A bridge downhill road section traffic risk assessment method based on reliability analysis

Abstract

This invention belongs to the field of bridge traffic risk assessment technology, and specifically relates to a method for assessing traffic risk on downhill bridge sections based on reliability analysis. The method comprises the following steps: using driving speed as a random variable, constructing a vehicle braking traffic risk function for the downhill bridge section based on the sight distance required for vehicles going downhill and the emergency stopping distance provided by the bridge deck; analyzing reliability indices and failure probabilities to determine traffic risk level classification standards; determining reliability indices based on the longitudinal force coefficient detection value of the bridge deck, thereby determining the traffic risk level of the section and assessing the risk of the downhill bridge section. This invention quantifies the impact of decreased bridge deck anti-skid performance on driving safety, predicts potential accidents from a probabilistic perspective, and thus achieves the purpose of timely risk warning and timely hazard elimination.

Description

Technical Field

[0001] This invention belongs to the field of bridge traffic risk assessment technology, and specifically relates to a method for assessing traffic risks on downhill sections of bridges based on reliability analysis. Background Technology

[0002] Traffic safety has always been a focal point of scholarly concern. With rising economic levels, the increasing number of motor vehicles, while facilitating travel, has also led to frequent traffic accidents, directly threatening people's lives and property. On downhill sections of bridges, vehicles brake more frequently, resulting in a more severe decrease in the bridge's anti-skid performance compared to other road sections. If the bridge surface cannot provide sufficient braking distance for vehicles, traffic accidents will occur. Therefore, the traffic safety issues on downhill bridge sections are particularly serious.

[0003] Risk theory was first applied to business management, but with economic and technological development, the risks faced by humanity have become increasingly complex. Higher returns often come with greater risks, and risk management can assist managers in decision-making, avoiding or reducing losses while maximizing returns. Currently, risk management is applied in many fields such as finance, construction, manufacturing, and aerospace, with different risk assessment methods used in different fields. Common risk assessment methods can be divided into three types: qualitative analysis, quantitative analysis, and semi-qualitative / semi-quantitative. These methods mainly analyze different stages and processes of risk events and are well-suited for production operations such as engineering construction and equipment manufacturing. However, for traffic risks that are difficult to quantify, traditional risk assessment methods have significant limitations and are difficult to apply to actual traffic risk assessments. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to provide a traffic risk assessment method for downhill bridge sections based on reliability analysis. This method quantifies the impact of reduced bridge deck anti-skid performance on driving safety, predicts potential accidents from a probabilistic perspective, and thus achieves timely risk warning and timely elimination of dangers.

[0005] The technical solution of this invention is: a method for traffic risk assessment of bridge downhill sections based on reliability analysis, comprising the following steps:

[0006] S1: Collect the vehicle speed on the downhill section and determine the mean and standard deviation of the speed;

[0007] S2: Using driving speed as a random variable, construct a vehicle braking traffic risk function for downhill bridge sections based on the sight distance required for vehicles going downhill and the emergency stopping distance provided by the bridge surface.

[0008] S3: Based on the vehicle braking traffic risk function of the bridge downhill section, analyze the reliability index β and failure probability P. f Determine the criteria for classifying traffic risk levels;

[0009] S4: Detect the longitudinal force coefficient of the bridge deck;

[0010] S5: Determine the reliability index β based on the longitudinal force coefficient detection value of the bridge deck, thereby determining the traffic risk level of the road section and assessing the risk of the downhill section of the bridge.

[0011] In step S1, the vehicle speed on the downhill section under different speed limit conditions is collected as a sample. After removing abnormal data, the mean speed and standard deviation of the vehicle speed are calculated.

[0012] The minimum number of samples to be collected is determined according to the following formula:

[0013]

[0014] In the formula: n is the minimum number of samples, z α / 2 Let σ be a constant at a given confidence level, σ be the standard deviation of the collected vehicle speeds, and E be the expected estimation error.

[0015] The formulas for calculating the mean and standard deviation of vehicle speed after removing outliers are as follows:

[0016]

[0017]

[0018] Where: μ v and σ v These represent the mean and standard deviation of the collected vehicle speeds, respectively. i Let be the i-th vehicle speed value, and N be the number of processed samples.

[0019] In step S2, the specific steps for constructing the vehicle braking traffic risk function for the downhill section of the bridge are as follows:

[0020] S21: When a vehicle travels on a bridge section, the vehicle and the bridge surface constitute a system. When the driver detects a hazard and takes emergency braking measures, the traffic risk function expression of the system is as follows:

[0021] Z = f R -f S (4)

[0022] In the formula: f S The required stopping sight distance to ensure vehicle safety is m; f R The actual anti-skid performance of the bridge deck provides an emergency stopping distance for vehicles, in meters.

[0023] S22: The stopping distance of a vehicle during emergency braking consists of two parts: reaction distance and braking distance. The braking distance is mainly determined by the bridge deck's anti-skid performance and longitudinal slope. On downhill sections, the bridge deck provides a braking distance f for the vehicle. R The expression is as follows:

[0024]

[0025] In the formula: v is the vehicle speed when the driver discovers the danger, in km / h, and is a random variable; t is the driver's reaction time, taken as 2.5s; g is the acceleration due to gravity, taken as 9.8m / s². 2 θ is the longitudinal slope of the bridge; BFC is the longitudinal force coefficient of the bridge deck.

[0026] In step S21, f S Depending on the design speed, the value shall be selected in accordance with the provisions of the "Highway Route Design Specification" (JTG D20-2017).

[0027] In step S3, based on the vehicle braking traffic risk function of the bridge downhill section, the JC method (equivalent normalization method) is used to solve for the reliability index β and the failure probability P. f The specific steps are as follows:

[0028] S31: In the traffic risk function for vehicle braking on a downhill section of a bridge, let the vehicle speed be a random variable V, μ V σ V Let these be the mean and standard deviation of the vehicle's operating speed, respectively. Then, normalize the random variable to its equivalent normality.

[0029] μ V′ =v * -Φ -1 [F V (v * )]σ V′ (6)

[0030]

[0031] Where: μ V′ and σ V′ These are the mean and standard deviation after normalization, respectively; v * μ is taken as the verification point for the random variable V in the initial calculation. V ;F V and f V These are the distribution function and probability density function of V, respectively, and Φ -1 [·]and These are the inverse function of the standard normal distribution function and its probability density function, respectively.

[0032] S32: Calculate the sensitivity coefficient cosθ V :

[0033]

[0034] S33: Verification point v * The reliability index β is calculated according to the following formula:

[0035]

[0036] v * =μ V′ +βσ V′ cosθ V (10)

[0037] Where Z(v) * ) is v = v * The function value of the traffic risk function for vehicle braking on a downhill section of a bridge; the meanings of other symbols are the same as before. Iterative calculations are performed using the above two equations as constraints, continuously updating v. * The iteration ends when β and v satisfy the following equation: * The corresponding reliability index β is the reliability value of the system under study;

[0038]

[0039] In the formula, ε takes the value of 10. -6 .

[0040] In step S3, the requirements for the pavement skid resistance index (SRI) in the "Technical Standard for Highway Engineering" (JTG B01-2014) are converted into the road surface skid control factor (BFC) and substituted into the traffic risk function to classify traffic risk levels. The conversion relationship between SRI and BFC is as follows:

[0041]

[0042] In the formula: SRI is the road surface skid resistance index, and BFC is the longitudinal force coefficient.

[0043] The technical advantages of this invention are as follows: Based on reliability analysis, this invention establishes a traffic risk assessment method for downhill bridge sections, describes the braking process of vehicles on downhill bridge sections, quantifies the impact of reduced bridge anti-skid performance on driving safety, and the proposed risk level classification standard can more intuitively reflect the risk status of road sections. It can predict possible accidents from a probabilistic perspective, which is beneficial for maintenance departments and traffic safety departments to make decisions, thereby achieving the purpose of timely risk warning and timely elimination of danger.

[0044] The following will provide further explanation in conjunction with the accompanying drawings. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating a traffic risk assessment method for bridge downhill sections based on reliability analysis, according to an embodiment of the present invention.

[0046] Figure 2 This is a flowchart of the JC method for solving a traffic risk assessment method for downhill sections of bridges based on reliability analysis, according to an embodiment of the present invention.

[0047] Figure 3 This is a diagram showing the changes in traffic risk at different measuring points in an embodiment of the present invention. Detailed Implementation

[0048] Example 1

[0049] A traffic risk assessment method for bridge downhill sections based on reliability analysis, such as... Figure 1 As shown, it includes the following steps:

[0050] S1: Collect the vehicle speed on the downhill section and determine the mean and standard deviation of the speed;

[0051] S2: Using driving speed as a random variable, construct a vehicle braking traffic risk function for downhill bridge sections based on the sight distance required for vehicles going downhill and the emergency stopping distance provided by the bridge surface.

[0052] S3: Based on the vehicle braking traffic risk function of the bridge downhill section, analyze the reliability index β and failure probability P. f Determine the criteria for classifying traffic risk levels;

[0053] S4: Detect the longitudinal force coefficient of the bridge deck;

[0054] S5: Determine the reliability index β based on the longitudinal force coefficient detection value of the bridge deck, thereby determining the traffic risk level of the road section and assessing the risk of the downhill section of the bridge.

[0055] In step S1, the vehicle speed on the downhill section under different speed limit conditions is collected as a sample. After removing abnormal data, the mean speed and standard deviation of the vehicle speed are calculated.

[0056] The minimum number of samples to be collected is determined according to the following formula:

[0057]

[0058] In the formula: n is the minimum number of samples, z α / 2 Let σ be a constant at a given confidence level, σ be the standard deviation of the collected vehicle speeds, and E be the expected estimation error.

[0059] The formulas for calculating the mean and standard deviation of vehicle speed after removing outliers are as follows:

[0060]

[0061]

[0062] Where: μ v and σ v These represent the mean and standard deviation of the collected vehicle speeds, respectively. i Let be the i-th vehicle speed value, and N be the number of processed samples.

[0063] In step S2, the specific steps for constructing the vehicle braking traffic risk function for the downhill section of the bridge are as follows:

[0064] S21: When a vehicle travels on a bridge section, the vehicle and the bridge surface constitute a system. When the driver detects a hazard and takes emergency braking measures, the traffic risk function expression of the system is as follows:

[0065] Z = f R -f S (4)

[0066] In the formula: f S The required stopping sight distance to ensure vehicle safety is m; f R The actual anti-skid performance of the bridge deck provides an emergency stopping distance for vehicles, in meters.

[0067] S22: The stopping distance of a vehicle during emergency braking consists of two parts: reaction distance and braking distance. The braking distance is mainly determined by the bridge deck's anti-skid performance and longitudinal slope. On downhill sections, the bridge deck provides a braking distance f for the vehicle. R The expression is as follows:

[0068]

[0069] In the formula: v is the vehicle speed (km / h) when the driver discovers the danger, which is a random variable; t is the driver's reaction time, taken as 2.5s; g is the acceleration due to gravity, taken as 9.8m / s². 2 θ is the longitudinal slope of the bridge; BFC is the longitudinal force coefficient of the bridge deck.

[0070] In step S21, f S Depending on the design speed, the value shall be selected in accordance with the provisions of the "Highway Route Design Specification" (JTG D20-2017).

[0071] In step S3, based on the vehicle braking traffic risk function of the bridge downhill section, the JC method (equivalent normalization method) is used to solve for the reliability index β and the failure probability P. f ,like Figure 2 As shown, the specific steps are as follows:

[0072] S31: In the traffic risk function for vehicle braking on a downhill section of a bridge, let the vehicle speed be a random variable V, μ V σ V Let these be the mean and standard deviation of the vehicle's operating speed, respectively. Then, normalize the random variable to its equivalent normality.

[0073] μ V′ =v * -Φ -1 [F V (v * )]σ V′ (6)

[0074]

[0075] Where: μ V′ and σ V′ These are the mean and standard deviation after normalization, respectively; v * μ is taken as the verification point for the random variable V in the initial calculation. V ;F V and f V These are the distribution function and probability density function of V, respectively, and Φ -1 [·]and These are the inverse function of the standard normal distribution function and its probability density function, respectively.

[0076] S32: Calculate the sensitivity coefficient cosθ V :

[0077]

[0078] S33: Verification point v * The reliability index β is calculated according to the following formula:

[0079]

[0080] v * =μ V′ +βσ V′ cosθ V (10)

[0081] Where Z(v) * ) is v = v * The function value of the traffic risk function for vehicle braking on a downhill section of a bridge; the meanings of other symbols are the same as before. Iterative calculations are performed using the above two equations as constraints, continuously updating v. * The iteration ends when β and v satisfy the following equation: * The corresponding reliability index β is the reliability value of the system under study;

[0082]

[0083] In the formula, ε takes the value of 10. -6 .

[0084] In step S3, the requirements for the pavement skid resistance index (SRI) in the "Technical Standard for Highway Engineering" (JTG B01-2014) are converted into the road surface skid control factor (BFC) and substituted into the traffic risk function to classify traffic risk levels. The conversion relationship between SRI and BFC is as follows:

[0085]

[0086] In the formula: SRI is the road surface skid resistance index, and BFC is the longitudinal force coefficient.

[0087] Example 2

[0088] This embodiment uses vehicle speed data and bridge deck detection data at two measuring points on a downhill section of a bridge on the Xikang Expressway as examples. The longitudinal slope of the section at measuring point 2 is greater than that of the section at measuring point 1. A traffic risk assessment method based on reliability analysis for downhill bridge sections, as described in Embodiment 1, is used for risk assessment, following these steps:

[0089] S1: Collect the vehicle speed on the downhill section and determine the mean and standard deviation of the speed;

[0090] In this embodiment, a radar speedometer is used to collect vehicle speed data, and the minimum sample size is calculated according to the following formula.

[0091]

[0092] Where: n is the minimum number of samples; z α / 2 Let z be a constant at a given confidence level, and z be a constant at a significance level of 0.05. α / 2 =1.96; σ is the standard deviation of the collected vehicle speed, taken as σ = 10km / h; E is the expected estimation error, taken as E = 2km / h;

[0093] After removing outlier data, the mean and standard deviation of vehicle speeds are calculated using the following formula.

[0094]

[0095]

[0096] Where: μ v and σ v These represent the mean and standard deviation of the collected vehicle speeds, respectively. i Let be the i-th vehicle speed value, and N be the number of processed samples;

[0097] S2: Using driving speed as a random variable, construct a vehicle braking traffic risk function for downhill bridge sections based on the sight distance required for vehicles going downhill and the emergency stopping distance provided by the bridge surface.

[0098]

[0099] The symbols in the formula have the same meaning as before. When the stopping sight distance required for safe driving of a vehicle exceeds the stopping distance that the bridge surface can provide, that is, Z = f R -f S When the speed is less than 0, the system consisting of the vehicle and the bridge deck can be considered to have failed, resulting in a traffic accident. In this embodiment, the design speed of the road segment is 80 km / h, and f is taken as... S =110m; bridge longitudinal slope θ=0.03;

[0100] S3: Based on the vehicle braking traffic risk function of the bridge downhill section, analyze the reliability index β and failure probability P. f Determine the criteria for classifying traffic risk levels;

[0101] The requirements for the skid resistance index (SRI) of pavement in the "Technical Standard for Highway Engineering" (JTG B01-2014) are converted to BFC using the following formula. The conversion results are shown in Table 1 below.

[0102]

[0103] Where: SRI is the pavement skid resistance index, and BFC is the longitudinal force coefficient;

[0104] Table 1 SRI Conversion Results

[0105] index excellent good middle Second-rate Difference SRI ≥90 ≥80，＜90 ≥70，＜80 ≥60，＜70 ＜60 BFC ≥57 ≥47，＜57 ≥39，＜47 ≥32，＜39 ＜32

[0106] The JC method is used to solve for the reliability index β and the failure probability P. f ;

[0107] First, normalize the vehicle speed equivalent:

[0108] μ V ′=v * -Φ -1 [F V (v * )]σ V ′ (6)

[0109]

[0110] Where: μ V′ and σ V′ These are the mean and standard deviation after normalization, respectively; v * μ is taken as the verification point for the random variable V in the initial calculation.V ;F V and f V These are the distribution function and probability density function of V, respectively, and Φ -1 [·]and These are the inverse function of the standard normal distribution function and its probability density function, respectively.

[0111] Calculate the sensitivity coefficient:

[0112]

[0113] In the formula, Z(v) * The value of the traffic risk function is the value of the above verification point.

[0114] Verification point v * The reliability index β is calculated according to the following formula:

[0115]

[0116] v * =μ V′ +βσ V′ cosθ V (10)

[0117] Using the above two equations as constraints, iterative calculations are performed to continuously update v. * The iteration ends when the following equation is satisfied: and β. The corresponding reliability index β is the reliability value of the downhill section;

[0118]

[0119] The criteria for classifying traffic risk levels are shown in Table 2 below.

[0120] Table 2 Traffic Risk Level Classification Standards

[0121] Risk level Level I Level II Level III Level IV Level V Reliability index ≤0.35 0.35～0.80 0.80～1.50 1.50～1.95 ≥1.95 Failure probability ≥50％ 25％～50％ 14％～25％ 8％～14％ ≤8％

[0122] S4: Detect the longitudinal force coefficient of the bridge deck;

[0123] S5: Determine the reliability index β based on the measured value of the longitudinal force coefficient of the bridge deck. The traffic risk level of this road section can then be determined based on the calculated reliability index. Figure 3 As shown.

[0124] Figure 3This study reflects the changes in reliability indices and traffic risk levels at monitoring points 1 and 2 between 2016 and 2022. It shows that the reliability index of bridges on downhill sections decreases year by year with increasing service life, while the traffic risk level increases accordingly, indicating a higher probability of traffic accidents. Meanwhile, because vehicles brake more frequently on the section where monitoring point 2 is located, the reliability index at this point is lower than that at monitoring point 1 in all years. This means that sections with steeper longitudinal slopes are more prone to traffic accidents, which is consistent with actual traffic accident statistics, demonstrating that this method can reflect changes in traffic risk.

[0125] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for traffic risk assessment of bridge downhill sections based on reliability analysis, characterized in that: The method comprises the following steps: S1: collecting the driving speed of the vehicle on a downhill section and determining the mean value and standard deviation of the driving speed; S2: taking the driving speed as a random variable, constructing a bridge downhill section vehicle braking traffic risk function function according to the required sight distance of the vehicle when downhill and the emergency stopping distance provided by the bridge deck, and the specific steps of constructing the bridge downhill section vehicle braking traffic risk function function are: S21: when the vehicle drives on the bridge section, the vehicle and the bridge deck form a system, and when the driver discovers danger and takes emergency braking measures, the traffic risk function function expression of the system is as follows: （4） In the formula: m is the stopping sight distance required to ensure the safety of the vehicle; m is the emergency stopping distance provided by the actual anti-skid performance of the bridge deck for the vehicle. S22: The stopping distance of the vehicle when emergency braking is composed of two parts of reaction distance and braking distance, wherein the braking distance is mainly determined by the anti-skid performance of the bridge deck and the longitudinal slope of the bridge deck, and the bridge deck provides braking distance for the vehicle on the downhill section The expression is as follows: （5） wherein: is the speed of the vehicle at which the driver finds the hazard, is the reaction time of the driver, taken as 2.5 is the acceleration due to gravity, taken as 9.8 is the bridge longitudinal grade; BFC is the bridge longitudinal force coefficient;​​​ S3: According to the bridge downhill road section vehicle braking traffic risk function function, analyze the reliability index And failure probability , Determine the traffic risk level classification standard, according to the bridge downhill road section vehicle braking traffic risk function function, solve the reliability index And failure probability , The specific steps are: S31: In the vehicle braking traffic risk function on the bridge downhill section, let the vehicle operating speed be a random variable V, , respectively the mean and standard deviation of the vehicle operating speed, and normalize the random variable as equivalent normal: （6） （7） wherein: and are the mean and the standard deviation after normalization, respectively; is the check point of the random variable V, which is taken as ; and are the distribution function and the probability density function of , respectively, and are the inverse function of the standard normal distribution function and its probability density function, respectively. S32: Calculate sensitivity coefficient : （8） S33: Check point and reliability index is calculated according to the following formula: （9） （10） in, for The function value of the traffic risk function for vehicle braking on a downhill section of a bridge; the meanings of other symbols are the same as before. Iterative calculations are performed using the above two equations as constraints, and the results are continuously updated. and The iteration ends when the following expression is satisfied. Corresponding reliability index This is the reliability value of the system under study; （11） In the formula, the value of ; S4: detecting the longitudinal force coefficient of the bridge deck; S5: determining the reliability index according to the bridge deck longitudinal force coefficient detection value Thus, the traffic risk grade of the road section is determined, and the risk of the bridge downhill road section is evaluated.

2. The bridge downhill road section traffic risk assessment method based on reliability analysis according to claim 1, characterized in that: In the step S1, the driving speed of the vehicle on a downhill section under different speed limit conditions is collected as a collection sample, and the mean value and standard deviation of the vehicle speed are calculated after removing abnormal data.

3. The method of claim 2, wherein the method further comprises: The minimum number of collection samples is determined according to the following formula: （1） wherein: is the minimum number of samples, is a constant at a given confidence level, is the standard deviation of the collected vehicle speeds, is the expected achieved estimation error; The mean value and standard deviation of the vehicle speed after removing abnormal data are calculated according to the following formula: （2） （3） In the formula: and are the mean and standard deviation of the collected vehicle speed, respectively, is the vehicle speed value, is the number of processed samples.

4. The bridge downhill road traffic risk assessment method based on reliability analysis according to claim 1, characterized in that: The step S21 According to the design speed, the value is taken according to the provisions in the "Highway Route Design Specification" (JTG D20-2017).

5. The method of claim 1, wherein the method further comprises: In the step S3, the requirement of the road surface anti-skid performance index SRI in the Technical Standard of Highway Engineering (JTG B01-2014) is converted into BFC and substituted into the traffic risk function function to divide the traffic risk level, and the conversion relationship between SRI and BFC is as follows: （12） In the formula: SRI is the road surface anti-skid performance index, and BFC is the longitudinal force coefficient.

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