A method for estimating road section delay loss based on water accumulation depth and traffic flow probability density

Abstract

The application discloses a road section delay loss estimation method based on waterlogging depth and traffic flow probability density, comprising the following steps: S1, establishing a road section waterlogging depth and distance relationship model; S2, formulating a maximum waterlogging depth probability density function based on the maximum waterlogging depth of the road section collected from the historical records of the same rainfall forecast; S3, formulating a road section traffic flow probability density function based on the road section traffic flow collected from the historical records of the same rainfall forecast; S4, calculating a free flow speed, calculating a vehicle average speed according to the road section traffic flow, and calculating a vehicle average passing time under the road section waterlogging condition; S5, calculating a vehicle average delay time on the waterlogging road section, and estimating a road section traffic delay loss total amount according to the average delay time and the passenger number probability distribution. The application establishes a scientific delay loss estimation model by comprehensively considering the uncertainty of the waterlogging depth, the traffic flow and the passenger number, and provides an important basis for preventing and treating the traffic congestion caused by the urban waterlogging.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of traffic operation evaluation, and particularly relates to a road section delay loss estimation method based on waterlogging depth and traffic flow probability density. BACKGROUND

[0002] In recent years, waterlogging secondary disasters caused by extreme rainfall have become increasingly serious, not only causing serious damage to urban infrastructure, but also directly threatening the normal operation of the transportation system and affecting the travel efficiency and safety of vehicles and pedestrians. Road waterlogging can directly cause a significant reduction in vehicle travel speed and efficiency, thus extending the travel time of vehicles on waterlogged road sections and exacerbating traffic delays and congestion, which not only affects the daily life of citizens, but also affects business logistics, and ultimately leads to the disruption of urban economic operations.

[0003] In actual situations, it is difficult to accurately estimate the impact of waterlogging on road traffic. First, due to factors such as rainfall, topographic features, and drainage facilities, the waterlogging condition of the road is uncertain, and the actual waterlogging depth and range are difficult to accurately predict. Second, due to weather forecasts, traffic control measures, and traffic guidance schemes, travel demand and travel modes often exhibit uncertainty characteristics, and road traffic flow changes cannot be fully grasped, making it difficult to accurately estimate. In addition, the number of passengers of various types of vehicles also changes within a certain range, subject to some distribution rules. Therefore, using a fixed value calculation method to estimate the road traffic delay loss caused by waterlogging has weak applicability.

[0004] In order to solve the above problems, it is necessary to establish a waterlogging depth probability density function and a traffic flow probability density function for evaluating road sections based on historical records of forecasted rainfall of the same amount. Combined with a road waterlogging depth and distance relationship model, the average travel time of vehicles on waterlogged road sections is calculated. Considering the flow size of different types of vehicles and their passenger number probability distribution function, the total amount of road traffic delay loss is estimated. Through the study of road traffic operation state and service level evaluation technology under waterlogging conditions, important reference basis can be provided for analyzing and managing urban traffic congestion under the influence of waterlogging. SUMMARY

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

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

[0007] The application provides a road section delay loss estimation method based on waterlogging depth and traffic flow probability density, and comprises the following steps:

[0008] S1. Establishing a road section waterlogging depth-distance relationship model according to geographic elevation information;

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

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

[0011] S4. Calculating the free flow speed of each point in the waterlogging area based on the road section waterlogging depth-distance relationship model, calculating the average vehicle speed based on the road section traffic flow, and calculating the average travel time of vehicles under the road section waterlogging condition based on the maximum waterlogging depth probability density function and the traffic flow probability density function;

[0012] S5. Calculating the average delay time of vehicles in the waterlogging road section based on the average travel time under the non-waterlogging condition and the average travel time under the waterlogging condition, and estimating the total road section traffic delay loss based on the average delay time and the passenger number probability distribution.

[0013] As a preferred technical solution, the road section waterlogging depth-distance relationship model is established according to geographic elevation information, and specifically:

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

[0015]

[0016] In the formula, f X (l) represents the waterlogging depth function relationship of the waterlogging position, l1 is the coordinate position of the starting point of the waterlogging road section, l2 is the coordinate position of the ending point of the waterlogging road section, the waterlogging depth of the starting point of the waterlogging road section is 0, the waterlogging depth of the ending point of the waterlogging road section is 0, and the waterlogging depth x (0) of the coordinate origin is the maximum waterlogging depth x.

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

[0018] According to the maximum accumulated water depth x of the road section collected by the water level detection device, the mean value of the maximum accumulated water depth of the road section is counted and variance The maximum accumulated water depth x of the road section is assumed to obey a truncated normal distribution model The probability density function of the maximum accumulated water depth of the road section is:

[0019]

[0020] In the formula, φ(·) is the probability density function of the normal distribution, Φ(·) is the cumulative distribution function of the normal distribution, x1 is the minimum value of the maximum accumulated water depth, which is 0 when there is no rainfall or no accumulated water, x2 is the maximum value of the maximum accumulated water depth, which is determined by the rainfall size, drainage condition and longitudinal section alignment, and the probability density function f PX (x) satisfies

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

[0022] The mean value of the road section traffic flow is counted and variance The road section traffic flow q is assumed to obey a truncated normal distribution model The probability density function of the road section traffic flow is:

[0023]

[0024] In the formula, 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 rainfall size, traffic control measures and traffic induction scheme, q2 is the maximum value of the traffic flow, which is determined by the signal timing scheme of the upstream intersection and the maximum traffic capacity, and the probability density function f PQ (q) satisfies

[0025] As a preferred technical solution, the free flow speed of each point in the accumulated water area is calculated based on the accumulated water depth-distance relationship model, the average vehicle speed is calculated based on the road section traffic flow, and the average travel time of vehicles under the accumulated water condition of the road section is calculated based on the probability density function of the maximum accumulated water depth and the probability density function of the traffic flow, specifically:

[0026] According to the accumulated water depth x of each point coordinate position l in the accumulated water area (l) , the free flow speed v fl of the point is calculated by using the hyperbolic tangent function

[0027]

[0028] wherein v f is the free flow speed, a is the median of the critical standing water depth, and b is the decay elasticity coefficient;

[0029] According to the standing water depth x (l) , the corresponding free flow speed v fl is calculated by using the Greenshields flow-density-speed model: q,l

[0030]

[0031] wherein p j is the road congestion density;

[0032] The average travel time of vehicles on the standing water road section is calculated

[0033]

[0034] As a preferred technical solution, the average delay time of vehicles on the standing water road section is calculated based on the average travel time under the condition of no standing water and the average travel time under the condition of standing water, and the total amount of traffic delay loss on the road section is estimated according to the average delay time and the passenger number probability distribution, specifically:

[0035] The average delay time of vehicles on the standing water road section is calculated

[0036]

[0037] wherein is the average travel time of vehicles under the condition of no standing water, which is calculated according to the length of the standing water road section and the average travel speed under the condition of no standing water:

[0038]

[0039] wherein v q is the average travel speed of the road section [l1, l2] under the condition of no standing water and traffic flow q, which is calculated according to the Greenshields flow-density-speed model:

[0040]

[0041] According to the flow size of different types of vehicles and the passenger number probability distribution function, the total amount of traffic delay loss on the standing water road section [l1, l2] per unit time is estimated ​

[0042]

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

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

[0045] (1) The present application can calculate the water depth of each position of the road section by establishing a relationship model between the water depth and the distance, and using the detected road water depth or water coverage, thereby reducing the water data collection cost and providing a feasible solution for road water depth detection.

[0046] (2) The present application establishes the water depth and traffic flow probability density functions for evaluating the road section according to the historical record information, without the need for fixed value prediction of the water depth and traffic flow, thereby reducing the dependence on scene data and having better generalization ability, applicability and reliability.

[0047] (3) The present application calculates the average travel time of vehicles on the waterlogged road section according to the water depth and traffic flow probability density functions, considers the traffic size and passenger number probability distribution function of different types of vehicles, and can comprehensively estimate the total amount of traffic delay loss, thereby providing an important basis for preventing and treating road traffic congestion under the influence of urban waterlogging. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0049] Figure 1 The flowchart of the road section delay loss estimation method based on water depth and traffic flow probability density according to an embodiment of the present application is shown in the figure.

[0050] Figure 2 The longitudinal section view of the road section according to an embodiment of the present application is shown in the figure.

[0051] Figure 3This is the probability density curve of the maximum water accumulation depth in the road section according to an embodiment of the present invention;

[0052] Figure 4 This is the probability density curve of traffic flow on the road segment in an embodiment of the present invention;

[0053] Figure 5 This illustrates how the average vehicle speed varies with the maximum water depth and average traffic flow in a road segment according to an embodiment of the present invention. Detailed Implementation

[0054] 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 with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

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

[0056] This embodiment selects a road segment with a total length of L = 0.5 km as the research object. It is known that the lowest point of the road segment is located at the center of the road segment, and the maximum distance from the horizontal plane is x. M =25cm, the slope of the road surface on both sides is fixed at tanθ1=tanθ2=0.001, and the free flow velocity v f = 60km / h. For example... Figure 1 As shown in the figure, this embodiment presents a method for estimating road segment delay loss based on water depth and traffic flow probability density. The specific steps are as follows:

[0057] Step S1: Establish a model of the relationship between water depth and distance in road sections based on geographic elevation information, specifically as follows:

[0058] The longitudinal cross-sectional diagram of the known embodiment road section is as follows: Figure 2 As shown, the lowest point in the waterlogged area of ​​the road section is taken as the origin O of the coordinate system, and the origin corresponds to the maximum water depth x. (0) Let l1 be the coordinates of the starting point of the flooded section, and l2 be the coordinates of the ending point of the flooded section. The longitudinal length of the flooded area, Δl, is calculated as l2 - l1. Based on the road structure and the slope angles θ1 and θ2 of the road surface on both sides of the lowest point, the maximum water depth can be calculated. According to the geographic elevation information, the water depth x of each point in the water accumulation area is determined (l) The relationship between the coordinate position l and the water depth x is as follows:

[0059]

[0060] Step S2: Based on the maximum water depth of the road section collected by the historical records of the forecast equivalent rainfall, the probability density function of the maximum water depth is determined, specifically:

[0061] For the historical records of the forecast equivalent rainfall, the maximum water depth x of the road section collected or converted by the road water detection equipment is as shown in the following table, assuming that the maximum water depth x of the road section in the interval [x1, x2] ([0, 25]) obeys the truncated normal distribution model The mean value of the maximum water depth x of the road section is calculated The standard deviation σ x = 2.65, and the probability density function of the maximum water depth of the road section is:

[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 the road section is as shown in Figure 3 .

[0065] Step S3: Based on the road traffic flow collected by the historical records of the forecast equivalent rainfall, the probability density function of the road traffic flow is determined, specifically:

[0066] According to the road traffic flow q collected by the traffic flow detection equipment, the road traffic flow q is as shown in the following table, assuming that the road traffic flow q in the interval [0, 2250] obeys the truncated normal distribution model The mean value of the road traffic flow q of the road section is calculated The standard deviation σ q = 28.29, and the probability density function of the road traffic flow of the road section is:

[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 road traffic flow of the road section is as shown in Figure 4 .

[0070] Step S4: Calculate the free-flow vehicle speed at each point within the flooded area based on the model relating road water depth to distance. Calculate the average vehicle speed based on the road traffic flow. Calculate the average travel time of vehicles under flooded road conditions based on the probability density function of the maximum water depth and the probability density function of the traffic flow. Specifically:

[0071] Based on the coordinates l of each point within the waterlogged area and the water depth x (l) The hyperbolic tangent function is used to calculate the free-flow vehicle speed v at the specified location. fl In the formula, v f =60km / h, a=15, b=6.

[0072]

[0073] Based on the water depth x (l) The corresponding free-flow vehicle speed v fl The average vehicle speed v was calculated using the Greenshields fluid-density-velocity model. q,l In the formula, ρ j =150veh / km.

[0074]

[0075] The changes in average vehicle speed on this section of road with maximum water depth and average traffic flow are as follows: Figure 5 As shown.

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

[0077]

[0078] Step S5: Calculate the average delay time of vehicles on flooded road sections based on the average travel time under no-flood conditions and the average travel time under flood conditions. Estimate the total traffic delay loss of the road section based on the average delay time and the probability distribution of passenger numbers. Specifically:

[0079] Based on the Greenshields flow-density-velocity model, calculate the average speed v of road segment [l1, l2] under the condition of no water accumulation and traffic flow q. q :

[0080]

[0081] Calculate the average travel time for vehicles in the absence of water based on the length of the flooded section and the average driving speed in the absence of water.

[0082]

[0083] Computing average delay time of vehicles on a waterlogged road segment

[0084]

[0085] According to the traffic volume of different types of vehicles and the probability distribution function of the number of passengers, the total traffic delay loss of the waterlogged road segment [l1, l2] per unit time is estimated

[0086]

[0087] Assuming that the traffic flow of the implementation example road segment is mainly composed of cars and buses, the car traffic volume ratio k1 = 0.8, the maximum number of passengers m1 = 5, the number of passengers between [1, 5] obeys the Poisson distribution with a mean of 2, the bus traffic volume ratio k2 = 0.2, the maximum number of passengers m2 = 30, the number of passengers between [1, 30] obeys the Poisson distribution with a mean of 18, the total traffic delay loss of the waterlogged road segment 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 a computer program instructing related hardware, 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 above-mentioned embodiments of each method. Any reference to memory, storage, database or other medium used in each embodiment provided by the present application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), 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), etc.

[0089] Any technical features in the above embodiments can be combined, and for the sake of brevity, not all possible combinations are described above, however, any combination of the technical features is deemed to be within the scope of the present disclosure.

[0090] The above embodiments are preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications, etc. made without departing from the spirit and principles of the present application are deemed to be equivalent replacement manners and are included in the protection scope of the present application.

Claims

1. A method for estimating delay loss of a road section based on water depth and traffic flow probability density, characterized in that, Comprise the following steps: S1. According to the geographic elevation information to establish the relationship between the road section water depth and distance model, specifically: Taking the lowest point of the accumulated water area of the road section as the coordinate origin, the coordinate origin corresponds to the maximum accumulated water depth, and the accumulated water depth x of each point in the accumulated water area is determined according to the geographic elevation information (l) Relationship with coordinate position l: In the formula, f X (l) represents the functional relationship between the location of water accumulation and the depth of water accumulation, where l1 is the coordinate position of the starting point of the water accumulation section, l2 is the coordinate position of the ending point of the water accumulation section, and the depth of water accumulation at the starting point of the water accumulation section is... The water depth at the end of the waterlogged section is 0. The water depth at the origin is 0. (0) x represents the maximum water depth. S2. Based on the forecast of the same amount of rainfall history record collection of road section maximum water depth to draft the maximum water depth probability density function, specifically: According to the maximum water depth x of the road section collected by the water level detection device, the mean value of the maximum water depth of the road section is calculated based on the historical records of the forecast equivalent rainfall and variance The maximum water depth x of the road section is assumed to follow a truncated normal distribution model The probability density function of the maximum water depth of the road section is: wherein (·) is the probability density function of the normal distribution, Φ(·) is the cumulative distribution function of the normal distribution, x1 is the minimum value of the maximum water depth that can occur, taken as 0 when there is no rainfall or no water, x2 is the maximum value of the maximum water depth that can occur, determined by the amount of rainfall, drainage conditions, and longitudinal section alignment, the probability density function f of the maximum water depth x PX (x) satisfies S3. Based on the forecast of the same amount of rainfall history record collection of road section traffic flow to draft the road section traffic flow probability density function; S4. Based on the road section water depth and distance relationship model to calculate the free flow speed of each point in the water area, according to the road section traffic flow to calculate the average vehicle speed, according to the maximum water depth probability density function and traffic flow probability density function to calculate the average travel time of vehicle in the road section water condition; S5. Based on the average travel time under no water condition and the average travel time under water condition to calculate the average delay time of vehicle in the water road section, according to the average delay time and the probability distribution of the number of passengers to estimate the total amount of road traffic delay loss. 2.The method of claim 1, wherein, Based on the forecast of the same amount of rainfall history record collection of road section traffic flow to draft the road section traffic flow probability density function, specifically: The mean value of the statistical section traffic flow and variance The section traffic flow q is assumed to obey a truncated normal distribution model The probability density function of the section traffic flow is wherein (·) is the probability density function of normal distribution, Φ(·) is the cumulative distribution function of normal distribution, q1 is the minimum value of traffic flow that can occur, influenced by rainfall, traffic control measures, and traffic guidance schemes, q2 is the maximum value of traffic flow that can occur, determined by the signal timing scheme of the upstream intersection and the maximum traffic capacity, the probability density function of the road section traffic flow q PQ (q) satisfies 3.The method of claim 2, wherein, Based on the road section water depth and distance relationship model to calculate the free flow speed of each point in the water area, according to the road section traffic flow to calculate the average vehicle speed, according to the maximum water depth probability density function and traffic flow probability density function to calculate the average travel time of vehicle in the road section water condition, specifically: According to the water depth x of each point coordinate position l in the water accumulation area (l) , the free flow speed v of the point position is calculated by using "hyperbolic tangent function" fl In the formula, v f denoted as the free-flow vehicle speed when there is no water accumulation, a is the median of the critical water depth at which the vehicle comes to a standstill, and b is the damping elasticity coefficient. According to the water depth x (l) The corresponding free-flow speed v fl The average vehicle speed v q,l : wherein p j is the road segment congestion density; Computing average transit time of a vehicle on a waterlogged road segment 4. The method of claim 3, wherein, Based on the average travel time under no water condition and the average travel time under water condition to calculate the average delay time of vehicle in the water road section, according to the average delay time and the probability distribution of the number of passengers to estimate the total amount of road traffic delay loss, specifically: Computing average delay time of a vehicle on a waterlogged road segment In the formula, is the average travel time of the vehicle in the case of no standing water, calculated from the length of the standing water section and the average travel speed in the case of no standing water: where v q The average travel speed of the road segment [l1, l2] with no water accumulation and traffic flow q is calculated according to the Greenshields flow-density-speed model: According to the flow size of different types of vehicles and the passenger number probability distribution function, the total traffic delay loss of the flooded road section [l1, l2] per unit time is estimated where i is the vehicle type serial number, n is the total number of vehicle types, k i is the traffic proportion of vehicle type i, j is the passenger number, m i is the maximum passenger number of vehicle type i, P (i,j) is the probability distribution of passenger number j of vehicle type i; the probability distribution P of passenger number of various vehicle types (i,j) satisfy

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