A method for deriving the location of the bridge transition section slab separation based on vehicle acceleration

Abstract

This invention relates to the field of road-bridge transition section health monitoring and intelligent transportation technology, specifically to a method for inferring the location of slab breakage in road-bridge transition sections based on vehicle acceleration. The method involves: collecting vibration signals from vehicles passing through the road-bridge transition section using an onboard acceleration sensor; denoising, noise reduction, and normalization of the collected data; extracting the actual acceleration collected by the sensor using wavelet transform and fast Fourier transform; constructing a physical-mechanical model of the road-bridge transition section and a vehicle-road coupled mechanical model to determine the slab breakage status; calibrating the slab breakage status using a Bayesian probability model, constructing a likelihood function and prior distribution; inferring the posterior distribution based on the likelihood function and prior distribution; and calculating the posterior distribution using the MCMC method. This invention infers the location of slab breakage in road-bridge transition sections using vehicle vibration data and Bayesian methods, enabling precise quantification and uncertainty assessment of road defects.

Description

Technical Field

[0001] This invention relates to the field of road and bridge transition section health monitoring and intelligent transportation technology, and in particular to a method for inferring the location of the detachment of the approach slab in a road and bridge transition section based on vehicle acceleration. Background Technology

[0002] Bridge approach slab detachment refers to the appearance of gaps between the bridge approach slab and the roadbed, causing the slab to lose effective support. This phenomenon can lead to a series of problems, seriously affecting road safety and service life. Problem description: Due to the detachment of the approach slab, vehicles experience significant bumps and jolts when passing over the bridge approach, reducing driving comfort, increasing driver fatigue, causing additional impact on the vehicle's suspension system, shortening vehicle life, and in severe cases, potentially leading to loss of vehicle control and traffic accidents. The detached area causes uneven stress on the approach slab, resulting in localized stress concentration, which may cause cracks, fractures, or even detachment of the slab. This leads to insufficient road support, resulting in cracks, potholes, and other defects. Water may accumulate in the detached area, causing the roadbed to soften and further exacerbating the problem. Bridge bearings may also be damaged due to uneven stress, leading to uneven settlement, further aggravating structural damage, increasing road maintenance costs, and affecting driving safety, especially for vehicles traveling at high speeds.

[0003] Existing methods for detecting the location of detachment of road and bridge transition slabs rely on manual inspections or fixed sensors, which are costly, inefficient, and cannot be monitored in real time. Furthermore, the detachment and settlement of road and bridge transition slabs are highly concealed, making it difficult for conventional detection methods to accurately locate and quantify them. In addition, existing research lacks sufficient study on the correlation between vehicle vibration signals and pavement defects, and there is a lack of systematic inversion models.

[0004] Therefore, this invention proposes a method for deriving the location of the bridge transition section slab detachment based on vehicle acceleration to solve the above problems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention develops a method for inferring the location of detachment of road and bridge transition slabs based on vehicle acceleration. This invention aims to provide a low-cost, high-efficiency, and real-time monitoring method for detecting detachment of road and bridge transition slabs. By inverting the defect parameters through vehicle acceleration data, it provides decision support for road maintenance.

[0006] The technical solution of this invention to solve the technical problem is a method for deriving the location of the detachment of the bridge transition section slab based on vehicle acceleration, comprising the following steps:

[0007] S1. Vibration signals of vehicles passing through the transition section of road bridges are collected using on-board acceleration sensors;

[0008] S2. The collected data is denoised, reduced in noise and normalized, and then the real acceleration collected by the sensor is extracted by wavelet transform and fast Fourier transform.

[0009] S3. Construct a physical and mechanical model of the road-bridge transition section and a vehicle-road coupling mechanical model. Use the vehicle-road coupling mechanical model to find the relationship between the acceleration of the vehicle passing through the road-bridge transition section and the vehicle-road interaction force. Use the physical and mechanical model of the road-bridge transition section to establish the relationship between the detachment status of the road-bridge transition section slab and the acceleration of the vehicle passing through the road-bridge transition section, and then find the detachment status of the road-bridge transition section slab.

[0010] S4. A Bayesian probability model is used to calibrate the detachment status of the bridge transition section slab. Vehicle acceleration data and vehicle type parameters are collected to construct a likelihood function and prior distribution. The posterior distribution is inferred based on the likelihood function and prior distribution. The posterior distribution is calculated using the MCMC Markov chain Monte Carlo method.

[0011] S5. Using the posterior distribution, the damage of the detachment is estimated, the vehicle type parameters corresponding to the acceleration and the deflection value of the road-bridge transition section are obtained, the maximum posterior estimate and confidence interval of the detachment location are calculated, and the vehicle type parameters and the deflection value of the road-bridge transition section are continuously updated to update and predict the detachment situation of the road-bridge transition section slab in real time.

[0012] S1 is as follows:

[0013] Accelerometers are installed on different types of vehicles, and sampling frequencies are set. The accelerometers are installed near the vehicle's center of gravity, with the X-axis of the accelerometer aligned with the vehicle's forward direction. The vehicle carrying the accelerometer passes through the transition section of the road bridge containing the clearance area at a constant speed. Vibration signals before and after the transition section are extracted. The vibration signals include vertical, lateral, and longitudinal acceleration data.

[0014] S2 is as follows:

[0015] S2.1 Data Preprocessing:

[0016] The collected data is preprocessed by using an adaptive Kalman slew rate to eliminate high-frequency noise and outliers, and wavelet denoising and normalization are performed on the collected acceleration data.

[0017] S2.2 Feature Extraction:

[0018] The impulse signal in the preprocessed data is extracted by wavelet transform, the dominant frequency component is extracted by fast Fourier transform, and the local frequency component of the non-stationary signal is extracted by wavelet transform to separate the true acceleration collected by the sensor.

[0019] S3 is as follows:

[0020] S3.1 Constructing the physical and mechanical model of the road-bridge transition section:

[0021] The abutments of the road and bridge are fixed, the roadbed is supported by an elastic foundation, and the physical and mechanical model of the road and bridge transition section is a Winkler foundation beam with one end simply supported, the other end free, and partially detached. The mechanical model of the road and bridge transition section follows the basic assumptions of Winkler.

[0022] According to Winkler's hypothesis, if the approach slab of the road-bridge transition section is located on a continuous elastic foundation and bends under the vertical load along the road-bridge transition section pavement, when the deflection value is smaller than the thickness of the approach slab, any point in the vertical direction of the approach slab will... Interaction forces It is directly proportional to the deflection value of the approach slab;

[0023] Based on the deformation of the approach slab reflecting road surface unevenness, any point in the vertical direction of the approach slab in the road-bridge transition section... deflection value The relationship between the interaction forces is as follows:

[0024] (1)

[0025] in, Indicates the subgrade coefficient. This indicates the difference in settlement between the bridge abutment and the roadbed;

[0026] The dimensions of the void in the bridge transition section slab are simplified by representing the void shape as a cube. The depth, length, and width of the void surface are all denoted as... ;

[0027] Side length of the hollow surface The relationship between the deflection value and the deflection value is as follows:

[0028] ,

[0029] The following relation is further derived:

[0030] (2)

[0031] in, and This represents two different parameters determined by the given thickness of the bridge transition slab, the surface layer thickness and the corresponding elastic modulus, the base layer thickness and the corresponding elastic modulus, and the subgrade thickness and the corresponding elastic modulus:

[0032] The side length of the detached surface is obtained from equations (1) and (2). Between and interaction forces The relationship between these factors is then established, thereby establishing the connection between the detachment of the approach slab in the bridge-road transition section and the acceleration of vehicles passing through the bridge-road transition section.

[0033] S3.2 Constructing a vehicle-road coupled mechanical model:

[0034] The vehicle-road interaction includes forward and inverse problems. The forward problem is to calculate the vehicle acceleration, velocity, and displacement of a specified road profile using a vehicle-road coupling model. The inverse problem is to evaluate the clearance of the bridge-road transition section using the obtained vehicle acceleration. When a vehicle passes through the clearance area, the vehicle's suspension system will be impacted due to the uneven road surface, resulting in changes in acceleration. The vehicle is simplified to a 2-DOF system, and the bridge-road transition section is simplified to a Winkler elastic foundation beam model. A multibody dynamics model of the vehicle suspension system and the road surface is constructed.

[0035] The vehicle is idealized as a combination of multiple rigid bodies connected by a series of springs and dampers. In the vehicle-road coupled mechanics model, the vehicle-road interaction forces are solved based on the collected vehicle acceleration data and the vehicle motion equations. Then, based on the physical and mechanical model of the bridge transition section, the deflection value is calculated, and finally the size of the slab detachment is obtained.

[0036] The vehicle's motion equations are established as follows:

[0037] ,

[0038] ,

[0039] ,

[0040] in, This indicates the determination of the sprung mass of the vehicle. Indicates unsprung mass. Indicates the damping coefficient of the suspension system. Indicates the spring stiffness. Indicates the vertical stiffness of the tire. This represents the vertical acceleration of the mass on the spring. Indicates the vertical velocity of the sprung mass. This indicates the vertical displacement of the mass on the spring. Represents the vertical acceleration and vertical velocity of the unsprung mass. Vertical displacement of unsprung mass Pitch angle around the vehicle's center of gravity Pitch angular velocity Pitch acceleration and road surface pitch excitation , It represents half of the wheelbase. Represents the pitch moment of inertia. This indicates the input of road surface unevenness. This represents the interaction force between the vehicle and the road surface;

[0041] The vehicle is represented by a quarter-sized car model. The sprung and unsprung masses in the car model are connected by springs and viscous dampers. Solve the dynamic equations for the vertical displacement, vertical velocity, and pitch angular velocity of the sprung mass.

[0042] The vehicle and road surface are coupled at the tire contact point through interaction force vectors. The inverse problem is solved using the Newmark-β method, which generalizes the linear acceleration method. , , , and Solve this problem, assuming the solution is at time step [time step] arrive The internal acceleration changes linearly. The calculation formula is as follows:

[0043] ,

[0044] ,

[0045] in, Indicates time step Vertical displacement of the mass on the spring Indicates time step Vertical velocity of the mass on the spring, Indicates time step Vertical acceleration of the mass on the spring, Indicates time step Vertical displacement of the mass on the spring Indicates time step Vertical velocity of the mass on the spring, Indicates time step Vertical acceleration of the mass on the spring, Indicates the time step. This represents the weight that controls the change in acceleration; set... =1 / 4, The weights representing the control of speed changes are set. =1 / 2;

[0046] Time step pitch angular velocity around the vehicle's center of mass The calculation formula is as follows:

[0047] ,

[0048] in, Indicates time step pitch angular velocity, Indicates time step Pitch acceleration, Indicates time step Pitch acceleration, Indicates time step pitch angular velocity at that time;

[0049] Based on the vertical acceleration of the mass on the spring Vertical acceleration of the sprung mass Pitch angular velocity and sprung mass Damping coefficient of suspension system Spring stiffness Calculation of unsprung mass displacement using the Newmark-β method The calculation formula is as follows:

[0050] ,

[0051] in, Represents the Laplace variable. , For the real part, It is the imaginary part;

[0052] The displacement of the unsprung mass is determined using the Newmark-β method. Calculate time steps acceleration of unsprung mass and speed The calculation formula is as follows;

[0053] ,

[0054] ,

[0055] in, It represents the change over the square of time. Indicates time step Vertical displacement of the unsprung mass Indicates time step Vertical displacement of the unsprung mass Indicates time step Vertical displacement of the unsprung mass;

[0056] Calculate the time-varying interaction force between the vehicle and the road surface. The calculation formula is as follows:

[0057] (3)

[0058] S3.3 is obtained by combining formulas (1) and (3):

[0059] (4)

[0060] From formulas (2) and (4), we can further derive the relationship between the slipway release and acceleration:

[0061] .

[0062] 5. The method for deriving the location of the bridge transition section slab detachment based on vehicle acceleration according to claim 4, characterized in that S4 is specifically as follows:

[0063] The Bayesian update method is used to calculate the deflection value of the approach slab in the road-bridge transition section by combining the specific values ​​of vehicle type parameters obtained from drop tests and acceleration data collected by on-board acceleration sensors with the vehicle-road coupling model, thereby determining the side length of the approach slab detachment. Wherein, any point on the road-bridge transition section represents , Indicates the first section of the road-bridge transition. The set of locations on the road-bridge transition section is represented as: , This represents the total number of locations, and the corresponding deflection value is expressed as... , express The deflection value at the location;

[0064] (1) Construct the likelihood function based on the collected data:

[0065] Using a simple independent Gaussian error model, the first The vehicle's acceleration iteration data is as follows:

[0066] ,

[0067] Where, the likelihood function This represents the probability of all acceleration data. This represents the set of accelerations corresponding to each vehicle type and road surface deflection value. Indicates the first The acceleration of the vehicle, Indicates the first The car is acceleration at that point Indicates the deflection value. Indicates the first Vehicle sprung mass Indicates the first Vehicle unsprung mass Indicates the first The damping coefficient of the vehicle's suspension system. Indicates the first Vehicle spring stiffness Indicates the first Vertical stiffness of vehicle tires Indicates the sampling variance;

[0068] (2) Construct the prior distribution:

[0069] Assign a prior distribution to the sprung mass of each vehicle. , This represents the distribution of vehicle mass among all vehicles used in the road-bridge transition section, assuming each vehicle has the same mass. This represents the set of mean and variance of sprung masses. Prior values ​​are independent for each vehicle, thus yielding all masses. Prior values, The total number of vehicles is represented by the following formula:

[0070] ,

[0071] Similarly, the prior distributions of unsprung mass, suspension system damping coefficient, spring stiffness, and tire vertical stiffness are calculated for each vehicle using the following formulas:

[0072] ,

[0073] ,

[0074] ,

[0075] ,

[0076] in, This represents the set of mean and variance of unsprung mass. This represents the set of mean and variance of the damping coefficients of the suspension system. This represents the set of mean and variance of spring stiffness. This represents the set of mean and variance of the vertical stiffness of a tire.

[0077] The prior distribution of road surface deflection values ​​adopts an inherent Gaussian process, and the calculation formula is as follows:

[0078] ,

[0079] in, The smoothing parameters representing the road profile. Represents the prior distribution of road surface deflection values;

[0080] (3) Posterior distribution inference and sampling:

[0081] Inferring the posterior distribution from the likelihood function and the prior distribution:

[0082] ,

[0083] in, This represents the probability that the vehicle type and the deflection during the transition section are within a specific range given the known acceleration data. This represents the probability of all acceleration data. express The sprung mass of a vehicle, express The unsprung mass of a vehicle, express The spring stiffness of a car express The vertical stiffness of a vehicle's tires. express The damping coefficient of the vehicle's suspension system. Indicates vehicle acceleration. .

[0084] The hindrance distribution is calculated using the MCMC Markov chain Monte Carlo method, specifically employing Gibbs sampling. The procedure is as follows:

[0085] (1) Define the initial set of vehicle types and initial deflection value Set the number of iterations , , and They represent The vehicle's initial sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient;

[0086] (2) Calculate the initial expected acceleration set corresponding to vehicle type and deflection value using the vehicle motion equations of the vehicle-road coupled mechanical model. ;

[0087] (3) Using the current deflection set Replace the initial deflection value

[0088] (4) Each iteration is based on the acceptance probability and Update vehicle type and bridge transition deflection value;

[0089] (4-1) Update vehicle type parameters:

[0090] In the In this iteration, for each vehicle type, new parameters are sampled from a normal distribution to generate candidate parameters. The generated candidate parameters are represented as follows:

[0091] ,

[0092] ,

[0093] ,

[0094] ,

[0095] ,

[0096] in, , , , and Indicates the first Candidate parameters for a vehicle , , , and These represent the variances of sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient, respectively. , , , and Each represents the first The sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient of the next iteration;

[0097] The acceleration set corresponding to each vehicle type and road surface deflection value is calculated using the vehicle motion equations of the vehicle-road coupling model at the road-bridge transition section. , ...,

[0098] , ..., ;

[0099] Calculate the probability of acceptance :

[0100] ,

[0101] in, Indicates the first The deflection value of the next iteration. This indicates taking the minimum value;

[0102] Generate a random number that is uniformly distributed between 0 and 1. ,like If, then accept candidate parameters, if If so, then candidate parameters are not accepted;

[0103] When accepting, , , , , ;

[0104] If not accepted, , , , , ;

[0105] The updated vehicle type parameter is represented as follows:

[0106] (4-2) Update the deflection value of the road-bridge transition section:

[0107] In the In this iteration, for the deflection value of the bridge transition section, candidate deflection values ​​are sampled from a normal distribution, and the generated candidate deflection values ​​are represented as follows:

[0108] ,

[0109] in, Indicates the candidate deflection value. Indicates the first The deflection value of the next iteration. This represents the variance of the deflection values;

[0110] Construct a new deflection set , Using a new deflection set Replace the current deflection set The acceleration set corresponding to each vehicle type and road surface deflection value is calculated using the vehicle motion equations of the vehicle-road coupling model at the road-bridge transition section. ;

[0111] Calculate the probability of acceptance :

[0112] ,

[0113] Generate a random number that is uniformly distributed between 0 and 1. ,like Then accept the new deflection set. ,like Then, a new deflection set will not be accepted. ;

[0114] When accepting, ;

[0115] If not accepted, ;

[0116] (4-3) The dataset for updating vehicle type and road-bridge transition deflection values ​​is represented as follows: , Indicates the first The data set updated in each iteration;

[0117] Repeat steps (1) to (4) above until... .

[0118] The effects described in the invention are merely those of the embodiments, and not all the effects of the invention. The above technical solutions have the following advantages or beneficial effects:

[0119] This invention collects vehicle vibration signals in real time using an onboard accelerometer. Combined with adaptive Kalman filtering and wavelet denoising techniques, it effectively eliminates high-frequency noise and outlier interference, improving detection efficiency. Furthermore, data acquisition does not require road closures, saving time and reducing maintenance costs. The invention constructs a physical-mechanical model of the bridge transition section and a vehicle-road coupling mechanical model, linking interaction forces, deflection values, vehicle acceleration, and deflection dimensions. Closed-loop mechanical verification ensures logical rigor. Employing a Bayesian-MCMC framework, it constructs a Gaussian error model using likelihood functions to quantify measurement uncertainty. By constructing a prior distribution to determine the smoothing constraints of the Gaussian process, and by iteratively updating vehicle parameters and deflection values ​​through Gibbs sampling in posterior inference, it effectively integrates data from multiple vehicle trips, suppressing the interference of single vehicle parameter errors on the results. Finally, through adaptive damage quantification and confidence assessment, it dynamically updates vehicle parameters and deflection values, enabling real-time prediction and reliability assessment of deflection conditions, providing a probabilistic basis for road and bridge maintenance decisions. Attached Figure Description

[0120] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0121] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0122] Figure 2 This is a schematic diagram comparing the predicted value and the actual value of the method of the present invention. Detailed Implementation

[0123] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0124] Example 1

[0125] like Figure 1 As shown, a method for deducing the location of the detachment of the approach slab in a road-bridge transition section based on vehicle acceleration is characterized by the following steps:

[0126] S1. Vibration signals of vehicles passing through the transition section of road bridges are collected using on-board acceleration sensors;

[0127] S2. The collected data is denoised, reduced in noise and normalized, and then the real acceleration collected by the sensor is extracted by wavelet transform and fast Fourier transform.

[0128] S3. Construct a physical and mechanical model of the road-bridge transition section and a vehicle-road coupling mechanical model. Use the vehicle-road coupling mechanical model to find the relationship between the acceleration of the vehicle passing through the road-bridge transition section and the vehicle-road interaction force. Use the physical and mechanical model of the road-bridge transition section to establish the relationship between the detachment status of the road-bridge transition section slab and the acceleration of the vehicle passing through the road-bridge transition section, and then find the detachment status of the road-bridge transition section slab.

[0129] S4. A Bayesian probability model is used to calibrate the detachment status of the bridge transition section slab. Vehicle acceleration data and vehicle type parameters are collected to construct a likelihood function and prior distribution. The posterior distribution is inferred based on the likelihood function and prior distribution. The posterior distribution is calculated using the MCMC Markov chain Monte Carlo method.

[0130] S5. Using the posterior distribution, the damage of the detachment is estimated, the vehicle type parameters corresponding to the acceleration and the deflection value of the road-bridge transition section are obtained, the maximum posterior estimate and confidence interval of the detachment location are calculated, and the vehicle type parameters and the deflection value of the road-bridge transition section are continuously updated to update and predict the detachment situation of the road-bridge transition section slab in real time.

[0131] In a specific implementation, S1 is as follows:

[0132] Accelerometers were installed on different types of vehicles, and a sampling frequency of 100Hz was set. The accelerometers were installed near the vehicle's center of gravity, with the X-axis of the accelerometers aligned with the vehicle's forward direction. The vehicles carrying the accelerometers were made to pass through the transition section of the road bridge containing the clearance area at a constant speed. Vibration signals before and after the transition section were extracted. The vibration signals included vertical, lateral, and longitudinal acceleration data. The vibration signals were extracted 10 meters before and after the transition section.

[0133] In a specific implementation, S2 is as follows:

[0134] S2.1 Data Preprocessing:

[0135] The collected data is preprocessed by using an adaptive Kalman slew rate to eliminate high-frequency noise and outliers, and wavelet denoising and normalization are performed on the collected acceleration data.

[0136] S2.2 Feature Extraction:

[0137] The impact signal in the preprocessed data is extracted by wavelet transform, which can easily excite high-frequency vibrations of 10-50 Hz. Then, the dominant frequency component is extracted by fast Fourier transform, and the local frequency component of the non-stationary signal is extracted by wavelet transform to separate the true acceleration collected by the sensor.

[0138] In a specific implementation, S3 is as follows:

[0139] S3.1 Constructing the physical and mechanical model of the road-bridge transition section:

[0140] The abutments of the road and bridge are fixed, the roadbed is supported by an elastic foundation, and the physical and mechanical model of the road and bridge transition section is a Winkler foundation beam with one end simply supported, the other end free, and partially detached. The mechanical model of the road and bridge transition section follows the basic assumptions of Winkler.

[0141] According to Winkler's hypothesis, if the approach slab of the road-bridge transition section is located on a continuous elastic foundation and bends under the vertical load along the road-bridge transition section pavement, when the deflection value is smaller than the thickness of the approach slab, any point in the vertical direction of the approach slab will... Interaction forces It is directly proportional to the deflection value of the approach slab;

[0142] Based on the deformation of the approach slab reflecting road surface unevenness, any point in the vertical direction of the approach slab in the road-bridge transition section... deflection value The relationship between the interaction forces is as follows:

[0143] (1)

[0144] in, Indicates the subgrade coefficient. This indicates the difference in settlement between the bridge abutment and the roadbed;

[0145] The dimensions of the void in the bridge transition section slab are simplified by representing the void shape as a cube. The depth, length, and width of the void surface are all denoted as... ;

[0146] Side length of the hollow surface The relationship between the deflection value and the deflection value is as follows:

[0147] ,

[0148] The following relation is further derived:

[0149] (2)

[0150] in, and This represents two different parameters determined by the given thickness of the bridge transition slab, the surface layer thickness and the corresponding elastic modulus, the base layer thickness and the corresponding elastic modulus, and the subgrade thickness and the corresponding elastic modulus:

[0151] When the thickness of the approach slab in the road-bridge transition section is 0.3m, the surface layer thickness is 0.25m, corresponding to an elastic modulus of 30000MPa; the base layer thickness is 0.5m, corresponding to an elastic modulus of 2500MPa; and the subgrade thickness is 8m, corresponding to an elastic modulus of 50MPa. Then, curve fitting is performed on the above parameters using finite element Abaqus numerical simulation to obtain... , ;

[0152] The side length of the detached surface is obtained from equations (1) and (2). Between and interaction forces The relationship between these factors is then established, thereby establishing the connection between the detachment of the approach slab in the bridge-road transition section and the acceleration of vehicles passing through the bridge-road transition section.

[0153] S3.2 Constructing a vehicle-road coupled mechanical model:

[0154] The vehicle-road interaction includes forward and inverse problems. The forward problem is to calculate the vehicle acceleration, velocity, and displacement of a specified road profile using a vehicle-road coupling model. The inverse problem is to evaluate the clearance of the bridge-road transition section using the obtained vehicle acceleration. When a vehicle passes through the clearance area, the vehicle's suspension system will be impacted due to the uneven road surface, resulting in changes in acceleration. The vehicle is simplified to a 2-DOF system, and the bridge-road transition section is simplified to a Winkler elastic foundation beam model. A multibody dynamics model of the vehicle suspension system and the road surface is constructed.

[0155] The vehicle is idealized as a combination of multiple rigid bodies connected by a series of springs and dampers. In the vehicle-road coupled mechanics model, the vehicle-road interaction forces are solved based on the collected vehicle acceleration data and the vehicle motion equations. Then, based on the physical and mechanical model of the bridge transition section, the deflection value is calculated, and finally the size of the slab detachment is obtained.

[0156] The vehicle's motion equations are established as follows:

[0157] ,

[0158] ,

[0159] ,

[0160] in, This indicates the determination of the sprung mass of the vehicle. Indicates unsprung mass. Indicates the damping coefficient of the suspension system. Indicates the spring stiffness. Indicates the vertical stiffness of the tire. This represents the vertical acceleration of the mass on the spring. Indicates the vertical velocity of the sprung mass. This indicates the vertical displacement of the mass on the spring. Represents the vertical acceleration and vertical velocity of the unsprung mass. Vertical displacement of unsprung mass Pitch angle around the vehicle's center of gravity Pitch angular velocity Pitch acceleration and road surface pitch excitation , It represents half the wheelbase, which is the distance from the center of gravity to the front and rear wheels. Represents the pitch moment of inertia. This indicates the input of road surface unevenness. This represents the interaction force between the vehicle and the road surface;

[0161] The vehicle is represented by a quarter-sized car model. The sprung and unsprung masses in the car model are connected by springs and viscous dampers. Solve the dynamic equations for the vertical displacement, vertical velocity, and pitch angular velocity of the sprung mass.

[0162] The vehicle and road surface are coupled at the tire contact point through interaction force vectors. The inverse problem is solved using the Newmark-β method, which generalizes the linear acceleration method. , , , and Solve this problem, assuming the solution is at time step [time step] arrive The internal acceleration changes linearly. The calculation formula is as follows:

[0163] ,

[0164] ,

[0165] in, Indicates time step Vertical displacement of the mass on the spring Indicates time step Vertical velocity of the mass on the spring, Indicates time step Vertical acceleration of the mass on the spring, Indicates time step Vertical displacement of the mass on the spring Indicates time step Vertical velocity of the mass on the spring, Indicates time step Vertical acceleration of the mass on the spring, Indicates the time step. This represents the weight that controls the change in acceleration; set... =1 / 4, The weights representing the control of speed changes are set. =1 / 2;

[0166] Time step pitch angular velocity around the vehicle's center of mass The calculation formula is as follows:

[0167] ,

[0168] in, Indicates time step pitch angular velocity, Indicates time step Pitch acceleration, Indicates time step Pitch acceleration, Indicates time step pitch angular velocity at that time;

[0169] Based on the vertical acceleration of the mass on the spring Vertical acceleration of the sprung mass Pitch angular velocity and sprung mass Damping coefficient of suspension system Spring stiffness Calculation of unsprung mass displacement using the Newmark-β method The calculation formula is as follows:

[0170] ,

[0171] in, Represents the Laplace variable. , For the real part, It is the imaginary part;

[0172] The displacement of the unsprung mass is determined using the Newmark-β method. Calculate time steps acceleration of unsprung mass and speed The calculation formula is as follows;

[0173] ,

[0174] ,

[0175] in, It represents the change over the square of time. Indicates time step Vertical displacement of the unsprung mass Indicates time step Vertical displacement of the unsprung mass Indicates time step Vertical displacement of the unsprung mass;

[0176] Calculate the time-varying interaction force between the vehicle and the road surface. The calculation formula is as follows:

[0177] (3)

[0178] S3.3 is obtained by combining formulas (1) and (3):

[0179] (4)

[0180] From formulas (2) and (4), we can further derive the relationship between the slipway release and acceleration:

[0181] .

[0182] In a specific implementation, S4 is as follows:

[0183] The Bayesian update method is used to calculate the deflection value of the approach slab in the road-bridge transition section by combining the specific values ​​of vehicle type parameters obtained from drop tests and acceleration data collected by on-board acceleration sensors with the vehicle-road coupling model, thereby determining the side length of the approach slab detachment. Wherein, any point on the road-bridge transition section represents , Indicates the first section of the road-bridge transition. The set of locations on the road-bridge transition section is represented as: , This represents the total number of locations, and the corresponding deflection value is expressed as... , express The deflection value at the location;

[0184] (1) Construct the likelihood function based on the collected data:

[0185] Using a simple independent Gaussian error model, the first The vehicle's acceleration iteration data is as follows:

[0186] ,

[0187] Where, the likelihood function This represents the probability of all acceleration data. This represents the set of accelerations corresponding to each vehicle type and road surface deflection value. Indicates the first The acceleration of the vehicle, Indicates the first The car is acceleration at that point Indicates the deflection value. Indicates the first Vehicle sprung mass Indicates the first Vehicle unsprung mass Indicates the first The damping coefficient of the vehicle's suspension system. Indicates the first Vehicle spring stiffness Indicates the first Vertical stiffness of vehicle tires Indicates the sampling variance;

[0188] (2) Construct the prior distribution:

[0189] Assign a prior distribution to the sprung mass of each vehicle. , This represents the distribution of vehicle mass among all vehicles used in the road-bridge transition section, assuming each vehicle has the same mass. This represents the set of mean and variance of sprung masses. Prior values ​​are independent for each vehicle, thus yielding all masses. Prior values, The total number of vehicles is represented by the following formula:

[0190] ,

[0191] Similarly, the prior distributions of unsprung mass, suspension system damping coefficient, spring stiffness, and tire vertical stiffness are calculated for each vehicle using the following formulas:

[0192] ,

[0193] ,

[0194] ,

[0195] ,

[0196] in, This represents the set of mean and variance of unsprung mass. This represents the set of mean and variance of the damping coefficients of the suspension system. This represents the set of mean and variance of spring stiffness. This represents the set of mean and variance of the vertical stiffness of a tire.

[0197] The prior distribution of road surface deflection values ​​adopts an inherent Gaussian process, and the calculation formula is as follows:

[0198] ,

[0199] in, The smoothing parameters representing the road profile. Represents the prior distribution of road surface deflection values;

[0200] (3) Posterior distribution inference and sampling:

[0201] Inferring the posterior distribution from the likelihood function and the prior distribution:

[0202] ,

[0203] in, This represents the probability that the vehicle type and the deflection during the transition section are within a specific range given the known acceleration data. This represents the probability of all acceleration data. express The sprung mass of a vehicle, express The unsprung mass of a vehicle, express The spring stiffness of a car express The vertical stiffness of a vehicle's tires. express The damping coefficient of the vehicle's suspension system. Indicates vehicle acceleration. .

[0204] In a specific implementation, the hindrance distribution is calculated using the MCMC Markov chain Monte Carlo method, specifically selecting Gibbs sampling. The operation process is as follows:

[0205] (1) Define the initial set of vehicle types and initial deflection value Set the number of iterations , , and They represent The vehicle's initial sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient;

[0206] (2) Calculate the initial expected acceleration set corresponding to vehicle type and deflection value using the vehicle motion equations of the vehicle-road coupled mechanical model. ;

[0207] (3) Using the current deflection set Replace the initial deflection value

[0208] (4) Each iteration is based on the acceptance probability and Update vehicle type and bridge transition deflection value;

[0209] (4-1) Update vehicle type parameters:

[0210] In the In this iteration, for each vehicle type, new parameters are sampled from a normal distribution to generate candidate parameters. The generated candidate parameters are represented as follows:

[0211] ,

[0212] ,

[0213] ,

[0214] ,

[0215] ,

[0216] in, , , , and Indicates the first Candidate parameters for a vehicle , , , and These represent the variances of sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient, respectively. , , , and Each represents the first The sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient of the next iteration;

[0217] The acceleration set corresponding to each vehicle type and road surface deflection value is calculated using the vehicle motion equations of the vehicle-road coupling model at the road-bridge transition section. , ...,

[0218] , ..., ;

[0219] Calculate the probability of acceptance :

[0220] ,

[0221] in, Indicates the first The deflection value of the next iteration. This indicates taking the minimum value;

[0222] Generate a random number that is uniformly distributed between 0 and 1. ,like If, then accept candidate parameters, if If so, then candidate parameters are not accepted;

[0223] When accepting, , , , , ;

[0224] If not accepted, , , , , ;

[0225] The updated vehicle type parameter is represented as follows:

[0226] (4-2) Update the deflection value of the road-bridge transition section:

[0227] In the In this iteration, for the deflection value of the bridge transition section, candidate deflection values ​​are sampled from a normal distribution, and the generated candidate deflection values ​​are represented as follows:

[0228] ,

[0229] in, Indicates the candidate deflection value. Indicates the first The deflection value of the next iteration. This represents the variance of the deflection values;

[0230] Construct a new deflection set , Using a new deflection set Replace the current deflection set The acceleration set corresponding to each vehicle type and road surface deflection value is calculated using the vehicle motion equations of the vehicle-road coupling model at the road-bridge transition section. ;

[0231] Calculate the probability of acceptance :

[0232] ,

[0233] Generate a random number that is uniformly distributed between 0 and 1. ,like Then accept the new deflection set. ,like Then, a new deflection set will not be accepted. ;

[0234] When accepting, ;

[0235] If not accepted, ;

[0236] (4-3) The dataset for updating vehicle type and road-bridge transition deflection values ​​is represented as follows: , Indicates the first The data set updated in each iteration;

[0237] Repeat steps (1) to (4) above until... .

[0238] Example 2

[0239] To demonstrate the beneficial effects of this invention, the voiding depth result obtained by the method of this invention is verified. The voiding depth is the side length of the voided surface calculated in the method of this invention, such as... Figure 2 As shown, the Bayesian predicted value in this invention is compared with the actual value. The vehicle in the experiment passed through the road-bridge transition test section at 60 km / h. Acceleration data from the accelerometer was extracted during the vehicle's passage. The MCMC method was run 5000 times, and 95% of the MCMC sample values ​​were used as the calculation results. The posterior mean of the detachment location was obtained as K10+230 (station number), and the posterior mean of the detachment depth was obtained as d=33.2 mm (95% confidence interval: 32.1-34.6 mm). Given that the actual detachment depth is 34 mm, the calculated deflection value is very close to the actual value. Laboratory verification showed an error of only 2%, a settlement error ≤3 mm, and a detachment depth inversion error ≤5 mm. Using this invention's method to detect the detachment location of the road-bridge transition section slab can reduce detection costs by more than 80% and expand coverage to the entire road section. The method of this invention, compared with the results of ground-penetrating radar detection, shows an error of less than 5%.

[0240] Example 3

[0241] During multi-vehicle detection, the known actual clearance depth was 34 mm, and the vehicle speed was 60 km / h. The posterior mean after the first 5 vehicles passed was d = 32.7 mm (confidence interval width 8 mm). The posterior mean after the 6th-10th vehicles passed was updated to d = 33.4 mm (confidence interval width narrowed to 4 mm). When the data of the 15th vehicle was added, the confidence interval width was ≤ 3 mm, reaching the maintenance decision threshold, proving that the method described in the invention can achieve dynamic updating of the clearance status of the road-bridge transition section when multiple vehicles pass.

[0242] Although the specific embodiments of the invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the invention. Based on the technical solutions of the invention, various modifications or variations that can be made by those skilled in the art without creative effort are still within the scope of protection of the invention.

Claims

1. A method for deriving the location of the detachment of the approach slab in a road-bridge transition section based on vehicle acceleration, characterized in that, Includes the following steps: S1. Vibration signals of vehicles passing through the transition section of road bridges are collected using on-board acceleration sensors; S2. The collected data is denoised, reduced in noise and normalized, and then the real acceleration collected by the sensor is extracted by wavelet transform and fast Fourier transform. S3. Construct a physical and mechanical model of the road-bridge transition section and a vehicle-road coupling mechanical model. Use the vehicle-road coupling mechanical model to find the relationship between the acceleration of the vehicle passing through the road-bridge transition section and the vehicle-road interaction force. Use the physical and mechanical model of the road-bridge transition section to establish the relationship between the detachment status of the road-bridge transition section slab and the acceleration of the vehicle passing through the road-bridge transition section, and then find the detachment status of the road-bridge transition section slab. S3.1 Constructing the physical and mechanical model of the road-bridge transition section: The abutments of the road and bridge are fixed, the roadbed is supported by an elastic foundation, and the physical and mechanical model of the road and bridge transition section is a Winkler foundation beam with one end simply supported, the other end free, and partially detached. The mechanical model of the road and bridge transition section follows the basic assumptions of Winkler. According to Winkler's hypothesis, if the approach slab of the road-bridge transition section is located on a continuous elastic foundation and bends under the vertical load along the road-bridge transition section pavement, when the deflection value is smaller than the thickness of the approach slab, any point in the vertical direction of the approach slab will... Interaction forces It is directly proportional to the deflection value of the approach slab; Based on the deformation of the approach slab reflecting road surface unevenness, any point in the vertical direction of the approach slab in the road-bridge transition section... deflection value The relationship between the interaction forces is as follows: ，（1） in, Indicates the subgrade coefficient. This indicates the difference in settlement between the bridge abutment and the roadbed; The dimensions of the void in the bridge transition section slab are simplified by representing the void shape as a cube. The depth, length, and width of the void surface are all denoted as... ; Side length of the hollow surface The relationship between the deflection value and the deflection value is as follows: ， The following relation is further derived: ，（2） in, and This represents two different parameters determined by the given thickness of the bridge transition slab, the surface layer thickness and the corresponding elastic modulus, the base layer thickness and the corresponding elastic modulus, and the subgrade thickness and the corresponding elastic modulus: The side length of the detached surface is obtained from equations (1) and (2). and interaction forces The relationship between these factors is then established, thereby establishing the connection between the detachment of the approach slab in the bridge transition section and the acceleration of vehicles passing through the bridge transition section. S3.2 Constructing a vehicle-road coupled mechanical model: The vehicle-road interaction includes forward and inverse problems. The forward problem is to calculate the vehicle acceleration, velocity, and displacement of a specified road profile using a vehicle-road coupling model. The inverse problem is to evaluate the clearance of the bridge-road transition section using the obtained vehicle acceleration. When a vehicle passes through the clearance area, the vehicle's suspension system will be impacted due to the uneven road surface, resulting in changes in acceleration. The vehicle is simplified to a 2-DOF system, and the bridge-road transition section is simplified to a Winkler elastic foundation beam model. A multibody dynamics model of the vehicle suspension system and the road surface is constructed. The vehicle is idealized as a combination of multiple rigid bodies connected by a series of springs and dampers. In the vehicle-road coupled mechanics model, the vehicle-road interaction forces are solved based on the collected vehicle acceleration data and the vehicle motion equations. Then, based on the physical and mechanical model of the bridge transition section, the deflection value is calculated, and finally the size of the slab detachment is obtained. Calculate the time-varying interaction force between the vehicle and the road surface. The calculation formula is as follows: ，（3） in, This indicates the determination of the sprung mass of the vehicle. Indicates the damping coefficient of the suspension system. Indicates the spring stiffness. Indicates the vertical stiffness of the tire. This represents the vertical acceleration of the unsprung mass. Indicates the vertical velocity of the unsprung mass. Indicates the vertical velocity of the sprung mass. This indicates the vertical displacement of the unsprung mass. This indicates the vertical displacement of the mass on the spring. This indicates the input of road surface unevenness. This represents the interaction force between the vehicle and the road surface; S3.3 is obtained by combining formulas (1) and (3): ，（4） From formulas (2) and (4), we can further derive the relationship between the slip slab detachment and acceleration: ； S4. A Bayesian probability model is used to calibrate the detachment status of the bridge transition section slab. Vehicle acceleration data and vehicle type parameters are collected to construct a likelihood function and prior distribution. The posterior distribution is inferred based on the likelihood function and prior distribution. The posterior distribution is calculated using the MCMC Markov chain Monte Carlo method. S5. Using the posterior distribution, the damage of the detachment is estimated, the vehicle type parameters corresponding to the acceleration and the deflection value of the road-bridge transition section are obtained, the maximum posterior estimate and confidence interval of the detachment location are calculated, and the vehicle type parameters and the deflection value of the road-bridge transition section are continuously updated to update and predict the detachment situation of the road-bridge transition section slab in real time.

2. The method for deriving the location of the bridge transition section slab detachment based on vehicle acceleration according to claim 1, characterized in that, S1 is as follows: Accelerometers are installed on different types of vehicles, and sampling frequencies are set. The accelerometers are installed near the vehicle's center of gravity, with the X-axis of the accelerometer aligned with the vehicle's forward direction. The vehicle carrying the accelerometer passes through the transition section of the road bridge containing the clearance area at a constant speed. Vibration signals before and after the transition section are extracted. The vibration signals include vertical, lateral, and longitudinal acceleration data.

3. The method for deriving the location of the bridge transition section slab detachment based on vehicle acceleration according to claim 2, characterized in that, S2 is as follows: S2.1 Data Preprocessing: The collected data is preprocessed by using an adaptive Kalman slew rate to eliminate high-frequency noise and outliers, and wavelet denoising and normalization are performed on the collected acceleration data. S2.2 Feature Extraction: The impulse signal in the preprocessed data is extracted by wavelet transform, the dominant frequency component is extracted by fast Fourier transform, and the local frequency component of the non-stationary signal is extracted by wavelet transform to separate the true acceleration collected by the sensor.

4. The method for deriving the location of the bridge transition section slab detachment based on vehicle acceleration according to claim 3, characterized in that, S3.2 Constructing a vehicle-road coupled mechanical model: The vehicle's motion equations are established as follows: ， ， ， in, This indicates the determination of the sprung mass of the vehicle. Indicates unsprung mass. Indicates the damping coefficient of the suspension system. Indicates the spring stiffness. Indicates the vertical stiffness of the tire. This represents the vertical acceleration of the mass on the spring. Indicates the vertical velocity of the sprung mass. This indicates the vertical displacement of the mass on the spring. Represents the vertical acceleration and vertical velocity of the unsprung mass. Vertical displacement of unsprung mass Pitch angle around the vehicle's center of gravity Pitch angular velocity Pitch acceleration and road surface pitch excitation , It represents half of the wheelbase. Represents the pitch moment of inertia. This indicates the input of road surface unevenness. This represents the interaction force between the vehicle and the road surface; The vehicle is represented by a quarter-sized car model. The sprung and unsprung masses in the car model are connected by springs and viscous dampers. Solve the dynamic equations for the vertical displacement, vertical velocity, and pitch angular velocity of the sprung mass. The vehicle and road surface are coupled at the tire contact point through interaction force vectors. The inverse problem is solved using the Newmark-β method, which generalizes the linear acceleration method. , , , and Solve this problem, assuming the solution is at time step [time step] arrive The internal acceleration changes linearly. The calculation formula is as follows: ， ， in, Indicates time step Vertical displacement of the mass on the spring. Indicates time step Vertical velocity of the mass on the spring, Indicates time step Vertical acceleration of the mass on the spring, Indicates time step Vertical displacement of the mass on the spring. Indicates time step Vertical velocity of the mass on the spring, Indicates time step Vertical acceleration of the mass on the spring, Indicates the time step. This represents the weight that controls the change in acceleration; set... =1 / 4, The weights representing the control of speed changes are set. =1 / 2; Time step pitch angular velocity around the vehicle's center of mass The calculation formula is as follows: ， in, Indicates time step pitch angular velocity, Indicates time step Pitch acceleration, Indicates time step Pitch acceleration, Indicates time step pitch angular velocity at that time; Based on the vertical acceleration of the mass on the spring Vertical acceleration of the sprung mass Pitch angular velocity and sprung mass Damping coefficient of suspension system Spring stiffness Calculation of unsprung mass displacement using the Newmark-β method The calculation formula is as follows: ， in, Represents the Laplace variable. , For the real part, It is the imaginary part; The displacement of the unsprung mass is determined using the Newmark-β method. Calculate time steps acceleration of unsprung mass and speed The calculation formula is as follows: ， ， in, It represents the change over the square of time. Indicates time step Vertical displacement of the unsprung mass Indicates time step Vertical displacement of the unsprung mass Indicates time step Vertical displacement of the unsprung mass.

5. The method for deriving the location of the bridge transition section slab detachment based on vehicle acceleration according to claim 4, characterized in that, S4 is as follows: The Bayesian update method is used to calculate the deflection value of the approach slab in the road-bridge transition section by combining the specific values ​​of vehicle type parameters obtained from drop tests and acceleration data collected by on-board acceleration sensors with the vehicle-road coupling model, thereby determining the side length of the approach slab detachment. Wherein, any point on the road-bridge transition section represents , Indicates the first section of the road-bridge transition. The set of locations on the road-bridge transition section is represented as: , This represents the total number of locations, and the corresponding deflection value is expressed as... , express The deflection value at the location; (1) Construct the likelihood function based on the collected data: Using a simple independent Gaussian error model, the first The vehicle's acceleration iteration data is as follows: ， Where, the likelihood function Represents the probability of all acceleration data. This represents the set of accelerations corresponding to each vehicle type and road surface deflection value. Indicates the first The acceleration of the vehicle, Indicates the first The car is acceleration at that point Indicates the deflection value. Indicates the first Vehicle sprung mass Indicates the first Vehicle unsprung mass Indicates the first The damping coefficient of the vehicle's suspension system. Indicates the first Vehicle spring stiffness Indicates the first Vertical stiffness of vehicle tires Indicates the sampling variance; (2) Construct the prior distribution: Assign a prior distribution to the sprung mass of each vehicle. , This represents the distribution of vehicle mass among all vehicles used in the road-bridge transition section, assuming that each vehicle has the same mass. Let represent the set of mean and variance of sprung masses. Prior values ​​are independent for each vehicle, thus yielding all masses. Prior values, The total number of vehicles is represented by the following formula: ， Similarly, the prior distributions of unsprung mass, suspension system damping coefficient, spring stiffness, and tire vertical stiffness are calculated for each vehicle using the following formulas: ， ， ， ， in, This represents the set of mean and variance of unsprung mass. This represents the set of mean and variance of the damping coefficients of the suspension system. This represents the set of mean and variance of spring stiffness. This represents the set of mean and variance of the vertical stiffness of a tire. The prior distribution of road surface deflection values ​​adopts an inherent Gaussian process, and the calculation formula is as follows: ， in, The smoothing parameters representing the road profile. Represents the prior distribution of road surface deflection values; (3) Posterior distribution inference and sampling: Inferring the posterior distribution from the likelihood function and the prior distribution: ， in, This represents the probability that the vehicle type and the deflection during the transition section are within a specific range given the known acceleration data. Represents the probability of all acceleration data. express The sprung mass of a vehicle, express The unsprung mass of a vehicle, express The spring stiffness of a car express The vertical stiffness of a vehicle's tires. express The damping coefficient of the vehicle's suspension system. Indicates vehicle acceleration. .

6. The method for deriving the location of the bridge transition section slab detachment based on vehicle acceleration according to claim 5, characterized in that, The hindrance distribution is calculated using the MCMC Markov chain Monte Carlo method, specifically employing Gibbs sampling. The procedure is as follows: (1) Define the initial set of vehicle types and initial deflection value Set the number of iterations , and They represent The vehicle's initial sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient; (2) Calculate the initial expected acceleration set corresponding to vehicle type and deflection value using the vehicle motion equations of the vehicle-road coupled mechanical model. ; (3) Using the current deflection set Replace the initial deflection value (4) Each iteration is based on the acceptance probability and Update vehicle type and bridge transition deflection value; (4-1) Update vehicle type parameters: In the In this iteration, for each vehicle type, new parameters are sampled from a normal distribution to generate candidate parameters. The generated candidate parameters are represented as follows: ， ， ， ， ， in, , , , and Indicates the first Candidate parameters for a vehicle , , , and These represent the variances of sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient, respectively. , , , and Each represents the first The sprung mass, unsprung mass, spring stiffness, tire vertical stiffness, and suspension system damping coefficient of the next iteration; The acceleration sets corresponding to each vehicle type and road surface deflection value are calculated using the vehicle motion equations of the vehicle-road coupling model at the road-bridge transition section. , ..., ，…， ； Calculate the probability of acceptance : ， in, Indicates the first The deflection value of the next iteration. This indicates taking the minimum value; Generate a random number that is uniformly distributed between 0 and 1. ,like If, then accept candidate parameters, if If so, then candidate parameters are not accepted; When accepting, , , , , ; If not accepted, , , , , ; The updated vehicle type parameter is represented as follows: (4-2) Update the deflection value of the road-bridge transition section: In the In this iteration, for the deflection value of the bridge transition section, candidate deflection values ​​are sampled from a normal distribution, and the generated candidate deflection values ​​are represented as follows: ， in, Indicates the candidate deflection value. Indicates the first The deflection value of the next iteration. This represents the variance of the deflection values; Construct a new deflection set , Using a new deflection set Replace the current deflection set The acceleration set corresponding to each vehicle type and road surface deflection value is calculated using the vehicle motion equations of the vehicle-road coupling model at the road-bridge transition section. ; Calculate the probability of acceptance : ， Generate a random number that is uniformly distributed between 0 and 1. ,like Then accept the new deflection set. ,like Then, a new deflection set will not be accepted. ; When accepting, ; If not accepted, ; (4-3) The dataset for updating vehicle type and road-bridge transition deflection values ​​is represented as follows: , Indicates the first The data set updated in each iteration; Repeat steps (1) to (4) above until... .

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