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