Road section delay loss estimation method based on ponding depth and traffic flow probability density

Abstract

The invention discloses a road section delay loss estimation method based on ponding depth and traffic flow probability density. The method comprises the following steps: S1, establishing a relation model of the ponding depth and the distance of a road section; s2, drawing up a probability density function of the maximum ponding depth based on the maximum ponding depth of the road section acquired by forecasting the historical record of the same rainfall; s3, drawing up a probability density function of the road section traffic flow based on the road section traffic flow collected by forecasting the same rainfall historical record; s4, calculating the free flow speed, calculating the average vehicle speed according to the road section traffic flow, and calculating the average passing time of the vehicle under the road section water accumulation condition; and S5, calculating the average delay time of the vehicle in the ponding road section, and estimating the total traffic delay loss amount of the road section according to the average delay time and the passenger number probability distribution. According to the method, the scientific delay loss estimation model is established by comprehensively based on the uncertainty of the ponding depth, the traffic flow and the number of passengers, and an important basis is provided for prevention and treatment of traffic congestion caused by urban waterlogging ponding.

Description

Technical Field

[0001] The invention belongs to the technical field of traffic operation evaluation, and in particular relates to a method for estimating road section delay losses based on water accumulation depth and traffic flow probability density. Background Art

[0002] In recent years, the impact of waterlogging and secondary disasters caused by extreme rainfall has become increasingly serious, not only causing serious damage to urban infrastructure, but also directly threatening the normal operation of the transportation system, affecting the travel efficiency and safety of vehicles and pedestrians. Road waterlogging will directly cause a significant reduction in vehicle speed and efficiency, thereby extending the driving time of vehicles in flooded sections, aggravating travel delays and traffic congestion, affecting not only the daily lives of citizens, but also commercial logistics, and ultimately hindering the operation of the city's economy.

[0003] In actual situations, it is difficult to accurately estimate the impact of waterlogging on road traffic. First, due to factors such as rainfall, terrain characteristics, and drainage facilities, the road waterlogging situation is uncertain, and the actual depth and range of waterlogging are difficult to accurately predict; secondly, due to the influence of weather forecasts, traffic control measures, and traffic induction plans, travel demand and travel methods often show uncertain characteristics, and the changes in road traffic flow cannot be fully grasped, making it difficult to accurately estimate; in addition, the number of passengers in various types of vehicles will also change, and obey a certain distribution law within a certain range. Therefore, the use of a fixed value calculation method to estimate the possible road traffic delay losses caused by waterlogging is less applicable.

[0004] In order to solve the above problems, it is necessary to establish the probability density function of water depth and traffic flow of the evaluation section based on the historical records of the same rainfall forecast; combine the relationship model between water depth and distance of the section to calculate the average travel time of vehicles in the flooded section; consider the flow size of different types of vehicles and the probability distribution function of the number of passengers, and estimate the total loss of traffic delays on the section. By studying the road traffic operation status and service level evaluation technology under waterlogging conditions, it can provide an important reference for analyzing and controlling urban traffic congestion under the influence of waterlogging. Summary of the invention

[0005] The main purpose of the present invention is to provide a method for estimating road section delay losses based on waterlogging depth and traffic flow probability density based on historical detection data and distribution patterns, to achieve travel time estimation and loss time calculation for flooded sections, and to provide technical support for evaluating the impact of urban waterlogging on road traffic operation efficiency.

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

[0007] The present invention provides a method for estimating road section delay losses based on waterlogging depth and traffic flow probability density, comprising the following steps:

[0008] S1. Establish a model of the relationship between water depth and distance of road sections based on geographic elevation information;

[0009] S2. Propose a probability density function of the maximum water depth based on the maximum water depth of the road section collected from historical records of the same rainfall amount;

[0010] S3. Propose a probability density function of the traffic flow of a road section based on the traffic flow of the road section collected from the historical records of the same rainfall amount;

[0011] S4. Calculate the free flow speed of each point in the flooded area based on the relationship model between the depth of flooding and the distance of the road section, calculate the average speed of vehicles based on the traffic flow of the road section, and calculate the average travel time of vehicles under flooding conditions based on the probability density function of the maximum flooding depth and the probability density function of the traffic flow;

[0012] S5. Calculate the average delay time of vehicles on flooded sections based on the average travel time without flooding and the average travel time under flooding conditions, and estimate the total traffic delay loss of the section based on the probability distribution of the average delay time and the number of passengers.

[0013] As a preferred technical solution, a model of the relationship between water depth and distance of road sections is established based on geographic elevation information, specifically:

[0014] The lowest point in the flooded area of ​​the road section is taken as the coordinate origin, and the coordinate origin corresponds to the maximum flooded depth. The water depth x of each point in the flooded area is determined based on the geographic elevation information. (l) The relationship between the coordinate position l:

[0015]

[0016] In the formula, f X (l) represents the functional relationship between the water depth and the water accumulation position, l 1 is the coordinate position of the starting point of the flooded road section, l 2 is the coordinate position of the end point of the flooded section, and the depth of the water at the starting point of the flooded section 0, the water depth at the end of the flooded section is 0, the water depth x at the origin of the coordinate system (0) is the maximum water depth x.

[0017] As a preferred technical solution, a probability density function of the maximum waterlogging depth is proposed based on the maximum waterlogging depth of the road section collected from historical records of the same rainfall amount, specifically:

[0018] According to the historical records of the same rainfall forecast, the average value of the maximum water depth x of the road section collected by the water level detection equipment is calculated. With variance The maximum water depth x of the proposed road section follows the truncated normal distribution model Then the probability density function of the maximum water depth of this section is:

[0019]

[0020] Where φ(·) is the probability density function of the normal distribution, Φ(·) is the cumulative distribution function of the normal distribution, and x 1 is the minimum possible value of the maximum water depth, which is 0 when there is no rainfall or water accumulation. 2 is the maximum value of the maximum waterlogging depth, which is determined by the rainfall, drainage conditions, and longitudinal profile. The probability density function f of the maximum waterlogging depth x is PX (x) Satisfaction

[0021] As a preferred technical solution, a probability density function of the traffic flow of a road section is proposed based on the traffic flow of the road section collected from the historical records of the same rainfall amount, specifically:

[0022] Statistical section traffic flow average With variance The traffic flow q of the proposed road section follows the truncated normal distribution model Then the traffic flow probability density function of this road section is:

[0023]

[0024] Where φ(·) is the probability density function of the normal distribution, Φ(·) is the cumulative distribution function of the normal distribution, and q 1 is the minimum value of traffic flow, which is affected by rainfall, traffic control measures, and traffic induction schemes. 2 is the maximum possible traffic flow, which is determined by the upstream intersection signal timing plan and the maximum traffic capacity. The probability density function f of the traffic flow q on the road section is PQ (q) Satisfaction

[0025] As a preferred technical solution, the free flow speed of each point in the flooded area is calculated based on the relationship model between the water depth and distance of the road section, the average vehicle speed is calculated according to the traffic flow of the road section, and the average travel time of vehicles under the condition of waterlogging on the road section is calculated according to the probability density function of the maximum water depth and the probability density function of the traffic flow. Specifically,

[0026] According to the water depth x of the coordinate position l of each point in the water accumulation area(l) , using the "hyperbolic tangent function" to calculate the free flow speed v at the point fl

[0027]

[0028] In the formula, v f is the free flow speed when there is no water accumulation, a is the median of the critical water accumulation depth for vehicle stagnation, and b is the attenuation elastic coefficient;

[0029] According to the depth of water x (l) The corresponding free flow speed v fl , the Greenshields flow-density-speed model is used to calculate the average vehicle speed v q,l :

[0030]

[0031] In the formula, ρ j is the road congestion density;

[0032] Calculate the average travel time of vehicles on flooded roads

[0033]

[0034] As a preferred technical solution, the average delay time of vehicles on flooded sections is calculated based on the average travel time without water accumulation and the average travel time under water accumulation, and the total traffic delay loss of the section is estimated according to the probability distribution of the average delay time and the number of passengers, specifically:

[0035] Calculate the average delay time of vehicles on flooded roads

[0036]

[0037] In the formula, is the average travel time of vehicles in the absence of waterlogging, calculated based on the length of the flooded road section and the average driving speed in the absence of waterlogging:

[0038]

[0039] In the formula, v q is the road section without water accumulation and with a traffic flow of q [l 1 ,l 2 The average driving speed of the vehicle is calculated based on the Greenshields flow-density-speed model:

[0040]

[0041] According to the flow size of different types of vehicles and the probability distribution function of the number of passengers, the number of flooded sections per unit time is estimated. 1 ,l 2 ] Total traffic delay losses

[0042]

[0043] In the formula, i is the vehicle type number, n is the total number of vehicle types, k is i is the traffic proportion of vehicle type i, j is the number of passengers, m i is the maximum number of passengers of vehicle type i, P (i,j) is the probability distribution of the number of passengers j of vehicle type i; the probability distribution of the number of passengers of various vehicle types P (i,j) All meet

[0044] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0045] (1) The present invention establishes a model for the relationship between water depth and distance on a road section, and can use the detected water depth or water coverage on the road to calculate the water depth at each location on the road section, thereby reducing the cost of collecting water data and providing a feasible solution for detecting water depth on the road.

[0046] (2) In view of the uncertainty of road waterlogging conditions and traffic travel demand, the present invention uses historical record information to establish probability density functions of waterlogging depth and traffic flow of the evaluation section respectively. There is no need to make fixed value predictions of waterlogging depth and traffic flow, which reduces the dependence on scene data and has greater generalization ability, applicability and reliability.

[0047] (3) The present invention calculates the average travel time of vehicles on flooded sections of road based on the water depth and the probability density function of traffic flow, taking into account the flow size of different types of vehicles and the probability distribution function of the number of passengers they carry. It can more comprehensively estimate the total amount of traffic delay losses on the road section, and provides an important basis for preventing and controlling road traffic congestion caused by urban waterlogging. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0049] Figure 1 This is a flow chart of a method for estimating road delay losses based on water depth and traffic flow probability density according to an embodiment of the present invention;

[0050] Figure 2 It is a longitudinal cross-sectional view of a road section according to an embodiment of the present invention;

[0051] Figure 3 is a probability density curve of the maximum waterlogging depth of the road section in the embodiment of the present invention;

[0052] Figure 4 is a probability density curve of the traffic flow of the road section according to the embodiment of the present invention;

[0053] Figure 5 The figure shows the change of the average vehicle speed of the road section according to the maximum water depth and the average traffic flow in the embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to enable those skilled in the art to better understand the present application, the technical solutions 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. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present application.

[0055] Reference to "embodiments" in this application means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described in this application may be combined with other embodiments.

[0056] This embodiment selects a road section with a total length of L = 0.5 km as the research object. It is known that the lowest point of the road section is located at the center of the road section, and the maximum distance x from the horizontal plane is M = 25cm, the slope of the road on both sides is fixed at tanθ 1 =tanθ 2 =0.001, free flow velocity v f =60km / h. Figure 1 As shown, in this embodiment, a method for estimating the delay loss of a road section based on the water depth and the probability density of traffic flow is provided, and the specific steps are as follows:

[0057] Step S1: Establish a road section water depth and distance relationship model based on geographic elevation information, specifically:

[0058] A longitudinal cross-sectional view of a known embodiment of the road section is shown in FIG. Figure 2 As shown in the figure, the lowest point in the flooded area of ​​the road section is taken as the coordinate origin O, and the coordinate origin corresponds to the maximum flood depth x(0) , l 1 is the coordinate position of the starting point of the flooded road section, l 2 is the coordinate position of the end point of the flooded section, and the longitudinal length of the flooded area is Δl=l 2 -l 1 , according to the road section structure and the road slope angle θ on both sides of the lowest point 1 With θ 2 , the maximum water depth can be calculated Determine the water depth x at each point in the waterlogged area based on geographic elevation information (l) The relationship between the coordinate position l is as follows:

[0059]

[0060] Step S2: Based on the maximum waterlogging depth of the road section collected from the historical records of the same rainfall amount, a probability density function of the maximum waterlogging depth is formulated, which is specifically:

[0061] According to the historical records of the same rainfall forecast, the maximum water depth x of the road section collected or converted by the road water detection equipment is shown in the following table. Assuming that the maximum water depth x of the road section is in the interval [x 1 ,x 2 ]([0,25]) obeys the truncated normal distribution model Calculate the mean of the maximum water depth x of the road section Standard deviation x =2.65, the probability density function of the maximum water depth of this section is obtained as:

[0062]

[0063] order 1 2 3 4 5 6 7 8 9 10 x(cm) 14.7 13.5 17.9 19.5 12.3 19.4 15.3 16.8 20.3 14.2

[0064] The probability density curve of the maximum water depth of this road section is as follows Figure 3 shown.

[0065] Step S3: Based on the forecast of the traffic flow of the road section collected from the historical records of the same rainfall amount, a probability density function of the traffic flow of the road section is formulated, which is specifically:

[0066] The traffic flow q collected by the traffic flow detection equipment is shown in the following table. It is assumed that the traffic flow q in the interval [0,2250] follows the truncated normal distribution model. Calculate the mean of the traffic flow q of the road section Standard deviation q =28.29, the probability density function of the traffic flow of this section is obtained as follows:

[0067]

[0068] order 1 2 3 4 5 6 7 8 9 10 q(veh / h) 358 412 366 421 443 362 395 378 396 429

[0069] The probability density curve of the traffic flow on this road section is as follows: Figure 4 shown.

[0070] Step S4: Calculate the free flow speed of each point in the flooded area based on the road section water depth and distance relationship model, calculate the average vehicle speed according to the road section traffic flow, and calculate the average travel time of vehicles under the condition of road section waterlogging according to the probability density function of the maximum water depth and the probability density function of the traffic flow, specifically:

[0071] According to the water depth x of the coordinate position l of each point in the water accumulation area (l) , using the "hyperbolic tangent function" to calculate the free flow speed v at the point fl , where v f =60km / h, a=15, b=6.

[0072]

[0073] According to the depth of water x (l) The corresponding free flow speed v fl , the Greenshields flow-density-speed model is used to calculate the average vehicle speed v q,l , where ρ j =150veh / km.

[0074]

[0075] The average vehicle speed of this road section changes with the maximum water depth and average traffic flow as shown in the figure below. Figure 5 shown.

[0076] According to the probability density function of water depth in the road section f PX (x) and traffic flow probability density function f PQ (q), calculate the average travel time of vehicles on flooded road sections

[0077]

[0078] Step S5: Calculate the average delay time of vehicles on the flooded road section based on the average travel time without water accumulation and the average travel time under water accumulation, and estimate the total traffic delay loss of the road section according to the probability distribution of the average delay time and the number of passengers, specifically:

[0079] According to the Greenshields flow-density-speed model, the road section [l 1 ,l2 ]’s average speed v q :

[0080]

[0081] Calculate the average travel time of vehicles without waterlogging based on the length of the flooded road section and the average driving speed without waterlogging.

[0082]

[0083] Calculate the average delay time of vehicles on flooded roads

[0084]

[0085] According to the flow size of different types of vehicles and the probability distribution function of the number of passengers, the number of flooded sections per unit time is estimated. 1 ,l 2 ] Total traffic delay losses

[0086]

[0087] Assume that the traffic flow on the road section of the embodiment is mainly composed of cars and buses, among which the car flow accounts for k 1 =0.8, maximum number of passengers m 1 =5, the number of passengers is between [1,5] and follows a Poisson distribution with a mean of 2, and the bus flow accounts for k 2 =0.2, maximum number of passengers m 2 =30, the number of passengers between [1,30] follows a Poisson distribution with a mean of 18, and the total amount of traffic delay losses in the flooded road section is calculated.

[0088] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0089] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0090] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A method for estimating road delay losses based on water depth and traffic flow probability density, characterized in that: The following steps are involved: S1. Establish a model of the relationship between water depth and distance of road sections based on geographic elevation information; S2. Propose a probability density function of the maximum water depth based on the maximum water depth of the road section collected from historical records of the same rainfall amount; S3. Propose a probability density function of the traffic flow of a road section based on the traffic flow of the road section collected from the historical records of the same rainfall amount; S4. Calculate the free flow speed of each point in the flooded area based on the relationship model between the depth of flooding and the distance of the road section, calculate the average speed of vehicles based on the traffic flow of the road section, and calculate the average travel time of vehicles under flooding conditions based on the probability density function of the maximum flooding depth and the probability density function of the traffic flow; S5. Calculate the average delay time of vehicles on flooded sections based on the average travel time without flooding and the average travel time under flooding conditions, and estimate the total traffic delay loss of the section based on the probability distribution of the average delay time and the number of passengers.

2. The method for estimating road delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that: The relationship model between waterlogging depth and distance of road sections is established based on geographic elevation information, specifically: The lowest point in the flooded area of ​​the road section is taken as the coordinate origin, and the coordinate origin corresponds to the maximum flooded depth. The water depth x of each point in the flooded area is determined based on the geographic elevation information. (l) The relationship between the coordinate position l: In the formula, f X (l) represents the functional relationship between the water depth and the water accumulation position. l1 is the coordinate position of the starting point of the water accumulation section, l2 is the coordinate position of the end point of the water accumulation section, and the water depth at the starting point of the water accumulation section is 0, the water depth at the end of the flooded section is 0, the water depth x at the origin of the coordinate system (0) is the maximum water depth x.

3. The method for estimating road delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that: The probability density function of the maximum waterlogging depth is proposed based on the maximum waterlogging depth of the road section collected from the historical records of the same rainfall amount, which is as follows: According to the historical records of the same rainfall forecast, the average value of the maximum water depth x of the road section collected by the water level detection equipment is calculated. With variance The maximum water depth x of the proposed road section follows the truncated normal distribution model Then the probability density function of the maximum water depth of this section is: Where φ(·) is the probability density function of the normal distribution, Φ(·) is the cumulative distribution function of the normal distribution, x1 is the minimum possible value of the maximum waterlogging depth, which is 0 when there is no rainfall or no waterlogging, and x2 is the maximum possible value of the maximum waterlogging depth, which is determined by the rainfall, drainage conditions, and longitudinal section line shape. The probability density function f of the maximum waterlogging depth x is PX (x) Satisfaction 4. The method for estimating road delay loss based on waterlogging depth and traffic flow probability density according to claim 1, characterized in that: The probability density function of the traffic flow of the road section is proposed based on the traffic flow of the road section collected from the historical records of the same rainfall forecast, which is: Statistical section traffic flow average With variance The traffic flow q of the proposed road section follows the truncated normal distribution model Then the traffic flow probability density function of this road section is: Where φ(·) is the probability density function of the normal distribution, Φ(·) is the cumulative distribution function of the normal distribution, q1 is the minimum value of the traffic flow, which is affected by the amount of rainfall, traffic control measures, and traffic induction schemes, q2 is the maximum value of the traffic flow, which is determined by the upstream intersection signal timing scheme and the maximum traffic capacity. The probability density function f of the traffic flow q on the road section is PQ (q) Satisfaction 5. The method for estimating road delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that: The free flow speed of each point in the flooded area is calculated based on the relationship model between the depth and distance of the road section. The average speed of vehicles is calculated based on the traffic flow of the road section. The average travel time of vehicles under flooded conditions is calculated based on the probability density function of the maximum flood depth and the probability density function of the traffic flow. Specifically, According to the water depth x of the coordinate position l of each point in the water accumulation area (l) , using the "hyperbolic tangent function", calculate the free flow speed v at the point fl In the formula, v f is the free flow speed when there is no water accumulation, a is the median of the critical water accumulation depth for vehicle stagnation, and b is the attenuation elastic coefficient; According to the depth of water x (l) The corresponding free flow speed v fl , the Greenshields flow-density-speed model is used to calculate the average vehicle speed v q,l : In the formula, ρ j is the road congestion density; Calculate the average travel time of vehicles on flooded roads 6. The method for estimating road delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that: The average delay time of vehicles on flooded sections is calculated based on the average travel time without water accumulation and the average travel time under water accumulation. The total traffic delay loss of the section is estimated based on the probability distribution of the average delay time and the number of passengers. Specifically, it is: Calculate the average delay time of vehicles on flooded roads In the formula, is the average travel time of vehicles in the absence of waterlogging, calculated based on the length of the flooded road section and the average driving speed in the absence of waterlogging: In the formula, v q is the average speed of the road section [l1,l2] when there is no water accumulation and the traffic flow is q, calculated according to the Greenshields flow-density-speed model: According to the flow size of different types of vehicles and the probability distribution function of the number of passengers, the total amount of traffic delay loss in the flooded section [l1,l2] per unit time is estimated In the formula, i is the vehicle type number, n is the total number of vehicle types, k is i is the traffic proportion of vehicle type i, j is the number of passengers, m i is the maximum number of passengers of vehicle type i, P (i,j) is the probability distribution of the number of passengers j of vehicle type i; the probability distribution of the number of passengers of various vehicle types P (i,j) All meet

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