A transportation network reliability evaluation method based on entropy weight-TOPSIS method

Abstract

A traffic network reliability evaluation method based on entropy weight TOPSIS method involves the field of traffic network evaluation. From the perspective of traffic flow operation, the three aspects of traffic network operation efficiency, time resources and space resources are considered. The speed deviation rate, high delay operation time ratio and frequently congested road mileage ratio are selected to construct evaluation indicators. The evaluation indicator weights are calculated based on the entropy weight method. The traffic network reliability is calculated based on the TOPSIS method. An example analysis is conducted on a traffic network in a town in Tongzhou District, Beijing. The results show that the calculation results of the present invention are consistent with those of the existing methods, and the minimum sum of square errors (SSE) is less than the existing methods, which verifies the advancement and applicability of the present invention. The present invention is conducive to fine management and precise governance of traffic networks and improves reliability.

Description

Technical Field

[0001] The present invention relates to the field of transportation network evaluation, and mainly aims at the reliability evaluation of transportation networks. A transportation network reliability evaluation method based on entropy weight-TOPSIS method is proposed, which can quantitatively describe the reliability of transportation networks from three dimensions: operating efficiency, time resources and space resources. Background Art

[0002] As my country enters a new era, the economy, culture, public services, and infrastructure of various regions and cities all require high-quality development. As an important carrier of residents' travel, the urban transportation network will also abandon the past high-speed, rough construction model and enter a new stage of optimizing stock and improving quality.

[0003] In many cities in my country, the roads are getting longer and longer, the road networks are getting denser and denser, but the traffic problems are becoming more and more prominent. The root cause is that the road length and road network density have been increased in quantity, but the quality has not met the requirements. The existing supply cannot meet the traffic demand, resulting in a situation of supply exceeding demand and an imbalance between supply and demand.

[0004] Therefore, only by quantitatively describing the reliability of the transportation network from the three dimensions of operating efficiency, time resources and space resources can we accurately evaluate the operating quality of the existing road network and propose practical road network optimization methods to better meet transportation needs.

[0005] At present, most of the traffic network reliability evaluation is based on complex network theory, and the reliability is obtained by judging the road network structure. However, once the road is built, the road network structure is basically formed and it is difficult to change fundamentally. If you want to improve the network reliability, you can only achieve the goal by building or renovating roads. This is not in line with the current concept of high-quality development. In addition, building new roads is often costly and time-consuming, which is not an economically reasonable and easy-to-operate method. Therefore, it is necessary to select appropriate indicators from other perspectives to evaluate the reliability of the traffic network, so as to improve the quality of the traffic network, optimize traffic supply, and improve the operation efficiency of the traffic network. Summary of the invention

[0006] The present invention fully considers the high efficiency of operation, the abundance of time resources and the smoothness of road space from the perspective of traffic flow operation, and selects speed deviation rate, high delay operation time ratio and mileage ratio of frequently congested sections as evaluation indicators to evaluate the reliability of the traffic network.

[0007] The significance and calculation methods of the evaluation indicators are as follows:

[0008] (1) Operation efficiency index

[0009] The operating efficiency of the road network can represent the operating conditions of the entire traffic network. Traffic flow theory believes that the smoother the speed of vehicles on the road, the smoother the road operation and the less likely traffic jams will occur. At this time, the road network has a higher operating efficiency. Therefore, this paper uses the speed deviation rate to represent the operating efficiency of roads in the network, that is, the ratio of the standard deviation of vehicle speeds on each road section within the scope of the road network in the study area to the average value.

[0010] Considering the stable running speed, there are two situations:

[0011] First, the overall road operation is smooth, the vehicle speed is high and the operation is stable, and the road network efficiency is high at this time;

[0012] The second is that the road is congested and the vehicle speed is low but stable, and the road network efficiency is low at this time.

[0013] The speed deviation rate in both cases is relatively small, but they correspond to two completely opposite cases. Therefore, the calculation of road network efficiency should also be calculated according to the situation. According to convention, whether a road is congested or not is not when the vehicle speed is reduced to 0, but when the speed is lower than 30km / h, the road is considered to be in a congested state. When the vehicle speed is lower than 10km / h, the road is in a serious congestion. Based on this, the road network efficiency calculation formula of the present invention is:

[0014]

[0015] Where: α is the running speed deviation rate; σ a is the speed standard deviation of section a; μ a is the average speed of section a.

[0016] In a non-congested state, the smaller the speed deviation rate, the greater the possibility that the vehicle speeds on the traffic network will tend to be consistent, the traffic operation will be smoother and more orderly, and the efficiency will be 0 in a congested state; conversely, the greater the vehicle speed fluctuation, the greater the possibility of conflict, thereby reducing the road network operation efficiency.

[0017] (2) Time resource indicators

[0018] Time is the primary consideration for travelers and an important indicator for measuring the quality of the road network. The present invention selects the proportion of high-delay operation time to measure the time resources of the traffic network, that is, the ratio of the cumulative operation time with a traffic delay index higher than 1.5 within the road network of the research area to the whole day. The calculation formula is:

[0019]

[0020] Where: β is the proportion of high-delay operation time of the road network; t is the cumulative operation time of the network delay index higher than 1.5 within a certain period of time; T is a research cycle. Among them, the road network delay index refers to the ratio of the actual operation time of the traffic network to the free flow time, and the calculation formula is:

[0021]

[0022] Where: τ is the delay index; is the actual running time of section a; is the free flow time of section a.

[0023] The greater the proportion of high-latency operation time, the greater the time load of the road network. The traffic network is busy for a long time, and is easily affected by interference events, resulting in reduced robustness, increased vulnerability, and damaged quality.

[0024] (3) Space resource indicators

[0025] The utilization of traffic network space resources can reflect the state of road congestion, but occasional congestion does not mean that road space resources are exhausted. Only frequent and severe congestion can truly reflect the utilization of road space resources. Therefore, the road network space resources are calculated by the mileage ratio of frequently congested sections, that is, the mileage ratio of sections in the road network that experience severe congestion (delay index higher than 1.5) with a certain frequency. The calculation formula is:

[0026]

[0027] Where: γ is the mileage ratio of frequently congested sections; l a is the length of the frequently congested section of section a; L a is the total length of section a.

[0028] The greater the proportion of frequently congested sections, the greater the load on the road network, which is more susceptible to interference and causes regional traffic congestion or paralysis.

[0029] The calculation method of the evaluation index in the present invention is discussed above, but the three evaluation indexes do not affect the reliability of the traffic network to the same extent, so it is necessary to calculate the weights of the evaluation indexes. The present invention selects the entropy weight method to calculate the index weights.

[0030] The entropy weight method is a quantitative method for calculating indicator weights. Compared with the hierarchical analysis method, the principal component method and the factor analysis method, it focuses more on describing the degree of difference between indicators and is suitable for calculating indicator weights when conducting reliability evaluation. The specific calculation steps are as follows:

[0031] (1) Each indicator is normalized using the maximum and minimum values, and the indicators are adjusted in the positive and negative directions.

[0032] (2) Calculate the proportion of the i-th sample value under the j-th indicator to the indicator

[0033]

[0034] (3) Calculate the entropy value of the jth indicator

[0035]

[0036] (4) Calculate information entropy redundancy

[0037] d j =1-e j ,j=1,2,3…,m (7)

[0038] (5) Calculate the weight of each indicator

[0039]

[0040] The above has completed the calculation of the evaluation index weights. Next, it is necessary to select a suitable method to comprehensively calculate the index weights and index values ​​to obtain the reliability of the transportation network.

[0041] This paper selects the TOPSIS method for reliable calculation. The basic idea of ​​the TOPSIS method is to use historical data to determine the optimal solution and the worst solution of the research target, which are called positive ideal solution and negative ideal solution respectively, and then calculate the distance between each object involved in the evaluation and the positive and negative ideal solutions, so as to obtain the closeness between each evaluation object and the ideal solution, and thus obtain the evaluation result of the scheme. The calculation process is as follows:

[0042] (1) Determine the positive and negative ideal solutions of the indicators

[0043] A + = {max x ij |i=1,2,3,…} (9)

[0044] A - = {min x ij |i=1,2,3,…} (10)

[0045] (2) Use the best and worst values ​​to normalize the data and consider the positive and negative adjustments of the indicators

[0046]

[0047]

[0048] (3) Use the Euclidean distance to calculate the distance to the best and worst targets and multiply it by the weight

[0049]

[0050]

[0051] (4) Calculate the relative closeness of each evaluation object, that is, the reliability of this article.

[0052]

[0053] So far, the reliability of the transportation network has been calculated. Next, we will select a suitable method to test its accuracy and use numerical solutions to illustrate the applicability of this method.

[0054] In order to test the accuracy of this method in evaluating the reliability of the road network, this paper uses the travel time as the standard to select the minimum error square sum method (SSE) to test the proximity between the evaluation result and the standard value. SSE is the sum of squares of the error between the evaluation result and the standard value. The smaller the error, the better. Therefore, the smaller the minimum error square sum, the closer the calculation result of this method is to the actual road situation. The calculation formula is:

[0055]

[0056] Where: SSE is the minimum error square sum; a represents the road section; R(T a ) is the travel time reliability of section a, and the calculation formula is:

[0057]

[0058] V(T a ) is the standard speed of section a, which refers to the speed after normalizing the average speed, and can be mapped between 0 and 1. The calculation formula is:

[0059]

[0060] Where: is the average speed of section a; is the minimum speed of section a; is the maximum speed of section a.

[0061] The standard value is calculated as follows: The network travel time T is calculated by the BPR function. a Then, according to the on-site traffic survey, the average travel time of each section is obtained, which is less than 1.1T a The vehicle proportion is used as the standard value of the travel time reliability of the measured road section.

[0062] In order to further illustrate the applicability of the reliability calculation method in the present invention, the existing method is selected as a control, and the traffic network reliability of the method of the present invention and the existing method is calculated respectively, and the minimum sum of square errors (SSE) between the two methods and the standard value is calculated. The applicability of the method of the present invention is illustrated by comparison using numerical solutions.

[0063] The existing reliability calculation method is as follows:

[0064]

[0065] Where: R n is the reliability of road section n; R stis the reliability of the OD link between s and t; q st is the traffic volume between OD pairs s and t. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a flow chart of the traffic network reliability evaluation based on the entropy weight-TOPSIS method of the present invention.

[0067] Figure 2 This is a flow chart for determining a frequently congested road section according to the present invention.

[0068] Figure 3 It is the numerical difference between the calculation results of the method of the present invention, the calculation results of the existing method and the reliability standard value. DETAILED DESCRIPTION

[0069] The technical solution of the present invention will be fully described below in conjunction with examples. The flow chart of the traffic network reliability evaluation method based on entropy weight-TOPSIS method of the present invention is as follows: Figure 1 shown.

[0070] The purpose of this invention is to evaluate the reliability of the traffic network from the perspective of road sections. The evaluation index is not based on the structural index of the complex network, but on the traffic flow operation index, and strives to improve the reliability of the traffic network from the perspective of management.

[0071] The specific implementation steps of the evaluation process are as follows:

[0072] First, basic road data and traffic flow operation data are obtained. The evaluation index calculation of the invention requires data such as operating speed, average speed, speed standard deviation, driving time, and road length.

[0073] Secondly, calculate the evaluation index. Calculate the traffic network reliability evaluation index from the three perspectives of efficiency, time and space. The index calculation method is as follows:

[0074] (1) Calculation of road network efficiency

[0075]

[0076] Where: α is the running speed deviation rate; σ a is the speed standard deviation of section a; μ a is the average speed of section a.

[0077] (2) Time resource calculation

[0078]

[0079] Where: β is the proportion of high-delay operation time of the road network; t is the cumulative operation time of the network delay index higher than 1.5 within a certain period of time; T is a research cycle. Among them, the road network delay index refers to the ratio of the actual operation time of the traffic network to the free flow time, and the calculation formula is:

[0080]

[0081] Where: τ is the delay index; is the actual running time of section a; is the free flow time of section a.

[0082] (3) Spatial resource calculation

[0083]

[0084] Where: γ is the mileage ratio of frequently congested sections; l a is the length of the frequently congested section of section a; L a is the total length of section a.

[0085] Next, the entropy weight-TOPSIS method is used to calculate the evaluation index weights and transportation network reliability. The steps are as follows:

[0086] (1) Each indicator is normalized using the maximum and minimum values, and the indicators are adjusted in the positive and negative directions.

[0087] (2) Calculate the proportion of the i-th sample value under the j-th indicator to the indicator

[0088]

[0089] (3) Calculate the entropy value of the jth indicator

[0090]

[0091] (4) Calculate information entropy redundancy

[0092] d j =1-e j ,j=1,2,3…,m (7)

[0093] (5) Calculate the weight of each indicator

[0094]

[0095] (6) Determine the positive and negative ideal solutions of the indicators

[0096] A + = {max x ij |i=1,2,3,…} (9)

[0097] A -= {min x ij |i=1,2,3,…} (10)

[0098] (7) Use the best and worst values ​​to normalize the data and consider the positive and negative adjustments of the indicators

[0099]

[0100]

[0101] (8) Use the Euclidean distance to calculate the distance to the best and worst targets and multiply it by the weight

[0102]

[0103]

[0104] (9) Calculate the relative closeness of each evaluation object, that is, the reliability of this article.

[0105]

[0106] Finally, the calculation results are tested. The present invention uses the minimum sum of square errors (SSE) method to test the accuracy of the evaluation results based on the reliability of the travel time. The SSE calculation method is as follows:

[0107]

[0108] Where: SSE is the minimum error square sum; a represents the road section; R(T a ) is the travel time reliability of section a, and the calculation formula is:

[0109]

[0110] V(T a ) is the standard speed of section a, which refers to the speed after normalizing the average speed, and can be mapped between 0 and 1. The calculation formula is:

[0111]

[0112] Where: is the average speed of section a; is the minimum speed of section a; is the maximum speed of section a

[0113] In order to further illustrate the accuracy of the calculation results of the present method, the present invention selects an existing reliability calculation method as a control, and compares the reliability calculation results of the two methods and the SSE between the two results and the standard value.

[0114] The calculation method of reliability standard value is as follows:

[0115] The road network travel time T is calculated by the BPR function a Then, according to the on-site traffic survey, the average travel time of each section is obtained, which is less than 1.1T a The vehicle proportion is used as the standard value of the travel time reliability of the measured road section.

[0116] The existing reliability calculation method is as follows:

[0117]

[0118] Where: R n is the reliability of road section n; R st is the reliability of the OD link between s and t; q st is the traffic volume between OD pairs s and t.

[0119] The above are the specific implementation steps of the present invention, which are described below with reference to case data.

[0120] The road attribute data and traffic flow operation data of 30 road sections in a city are known, as shown in Table 1:

[0121] Table 1 Traffic network attribute data

[0122]

[0123] Based on the traffic network attribute data in Table 1, the speed deviation rate of each road section is calculated using formula (1), and the high-delay operation time ratio is calculated using formula (2). The delay index is calculated using formula (3), and a delay index greater than or equal to 1.5 is considered to be high delay. The mileage ratio of frequently congested sections is calculated using formula (4). The judgment process of frequently congested sections is as follows: Figure 2 The calculation results of the evaluation index are shown in Table 2:

[0124] Table 2 Transportation network evaluation indicators

[0125]

[0126] Based on Table 2, the weights of the evaluation indicators are calculated using formulas (5) to (8). The results are shown in Table 3:

[0127] Table 3 Reliability evaluation index weights

[0128]

[0129] Table 3 shows that among the three evaluation indicators, the mileage ratio of frequently congested sections (γ) has the highest weight, reaching 0.412; the proportion of high-delay operation time (β) is the lowest, which is 0.210.

[0130] Next, the traffic network reliability of the method of the present invention is calculated using equations (9) to (15), and the traffic network reliability of the existing method is calculated using equation (19). The results are shown in Table 4:

[0131] Table 4. Transportation network reliability

[0132]

[0133] Table 4 shows that the traffic network reliability calculated by the method of the present invention is consistent with the calculation results of the existing method, which verifies the applicability of the method, that is, the present invention can be used to calculate the traffic network reliability. In addition, in order to further illustrate the accuracy of the method, the present invention uses SSE for verification.

[0134] The SSE of the two methods are calculated using formula (16). The results are shown in Table 5:

[0135] Table 5 Calculation results SSE test

[0136]

[0137] As shown in Table 5, the SSE of the method of the present invention is smaller than that of the existing method. SSE represents the minimum sum of squares of the error between the calculated value and the standard value. The smaller the error, the more accurate the calculation result. Therefore, the method of the present invention has higher accuracy, smaller error, and more reliable calculation results. The numerical difference between the calculation results and the standard values ​​of the two methods is shown in Figure 3 shown. Figure 3 In the figure, error 1 is the error between the traditional method and the standard value, with an average absolute error of 0.1, a maximum of 0.28, and a minimum of 0.01; error 2 is the error between the method of the present invention and the standard value, with an average absolute error of 0.04, a maximum of 0.1, and a minimum of 0. By comparing error 1 and error 2, it can be seen that the calculation of the method of the present invention is more accurate.

[0138] The present invention calculates the reliability of the traffic network based on the entropy weight-TOPSIS method. From the perspective of traffic flow operation, the present invention considers the three aspects of operation efficiency, time resources and space resources, selects the speed deviation rate, high delay operation time ratio and frequently congested road mileage ratio to construct evaluation indicators, and conducts an example analysis on a town in Tongzhou District, Beijing. The results show that the calculation results of the present invention are consistent with those of the existing methods, and the minimum sum of square errors (SSE) is less than that of the existing methods, which verifies the advancement and applicability of the present invention. The present invention is conducive to the refined management of the traffic network and improves the reliability of the traffic network.

[0139] The above implementation example is only an example selected to clearly illustrate the present invention, and does not limit the implementation method of the present invention in any form. Any changes in the form and details of the technical essence of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A transportation network reliability evaluation method based on entropy weight-TOPSIS method, characterized in that: The following steps are involved: Step 1: Collect basic road data and traffic flow operation data based on the characteristics of the traffic network. First, obtain basic road data and traffic flow data, calculate network efficiency, time resources and space resources based on road length, design speed, operating speed, average speed, free flow time and actual travel time, and select speed deviation rate, high delay operation time ratio and mileage ratio of frequently congested sections for measurement; Step 2: Use the entropy weight method to calculate the weight of the evaluation index; first calculate the weight coefficient of the index under each sample, and then obtain the comprehensive weight of the evaluation index according to the information entropy redundancy; Step 3: Use the TOPSIS method to calculate the reliability of the transportation network. It is necessary to fix the optimal solution and the worst solution based on historical data and adjust the indicators in the positive and negative directions, calculate the Euclidean distance from each data to the optimal and worst solutions, and then obtain the relative closeness as the reliability of the transportation network. The specific implementation process of step one is as follows: (1) Obtain road basic data and traffic flow operation data; (2) Calculate the evaluation index: Operation efficiency indicators: Where: α is the running speed deviation rate; σ a is the speed standard deviation of section a; μ a is the average speed of section a; Time Resource Indicators: Where: β is the proportion of high-delay operation time of the road network; t is the cumulative operation time of the network delay index higher than 1.5 within a certain period of time; T is a research cycle; the road network delay index refers to the ratio of the actual operation time of the traffic network to the free flow time, and the calculation formula is: Where: τ is the delay index; is the actual running time of section a; is the free flow time of section a; Space resource indicators: Where: γ is the mileage ratio of frequently congested sections; l a is the length of the frequently congested section of section a; L a is the total length of section a; Road sections where the average travel speed is less than 50% of the free flow speed are considered to be congested, and sections where the congestion duration ratio exceeds 50% during the observation period are considered to be frequently congested sections. The specific implementation process of step 2 is as follows: (1) Each indicator is normalized using the maximum and minimum values, and the indicators are adjusted in the positive and negative directions. (2) Calculate the proportion of the i-th sample value under the j-th indicator to the indicator (3) Calculate the entropy value of the jth indicator (4) Calculate information entropy redundancy d j =1-e j ,j=1,2,3…,m (7) (5) Calculate the weight of each indicator 2. According to claim 1, a traffic network reliability evaluation method based on entropy weight-TOPSIS method is characterized in that: The specific implementation process of step three is as follows: (1) Determine the positive and negative ideal solutions of the indicators Where: i—the i-th sample; j—the j-th indicator; (2) Use the best and worst values ​​to normalize the data and consider the positive and negative adjustments of the indicators Where: i—the i-th sample; j—the j-th indicator; (3) Use the Euclidean distance to calculate the distance to the best and worst targets and multiply it by the weight Where: i—the i-th sample; j—the j-th indicator; (4) Calculate the relative closeness of each evaluation object, that is, the reliability of this article; Where: i—the i-th sample.

3. The method for evaluating the reliability of a transportation network based on entropy weight-TOPSIS method according to claim 1 is characterized in that: The specific implementation process of step 4 is as follows: (1) Calculate the travel time reliability standard value: Calculate the network travel time T using the BPR function a Then, according to the on-site traffic survey, the average travel time of each section is obtained, which is less than 1.1T a The vehicle probability is used as the standard value of the reliability of the measured road section travel time; (2) Calculate SSE: Where: SSE is the minimum error square sum; a represents the road section; N is the number of road sections; R(T a ) is the travel time reliability of section a, and the calculation formula is: Where: P is probability; is the actual running time of section a; is the free flow time of section a; V(T a ) is the standard speed of section a, which refers to the speed after normalizing the average speed and mapping it between 0 and 1; the calculation formula is: Where: is the average speed of section a; is the minimum speed of section a; is the maximum speed of section a.

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