A risk analysis method for multi-vehicle rear-end collision in adverse weather conditions

Abstract

The present invention relates to a method for analyzing the risk of multi-vehicle rear-end collision under adverse weather conditions, and belongs to the field of traffic safety. The method first obtains vehicle data, meteorological data, road surface conditions and lighting conditions of the current road section, and screens out the data of three-vehicle group following; then quantifies the risk of rear-end collision of the three-vehicle group based on the artificial potential field theory; the data of the three-vehicle group are grouped according to weather conditions, and according to the superthreshold theory, the rear-end collision risk threshold of the three-vehicle following scene under different weather conditions is determined based on the average remaining life graph and the threshold stability graph; finally, the generalized Pareto log-likelihood function is used as the splitting function of the regression tree to construct a generalized Pareto regression tree, and the factors affecting the risk of rear-end collision of the three-vehicle group under different weather conditions are identified according to the generalized Pareto regression tree, and the risk of rear-end collision is warned based on the factors. The vehicle driving data and meteorological data used in the present invention are completely matched in time and space, and the rear-end collision risk of the three-vehicle group can be evaluated, and the heterogeneity of conflict events with higher risk of rear-end collision can be analyzed.

Description

Technical Field

[0001] The invention belongs to the technical field of road traffic safety, and in particular relates to a method for analyzing the risk of multi-vehicle rear-end collision under adverse weather conditions. Background Art

[0002] The risk of rear-end collision is easily affected by factors such as the driver's individual physiological and psychological factors, the natural environment, and the road environment. Among them, adverse weather conditions are an important factor causing rear-end collision accidents. Adverse weather conditions can affect road conditions, vehicle handling, reduce road visibility, and affect the driver's judgment. At present, most studies on the impact of weather conditions on car-following behavior use meteorological data released by meteorological information service providers. Such meteorological data are difficult to fully match with the vehicle driving characteristic data detected by vehicle detectors in terms of time and space scales. Most common rear-end collision risk studies involve only two vehicles, namely the leading vehicle in front and the following vehicle behind, and usually use alternative safety indicators to quantify the risk of rear-end collision. Existing alternative safety indicators are mainly divided into the following four categories: time-based indicators, deceleration-based indicators, distance-based indicators, and energy-based indicators. However, these alternative safety indicators are limited to measuring the risk of rear-end collision between two vehicles and are not suitable for evaluating the risk of rear-end collision between multiple vehicles (more than two vehicles). The probability of a chain rear-end collision caused by multiple vehicles following each other is relatively small. Once it occurs, it is easy to cause serious injuries and traffic congestion. However, in existing research, there are relatively few studies on multi-vehicle rear-end collisions. In addition, on actual roads, vehicles are at risk of collision throughout the entire following process, but risk does not mean that an accident will occur. According to the traffic safety pyramid theory, high-risk conflict events with a lower probability have a greater probability of converting into rear-end collisions or more serious consequences of the collision. Therefore, rear-end collision risk analysis should focus on low-probability but high-risk extreme following conflict events, that is, events with a rear-end collision risk greater than a certain threshold. However, there is no relevant research in the prior art. Summary of the invention

[0003] The purpose of the present invention is to address the deficiencies of the prior art and to provide a method for analyzing the risk of multi-vehicle rear-end collisions under adverse weather conditions. The method is based on artificial potential field theory and can evaluate the risk of rear-end collisions of multiple vehicles. By constructing a generalized Pareto regression tree, the method focuses on analyzing the heterogeneity of conflict events with higher risk of rear-end collisions.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0005] A method for analyzing the risk of multi-vehicle rear-end collision under adverse weather conditions comprises the following steps:

[0006] Step 1: Obtain vehicle data, weather data, road surface conditions, and lighting conditions of the current road section, and distinguish whether the vehicle is in a free flow state or a following state, and select the following data of the three-vehicle group;

[0007] Step 2: Quantify the risk of multi-vehicle rear-end collision based on artificial potential field theory;

[0008] Step 3: Group the multi-vehicle data according to sunny days, rainy days, and snowy days. According to the super-threshold model theory, based on the average remaining life graph and the threshold stability analysis graph, determine the rear-end collision risk threshold of the three-vehicle following scenario under different weather conditions, and filter out the data that exceeds the threshold;

[0009] Step 4: Combine the standard CART algorithm with the generalized Pareto distribution, use the generalized Pareto log-likelihood function as the splitting function of the regression tree, construct a generalized Pareto regression tree, identify the factors that affect the rear-end collision risk of the three-vehicle group under different weather conditions based on the generalized Pareto regression tree, and issue a rear-end collision risk warning based on this factor.

[0010] Further, preferably, in step 1, the vehicle data of the current road section is collected by a roadside vehicle detector, and the vehicle data includes the speed, time, vehicle length, vehicle weight and time interval data of each passing vehicle;

[0011] Meteorological data are obtained through meteorological detectors; meteorological data include precipitation intensity, precipitation type, temperature, relative humidity, wind speed and wind direction;

[0012] The weather detector is equipped with a camera for taking photos of the road surface and identifying the road surface status;

[0013] Light conditions are divided into daytime, dusk and nighttime, where dusk refers to the hour before sunrise and sunset and the hour after sunset.

[0014] Furthermore, preferably, in step one, the road surface conditions include four categories: dry, wet, snow-covered and with visible snow traces; and the vehicle detector and the weather detector are arranged in close proximity.

[0015] Further, preferably, in step 1, the time interval is used as a basis to determine whether the vehicle is in a free flow state or a following state; adjacent vehicles with a time interval of less than 5 seconds are considered to be in a following state;

[0016] When screening the following data of three-car groups, it is necessary to ensure that the lead car and the first following car, and the first following car and the second following car are in a following state, while the lead car and the car in front of the lead car, and the second following car and the car behind the second following car are not in a following state.

[0017] Further, preferably, the specific method of step 2 is:

[0018] (1) Calculate the probability of rear-end collision

[0019] The current time is recorded as t0, and p(n,s|τ) is the estimated rear-end collision probability of vehicle s and vehicle n after τ seconds, that is, the rear-end collision probability at time t0+τ is calculated;

[0020] For the three-car group following data, the average value of the time interval is used as τ for calculation;

[0021] The rear-end collision probability calculation formula is:

[0022]

[0023] Where N is the probability density function of the acceleration of vehicle n, μ and σ represent the mean and standard deviation of the probability density function respectively; ΔX represents the relative distance between the vehicles in the longitudinal direction; ΔV represents the relative speed of the two vehicles;

[0024] (2) Calculate the severity of the collision

[0025] Assuming that the collision is an inelastic collision, the calculation formula for the severity of the rear-end collision is:

[0026] CS=0.5W s β 2 |ΔV s,n | 2

[0027] Where CS represents the severity of rear-end collision; W s represents the weight of vehicle s; |ΔV s,n |=|V s -V n |, represents the relative speed between vehicle s and vehicle n; V s 、V n They represent the speed of vehicle s and vehicle n respectively; Indicates the mass ratio; W n represents the weight of vehicle n;

[0028] (3) Calculating rear-end collision risk

[0029] The calculation formula for the rear-end collision risk caused by vehicle n to target vehicle s is:

[0030] r n,s =CS·p(n,s|τ)

[0031] In the formula, r n,s is the rear-end collision risk caused by vehicle n to target vehicle s;

[0032] The total rear-end collision risk r borne by the target vehicle s is composed of the dynamic risks caused by multiple adjacent vehicles. The calculation formula of the total risk r is:

[0033] r=∑r n,s ;

[0034] The calculation of the total risk of rear-end collision of three vehicles is to take the first following vehicle as the target vehicle, and calculate the rear-end collision risks between the first following vehicle and the lead vehicle, and between the first following vehicle and the second following vehicle respectively. According to the superposition of field effects, the total risk of rear-end collision of the first following vehicle is the sum of the two.

[0035] Further, preferably, in step 3, based on the average remaining life graph and the threshold stability analysis graph, the specific method for determining the threshold of rear-end collision risk under different weather conditions and different following scenarios is:

[0036] (1) According to the average remaining life graph, an interval range U1 in which a threshold exists is selected so that the average remaining life graph within the interval is linear or approximately linear;

[0037] (2) According to the threshold stability diagram, an interval U2 is determined, so that the corrected scale parameter and shape parameter can remain stable or basically stable within the interval;

[0038] (3) Take the intersection U of the above two intervals, U = U1 ∩ U2, and take the lower limit value of the set U as the final threshold μ0.

[0039] Further, preferably, in step 4, for a given data set D=(R i , X i ) 1≤i≤n , R is the dependent variable, representing the total risk of rear-end collision; X represents the set of independent variables, represents d-dimensional space, that is, X=(X (1) ,…,X (d) ), d is the total number of independent variables; the constructed generalized Pareto regression tree is a binary tree. For each value x of the independent variable, assuming that the conditional distribution of R|X=x is a heavy-tailed distribution, the scale parameter σ and shape parameter γ of the generalized Pareto distribution depend on x, and the generalized Pareto log-likelihood function is obtained as follows:

[0040]

[0041] Wherein, φ is the generalized Pareto log-likelihood function and also the splitting function of the generalized Pareto regression tree; r represents a specific total risk value of rear-end collision; σ(x) is the function of the scale parameter σ of the generalized Pareto distribution with respect to x; γ(x) is the function of the shape parameter γ of the generalized Pareto distribution with respect to x; m(x) = (σ(x), γ(x)) is a function composed of σ(x) and γ(x); the standard CART algorithm uses the mean square error as the splitting function of the regression tree, and the generalized Pareto regression tree uses the generalized Pareto log-likelihood function as the splitting function of the regression tree based on the CART algorithm.

[0042] In the present invention, the weather detector and the vehicle detector are placed very close to each other so as to obtain weather conditions that can truly reflect and match the vehicle driving characteristic data in time and space.

[0043] In the present invention, the super-threshold model is specifically:

[0044] Assume Z i is a series of independent samples from the same distribution F, i = 1, ..., n, a threshold μ is selected from the samples, when μ is large enough, all samples greater than the threshold are regarded as extreme value samples; a sample Z is randomly selected from the samples, and the distribution function F of the part of sample Z that exceeds the threshold (i.e., Z-μ) is defined as:

[0045]

[0046] Wherein, r=Z-μ, represents the threshold exceeding value; Pr(Z>μ+r|Z>μ) represents the probability of Z>μ+r under the condition of Z>μ.

[0047] In practical applications, F is unknown, so the distribution of r is also unknown. The distribution of r can be approximately estimated based on the relevant theory of generalized extreme value distribution:

[0048]

[0049] The distribution represented by H(r) is the generalized Pareto distribution, where σ is the scale parameter and γ is the shape parameter;

[0050] The average value of r, E(r), is:

[0051]

[0052] r is the total risk.

[0053] In the present invention, the average remaining life graph is specifically:

[0054] Assume that there is a generalized Pareto distribution model whose threshold μ0 comes from a set of independent and identically distributed random observations Z i, i=1,…,n,, according to the super-threshold theory, if the samples exceeding the threshold μ0 (i.e., extreme value samples) obey the generalized Pareto distribution, then for any value μ greater than μ0, its threshold exceeding value also obeys the generalized Pareto distribution, the shape parameter γ remains unchanged, and the scale parameter changes to is the scale parameter corresponding to the threshold value μ0; σ μ is the scale parameter corresponding to any value μ greater than μ0;

[0055] Therefore, for any value μ greater than μ0, the average value of the threshold exceeding is

[0056]

[0057] When μ>μ0, E(Z-μ|Z>μ0) is a linear function of μ, and the graph consisting of a series of points representing this linear relationship is the average remaining life graph; Figure 5 As shown, the uppermost line and the lowermost line (lighter colored line) in the average remaining life graph define the range of value variation.

[0058] In the present invention, the threshold stability analysis diagram is specifically:

[0059] According to the super-threshold theory, if the samples exceeding the threshold μ0 (i.e., extreme value samples) obey the generalized Pareto distribution, then for any value μ greater than μ0, its threshold exceeding value also obeys the generalized Pareto distribution, the shape parameter γ remains unchanged, and the scale parameter changes to σ μ It changes with the change of μ; is the scale parameter corresponding to the threshold value μ0; σ μ is the scale parameter corresponding to any value μ greater than μ0;

[0060] Definition: σ * =σ μ +γμ

[0061] In the formula, σ * is the corrected scale parameter, which does not change with the change of μ and remains stable; the graph describing the relationship between the corrected scale parameter and shape parameter and μ is called the threshold stability analysis graph.

[0062] In the present invention, (1) according to the average remaining life graph, an interval range U1 in which a threshold exists is selected, so that the average remaining life graph within the interval is linear or approximately linear;

[0063] (2) According to the threshold stability diagram, an interval U2 is determined, so that the corrected scale parameter and shape parameter can remain stable or basically stable within the interval;

[0064] (3) Take the intersection U of the above two intervals, U = U1 ∩ U2, and take the lower limit value of the set U as the final threshold μ0.

[0065] The average remaining life graph should be linear in an ideal state, but in actual applications, it is almost impossible to be completely linear, so approximate linearity is used as a judgment standard. The specific operation can be carried out according to the existing technology.

[0066] The threshold stability diagram should be stable and unchanged in an ideal state, but in actual applications, it is almost impossible to be completely stable and unchanged, so basically maintaining stability is used as the judgment standard. The specific operation can be carried out according to the existing technology.

[0067] In step three of the present invention, vehicles whose rear-end collision risk exceeds the rear-end collision risk threshold have a higher rear-end collision risk. The present invention focuses on analyzing the heterogeneity of such conflict events with a higher rear-end collision risk, and screens out data that exceeds the rear-end collision risk threshold as the research object of the present invention.

[0068] In step 4 of the present invention, x represents the variable value of the independent variable, X represents the random variable of the independent variable, and X=x indicates that the value of the independent variable is x; R represents the variable of the total risk of rear-end collision, and r represents the variable value of the total risk of rear-end collision. Except for using the generalized Pareto log-likelihood function as the splitting function of the regression tree, the other parts in step 4 are all standard CART algorithms.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1. Most of the current studies on the impact of weather conditions on car-following behavior use meteorological data released by meteorological information service providers. Such meteorological data and vehicle driving characteristic data detected by vehicle detectors have deviations in time and space scales and are difficult to fully match. The present invention uses data that fully matches vehicle driving data and meteorological data in time and space to analyze the impact of adverse weather on rear-end collision risk;

[0071] 2. Most of the current studies on rear-end collision risk only involve two vehicles. The present invention quantifies the rear-end collision risk of three vehicles at the same time based on artificial potential field theory;

[0072] 3. The present invention focuses on extreme events with high rear-end collision risk and constructs a generalized Pareto regression tree to analyze the heterogeneity of the impact of adverse weather on the risk of three-vehicle rear-end collision. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0074] Figure 1 It is a flow chart of a method for analyzing the risk of rear-end collision of multiple vehicles under adverse weather conditions of the present invention;

[0075] Figure 2 This is a schematic diagram of a three-car group vehicle following scenario;

[0076] Figure 3 It is a schematic diagram of rear-end collision probability calculation;

[0077] Figure 4 is the empirical cumulative probability distribution diagram of rear-end collision risk;

[0078] Figure 5 Schematic diagram of the rear-end collision risk threshold selection process: (a) average remaining life of three vehicle groups under sunny conditions; (b) average remaining life of three vehicle groups under rainy conditions; (c) average remaining life of three vehicle groups under snowy conditions; (d) threshold stability analysis diagram of three vehicle groups under sunny conditions; (e) threshold stability analysis diagram of three vehicle groups under rainy conditions; (f) threshold stability analysis diagram of three vehicle groups under snowy conditions;

[0079] Figure 6 It is the generalized Pareto regression tree diagram of the three-vehicle group under sunny conditions;

[0080] Figure 7 is the generalized Pareto regression tree diagram of the three-vehicle group under rainy conditions;

[0081] Figure 8 It is the generalized Pareto regression tree diagram of the three-vehicle group under snowy conditions. DETAILED DESCRIPTION

[0082] The present invention is further described in detail below in conjunction with embodiments.

[0083] Those skilled in the art will appreciate that the following examples are only used to illustrate the present invention and should not be considered to limit the scope of the present invention. If no specific techniques or conditions are specified in the examples, the techniques or conditions described in the literature in the art or the product specifications are used. If the manufacturer of the materials or equipment used is not specified, they are all conventional products that can be purchased.

[0084] A method for analyzing the risk of multi-vehicle rear-end collision under adverse weather conditions comprises the following steps:

[0085] Step 1: Obtain vehicle data, weather data, road surface conditions, and lighting conditions of the current road section, and distinguish whether the vehicle is in a free flow state or a following state, and select the following data of the three-vehicle group;

[0086] Step 2: Quantify the risk of multi-vehicle rear-end collision based on artificial potential field theory;

[0087] Step 3: Group the multi-vehicle data according to sunny days, rainy days, and snowy days. According to the super-threshold model theory, based on the average remaining life graph and the threshold stability analysis graph, determine the rear-end collision risk threshold of the three-vehicle following scenario under different weather conditions, and filter out the data that exceeds the threshold;

[0088] Step 4: Combine the standard CART algorithm with the generalized Pareto distribution, use the generalized Pareto log-likelihood function as the splitting function of the regression tree, construct a generalized Pareto regression tree, identify the factors that affect the rear-end collision risk of the three-vehicle group under different weather conditions based on the generalized Pareto regression tree, and issue a rear-end collision risk warning based on this factor.

[0089] In step 1, vehicle data of the current road section is collected by a roadside vehicle detector, and the vehicle data includes speed, time, vehicle length, vehicle weight and time interval data of each passing vehicle;

[0090] Meteorological data are obtained through meteorological detectors; meteorological data include precipitation intensity, precipitation type, temperature, relative humidity, wind speed and wind direction;

[0091] The weather detector is equipped with a camera for taking photos of the road surface and identifying the road surface status;

[0092] Light conditions are divided into daytime, dusk and nighttime, where dusk refers to the hour before sunrise and sunset and the hour after sunset.

[0093] In step one, the road conditions include four categories: dry, wet, snow-covered, and visible snow traces; the vehicle detector and the weather detector are set up close to each other.

[0094] In step 1, the time interval is used as a basis to determine whether the vehicle is in a free flow state or a following state; adjacent vehicles with a time interval of less than 5 seconds are considered to be in a following state;

[0095] When screening the following data of three-car groups, it is necessary to ensure that the lead car and the first following car, and the first following car and the second following car are in a following state, while the lead car and the car in front of the lead car, and the second following car and the car behind the second following car are not in a following state.

[0096] The specific method of step 2 is:

[0097] (1) Calculate the probability of rear-end collision

[0098] The current time is recorded as t0, and p(n,s|τ) is the estimated rear-end collision probability of vehicle s and vehicle n after τ seconds, that is, the rear-end collision probability at time t0+τ is calculated;

[0099] For the three-car group following data, the average value of the time interval is used as τ for calculation;

[0100] The rear-end collision probability calculation formula is:

[0101]

[0102] Where N is the probability density function of the acceleration of vehicle n, μ and σ represent the mean and standard deviation of the probability density function respectively; ΔX represents the relative distance between the vehicles in the longitudinal direction; ΔV represents the relative speed of the two vehicles;

[0103] (2) Calculate the severity of the collision

[0104] Assuming that the collision is an inelastic collision, the calculation formula for the severity of the rear-end collision is:

[0105] CS=0.5W s β 2 |ΔV s,n | 2

[0106] Where CS represents the severity of rear-end collision; W s represents the weight of vehicle s; |ΔV s,n |=|V s -V n |, represents the relative speed between vehicle s and vehicle n; V s 、V n They represent the speed of vehicle s and vehicle n respectively; Indicates the mass ratio; W n represents the weight of vehicle n;

[0107] (3) Calculating rear-end collision risk

[0108] The calculation formula for the rear-end collision risk caused by vehicle n to target vehicle s is:

[0109] r n,s =CS·p(n,s|τ)

[0110] In the formula, r n,s is the rear-end collision risk caused by vehicle n to target vehicle s;

[0111] The total rear-end collision risk r borne by the target vehicle s is composed of the dynamic risks caused by multiple adjacent vehicles. The calculation formula of the total risk r is:

[0112] r=∑r n,s ;

[0113] The calculation of the total risk of rear-end collision of three vehicles is to take the first following vehicle as the target vehicle, and calculate the rear-end collision risks between the first following vehicle and the lead vehicle, and between the first following vehicle and the second following vehicle respectively. According to the superposition of field effects, the total risk of rear-end collision of the first following vehicle is the sum of the two.

[0114] In step 3, based on the average remaining life graph and the threshold stability analysis graph, the specific method for determining the threshold of rear-end collision risk under different weather conditions and different following scenarios is as follows:

[0115] (1) According to the average remaining life graph, an interval range U1 in which a threshold exists is selected so that the average remaining life graph within the interval is linear or approximately linear;

[0116] (2) According to the threshold stability diagram, an interval U2 is determined, so that the corrected scale parameter and shape parameter can remain stable or basically stable within the interval;

[0117] (3) Take the intersection U of the above two intervals, U = U1 ∩ U2, and take the lower limit value of the set U as the final threshold μ0.

[0118] In step 4, for a given data set D = (R i , X i ) 1≤i≤n , R is the dependent variable, representing the total risk of rear-end collision; X represents the set of independent variables, represents d-dimensional space, that is, X=(X (1) ,…,X (d) ), d is the total number of independent variables; the constructed generalized Pareto regression tree is a binary tree. For each value x of the independent variable, assuming that the conditional distribution of R|X=x is a heavy-tailed distribution, the scale parameter σ and shape parameter γ of the generalized Pareto distribution depend on x, and the generalized Pareto log-likelihood function is obtained as follows:

[0119]

[0120] Wherein, φ is the generalized Pareto log-likelihood function and also the splitting function of the generalized Pareto regression tree; r represents a specific total risk value of rear-end collision; σ(x) is the function of the scale parameter σ of the generalized Pareto distribution with respect to x; γ(x) is the function of the shape parameter γ of the generalized Pareto distribution with respect to x; m(x) = (σ(x), γ(x)) is a function composed of σ(x) and γ(x); the standard CART algorithm uses the mean square error as the splitting function of the regression tree, and the generalized Pareto regression tree uses the generalized Pareto log-likelihood function as the splitting function of the regression tree based on the CART algorithm.

[0121] Figure 1 Shown is a flow chart of a method for analyzing the risk of multi-vehicle rear-end collisions under adverse weather conditions provided by the present invention, and each step will be described in detail below.

[0122] Step 1: Obtain vehicle data, weather data, road surface conditions, and lighting conditions of the current road section, distinguish whether the vehicle is in a free-flow state or a following state, and filter out the following data of multiple vehicle groups.

[0123] 1. Data Collection

[0124] By installing vehicle detectors and meteorological detectors on the roadside and adjacent to each other, vehicle driving characteristic data and meteorological data that can be matched in time and space are obtained. The vehicle detector collects the speed, time, vehicle length, and vehicle weight data of each passing vehicle. Meteorological data is obtained through meteorological detectors, which include precipitation intensity, precipitation type, temperature, relative humidity, wind speed, and wind direction. Among them, precipitation intensity is divided into four categories, namely "no precipitation (precipitation equal to 0mm / 10min)", "low-intensity precipitation (precipitation greater than 0mm / 10min and less than or equal to 1mm / 10min)," "medium-intensity precipitation (precipitation greater than 1mm / 10min and less than or equal to 5mm / 10min)" and "high-intensity precipitation (precipitation greater than 5mm / 10min)"; precipitation types include sunny, rainy, and snowy. The meteorological detector is equipped with a camera that takes a road surface photo every 10 minutes. These photos are used to identify the road surface status and divide the road surface status into four categories: "dry", "wet", "snow-covered" and "visible snow traces". "Snow covered" means the entire road is completely covered with snow, and "visible snow traces" means the road is covered with snow but the road surface is still exposed. Using the ephemeris, the lighting conditions are determined based on the spatial position of the detector and the time point of each vehicle detection event. The lighting conditions are divided into daytime, dusk and nighttime, where dusk refers to the hour before sunrise and sunset and the hour after sunset.

[0125] Table 1. Variable names and their meanings

[0126] Variable Name Three-car group Vs The speed of vehicle s W Vehicle weight V1 Speed ​​of vehicle 1 W1 Weight of vehicle 1 V2 Speed ​​of vehicle 2 W2 Weight of vehicle 2 H1 Headway time between vehicle s and vehicle 1 H2 Headway time between vehicle s and vehicle 2

[0127] 2. Filtering of car-following data

[0128] The time interval is used as the basis for judging whether the vehicle is in a free flow state or a following state. Adjacent vehicles with a time interval of less than 5 seconds are considered to be in a following state. The present invention studies the multi-vehicle rear-end collision with three consecutive following vehicles. When screening the following data of the three-vehicle group, if Figure 2As shown, when screening the three-vehicle group following data, it is necessary to ensure that the target vehicle s is in a following state with vehicle 1 and vehicle 2, while vehicle 1 and vehicle 2 are not in a following state with other adjacent vehicles.

[0129] Step 2: Quantify the rear-end collision risk based on artificial potential field theory and apply it to multi-vehicle following risk assessment. The risk assessment indicator used is the single-step driving probability risk field method, referred to as S-PDRF. The calculation is divided into the following steps:

[0130] 1. Calculate the probability of rear-end collision

[0131] S-PDRF estimates the rear-end collision probability at a certain time in the future. Therefore, the rear-end collision probability is only related to the spatial overlap probability. If the current time is recorded as t0, p(n,s|τ) is the estimated rear-end collision probability of vehicle s and vehicle n after τ seconds, that is, the rear-end collision probability at time t0+τ is calculated. For a three-vehicle group, the average time interval is used as τ for calculation. Figure 3 This is a schematic diagram of the rear-end collision probability calculation. At time t0, the distance between vehicle s and the adjacent vehicle n is ΔX. After τ seconds, the two vehicles collide at time t0+τ. For vehicle s, it is assumed that its velocity and direction remain unchanged (that is, the acceleration is 0); for vehicle n, it is assumed that its acceleration follows a Gaussian distribution. By treating the acceleration as a random variable, the probability density function of the acceleration can be estimated. Vehicle s maintains its motion state unchanged, and the motion state of vehicle n is unknown (treating the acceleration as a random variable). After τ seconds, the spatial overlap probability of the two vehicles is the collision probability, which is calculated as follows:

[0132]

[0133] Where N is the probability density function of the acceleration of vehicle n, u and σ represent the mean and standard deviation of the probability density function respectively; ΔX represents the relative distance between the vehicles in the longitudinal direction; ΔV represents the relative speed of the two vehicles.

[0134] 2. Calculate the severity of the collision

[0135] Assuming that the collision is an inelastic collision, that is, the vehicles move together after the first collision contact, the rear-end collision severity calculation formula is:

[0136] CS=0.5W s β 2 |ΔV s,n | 2

[0137] Where CS represents the severity of rear-end collision; W s represents the weight of vehicle s; |ΔV s,n |=|V s -Vn |, represents the relative speed between vehicle s and vehicle n; V s 、V n They represent the speed of vehicle s and vehicle n respectively; Indicates the mass ratio; W n represents the weight of vehicle n.

[0138] 3. Rear-end collision risk

[0139] S-PDRF takes into account two important aspects of rear-end collision risk: rear-end collision probability and rear-end collision severity, and its calculation formula is:

[0140] r n,s =CS·p(n,s|τ)

[0141] In the formula, r n,s is the rear-end collision risk caused by vehicle n to target vehicle s.

[0142] At a given moment, the total rear-end collision risk r borne by the target vehicle is composed of the dynamic risks caused by multiple adjacent vehicles. Assuming that the risk posed by one obstacle is independent of the risk posed by another obstacle, the total risk r can be calculated as follows:

[0143] r=∑r n,s

[0144] Therefore, if Figure 2 For the three-car following scenario shown in the figure, the total rear-end collision risk is calculated as follows:

[0145] r=r 1,s +r 2,s

[0146] In the formula, r 1,s is the rear-end collision risk caused by vehicle 1 to target vehicle s, r 2,s is the rear-end collision risk caused by vehicle 2 to target vehicle s.

[0147] The rear-end collision risk is calculated through the above steps. Figure 4 This is the empirical cumulative probability distribution diagram of the rear-end collision risk of the three-vehicle group. It can be found that the heavy-tail phenomenon of the data is very obvious, which means that the risk of rear-end collision accidents for most vehicles in the following state is very small, and the extreme value events with higher rear-end collision risks are more worthy of special attention.

[0148] Step 3: Group the multi-vehicle data according to sunny days, rainy days, and snowy days. According to the super-threshold model theory, based on the average remaining life graph and the threshold stability analysis graph, determine the rear-end collision risk threshold of the three-vehicle following scenario under different weather conditions, and filter out the data that exceeds the threshold.

[0149] In order to focus on analyzing the heterogeneity of extreme value events of rear-end collisions with higher risk under different weather conditions and different following scenarios, the calculated rear-end collision risk is regarded as a set of independent and identically distributed observations, from which a suitable threshold needs to be selected to define the extreme value samples. The extreme value samples exceeding the threshold are fitted using the generalized Pareto distribution. The threshold is selected using the mean remaining life graph and the threshold stability graph. The selection process of the threshold μ0 is as follows:

[0150] (1) According to the average remaining life graph, an interval range U1 where a threshold exists is selected so that the average remaining life graph within the interval is approximately linear;

[0151] (2) According to the threshold stability analysis diagram, determine an interval U2 so that the corrected scale parameters and shape parameters can remain basically stable within the interval;

[0152] (3) Take the intersection U of the above two intervals, U = U1 ∩ U2. In order to ensure the amount of data for extreme value events, the lower limit of the set is taken as the final threshold μ0.

[0153] The rear-end collision risk threshold selection process of three vehicles under sunny conditions is taken as an example to illustrate. Figure 5 (a), (b), and (c) are the average remaining life graphs of the three vehicle groups under sunny, rainy, and snowy conditions, respectively; Figure 5 (d), (e), and (f) are the threshold stability analysis diagrams of the three-vehicle group under sunny, rainy, and snowy conditions, respectively. It can be observed that the average remaining life diagram is approximately linear in the interval U1 = [1,15], and the corrected scale parameter and shape parameter remain basically stable in the interval U2 = [11.25,12.19]. Therefore, the threshold of the three-vehicle group under sunny conditions is determined to be 11.25. Similarly, the threshold of the rear-end collision risk of the three-vehicle group under rainy and snowy conditions can be determined as 0.955 and 0.435, respectively. It can be found that the threshold decreases as the weather deteriorates.

[0154] Step 4: Combine the standard CART (Classification and Regression Trees) algorithm with the generalized Pareto distribution, use the generalized Pareto log-likelihood function as the splitting function of the regression tree, and construct a generalized Pareto regression tree.

[0155] For a given data set D = (R i , X i ) 1≤i≤n , R is the dependent variable, which represents the total risk of rear-end collision in the present invention; X represents the set of independent variables, represents d-dimensional space, that is, X=(X (1) ,…,X (d)), d is the total number of independent variables; in the present invention, d=5, X (1) ,…,X (5) They represent road conditions, lighting conditions, vehicle speed, vehicle weight, and time interval respectively.

[0156] The generalized Pareto regression tree constructed in the present invention draws on the standard CART algorithm, and its purpose is to retrieve a regression function:

[0157] m * =arg min E[φ(R,m(X)]

[0158] Where φ is the loss function and also the splitting function of the regression tree; arg min is a mathematical term that indicates the parameter value (the value of the independent variable) at which a function achieves the minimum value in its domain; R is the total risk of rear-end collision; m(X) is the number of variables that satisfy rule G. j (X) is the possible value of the tree node; m * represents the value of m(X) that minimizes the average loss;

[0159] The generalized Pareto regression tree branches through the splitting rule and can be represented by a binary tree. The tree construction process includes two stages, namely the "growing" and "pruning" stages of the tree.

[0160] In the tree growth phase, by determining a set of splitting rules, the input space x = (x (1) ,…,x (d) ) is divided into different units. j (x) represents the jth splitting rule, G j′ (x) represents the difference between G j (x). Specifically, for each possible value x of the independent variable of the current step, G j The value of (x) can be 1 or 0, G j (x)G j′ (x) = 0, and ∑ j G j (x) = 1. If d = 1, the splitting rule can be considered as a segment splitting line; if d = 2, the splitting rule can be considered as a segment splitting rectangle; if d>2, the splitting rule can be considered as a segment splitting hyperrectangle. For regression trees, the splitting rule must be determined according to the components of x, that is, for some and Can be written as This means that when x satisfies x1≤x<x2, G j (x) is 1, otherwise G j The value of (x) is 0. For the splitting rule G obtained at step k j , two new rules G will be generated at step k+1j1 and G j2 (If G j (x)=0, then G j1 (x)+G j2 (x)=0), the two new rules generated indicate that the regression tree diagram will generate two new branches in the current step. The algorithm of the growth stage can be summarized as follows:

[0161] Step 1: For all x, G1(x) = 1, n1 = 1 (corresponding to the root node of the tree).

[0162] Step k+1: Assume represents the rule obtained in step k. For j = 1, ..., n k :

[0163] (1) If G j (X i )=1 have the same characteristics, then the jth rule is retained because the population cannot be split any further;

[0164] (2) Otherwise, rule G j The two new rules G are determined in the following way j1 and G j2 replace:

[0165] 1) For X = (X (1) ,…,X (d) ) for each X (l) , X (l) represents the lth independent variable, l = 1, 2, .., d, defining the optimal threshold To split the data:

[0166]

[0167] In the formula,

[0168]

[0169] In the formula, x (l) represents the value of the lth independent variable; arg min is a mathematical term that indicates the parameter value (the value of the independent variable) at which a function achieves the minimum value in its domain; φ is the splitting function; R is the total risk of rear-end collision; Indicates when satisfied hour The value is 1, otherwise The value is 0, and the same applies to other similar symbols; is the optimal estimated value of the tree node when the rule Gj is satisfied, m l- (x,G j ) and m l+ (x,Gj ) are respectively to satisfy the rule G j The tree node is further split into estimated values ​​of left and right child nodes.

[0170] For the value x of the independent variable, assuming that the conditional distribution of Y|X=x is a heavy-tailed distribution, the scale parameter σ and shape parameter γ of the generalized Pareto distribution depend on x. This leads to the generalized Pareto log-likelihood function:

[0171]

[0172] Where φ is the generalized Pareto log-likelihood function, which is also the splitting function of the generalized Pareto regression tree; r represents the total risk value of a specific rear-end collision; σ(x) is the function of the scale parameter σ of the generalized Pareto distribution with respect to x; γ(x) is the function of the shape parameter γ of the generalized Pareto distribution with respect to x; m(x) = (σ(x), γ(x)) is the function composed of σ(x) and γ(x).

[0173] 2) Select the best split variable index to consider: Two new rules are defined and The two new rules generated represent the two new branches that the regression tree diagram will generate at the current step.

[0174] (3) Let n k+1 represents the new number of rules. The stopping rule is if n k+1 =n k , then stop.

[0175] From the tree growth stage, we can get the set of tree splitting rules, namely Where j = 1, ..., s; s is the last step of the regression tree split. From the generalized Pareto regression tree, the estimated quantity of the regression model can be derived

[0176]

[0177] The final rule obtained It is called the maximum tree.

[0178] The tree pruning stage is a model selection process that can avoid overfitting problems. The standard pruning method uses a penalty method to select appropriate subtrees. The subtree of the largest tree With cardinality n s Ruleset Then, the subtree that minimizes the criterion is selected.

[0179]

[0180] α is a penalty constant across all subtrees of the largest tree. Thus, trees with a large number of leaves (i.e., regularities) are penalized compared to smaller trees. To determine the tree It is not necessary to compute all subtrees from the maximum tree. For all K ≥ 0, as long as All subtrees of Determine the subtree that minimizes the above formula Then choose the tree that minimizes the criterion with respect to K The penalty constant α is selected by using the k-fold cross-validation method, which randomly divides the original sample into k parts and uses them as training samples or test samples in turn to calibrate α.

[0181] The hierarchical structure of the generalized Pareto regression tree can be used to evaluate the importance of each independent variable to the dependent variable. The hierarchical structure of the regression tree is constructed by partitioning the data. Each node corresponds to a feature that takes a specific value, which only represents the optimal partition at the current step. If an independent variable is located in the upper node of the tree and is frequently used for segmentation, then it has a key influence on the dependent variable and has a high importance. When determining the root node, the feature selected is the feature with the greatest partitioning ability in the entire model, which means that the feature corresponding to the root node has the highest importance in the entire model.

[0182] Figure 6 , Figure 7 , Figure 8 The generalized Pareto regression tree diagrams of the three-vehicle group under sunny, rainy and snowy conditions are shown respectively. The generalized Pareto regression tree diagram of the three-vehicle group under sunny conditions consists of 5 internal nodes and 6 leaf nodes. The root node is divided according to whether the weight of vehicle 2 is greater than 21080kg, which shows that on sunny days, whether the weight of the vehicle is greater than 21080kg has a significant impact on the rear-end collision risk of the three vehicles; for example, a rear-end collision warning is given to vehicles with a weight greater than 21080kg. The root node of the generalized Pareto regression tree diagram under rainy conditions is divided according to whether the speed of vehicle 2 is greater than 79.5km / h; for example, a prompt of a speed limit of less than 79.5km / h is given to all vehicles, and if it exceeds 79.5km / h, a rear-end collision risk warning is issued; the root node of the generalized Pareto regression tree diagram under snowy conditions is divided according to whether the weight of vehicle 1 is greater than 5678kg, which shows that the factors that most affect the risk of rear-end collision under different weather conditions are different. By observing all the regression tree diagrams, it can be found that the splitting of the root node, internal node and leaf node of the tree all starts with the speed, weight and time interval of the vehicle, which means that the main factors affecting the risk of rear-end collision are vehicle speed, vehicle weight and time interval.

[0183] Based on a method for analyzing the risk of multi-vehicle rear-end collision under adverse weather conditions provided by an embodiment of the present invention, a corresponding generalized Pareto regression tree can be constructed for the rear-end collision risk of three-vehicle following scenarios under different weather conditions, and the degree of influence of factors such as adverse weather on the rear-end collision risk can be analyzed, which has strong operability.

[0184] Those skilled in the art can understand that: all or part of the steps of implementing the above-mentioned method embodiment can be completed by hardware or software systems related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above-mentioned method embodiment; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk, etc. Various media that can store program codes.

[0185] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for analyzing the risk of multi-vehicle rear-end collisions in adverse weather conditions, characterized in that: The steps include: Step 1: Obtain vehicle data, weather data, road surface conditions, and lighting conditions of the current road section, and distinguish whether the vehicle is in a free flow state or a following state, and select the following data of the three-vehicle group; Step 2: Quantify the risk of multi-vehicle rear-end collision based on artificial potential field theory; Step 3: Group the multi-vehicle data according to sunny days, rainy days, and snowy days. According to the super-threshold model theory, based on the average remaining life graph and the threshold stability analysis graph, determine the rear-end collision risk threshold of the three-vehicle following scenario under different weather conditions, and filter out the data that exceeds the threshold; Step 4: Combine the standard CART algorithm with the generalized Pareto distribution, use the generalized Pareto log-likelihood function as the splitting function of the regression tree, construct a generalized Pareto regression tree, identify the factors that affect the rear-end collision risk of the three-vehicle group under different weather conditions based on the generalized Pareto regression tree, and issue a rear-end collision risk warning based on the factors; The specific method of step 2 is: (1) Calculate the probability of rear-end collision The current time is recorded as t0, and p(n,s|τ) is the estimated rear-end collision probability of vehicle s and vehicle n after τ seconds, that is, the rear-end collision probability at time t0+τ is calculated; For the three-car group following data, the average value of the time interval is used as τ for calculation; The rear-end collision probability calculation formula is: Where N is the probability density function of the acceleration of vehicle n, μ and σ represent the mean and standard deviation of the probability density function respectively; ΔX represents the relative distance between the vehicles in the longitudinal direction; ΔV represents the relative speed of the two vehicles; (2) Calculate the severity of the collision Assuming that the collision is an inelastic collision, the calculation formula for the severity of the rear-end collision is: CS=0.5W s b 2 |ΔV s,n | 2 Where CS represents the severity of rear-end collision; W s represents the weight of vehicle s; |ΔV s,n |=|V s -V n |, represents the relative speed between vehicle s and vehicle n; V s 、V n They represent the speed of vehicle s and vehicle n respectively; Indicates the mass ratio; W n represents the weight of vehicle n; (3) Calculating rear-end collision risk The calculation formula for the rear-end collision risk caused by vehicle n to target vehicle s is: r n,s =CS·p(n,s∣τ) In the formula, r n,s is the rear-end collision risk caused by vehicle n to target vehicle s; The total rear-end collision risk r borne by the target vehicle s is composed of the dynamic risks caused by multiple adjacent vehicles. The calculation formula of the total risk r is: r＝∑r n,s ； The total rear-end collision risk of the three-vehicle group is calculated by taking the first following vehicle as the target vehicle, and calculating the rear-end collision risk between the first following vehicle and the leading vehicle, and between the first following vehicle and the second following vehicle. According to the superposition of the field effect, the total rear-end collision risk of the first following vehicle is the sum of the two. In step 3, based on the average remaining life graph and the threshold stability analysis graph, the specific method for determining the threshold of rear-end collision risk under different weather conditions and different following scenarios is as follows: (1) According to the average remaining life graph, an interval range U1 in which a threshold exists is selected so that the average remaining life graph within the interval is linear or approximately linear; (2) According to the threshold stability diagram, an interval U2 is determined, so that the corrected scale parameter and shape parameter can remain stable or basically stable within the interval; (3) Take the intersection U of the above two intervals, U = U1∩U2, and take the lower limit of the set U as the final threshold μ0; In step 1, the time interval is used as a basis to determine whether the vehicle is in a free flow state or a following state; Adjacent vehicles with a time interval of less than 5 seconds are considered to be in a following state; When screening the following data of three-car groups, it is necessary to ensure that the lead car and the first following car, and the first following car and the second following car are in a following state, while the lead car and the car in front of the lead car, and the second following car and the car behind the second following car are not in a following state.

2. The method for analyzing the risk of multi-vehicle rear-end collision in adverse weather conditions according to claim 1, characterized in that: In step 1, vehicle data of the current road section is collected by a roadside vehicle detector, and the vehicle data includes speed, time, vehicle length, vehicle weight and time interval data of each passing vehicle; Meteorological data are obtained through meteorological detectors; meteorological data include precipitation intensity, precipitation type, temperature, relative humidity, wind speed and wind direction; The weather detector is equipped with a camera for taking photos of the road surface and identifying the road surface status; Light conditions are divided into daytime, dusk and nighttime, where dusk refers to the hour before sunrise and sunset and the hour after sunset.

3. The method for analyzing the risk of multi-vehicle rear-end collision in adverse weather conditions according to claim 2, characterized in that: In step one, the road conditions include four categories: dry, wet, snow-covered, and visible snow traces; the vehicle detector and the weather detector are set up close to each other.

4. The method for analyzing the risk of multi-vehicle rear-end collision in adverse weather conditions according to claim 1, characterized in that: In step 4, for a given data set D = (R i , X i ) 1≤i≤n , R is the dependent variable, representing the total risk of rear-end collision; X represents the set of independent variables, represents d-dimensional space, that is, X=(X (1) ,…,X (d) ), d is the total number of independent variables; the constructed generalized Pareto regression tree is a binary tree. For each value x of the independent variable, assuming that the conditional distribution of R|X=x is a heavy-tailed distribution, the scale parameter σ and shape parameter γ of the generalized Pareto distribution depend on x, and the generalized Pareto log-likelihood function is obtained as follows: Wherein, φ is the generalized Pareto log-likelihood function and also the splitting function of the generalized Pareto regression tree; r represents a specific total risk value of rear-end collision; σ(x) is the function of the scale parameter σ of the generalized Pareto distribution with respect to x; γ(x) is the function of the shape parameter γ of the generalized Pareto distribution with respect to x; m(x) = (σ(x), γ(x)) is a function composed of σ(x) and γ(x); the standard CART algorithm uses the mean square error as the splitting function of the regression tree, and the generalized Pareto regression tree uses the generalized Pareto log-likelihood function as the splitting function of the regression tree based on the CART algorithm.

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