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

Abstract

A road section delay loss estimation method based on a ponding depth probability density and a traffic flow probability density. The method comprises: S1, establishing a model for the relationship between the ponding depth of a road section and distance; S2, on the basis of the maximum ponding depth of the road section collected from a historical record with a forecasted equivalent rainfall, formulating a probability density function for the maximum ponding depth; S3, on the basis of the traffic flow of the road section collected from the historical record with the forecasted equivalent rainfall, formulating a probability density function for the traffic flow of the road section; S4, calculating free-flow vehicle speeds, and on the basis of the traffic flow of the road section, calculating the average vehicle speed of a vehicle, and calculating the average travel time of the vehicle under a road-section ponding condition; and S5, calculating the average delay time of the vehicle in a ponded road section, and on the basis of the average delay time and the probability distribution of passenger occupancy, estimating the total traffic delay loss of the road section. By means of taking the uncertainty based on the ponding depth, the traffic flow and the passenger occupancy into consideration, a scientific delay loss estimation model is established, thereby providing an important basis for the management of traffic congestion caused by urban flooding and ponding.

Description

A method for estimating road segment delay loss based on water depth and traffic flow probability density Technical Field

[0001] This invention belongs to the field of traffic operation evaluation technology, specifically relating to a method for estimating road segment delay losses based on water depth and traffic flow probability density. Background Technology

[0002] In recent years, the secondary disasters of waterlogging and flooding caused by extreme rainfall have become increasingly severe. These disasters not only cause serious damage to urban infrastructure but also directly threaten the normal operation of transportation systems, affecting the efficiency and safety of vehicles and pedestrians. Road flooding significantly reduces vehicle speed and efficiency, leading to longer travel times in flooded areas, exacerbating delays and traffic congestion. This not only affects citizens' daily lives but also disrupts commercial logistics, ultimately hindering the city's economic operations.

[0003] In reality, the impact of urban flooding on road traffic is difficult to estimate accurately. First, factors such as rainfall, terrain features, and drainage facilities introduce uncertainty into road flooding conditions, making it difficult to accurately predict the actual depth and extent of flooding. Second, weather forecasts, traffic control measures, and traffic guidance schemes often lead to uncertainties in travel demand and modes of transportation, making it impossible to fully grasp changes in road traffic flow and thus difficult to accurately predict. Furthermore, the number of passengers carried by different types of vehicles also varies, following a certain distribution pattern within a certain range. Therefore, using fixed-value calculation methods to estimate potential road traffic delays caused by urban flooding has limited applicability.

[0004] To address these issues, it is necessary to establish probability density functions for water depth and traffic flow on the assessed road sections based on historical records of similar forecast rainfall amounts. Combining this with a model of the relationship between water depth and distance, the average travel time for vehicles on waterlogged sections can be calculated. Furthermore, considering the flow rate of different vehicle types and their passenger number probability distribution functions, the total traffic delay losses on the road sections can be estimated. By studying road traffic operation status and service level evaluation techniques under waterlogging conditions, important reference data can be provided for analyzing and managing urban traffic congestion caused by urban flooding. Summary of the Invention

[0005] The main objective of this invention is to provide a method for estimating road segment delay losses based on water depth and traffic flow probability density, based on historical detection data and distribution patterns. This method enables the estimation of travel time and calculation of lost time for waterlogged road segments, providing technical support for assessing the impact of urban flooding on road traffic efficiency.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides a method for estimating road segment delay losses based on water depth and traffic flow probability density, comprising the following steps:

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

[0009] S2. Determine the probability density function of the maximum water accumulation depth based on the maximum water accumulation depth of road sections collected from historical records of the same forecast rainfall.

[0010] S3. Determine the probability density function of road segment traffic flow based on historical data of road segment traffic flow collected for the same forecast rainfall.

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

[0012] S5. Calculate the average delay time of vehicles on flooded road sections based on the average travel time under no water accumulation conditions and the average travel time under water accumulation conditions. Estimate the total traffic delay loss of the road section based on the probability distribution of the average delay time and the number of passengers.

[0013] As a preferred technical solution, a model relating road section water depth to distance is established based on geographic elevation information, specifically as follows:

[0014] Using the lowest point within the waterlogged area as the origin of the coordinate system, which corresponds to the maximum water depth, the water depth x at each point within the waterlogged area is determined based on geographic elevation information. (l) The relationship with the coordinate position l:

[0015] 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) Let x be the maximum water depth.

[0016] As a preferred technical solution, a probability density function for the maximum water accumulation depth is determined based on the maximum water accumulation depth of road sections collected from historical records of the same forecast rainfall. Specifically:

[0017] Based on historical records of the same forecast rainfall, the average maximum water depth of each road segment was calculated using data from water level monitoring equipment. With variance The proposed maximum water depth x of the road section follows a truncated normal distribution model. The probability density function for the maximum water depth in this road section is:

[0018] 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 possible maximum water depth (0 when there is no rainfall or water accumulation), x2 is the maximum possible maximum water depth (determined by rainfall amount, drainage conditions, and longitudinal profile), and f is the probability density function of the maximum water depth x. PX (x) satisfies

[0019] As a preferred technical solution, the probability density function of road segment traffic flow is determined based on historical data of road segment traffic flow for the same predicted rainfall, specifically as follows:

[0020] Average traffic flow of the statistical road segment With variance The proposed road segment traffic flow q follows a truncated normal distribution model. The traffic flow probability density function for this road segment is:

[0021] 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 possible traffic flow, which is affected by rainfall, traffic control measures, and traffic guidance schemes, q2 is the maximum possible traffic flow, which is determined by the signal timing scheme of the upstream intersection and the maximum capacity, and f is the probability density function of the traffic flow q of the road segment. PQ (q) satisfies

[0022] As a preferred technical solution, the free-flow vehicle speed at each point within the flooded area is calculated based on a model relating road water depth to distance. The average vehicle speed is calculated based on the road traffic flow. The average travel time of vehicles under flooded road conditions is calculated based on the probability density function of the maximum water depth and the probability density function of the traffic flow. Specifically:

[0023] Based on the coordinates l of each point within the waterlogged area and the water depth x (l) The free-flow vehicle speed v at the point is calculated using the hyperbolic tangent function. fl

[0024] 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.

[0025] 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 :

[0026] In the formula, ρ j Congestion density of the road segment;

[0027] Calculate the average travel time of vehicles in flooded road sections.

[0028] As a preferred technical solution, the average delay time of vehicles on flooded road sections is calculated based on the average travel time under conditions of no water accumulation and the average travel time under conditions of water accumulation. The total traffic delay loss of the road section is estimated based on the probability distribution of the average delay time and the number of passengers. Specifically:

[0029] Calculate the average delay time of vehicles on flooded road sections.

[0030] In the formula, The average travel time for vehicles under conditions without water accumulation is calculated based on the length of the flooded section and the average driving speed under conditions without water accumulation.

[0031] In the formula, v q The average driving speed on road segment [l1, l2] is calculated based on the Greenshields flow-density-velocity model under the condition of no water accumulation and traffic flow of q:

[0032] Based on the flow rate of different types of vehicles and their passenger number probability distribution function, estimate the total traffic delay loss per unit time for the flooded road section [l1,l2].

[0033] In the formula, i is the vehicle type number, n is the total number of vehicle types, and k is the vehicle type index. i Let m be the traffic share of vehicle type i, j be the number of passengers, and m be the number of passengers. i P represents the maximum number of passengers that vehicle type i can carry. (i,j) Let P be the probability distribution of the number of passengers j for vehicle type i; and the probability distribution of the number of passengers P for each vehicle type. (i,j) All meet

[0034] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0035] (1) By establishing a model of the relationship between road water depth and distance, this invention can calculate the water depth at each location of the road section using the detected road water depth or water coverage area, thereby reducing the cost of water data collection and providing a feasible solution for road water depth detection.

[0036] (2) In view of the uncertainty of road water accumulation and traffic demand, the present invention uses historical data to establish probability density functions of water accumulation depth and traffic flow of the evaluation road section respectively. It does not require fixed value prediction of water accumulation depth and traffic flow, reduces the dependence on scene data, and has greater generalization ability, applicability and reliability.

[0037] (3) This invention calculates the average travel time of vehicles on flooded road sections based on the water depth and traffic flow probability density function. It takes into account the flow of different types of vehicles and their passenger number probability distribution function, and can comprehensively estimate the total traffic delay loss of road sections, providing an important basis for preventing and controlling road traffic congestion caused by urban flooding. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 is a flowchart of a method for estimating road segment delay loss based on water depth and traffic flow probability density according to an embodiment of the present invention;

[0040] Figure 2 is a longitudinal cross-sectional view of a road segment according to an embodiment of the present invention;

[0041] Figure 3 shows the probability density curve of the maximum water accumulation depth in the road section according to an embodiment of the present invention;

[0042] Figure 4 shows the probability density curve of traffic flow on the road segment in an embodiment of the present invention;

[0043] Figure 5 shows the variation of average vehicle speed on the road section with maximum water depth and average traffic flow in an embodiment of the present invention. Detailed Implementation

[0044] 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.

[0045] 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.

[0046] 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. As shown in Figure 1, this embodiment presents a method for estimating road segment delay losses based on water depth and traffic flow probability density. The specific steps are as follows:

[0047] Step S1: Establish a model of the relationship between water depth and distance in road sections based on geographic elevation information, specifically as follows:

[0048] The longitudinal cross-sectional view of the road section in the known embodiment is shown in Figure 2. The lowest point of the terrain in the waterlogged area of ​​the road section is taken as the origin O of the coordinate system, and the origin of the coordinate system corresponds to the maximum waterlogging 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. Determine the water depth (x) at various points within the waterlogged area based on geographic elevation information. (l) The relationship between the coordinate position l and the coordinate position l is as follows:

[0049] Step S2: Based on the historical data of the maximum water accumulation depth of the road section collected for the same forecast rainfall, determine the probability density function of the maximum water accumulation depth, specifically:

[0050] Based on historical records of the same forecast rainfall, the maximum water depth x of the road section obtained from the data collected or calculated by the road water accumulation detection equipment is shown in the table below. It is assumed that the maximum water depth x of the road section follows a truncated normal distribution model in the interval [x1,x2] ([0,25]). Calculate the mean value of the maximum water depth x of the road section Standard deviation σ x =2.65, so the probability density function for the maximum water depth of this road section is:

[0051] The probability density curve of the maximum water depth in this section of road is shown in Figure 3.

[0052] Step S3: Based on the historical data of road segment traffic flow collected for the same predicted rainfall, determine the probability density function of the road segment traffic flow, specifically as follows:

[0053] The traffic flow q collected by the traffic flow detection equipment is shown in the table below. It is assumed that the traffic flow q in the interval [0, 2250] follows a truncated normal distribution. Calculate the mean traffic flow q of the road segment Standard deviation σ q =28.29, so the probability density function of the traffic flow for this road segment is:

[0054] The probability density curve of traffic flow on this road segment is shown in Figure 4.

[0055] 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:

[0056] Based on the coordinates l of each point within the waterlogged area and the water depth x (l) The free-flow vehicle speed v at the point is calculated using the hyperbolic tangent function. fl In the formula, v f =60km / h, a=15, b=6.

[0057] 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.

[0058] Figure 5 shows the variation of average vehicle speed on this section of road with maximum water depth and average traffic flow.

[0059] 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.

[0060] 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:

[0061] 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 :

[0062] 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.

[0063] Calculate the average delay time of vehicles on flooded road sections.

[0064] Based on the flow rate of different types of vehicles and their passenger number probability distribution function, estimate the total traffic delay loss per unit time for the flooded road section [l1,l2].

[0065] Assuming the traffic flow on the example road segment mainly consists of cars and buses, with cars accounting for a certain percentage (k1 = 0.8), having a maximum passenger capacity (m1 = 5), and following a Poisson distribution with a mean of 2 between [1, 5], and buses accounting for a certain percentage (k2 = 0.2), having a maximum passenger capacity (m2 = 30), and following a Poisson distribution with a mean of 18 between [1, 30], calculate the total traffic delay loss on the flooded road segment.

[0066] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this 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. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0067] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.

[0068] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for estimating road segment delay losses based on water depth and traffic flow probability density, characterized in that, Includes the following steps: S1. Establish a model of the relationship between water accumulation depth and distance in road sections based on geographic elevation information; S2. Determine the probability density function of the maximum water accumulation depth based on the maximum water accumulation depth of road sections collected from historical records of the same forecast rainfall. S3. Determine the probability density function of road segment traffic flow based on historical data of road segment traffic flow collected for the same forecast rainfall. S4. Calculate the free-flow vehicle speed at each point in the waterlogged area based on the model of the relationship between water depth and distance in the road section, calculate the average vehicle speed based on the traffic flow of the road section, and calculate the average travel time of vehicles under the condition of waterlogging in the road section based on the probability density function of the maximum water depth and the probability density function of the traffic flow. S5. Calculate the average delay time of vehicles on flooded road sections based on the average travel time under no water accumulation conditions and the average travel time under water accumulation conditions. Estimate the total traffic delay loss of the road section based on the probability distribution of the average delay time and the number of passengers.

2. The method for estimating road segment delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that, A model relating road section water depth to distance was established based on geographic elevation information, specifically as follows: Using the lowest point within the waterlogged area as the origin of the coordinate system, which corresponds to the maximum water depth, the water depth x at each point within the waterlogged area is determined based on geographic elevation information. (l) The relationship with the 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) Let x be the maximum water depth.

3. The method for estimating road segment delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that, The probability density function for determining the maximum water accumulation depth is based on the maximum water accumulation depth of road sections collected from historical records of the same forecast rainfall. Specifically: Based on historical records of the same forecast rainfall, the average maximum water depth of each road segment was calculated using data from water level monitoring equipment. With variance The proposed maximum water depth x of the road section follows a truncated normal distribution model. The probability density function for the maximum water depth in this road section is: 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 possible maximum water depth (0 when there is no rainfall or water accumulation), x2 is the maximum possible maximum water depth (determined by rainfall amount, drainage conditions, and longitudinal profile), and f is the probability density function of the maximum water depth x. PX (x) satisfies 4. The method for estimating road segment delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that, The probability density function of traffic flow for a road segment is determined based on historical data of traffic flow for the same predicted rainfall. Specifically: Average traffic flow of the statistical road segment With variance The proposed road segment traffic flow q follows a truncated normal distribution model. The traffic flow probability density function for this road segment is: 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 possible traffic flow, which is affected by rainfall, traffic control measures, and traffic guidance schemes, q2 is the maximum possible traffic flow, which is determined by the signal timing scheme of the upstream intersection and the maximum capacity, and f is the probability density function of the traffic flow q of the road segment. PQ (q) satisfies 5. The method for estimating road segment delay loss based on water depth and traffic flow probability density according to claim 1, characterized in that, The free-flow vehicle speed at each point within the flooded area is calculated based on a model relating road water depth to distance. The average vehicle speed is calculated based on the road traffic flow. Finally, the average travel time for vehicles under flooded road conditions is calculated using the probability density functions of the maximum water depth and traffic flow. Based on the coordinates l of each point within the waterlogged area and the water depth x (l) The free-flow vehicle speed v at the point is calculated using the 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. 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 Congestion density of the road segment; Calculate the average travel time of vehicles in flooded road sections.

6. The method for estimating road segment 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 road sections is calculated based on the average travel time under conditions of no water accumulation and the average travel time under conditions of water accumulation. The total traffic delay loss of the road section is estimated based on the probability distribution of the average delay time and the number of passengers. Specifically: Calculate the average delay time of vehicles on flooded road sections. In the formula, The average travel time for vehicles under conditions without water accumulation is calculated based on the length of the flooded section and the average driving speed under conditions without water accumulation. In the formula, v q The average driving speed on road segment [l1, l2] is calculated based on the Greenshields flow-density-velocity model under the condition of no water accumulation and traffic flow of q. Based on the flow rate of different types of vehicles and their passenger number probability distribution function, estimate the total traffic delay loss of the flooded road section [l1,l2] per unit time. In the formula, i is the vehicle type number, n is the total number of vehicle types, and k is the vehicle type index. i Let m be the traffic share of vehicle type i, j be the number of passengers, and m be the number of passengers. i P represents the maximum number of passengers that vehicle type i can carry. (i,j) Let P be the probability distribution of the number of passengers j for vehicle type i; and the probability distribution of the number of passengers P for each vehicle type. (i,j) All meet

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