CN115938105A - A mileage measurement method for highway sections based on ETC big data - Google Patents

Abstract

The invention discloses an ETC big data-based highway section mileage measurement method, which comprises the following steps of: acquiring the geographic position coordinates of a starting point and a finishing point of a highway section, and acquiring the total mileage of the section by using a map API (application programming interface); acquiring the running time of the vehicle on the whole road section, and calculating the average running speed of the vehicle on the whole road section by combining the mileage of the whole road section; dividing the whole road section into a plurality of sections, respectively acquiring the residence time of the vehicle in each section, and calculating the section driving mileage by taking the average speed of the whole road section as the driving speed of each section; and constructing a section mileage generation model according to the driving mileage of different sections of the vehicle. The model constructed by the method realizes the measurement of the mileage of the highway section only by relying on the ETC big data, has small measurement error and stable performance, and is beneficial to the fine management of the highway and the improvement of the application value of the ETC big data.

Description

A highway section mileage measurement method based on ETC big data

Technical Field

The present invention relates to the technical field of highway management, and in particular to a highway section mileage measurement method based on ETC big data.

Background Art

By the end of 2020, the total mileage of my country's expressways reached 161,000 kilometers, ranking first in the world. To further improve the operational efficiency of my country's expressways, by the end of 2019, my country's expressway non-stop electronic toll collection (ETC) system had been connected to 29 provinces across the country, with a total of 24,588 ETC gantry systems built, 48,211 ETC lanes renovated, and more than 200 million ETC users nationwide.

In order to realize the correct and reasonable ETC network charging, according to the document of my country's new expressway charging method, before the ETC network charging of new expressways is built, the mileage of the road section needs to be measured on the spot to determine the actual toll mileage and calculate the toll amount accordingly. However, facing my country's vast and complex expressway network, the traditional measurement method not only consumes a lot of manpower, material and financial resources, but also has safety hazards in the field measurement.

Summary of the invention

The purpose of the present invention is to provide a highway section mileage measurement method based on ETC big data, which greatly reduces the cost of manual surveying and mapping and improves the safety factor.

The technical solution adopted by the present invention is:

A method for measuring the mileage of a highway section based on ETC big data comprises the following steps:

Step 1, obtain the geographic coordinates of the starting point and end point of the highway section, and use the map API to obtain the total mileage of the section;

Step 2, obtaining the driving time of the vehicle on the entire road section and calculating the average driving speed of the vehicle on the entire road section;

Step 3, obtaining the residence time of the vehicle in each section, and calculating the section mileage by taking the average speed of the section as the driving speed of each section;

Specifically, firstly obtain the mileage of the entire road section according to step 1, then obtain the driving time of the vehicle on the entire road section according to the vehicle data, and calculate the driving speed.

Then calculate the average driving speed of the entire section, obtain the vehicle's residence time in each section, use the average speed as the section's driving speed, and then obtain the section mileage of each section.

Step 4: According to the segment mileage of the vehicle, a segment mileage generation model is constructed as follows:

ΔD～N(μ,Γ _Δd )

表示每个区段的方差，m表示经过区段的m辆车；N表示正态分布的意思。。即根据通行的车辆计算出每一辆车在不同区段的通行里程，输入模型中获取整个路段的里程，以及每个区段的里程。Where ΔD is a Gaussian random vector, whose mean vector μ = [μ ₁ ,μ ₂ ,…,μ _n-1 ], μ _n represents the mean distance of the nth segment, which is calculated based on the mileage of the passing vehicles; the covariance matrix is

represents the variance of each section, m represents the number of vehicles passing through the section, and N represents the normal distribution. That is, the mileage of each vehicle in different sections is calculated based on the number of vehicles passing through, and the mileage of the entire section and each section is obtained by inputting the model.

Furthermore, the map API in step 1 is the Amap API.

Furthermore, the average speed formula is used in step 2 to calculate the average speed of the vehicle:

表示第j辆车在该路段的行驶时间，Where d is the total mileage of the road section,

represents the travel time of the jth vehicle on this road section,

Furthermore, in step 3, a noise data cleaning method based on a box plot is used to obtain the residence time and mileage of the vehicle in each section.

Furthermore, the specific steps of step 3 are as follows:

Step 301, select a road section LD with a free traffic flow, and the number of lanes in each section of the road section is the same; if the traffic condition of the road section does not meet the requirements, select a time period such as the second half of the night that meets the free traffic flow requirements; if the number of lanes in each section is different, divide the sections into multiple sections and process them independently;

Step 302: Since different vehicles and different driving habits may lead to different driving speeds, the ratio of the dwelling time of a vehicle passing through a certain section to the total travel time of the section is called the section time ratio r:

Among them, Δt is the dwell time of the section, _Δtj is the dwell time of the entire section,

Step 303, normalize the section residence time to obtain the time ratio R of the m vehicles in the entire road section;

Among them, m refers to the mth vehicle; n refers to the nth section;

Step 304: Use a box plot to clean the noise data generated by vehicles passing through the service area to obtain a valid vehicle subset M" of the road section:

The valid subset of vehicles is the set of vehicles on the road segment used;

Step 305, obtaining the segment mileage ΔD:

表示第m辆车在第n-1个区段的行驶里程；m表示有效车辆子集M”中车辆的数目；Wherein, V = diag (v ¹ , v ² , D, v ^n-1 ) represents the speed of each vehicle in the subset;

represents the mileage of the mth vehicle in the n-1th segment; m represents the number of vehicles in the valid vehicle subset M”;

Step 3041: When a vehicle passes through a service area, it is divided into the case where the vehicle stays in the service area and the case where the vehicle does not stay in the service area. Different time usage ratios of different sections can be obtained. The time usage ratio of the vehicle not staying in the service area is:

Among them, Δt ₁ is the residence time in the section when not stopping, and Δt is the residence time of the entire section including the section;

The time ratio of vehicles staying in the service area is:

Among them, Δt ₁ is the residence time of the vehicle in the section, not included in the service area time; Δt _s is the residence time in the service area;

Step 3042, since the vehicle staying in the service area will cause the section time ratio to deviate from the overall true distribution, it is necessary to use a box plot to clean the data; obtain the various data of the box plot, of which the following are needed: Q1 is the first quartile; Q2 is the second quartile, also known as the median; Q3 is the third quartile; IQR = Q3-Q1 is the interquartile range; Q1-1.5×IQR is the lower limit Lower and Q3+1.5×IQR is the upper limit Upper; Outliers are noise points, whose values are greater than Q3+1.5×IQR or less than Q1-1.5×IQR, also known as outliers or abnormal points;

Step 3043, constructing a subset of vehicles I _j that stop at the service area according to the results of the box plot:

为第i辆车在区段j的区段用时比例；

为区段j的用时比例在箱线图中的第三四分位数；

为区段j的用时比例在箱线图中的四分位数间距；

为区段j的用时比例在箱线图中的第一四分位数；Wherein, J = {j} (j∈[1,n-1]) is the set of sections where the service area is located;

is the time ratio of the i-th vehicle in section j;

is the third quartile of the time proportion of segment j in the box plot;

is the interquartile range of the time proportion of segment j in the box plot;

is the first quartile of the time proportion of segment j in the box plot;

Step 3044, construct the vehicle subset M' of the road segment:

Among them, M is the original vehicle set, and M' is the vehicle set after eliminating the vehicles that stop at the service area;

Step 3045: Due to the complex and changeable traffic conditions, traffic flow, road maintenance and emergencies, it is necessary to further clean M' and then construct the abnormal vehicle subset I' _j in the section:

为异常车辆的区段用时比例；

为箱线图中的第三四分位数；

为箱线图中的四分位数间距；

为箱线图中的第一四分位数；in,

The proportion of time used in the section for abnormal vehicles;

is the third quartile in the box plot;

is the interquartile range in the box plot;

is the first quartile in the box plot;

Step 3046, further obtaining a valid vehicle subset M" of the road segment:

The valid subset of vehicles is the set of vehicles on the road segment used.

Furthermore, the steps of constructing the gantry section mileage generation model using the law of large numbers in step 4 are as follows:

Step 401: According to the segment mileage obtained in step 3, it can be known that the mileage of each vehicle in different segments is independent of each other and follows the same distribution with mathematical expectation:

表示第i辆车在区段j的行驶里程，μ_j为路段j的里程的数学期望值，in,

represents the mileage of the i-th vehicle in section j, μ _j is the mathematical expectation of the mileage of section j,

依概率收敛于μ_j，即

设

具有方差

由中心极限定理可知，Δd_j之和

的标准化变量Y_m为：Step 402, according to the law of large numbers, the sequence

Converges to μ _j with probability, that is

set up

With variance

From the central limit theorem, we know that the sum of Δd _j

The standardized variable Y _m is:

Among them, the distribution function F _m (x) of Y _m satisfies for any x:

Among them, F _m (x) is the distribution function, Φ(x) is the standard normal distribution function;

的均值

将近似服从均值为μ_j，方差为

的正态分布。因此，可构建基于ETC大数据的门架区段里程生成模型MGM(Mileage GenerationModel)：Step 403, when m is large enough (m≥30), the mean of Δd _j converges to a normal distribution after proper standardization.

The mean

The approximate mean is μ _j and the variance is

Therefore, a gantry section mileage generation model MGM (Mileage Generation Model) based on ETC big data can be constructed:

ΔD～N(μ,Γ _Δd )

表示每个区段的方差，m表示经过区段的m辆车。Among them, ΔD is the generated segment mileage, and its mean vector μ = [μ ₁ ,μ ₂ ,…,μ _n-1 ], μ _n represents the mean distance of the nth segment, which is calculated based on the mileage of the passing vehicles; the covariance matrix is

represents the variance of each segment, and m represents the number of vehicles passing through the segment.

The present invention adopts the above technical scheme and realizes the measurement of section mileage based on ETC big data, with high measurement accuracy and stable performance, which changes the traditional highway mileage measurement operation mode, not only greatly reduces the cost of manual surveying and mapping, but also improves the safety factor. At the same time, it improves the basic information of the ETC system, which is conducive to the refined management of highways and improves the application value of ETC big data.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments;

FIG1 is a schematic diagram of the structure of a highway section mileage measurement method based on ETC big data according to the present invention;

FIG2 is a schematic diagram of a noise data cleaning model for a box plot;

Fig. 3 is a schematic diagram of LD ₁ ;

Fig. 4 is a schematic diagram of LD ₂ ;

Figure 5 is a schematic diagram showing the comparison of the mileage data distribution in the segment before and after LD ₁ data cleaning;

Figure 6 is a schematic diagram showing the comparison of relative errors of segment mileage before and after LD ₁ data cleaning;

Figure 7 is a schematic diagram showing the comparison of the mileage data distribution in the segment before and after LD ₂ data cleaning;

Figure 8 is a schematic diagram showing the comparison of relative errors of segment mileage before and after LD ₂ data cleaning;

Figure 9 is a schematic diagram of the overall mileage error of LD ₁ ;

Figure 10 is a schematic diagram of the overall mileage error of LD ₂ ;

FIG11 is a schematic diagram of the error accumulation probability of a single segment in LD ₁ ;

FIG12 is a schematic diagram of the error accumulation probability of a single segment in LD ₂ ;

Figure 13 is a schematic diagram showing the effect of different parameters on model error in LD ₁ ;

Figure 14 is a schematic diagram showing the effect of different parameters in LD ₂ on the model error.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution 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.

As shown in any one of FIGS. 1 to 14 , the present invention discloses a method for measuring the mileage of a highway section based on ETC big data, which comprises the following steps:

Step 1, obtain the geographic coordinates of the starting point and end point of the highway section, and use the map API to obtain the total mileage of the section;

Step 2, obtaining the driving time of the vehicle on the entire road section and calculating the average driving speed of the vehicle on the entire road section;

Step 3, obtain the residence time of the vehicle in each section, and use the average speed of the road section as the driving speed of each section to calculate the section mileage;

Step 4: According to the segment mileage of the vehicle, the segment mileage generation model is constructed as follows:

ΔD～N(μ,Γ _Δd )

表示每个区段的方差，m表示经过区段的m辆车。Where ΔD is a Gaussian random vector, whose mean vector μ = [μ ₁ ,μ ₂ ,…,μ _n-1 ], μ _n represents the mean distance of the nth segment, which is calculated based on the mileage of the passing vehicles; the covariance matrix is

represents the variance of each segment, and m represents the number of vehicles passing through the segment.

Furthermore, the map API in step 1 is the Amap API.

Furthermore, the average speed formula is used in step 2 to calculate the average speed of the vehicle:

表示第j辆车在该路段的行驶时间，Where d is the total mileage of the road section,

represents the travel time of the jth vehicle on this road section,

Furthermore, in step 3, a noise data cleaning method based on a box plot is used to obtain the residence time and mileage of the vehicle in each section.

Furthermore, the specific steps of step 3 are as follows:

Step 301, select a road section LD with a free traffic flow, and the number of lanes in each section of the road section is the same; if the traffic condition of the road section does not meet the requirements, select a time period such as the second half of the night that meets the free traffic flow requirements; if the number of lanes in each section is different, divide the sections into multiple sections and process them independently;

Step 302: Since different vehicles and different driving habits may lead to different driving speeds, the ratio of the dwelling time of a vehicle passing through a certain section to the total travel time of the section is called the section time ratio r:

Among them, Δt is the dwell time of the section, _Δtj is the dwell time of the entire section,

Step 303, normalize the section residence time to obtain the time ratio R of the m vehicles in the entire road section;

Among them, m refers to the mth vehicle; n refers to the nth section;

Step 304: Use a box plot to clean the noise data generated by vehicles passing through the service area to obtain a valid vehicle subset M" of the road section:

The valid subset of vehicles is the set of vehicles on the road segment used;

Step 305, obtaining the segment mileage ΔD:

表示第m辆车在第n-1个区段的行驶里程；m表示有效车辆子集M”中车辆的数目；Wherein, V = diag (v ¹ , v ² , …, v ^n-1 ) represents the speed of each vehicle in the subset;

represents the mileage of the mth vehicle in the n-1th segment; m represents the number of vehicles in the valid vehicle subset M”;

Furthermore, the specific steps of step 304 are as follows:

Step 3041: When a vehicle passes through a service area, it is divided into the case where the vehicle stays in the service area and the case where the vehicle does not stay in the service area. Different time usage ratios of different sections can be obtained. The time usage ratio of the vehicle not staying in the service area is:

Among them, Δt ₁ is the residence time in the section when not stopping, and Δt is the residence time of the entire section including the section;

The time ratio of vehicles staying in the service area is:

Among them, Δt ₁ is the residence time of the vehicle in the section, not included in the service area time; Δt _s is the residence time in the service area;

Step 3042, since the vehicle staying in the service area will cause the section time ratio to deviate from the overall true distribution, it is necessary to use a box plot to clean the data; obtain the various data of the box plot, of which the following are needed: Q1 is the first quartile; Q2 is the second quartile, also known as the median; Q3 is the third quartile; IQR = Q3-Q1 is the interquartile range; Q1-1.5×IQR is the lower limit Lower and Q3+1.5×IQR is the upper limit Upper; Outliers are noise points, whose values are greater than Q3+1.5×IQR or less than Q1-1.5×IQR, also known as outliers or abnormal points;

Step 3043, constructing a subset of vehicles I _j that stop at the service area according to the results of the box plot:

为第i辆车在区段j的区段用时比例；

为区段j的用时比例在箱线图中的第三四分位数；

为区段j的用时比例在箱线图中的四分位数间距；

为区段j的用时比例在箱线图中的第一四分位数；Wherein, J = {j} (j∈[1,n-1]) is the set of sections where the service area is located;

is the time ratio of the i-th vehicle in section j;

is the third quartile of the time proportion of segment j in the box plot;

is the interquartile range of the time proportion of segment j in the box plot;

is the first quartile of the time proportion of segment j in the box plot;

Step 3044, construct the vehicle subset M' of the road segment:

Among them, M is the original vehicle set, and M' is the vehicle set after eliminating the vehicles that stop at the service area;

Step 3045: Due to the complex and changeable traffic conditions, traffic flow, road maintenance and emergencies, it is necessary to further clean M' and then construct the abnormal vehicle subset I' _j in the section:

为异常车辆的区段用时比例；

为箱线图中的第三四分位数；

为箱线图中的四分位数间距；

为箱线图中的第一四分位数；in,

The proportion of time used in the section for abnormal vehicles;

is the third quartile in the box plot;

is the interquartile range in the box plot;

is the first quartile in the box plot;

Step 3046, further obtaining a valid vehicle subset M" of the road segment:

The valid subset of vehicles is the set of vehicles on the road segment used.

Furthermore, the steps of constructing the gantry section mileage generation model using the law of large numbers in step 4 are as follows:

Step 401: According to the segment mileage obtained in step 3, it can be known that the mileage of each vehicle in different segments is independent of each other and follows the same distribution with mathematical expectation:

表示第i辆车在区段j的行驶里程，μ_j为路段j的里程的数学期望值，in,

represents the mileage of the i-th vehicle in section j, μ _j is the mathematical expectation of the mileage of section j,

依概率收敛于μ_j，即

设

具有方差

由中心极限定理可知，Δd_j之和

的标准化变量Y_m为：Step 402, according to the law of large numbers, the sequence

Converges to μ _j with probability, that is

set up

With variance

From the central limit theorem, we know that the sum of Δd _j

The standardized variable Y _m is:

Among them, the distribution function F _m (x) of Y _m satisfies for any x:

Among them, F _m (x) is the distribution function, Φ(x) is the standard normal distribution function;

的均值

将近似服从均值为μ_j，方差为

的正态分布。因此，可构建基于ETC大数据的门架区段里程生成模型MGM(Mileage GenerationModel)：Step 403, when m is large enough (m≥30), the mean of Δd _j converges to a normal distribution after proper standardization.

The mean

The approximate mean is μ _j and the variance is

Therefore, a gantry section mileage generation model MGM (Mileage Generation Model) based on ETC big data can be constructed:

ΔD～N(μ,Γ _Δd )

表示每个区段的方差，m表示经过区段的m辆车。Among them, ΔD is the generated segment mileage, and its mean vector μ = [μ ₁ ,μ ₂ ,…,μ _n-1 ], μ _n represents the mean distance of the nth segment, which is calculated based on the mileage of the passing vehicles; the covariance matrix is

represents the variance of each segment, and m represents the number of vehicles passing through the segment.

The specific principle of the present invention is described in detail below:

Assume that the geographic coordinates (latitude and longitude) of the starting and ending nodes of the road section LD are known. If a road section LD does not meet assumption 1, nodes with clear geographic coordinates such as the entrance and exit of the toll station can be selected as the starting and ending nodes of the road section. Obviously, this assumption is reasonable.

Therefore, according to the geographic coordinates of the start and end nodes of the road section LD, the total mileage of the road section LD can be obtained through the Amap driving route planning API as d, and the average driving speed of the vehicle in the entire road section is v:

However, factors such as the number of lanes on a road section, emergencies, and driving behavior inevitably affect the vehicle's speed. In order to achieve a more ideal effect and meet the requirements of the MGM model, the following constraints are imposed on the study section:

L1＝L2＝…＝Ln-1, Lj is the number of lanes in section j;

The traffic condition of the selected road section LD is free flow traffic.

If a road section does not meet constraint 1, it can be divided into multiple sections and processed independently; if the road condition of a section does not meet constraint 2, a time period that meets the free flow of traffic, such as the second half of the night, can be selected. Therefore, this constraint is reasonable.

It is assumed that all vehicles are operating under ideal traffic conditions, there is no interference or influence between vehicles, and the vehicles have free flow speed.

相互独立，服从同一分布且具有数学期望

根据大数定律可得，序列

依概率收敛于μ_j，即

不妨设

具有方差

由中心极限定理可知，Δd_j之和

的标准化变量Y_m为：According to the word hypothesis, it is obvious that

Independent of each other, follow the same distribution and have mathematical expectations

According to the law of large numbers, the sequence

Converges to μ _j with probability, that is

Let's assume

With variance

From the central limit theorem, we know that the sum of Δd _j

The standardized variable Y _m is:

Among them, the distribution function F _m (x) of Y _m satisfies for any x:

的均值

将近似服从均值为μ_j，方差为

的正态分布。因此，可构建基于ETC大数据的门架区段里程生成模型MGM(Mileage Generation Model)：From the above formula, we can see that when m is large enough (usually a large sample size of m≥30 is required), the mean of Δd _j converges to the normal distribution after proper standardization.

The mean

The approximate mean is μ _j and the variance is

Therefore, a gantry section mileage generation model MGM (Mileage Generation Model) based on ETC big data can be constructed:

ΔD～N(μ,Γ _Δd )

ΔD is a Gaussian random vector, whose mean vector μ = [μ ₁ ,μ ₂ ,…,μ _n-1 ] and covariance matrix

Table 1: Description of some fields of ETC transaction data

Table 1 shows the description of some fields of ETC transaction data. After data cleaning and generation model were effectively verified, the distribution characteristics of ETC transaction data of LD ₁ and LD ₂ were analyzed. The data distribution comparison before and after cleaning of the segment mileage is shown in Figures 5 and 6. Before data cleaning, although the mileage data distribution basically has the prototype of Gaussian distribution, there are still a lot of noise data, which makes it present a skewed distribution. Specifically, QD1, QD2 and QD3 are all sections without service areas, and a large number of mileage data points are scattered on the left side of the real mileage, resulting in a longer tail on the left side of the fitting curve (top), showing a negative skewed distribution; while QD4 is a service area section, and a large number of mileage data points are scattered on the right side of the real mileage, resulting in a longer tail on the right side of the fitting curve (top), showing a positive skewed distribution. The outlier mileage data is further cleaned by the ODC algorithm. It can be seen from Figures 5 and 6 that compared with the horizontal axis coordinates of each section before cleaning, all vertical axis coordinates are reduced to a certain range, indicating that all mileage data are close to the actual mileage after cleaning; at the same time, it can be seen from the fitting curves of each section after cleaning (right side) that the mileage data distribution of all sections shows a good Gaussian distribution characteristic, indicating that most of the abnormal mileage data has been well cleaned.

The mileage data before and after cleaning are further used to estimate the mileage of each section, and MRE is used as an evaluation indicator. Specifically, 100 groups are randomly sampled from the LD ₁ and LD ₂ data sets, with sample sizes of 1 to 200 in each group, to study the fluctuation evolution of MRE. The results are shown in Figures 7 and 8. All sections show that the smaller the sample size, the more violent the MRE fluctuation. Specifically, before data cleaning, the MRE values of all sections fluctuate in a wide range, and the sections without service areas converge to negative values, while the sections with service areas converge to positive values, showing the same distribution characteristics as before cleaning, further reflecting the skewness of data distribution; after cleaning, the MRE of all sections fluctuates only in a small range, reflecting a rapid convergence to 0 value after slight oscillation. In addition, from the degree of mileage deviation after the final convergence, it is found that both the service area section and the section without service area have the characteristics that the longer the section mileage, the greater the deviation. After cleaning, the total number of complete trajectories obtained for LD ₁ and LD ₂ were 1033 and 1302, respectively, and the data distribution characteristics and MRE of each segment before and after data cleaning were compared and analyzed.

On the basis of ensuring data quality, sample size will directly affect the size of the error of the generative model. In order to fully study the impact of sample size on the error, MAE is used as an evaluation indicator. Specifically, random sampling is performed from the LD ₁ and LD ₂ data sets, with sample sizes ranging from 1 to 1000, and repeated 100 times to study the fluctuation evolution law of MAE. As shown in Figures 9 and 11, MAE decreases rapidly with the increase of sample size, and its error fluctuation range gradually decreases and eventually tends to be stable. According to the requirements for sample size in Section 2, m = 30 is a watershed of sample size. When m < 30, the MAE error fluctuates violently and widely, and some of its errors exceed 200m, indicating that the performance of the generative model is poor under small sample size; when m > 30, the MAE fluctuation range is small, and its mean fluctuation changes smoothly and is less than 50m, indicating that the performance of the generative model has been greatly improved under large sample size, which further verifies the requirements of the generative model for large sample size in Section 2.

Further, multiple experiments are conducted on each section of the road section, and the overall probability distribution of MAE is calculated. Let δ = 100m, α = 0.02. Since the standard deviation σ is unknown, 10,000 groups can be randomly selected from the data set, with 30 samples in each group, and the standard deviation of each section can be calculated. Taking the maximum value, we can get: σ ₁ ≈[379,86,279,348] (unit: m, the same below) for each section of LD ₁ , and σ ₂ ≈[115,315,152,370] for each section of LD _2. Therefore, let σ _max of LD ₁ and LD ₂ be 379m and 370m respectively. According to Corollary 1, the required sample size of LD ₁ and LD ₂ is at least 78 and 75 respectively, so we only need to set m1 = 78 and m2 = 75. In order to approximate the true error probability distribution of each section, 10,000 groups of experiments (the same below) were conducted on each section and the error cumulative probability distribution (CDF) curve was drawn. As shown in Figures 10 and 12, all sections can control the error within 100m with a 100% confidence probability, and the probability value is stably higher than the preset value of 98%. At the same time, when the confidence probability is 98%, each section in LD ₁ can control the error within 73m, and each section in LD ₂ can control the error within 66m, indicating that the performance of the generative model is significant. In particular, under the same sample size, QD2 of LD ₁ and QD1 of LD ₂ perform better, and control the error within 30m and 32m respectively with a 100% confidence probability. Further research found that the mileage of the two sections is shorter, and their generative model performance is better.

In order to further study the impact of sample size on the error of the generated model under different parameters, the following experiment is conducted using the control variable method:

To study the effect of parameter σ, let α and δ be fixed values. Let α = 0.02, δ = 100m, and the standard deviations of the two sections be σ ₁ and σ ₂ respectively. The required sample sizes for LD ₁ and LD ₂ are [78, 30, 42, 66] and [30, 53, 30, 75] respectively. The corresponding CDF curves are shown in Figures 13(a) and (c). Under different σ, the confidence probabilities of LD ₁ and LD ₂ within an error of 100m are [100%, 100%, 99.6%, 99.9%] and [100%, 99.8%, 100%, 100%] respectively, which are both stable and higher than the preset value of 98%. At the same time, when the confidence probability is 98%, LD ₁ and LD ₂ can control the error within [64.0, 28.8, 82.9, 77.6] and [31.9, 75.6, 54.3, 62.9] respectively, which are far lower than the preset value of 100m.

To study the effect of parameter δ, α and σ are fixed. Let α = 0.02, σ = σ _max , δ = [50, 100, 150, 200], and the sample sizes required for LD ₁ and LD ₂ are [315, 78, 35, 30] and [297, 75, 33, 30], respectively. This indicates that the larger δ is, the smaller the sample size is required. After δ > 150, the required sample size basically does not change due to the large sample size. According to the experimental parameter settings, the CDF curves corresponding to the two sections are shown in Figure 13 (b) and Figure 14 (e). As the sample size increases, the error becomes smaller under the same confidence probability. When the confidence probability is 98%, the errors corresponding to LD ₁ and LD ₂ are [25.7, 41.3, 58.0, 62.0] and [22.1, 36.9, 54.3, 56.1], respectively, which are much smaller than the corresponding preset values; at the same time, the confidence probability at the preset value δ is 100%, and the effect is significant. At the same time, when δ is smaller, the required sample size increases in square series, and the steepness of its probability distribution curve increases successively, indicating that the change of parameter δ has a greater impact on the error of the generated model.

To study the effect of parameter α, δ and σ are fixed. Let δ = 100m, σ = σ _max , α = [0.02, 0.04, 0.06, 0.08, 0.10], and the required sample sizes for LD ₁ and LD ₂ are [78, 61, 51, 44, 39] and [75, 58, 48, 42, 38], respectively. Their CDF curves are shown in Figures 13(c) and 14(f). When the confidence probability (1-α) is the set value, the errors corresponding to LD ₁ and LD ₂ are basically distributed between 33 and 44m and 28 and 38m, respectively, which are significantly lower than the set threshold of 100m, and the effect is significant. Further research found that the sample size distribution span under different α is small, so that their probability distribution curves are basically consistent, indicating that the change of parameter α has little effect on the error of the generated model.

The present invention adopts the above technical scheme to construct a highway section mileage generation model based on ETC transaction data, and derives the functional relationship between the data sample capacity and the generation model error. The field experimental results show that the average error of the section mileage generated by the model reaches the accuracy requirement of 10m, and has strong robustness and applicability. Finally, the ETC transaction data from September 3 to 5, 2020 were used to conduct field verification on two sections of the Shenhai Expressway (Caopuyuan Hub~Neikeng Hub, Ganghou Hub~Xipu Hub). Theoretical analysis and experimental results show that the average error of the section mileage generated by the model reaches the accuracy requirement of 10m, and has strong robustness and applicability. The model constructed by the present invention relies solely on ETC big data to realize the measurement of highway section mileage, and has small measurement error and stable performance, which is conducive to the refined management of highways and improves the application value of ETC big data.

Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. In the absence of conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians of the art without making creative work are within the scope of protection of the present application.

Claims (8)

1. A highway section mileage measurement method based on ETC big data, characterized in that it includes the following steps: Step 1, obtain the geographic coordinates of the starting point and end point of the highway section, and use the map API to obtain the total mileage of the section; Step 2, obtaining the driving time of the vehicle on the entire road section, and calculating the average driving speed of the vehicle on the entire road section in combination with the mileage of the entire road section; Step 3, divide the entire road section into several sections, obtain the vehicle's residence time in each section respectively, and use the average speed of the entire road section as the driving speed of each section to calculate the section mileage; Step 4: According to the mileage of different sections of the vehicle, a section mileage generation model is constructed as follows: ΔD～N(μ,Γ _Δd ) Where ΔD is a Gaussian random vector, whose mean vector μ = [μ ₁ ,μ ₂ ,…,μ _n-1 ], μ _n represents the mean distance of the nth segment, which is calculated based on the mileage of the passing vehicles; the covariance matrix is

Represents the variance of each segment, m represents the number of vehicles passing through the segment; N represents normal distribution. 2. According to a method for measuring mileage of a highway section based on ETC big data in claim 1, it is characterized in that the map API in step 1 is Amap API. 3. A highway section mileage measurement method based on ETC big data according to claim 1, characterized in that: in step 2, the average speed formula is used to calculate the average speed of the vehicle:

Where d is the total mileage of the road section,

represents the travel time of the jth vehicle on this road section. 4. A highway section mileage measurement method based on ETC big data according to claim 3, characterized in that: the specific steps of using a noise data cleaning method based on a box plot in step 3 to obtain the residence time and mileage of the vehicle in each section are as follows: Step 301, select a road section LD with a free traffic flow, and the number of lanes in each section of the road section is the same; if the traffic condition of the road section does not meet the requirements, select a time period such as the second half of the night that meets the free traffic flow requirements; if the number of lanes in each section is different, divide the sections into multiple sections and process them independently; Step 302: Since different vehicles and different driving habits may lead to different driving speeds, the ratio of the dwelling time of a vehicle passing through a certain section to the total travel time of the section is called the section time ratio r:

Among them, Δt is the dwell time of the section, _Δtj is the dwell time of the entire section, Step 303, normalize the section residence time to obtain the time ratio R of the m vehicles in the entire road section;

Among them, m refers to the mth vehicle; n refers to the nth section; Step 304, using a box plot to clean the noise data generated by vehicles passing through the service area, to obtain a valid vehicle subset M" of the road section:

The valid subset of vehicles is the set of vehicles on the road segment used; Step 305, obtaining the segment mileage ΔD:

Wherein, V = diag (v ¹ , v ² , …, v ^n-1 ) represents the speed of each vehicle in the subset;

represents the mileage of the m-th vehicle in the n-1-th section; m represents the number of vehicles in the valid vehicle subset M". 5. The method for measuring the mileage of a highway section based on ETC big data according to claim 4 is characterized in that: the specific steps of step 304 are as follows: Step 3041: When a vehicle passes through a service area, it is divided into the vehicle staying in the service area and the vehicle not staying in the service area, and the time ratio of different sections is obtained. The time ratio of not staying in the service area is:

Among them, Δt ₁ is the residence time in the section when not stopping, and Δt is the residence time of the entire section including the section; The time ratio of vehicles staying in the service area is:

Among them, Δt ₁ is the residence time of the vehicle in the section, not included in the service area time; Δt _s is the residence time in the service area; Step 3042, The data needed to obtain the box plot are: Q1 is the first quartile; Q2 is the second quartile, also known as the median; Q3 is the third quartile; IQR = Q3-Q1 is the interquartile range; Q1-1.5×IQR is the lower limit Lower and Q3+1.5×IQR is the upper limit Upper; Outliers are noise points, whose values are greater than Q3+1.5×IQR or less than Q1-1.5×IQR, also known as outliers or abnormal points; Step 3043, constructing a subset of vehicles I _j that stop at the service area according to the results of the box plot:

Wherein, J = {j} (j∈[1,n-1]) is the set of sections where the service area is located;

is the time ratio of the i-th vehicle in section j;

is the third quartile of the time proportion of segment j in the box plot;

is the interquartile range of the time proportion of segment j in the box plot;

is the first quartile of the time proportion of segment j in the box plot; Step 3044, construct a vehicle subset M′ of the road section that does not contain vehicles stopping at the service area:

Among them, M is the original vehicle set, and M′ is the vehicle set after eliminating the vehicles that stopped at the service area; Step 3045, M' is further cleaned to obtain vehicles affected by traffic abnormalities, and then the abnormal vehicle subset I _j ' of the section is constructed:

in,

The proportion of time used in the section for abnormal vehicles;

is the third quartile in the box plot;

is the interquartile range in the box plot;

is the first quartile in the box plot; Step 3046, further obtaining a valid vehicle subset M" of the road section:

The valid subset of vehicles is the set of vehicles on the road segment used. 6. A highway section mileage measurement method based on ETC big data according to claim 5, characterized in that: the traffic abnormality factors in step 3045 include traffic flow, road maintenance and emergencies. 7. According to a method for measuring highway section mileage based on ETC big data as described in claim 1, it is characterized in that: in step 4, the law of large numbers is used to construct a gantry section mileage generation model. Step 401: According to the segment mileage obtained in step 3, it can be known that the mileage of each vehicle in different segments is independent of each other and follows the same distribution with mathematical expectation:

in,

represents the mileage of the i-th vehicle in section j, μ _j is the mathematical expectation of the mileage of section j, Step 402, according to the law of large numbers, the sequence

Converges to μ _j with probability, that is

set up

…with variance

From the central limit theorem, we know that the sum of Δd _j

The standardized variable Y _m is:

Among them, the distribution function F _m (x) of Y _m satisfies for any x:

Among them, F _m (x) is the distribution function, Φ(x) is the standard normal distribution function; Step 403, when m is not less than the minimum value, the mean of Δd _j converges to the normal distribution after proper standardization, then any

The mean

The approximate mean is μ _j and the variance is

If the normal distribution of is obtained, the gantry section mileage generation model MGM based on ETC big data is constructed: ΔD～N(μ,Γ _Δd ). 8. A highway section mileage measurement method based on ETC big data according to claim 7, characterized in that: the minimum value in step 403 is 30, that is, m≥30.

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