Extreme value prediction method and application of vehicle load effect on long-span concrete beam bridges

Abstract

This invention provides a method and application for predicting the extreme values ​​of vehicle load effects on long-span concrete beam bridges. The method involves the following steps: Classifying vehicles by axle number, using the axle weight and lane spacing of different vehicle models as traffic load parameters, and obtaining the marginal distribution function F for each traffic load parameter; Taking into account the correlation of vehicle axle weights, combining the marginal distribution functions of all axle weights of the same vehicle model to obtain the joint distribution function H of axle weights; Based on the joint distribution function of axle weights and the marginal distribution function of lane spacing, a random traffic load sample set is sampled to consider the correlation of axle weights; and a mapping relationship model between traffic load parameters and bridge response extreme values ​​is established to obtain the bridge response extreme value and corresponding extreme value distribution for the current random traffic load sample. By establishing a mapping relationship between traffic load parameters and bridge response extreme values, the extreme value of the traffic load response to the bridge at any time can be quickly and accurately calculated.

Description

Technical Field

[0001] The present invention belongs to the field of health monitoring and safety assessment of civil engineering structures, and proposes a method and application for predicting the extreme value of vehicle load effects on long-span concrete beam bridges, which is used for assessing the vehicle load effects on long-span concrete beam bridges. Background Art

[0002] Bridge structures, particularly long-span concrete beam bridges, are a vital component of the road transportation system. Their operational safety is directly linked to the smooth functioning of the transportation network. Vehicle loads are the primary external load on bridges, easily causing damage to the bridge structure. With economic development, transportation has become increasingly convenient, and the increasing number of heavy vehicles, in particular, has led to a growing problem of overloading. Bridge damage caused by vehicle loads has become an increasingly significant issue. In recent years, incidents of partial damage or even collapse of bridges due to overweight vehicles have occurred frequently.

[0003] The current method is to use finite element software (such as Abaqus or Madis Civil) to build a bridge model, substitute vehicle load data, and use the software to calculate the response. This is a common method for calculating the structural response of bridges caused by external loads, but this method is time-consuming, especially for stochastic analysis. Therefore, it is crucial to quickly and accurately calculate the response of bridge structures to vehicle loads.

[0004] Zhao Hui et al. (Zhao Hui, Chen Shuisheng, Li Jinhua, et al. Prediction of extreme values ​​of vehicle-induced displacement of bridges under random vehicle loads [J]. Journal of Harbin Engineering University, 2023, 44(02): 219-225.) calculated the vehicle-induced displacement of bridges under random vehicle loads. When generating random traffic flow, the axle weight of each axle is proportionally distributed according to the total vehicle weight, without considering the correlation of axle weights. In general, it is assumed that different axle weights of the same vehicle are independent of each other, ignoring the influence of the connecting axle and the correlation of axle weights. Especially for multi-axle vehicles (such as six-axle vehicles), the mutual influence between axle weights is more obvious. Assuming that axle weights are independently distributed cannot better reflect the actual axle weight of the vehicle.

[0005] Zong Zhouhong et al. (Zong Zhouhong, Xue Cheng, Yang Zegang, et al. Automobile load model of Jiangsu Province highway bridges based on WIM [J]. Journal of Southeast University (Natural Science Edition), 2020, 50(01): 143-152.) established a automobile load model of Jiangsu Province highway bridges and calculated the load effect of the bridges. The calculation amount was huge, and it took 45 days to calculate using 4 computers.

[0006] In order to make the traffic flow model more consistent with actual vehicles and accurately and quickly calculate the response of vehicle loads to bridges, the method of the present invention first improves the accuracy of the random traffic flow model by considering the correlation of axle weights, uses load tests to calculate the influence lines of the bridge, instead of using finite element software modeling to extract them, and then establishes a mapping relationship model between traffic flow load parameters and bridge response extremes. By substituting the required calculated traffic flow loads into the model, the bridge response extremes can be directly obtained, without the need for complex calculations using finite element software, thereby improving calculation efficiency. Summary of the Invention

[0007] This paper aims to propose a method and application for predicting the extreme values ​​of vehicle load effects on long-span concrete beam bridges. This method considers the correlation between vehicle axle loads and constructs a mapping relationship between traffic load parameters and bridge response extremes. This allows for the rapid calculation of the extreme value response and probability distribution of bridge structures under random traffic flow. This allows for the evaluation of vehicle load effects on long-span concrete beam bridges.

[0008] The technical solution of the present invention is:

[0009] In a first aspect, the present invention provides a method for predicting the extreme value of vehicle load effects on a long-span concrete beam bridge, the process of the method being:

[0010] Step 1: Obtain vehicle data measured by the bridge dynamic weighing system, classify vehicles according to the number of axles, and use the axle weight and lane distance of different vehicle models as traffic load parameters. The number of traffic load parameters is the sum of the axle weights of all vehicle models + the number of lane distances. Use the non-parametric kernel density fitting estimation method to determine the probability density distribution of each traffic load parameter, and then obtain the marginal distribution function F of each traffic load parameter. Considering the correlation of vehicle axle weights, the marginal distribution functions of all axle weights of the same vehicle model are combined according to the following formula to obtain the joint distribution function of axle weight H;

[0011] H(x 1 ,…,x n )=Φ ρ (Φ -1 (x 1 ),…,Φ -1 (x n ))(F1(x 1 ),…F n (xn))

[0012] Where: n is the number of axle loads in a certain type of vehicle, Φ ρ is the distribution function of the multivariate standard normal distribution with the correlation coefficient matrix ρ; Φ -1 Represents the inverse function of the standard normal distribution; x 1 represents the first axle weight sample; x n represents the sample of the nth axle weight;

[0013] Based on the joint distribution function of axle load and the marginal distribution function of lane distance, a random traffic load sample set considering axle load correlation is established.

[0014] Step 2: Obtain a reasonable value range for axle load and lane distance, and use stratified sampling method to generate a traffic load sample set within this reasonable value range;

[0015] Step 3: Obtain the influence line of each span section of the bridge through load testing;

[0016] Step 4: Load the traffic load sample set from step 2 onto the influence line and calculate the traffic load response extreme value dataset for the bridge. Use these calculated response extreme value datasets and the corresponding traffic load sample set to establish a mapping relationship model between traffic load parameters and bridge response extreme values:

[0017]

[0018] Where S is the extreme value of the response; M is the number of polynomials; r m is the coefficient; γ m (X) is a polynomial function; X is the traffic load parameter, corresponding to the axle weight and lane distance of all types of axles; ε is a function with mean 0 and variance σ 2 Normal distribution;

[0019] For each coefficient r m Introduce the prior distribution, construct the likelihood function, calculate the posterior distribution, and define the coefficient of variation ξ as:

[0020]

[0021] Where x new is a new variable point, the axle weight and lane distance of all types of all axles are a traffic load sample, and each traffic load sample is a point; S * 、 are the new variable points x new The mean and variance of the predicted response at ; is the prior variance; μ N is the posterior mean; σ N 2 is the posterior variance;

[0022] Each time, the first l1 data with the smallest coefficient of variation are selected to update the mapping relationship model until the model converges to obtain a converged mapping relationship model;

[0023] In step 5, the random traffic load sample set obtained in step 1 considering axle weight is input into the convergence mapping relationship model in step 4, that is, the bridge response extreme value of the current random traffic load sample is obtained, and then the corresponding extreme value distribution is further fitted.

[0024] Furthermore, the method is used in the assessment of vehicle load effects on long-span concrete beam bridges: based on national or regional bridge design codes and standards and combined with statistical analysis of historical monitoring data, the maximum allowable response value – the threshold – is determined;

[0025] Combined with the extreme value distribution of the response obtained in step 5, the probability of exceeding the threshold is calculated. This probability is the failure probability. The vehicle load effect on the bridge is evaluated based on the failure probability. If the failure probability is greater than 5%, it is determined that the vehicle load causes the bridge structure to fail.

[0026] Furthermore, the traffic load sample set generated in step 2 is defined as A q , select the initial traffic load sample l and the corresponding bridge response extreme value to train the mapping relationship model of traffic load parameters-bridge response extreme value;

[0027]

[0028] Where, l is the number of initial traffic load samples; j is the number of random traffic load parameters;

[0029] Then the remaining traffic load sample A q -l, substitute into In the calculation of S * and Take l1 traffic load samples with the smallest coefficient of variation and add them to the initial traffic load sample l, which is l+l1. Substitute l+l1 into Update the traffic load parameter-bridge response extreme value relationship model; then calculate the remaining traffic load sample A q -l+l1 corresponding to S * and Then take l1 traffic load samples with the smallest coefficient of variation and add them to the initial traffic load sample l, and repeat the above process until the model converges.

[0030] Preferably, the condition for model convergence is: ξ is less than or equal to 2.

[0031] In a second aspect, the present invention provides a vehicle load effect assessment device for a long-span concrete beam bridge, the device comprising:

[0032] Vehicle Information Collection Unit: This unit, with a dynamic weighing system as its core and equipped with high-precision sensors and signal receivers, is responsible for collecting real-time information on axle weights and lane distances of vehicles crossing the bridge. It pre-processes the data using an integrated chip and digital signal processor to eliminate outliers and stores the processed data in a storage module connected to an external interface.

[0033] Random traffic flow generation unit: uses the vehicle parameter information transmitted by the vehicle information acquisition unit to generate a random traffic flow load sample set considering the axle weight;

[0034] Mapping relationship establishment unit: The influence lines of each mid-span section of the bridge are obtained through load testing. Considering the reasonable value range of axle load and lane spacing, a stratified sampling method is used to generate a traffic load sample set within this reasonable value range. The bridge response extreme value corresponding to the traffic load sample set is calculated. The mapping relationship between traffic load parameters and bridge response extreme values ​​is established in the form of a polynomial. The random traffic load sample data generated by the random traffic generation unit, which considers the axle weight, is substituted into the mapping relationship to calculate the bridge response extreme value and obtain the bridge response extreme value distribution.

[0035] Evaluation unit: Set the maximum allowable response value of the bridge as the threshold, find the probability of exceeding the threshold in the extreme value distribution of the bridge response obtained by the mapping relationship, and this probability is the failure probability. The vehicle load effect of the bridge is evaluated based on the failure probability;

[0036] Control unit: The control unit is responsible for adjusting the input frequency and time nodes of vehicle information, including hour, day, month, quarter and year.

[0037] Compared with the prior art, the present invention has the following beneficial effects: First, the axle weight correlation of vehicles is taken into account. The present invention no longer performs independent sampling of axle weights, but considers the sampling of the joint distribution of vehicle axle weights; second, fast extreme value calculation. By establishing a mapping relationship between traffic load parameters and bridge response extreme values, the extreme response of traffic loads to bridges at any time passing through the bridge can be quickly and accurately calculated. The traditional finite element analysis method takes about 20 days to calculate one million random traffic load samples, but after using this method, it only takes 50 minutes to obtain the response value. Third, the results are accurate. When observing the extreme value data corresponding to the 95% quantile of the extreme value distribution of bridge response, the error between the finite element calculation data and the traditional method is only 0.7%, showing the significant advantages of this method in accuracy and efficiency.

[0038] The device of the present invention combines advanced sensor technology, digital signal processing and high-performance computing to provide comprehensive and accurate rapid calculation capabilities of bridge response extremes. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1This is a flow chart of the method for predicting the extreme value of vehicle load effects on long-span concrete beam bridges;

[0040] Figure 2 It is the probability density fitting diagram of the axle weight of the first axle of the six-axle vehicle;

[0041] Figure 3 This is the probability density fitting diagram of the axle weight of the second axle of the six-axle vehicle;

[0042] Figure 4 This is the probability density fitting diagram of the axle weight of the third axle of a six-axle vehicle;

[0043] Figure 5 This is the probability density fitting diagram of the axle weight of the fourth axle of a six-axle vehicle;

[0044] Figure 6 This is the probability density fitting diagram of the axle weight of the fifth axle of a six-axle vehicle;

[0045] Figure 7 It is the probability density fitting diagram of the axle weight of the sixth axle of the six-axle vehicle;

[0046] Figures 2 to 7 The probability density curve is fitted according to the axle weight data in order to integrate the probability density and obtain the marginal distribution of each axle weight.

[0047] Figure 8 This is a sampling of the correlated axle loads for the fifth and sixth axles of a six-axle vehicle. After accounting for axle load correlation, the axle loads sampled and obtained within the vehicle load data are correlated. Using the fifth and sixth axle loads of a six-axle vehicle as an example, the figure shows that the axle loads are not dispersed but rather have a certain linear relationship.

[0048] Figures 9 and 10 This figure compares two methods for calculating the probability density of extreme bridge deflections and stresses. MCS is calculated using the finite element method. The figure shows that the distributions obtained by the two methods closely match, indicating that the new method's results are reliable.

[0049] Figure 11 It is a schematic diagram of the block unit structure of the device of the present invention.

[0050] Figure 12 It is a schematic diagram of the equipment connection of the hardware required for the device of the present invention. DETAILED DESCRIPTION

[0051] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0052] The bridge dynamic weighing system in the present invention is a device installed on the bridge entity to collect information about vehicles passing through the bridge, which is a well-known technology in the art.

[0053] The present invention uses non-parametric kernel density estimation method to estimate the probability density of vehicle axle weight and lane distance, instead of using normal distribution, gamma distribution, generalized extreme value distribution, etc. to fit the data, so that the fitting curve is very consistent with the actual data. Figures 2 to 7 .

[0054] Example 1

[0055] The method for predicting the extreme value of vehicle load effect on a long-span concrete beam bridge in this embodiment comprises the following specific steps:

[0056] Step 1: Establish a random traffic load sample set considering axle load

[0057] (1) Collect vehicle load information on the bridge over a one-year period, including vehicle type, axle weight, wheelbase, lane spacing, etc. In this embodiment, the axle weight of the vehicle and the distance between vehicles in each lane (i.e., lane spacing) are used to represent random traffic load samples.

[0058] Vehicles are classified by the number of axles: two-axle, three-axle, four-axle, five-axle, and six-axle vehicles, for a total of five categories. Outliers, such as abnormal axle weights and lane distances, are removed from the data. In this example, five-axle vehicles are not considered because they account for a small proportion.

[0059] (2) Fit the probability density function of the axle weight and lane distance of each type of vehicle (classified by the number of axles). Each type of vehicle has a probability density function for a single axle weight. Integrate each probability density function to obtain its corresponding cumulative probability function, which is the marginal distribution function of each traffic load parameter.

[0060] A probabilistic statistical analysis was performed on 18 traffic load parameters: axle weights for all vehicle types (the sum of the axle weights for different vehicle types, i.e., 2+3+4+6, for a total of 15 parameters) and lane distances (3 parameters for the three lanes in this example). The probability density distributions of axle weights and lane distances were obtained using a nonparametric kernel density fitting method. Lane distances are calculated by lane, i.e., the distance between vehicles traveling in each lane.

[0061]

[0062] Where, is x j The probability density function at , e is the number of corresponding models or the number of spacings on the corresponding lanes, h is the bandwidth, K(·) is the kernel function, and this embodiment uses the Gaussian kernel function, i.e. x j is the jth traffic load parameter variable, and its value is [1,18]; Represents the i-th sample of the j-th traffic load parameter (either axle weight value or lane distance value).

[0063] The marginal distribution function F(x j )for:

[0064]

[0065] The t in the integral function is an integral variable, which is used to represent the value of the integrand at different points during the integration process and is "accumulated" or "summed" after the integration is completed.

[0066] Considering the correlation of axle weights of various types of vehicles, the marginal distribution functions of the corresponding axle weights of the same type of vehicles are connected to form a joint distribution function of axle weights, which is expressed as

[0067] H(x 1 ,…,x n )=Φ ρ (Φ -1 (x 1 ),…,Φ -1 (x n ))(F1(x 1 ),…F n (x n ))

[0068] Where: H is the n-dimensional joint distribution function, n is the number of axle weights in a certain type of vehicle, F n is the marginal distribution function of the nth axle weight of a certain type of vehicle, Φ ρ is the distribution function of the multivariate standard normal distribution with the correlation coefficient matrix ρ; Φ -1 Represents the inverse function of the standard normal distribution; ρ is a linear correlation coefficient matrix with all diagonal elements equal to 1.

[0069] Based on the joint distribution function of axle weight and the marginal distribution function of lane distance, a random traffic load sample set considering axle weight is established by sampling. Each random traffic load sample contains the axle weight and the corresponding lane distance.

[0070] Step 2: Obtain a reasonable range of values ​​for axle weight and lane distance, and use stratified sampling method to generate a traffic load sample set within this reasonable range.

[0071] The stratified sampling method divides the reasonable value range of each variable (axle weight and lane spacing) into several equal intervals (layers), and stratified sampling is used to establish a traffic load sample set. If there are N samples in the traffic load sample set, the range of each variable is divided into N layers. For each variable, a sample point is randomly selected from the respective layer. This ensures that a sample point can be selected in each layer, avoiding the concentrated distribution of samples. The sample points of each variable in the traffic flow passing through the bridge are combined to form a sample matrix. Each row of this sample matrix represents a traffic load sample, and each column corresponds to a traffic load parameter.

[0072] Step 3: Directly test the working state of the bridge structure through load tests to obtain the deflection influence lines and stress influence lines of each mid-span section of the experimental test bridge;

[0073] Step 4: Load the traffic load sample set from Step 2 along the two influence lines. Calculate the bridge response each time the traffic load sample advances 0.1 meters, until the entire convoy (one traffic load sample) has completely crossed the bridge. The maximum value of all calculated response values ​​is taken as the extreme value of the bridge response for that traffic load sample. Calculate the extreme value response data for all bridges corresponding to the traffic load sample set, and obtain the extreme value response dataset for the bridges corresponding to the traffic load sample set.

[0074] A mapping relationship is established using traffic load parameters and response extreme values. Each influence line corresponds to a mapping relationship, and the system output is expressed as a polynomial combination of input variables:

[0075]

[0076] It can also be written as: F = rΓ + ε

[0077] Where S is the extreme value of the response; M is the number of polynomials; r m is the coefficient; γ m (X) is a polynomial function; X is the traffic load parameter; ε is a parameter with a mean of 0 and a variance of σ 2 Normal distribution; r is the weight vector to be determined, Γ is a Q×M matrix, Q rows represent Q traffic load samples, and each row has M basis functions.

[0078] By inputting the probability distribution of random variables, the probability distribution of the system output can be predicted through polynomial expansion, which can effectively evaluate the uncertainty and risk of the output. The direct calculation of the coefficient output is a point estimate of the regression coefficient, which does not directly reflect the uncertainty and may be affected by outliers, resulting in estimation bias. Therefore, in order to quantify the uncertainty of the model coefficient, the coefficient r is m Probability estimation. For each coefficient r m Introducing the prior distribution,

[0079]

[0080] Where μ0 is the prior mean. is the prior variance, r is the coefficient, N represents the normal distribution, and p(r) represents the prior probability.

[0081] Based on the observed data and model output, the likelihood function of S is:

[0082]

[0083] Combining the prior distribution and the likelihood function, calculate the posterior distribution p(r|S),X):

[0084]

[0085] The quantification of uncertainty is achieved through the posterior distribution.

[0086] Posterior mean:

[0087]

[0088] Posterior variance:

[0089]

[0090] Get the variable point x new The predicted response mean S at * and its variance

[0091] S * =γ m (x new )μ N ,

[0092]

[0093] In the mapping relationship model between traffic load parameters and bridge response extremes, sample data closer to the test point has a greater impact on the predicted value, while samples farther away have a smaller impact. Selecting a sufficient number of sample points can more comprehensively cover data that significantly influence the test point, thereby establishing a more accurate nonlinear relationship. However, this results in lower efficiency. Therefore, to more efficiently select optimal data, the coefficient of variation ξ is defined as the ratio of the predicted response mean to its variance. This represents the degree of data dispersion. Each time a point is selected, the first l1 data points with the smallest coefficient of variation are used to update the mapping relationship model.

[0094]

[0095] The traffic load sample set generated in step 2 is defined as A q, select a certain initial traffic load sample l and the corresponding bridge response extreme value to train the mapping relationship model of traffic load parameter-bridge response extreme value, that is, in

[0096]

[0097] Where, l is the number of initial traffic load samples; j is the number of traffic load parameters;

[0098] Then the remaining traffic load sample A q -l, substitute into In the calculation of S * and Take l1 traffic load samples with the smallest coefficient of variation and add them to the initial traffic load sample l, which is l+l1. Substitute l+l1 into Update the traffic load parameter-bridge response extreme value relationship model; then calculate the remaining traffic load sample A q -l+l1 corresponding to S * and Then take l1 traffic load samples with the smallest coefficient of variation and add them to the initial traffic load sample l, and repeat the above process until the model converges. * +σ * With S * -σ * The closer the two are, the more convergence they have reached, or the convergence condition is satisfied when ξ is defined to be less than or equal to 2.

[0099] In step 5, the random traffic load sample set considering axle weight is input into the convergence mapping relationship model of step 4, that is, the bridge response extreme value of the current random traffic load sample is obtained, and then the corresponding extreme value distribution is further fitted.

[0100] Sample U1, U2, ... U from the uniform distribution U(0, 1) d . (d is the number of random variables), U i Mapped to the original spatial data, for each marginal distribution F i , using its inverse function F i -1

[0101] X i =F i -1 (U i )

[0102] X iThis is the result of joint distribution sampling, and the generated data takes into account the axle load dependence of actual vehicle loads. Repeated sampling yields a random traffic load sample set C2 that accounts for axle load dependence. Substituting this into the convergent mapping relationship model between traffic load parameters and bridge response extreme values ​​yields the corresponding bridge response extreme values. Nonparametric kernel density estimation is used to fit the response extreme value data and establish a bridge response extreme value distribution.

[0103] Step 6: Evaluate the effects of vehicle loads on the bridge.

[0104] Based on national or regional bridge design codes and standards, combined with statistical analysis of historical monitoring data, the maximum allowable response value—the threshold—is determined. Based on the resulting extreme value distribution of the response, the probability of exceeding the threshold is calculated. This probability is the failure probability, which is then used to assess the effects of vehicle loads on the bridge. If the failure probability is greater than 5%, the bridge structure is deemed to have failed due to vehicle loads.

[0105] When the calculated extreme value of the response is greater than the threshold, it indicates failure. The final calculated extreme value of the response is an extreme value distribution function. We can see how many values ​​of this distribution function are greater than the threshold. The ratio of these values ​​greater than the threshold to the total number is the failure probability.

[0106] Example 2

[0107] The effectiveness of this method was verified using nearly a year of vehicle data from the Xingtai North Ring South-to-North Water Diversion Bridge. During data preprocessing, outliers in axle weights and lane spacing were removed to ensure the accuracy of the verification results.

[0108] The details are as follows:

[0109] (1) The parameter variables of random traffic flow include axle weight and lane distance. First, the vehicle types are classified according to the number of axles, and the axle weight probability model of vehicles with different axle numbers is established. The data is fitted using the non-parametric kernel density estimation method. Taking the Xingtai North Ring South-to-North Water Diversion Bridge as an example, six-axle vehicles account for 64.9%, and the axle weight correlation of six-axle vehicles is the strongest. The axle weight kernel density fitting results of six-axle vehicles are shown in the figure below. Figures 2 to 7 shown.

[0110] (2) Using Matlab's copulastat function, we calculated the Spearman rank correlation coefficient of axle loads and used it to establish a joint distribution function related to axle loads. We sampled this joint distribution and the marginal distribution function of lane spacing to generate a random traffic load sample set that considered axle load correlation. Figure 8 The relevant axle load sampling points for a six-axle vehicle are shown.

[0111] Table 1 shows the Spearman rank correlation coefficients for axle loads. Larger values ​​indicate stronger correlations. For a six-axle vehicle, the table shows the strongest correlation between the fifth and sixth axles, followed by the fourth and fifth axles. The closer the distance between axles, the stronger the correlation. This demonstrates that correlations between axle loads do exist in real-world vehicles and need to be considered when developing random traffic load models.

[0112] Table 1 Spearman rank correlation coefficient of six-axle axle weight

[0113]

[0114] (3) After determining the reasonable value range of each parameter of axle weight and lane distance, stratified sampling is performed on the parameters, and 1000 samples are extracted for each parameter to form sample library A. q . Calculate sample library A by influence line loading q The bridge response extreme value of each sample in the database B is obtained. q . Select A q and B q The initial sample points in the model are substituted into the model to establish a mapping relationship between traffic load parameters and bridge response extreme values. Each time, 50 sample points (i.e., l1 = 50) are selected from the remaining candidate samples and substituted into the training of the mapping relationship model. Based on the calculated mean and variance, the coefficient of variation is introduced. The point with the smallest value is added to the initial sample points for iteration. Once the error range is within the allowable range, the mapping relationship is established and a converged mapping relationship model is obtained.

[0115] (4) The generated random traffic load sample set considering axle weight is input into the convergence mapping relationship model to obtain the extreme value distribution of the bridge response. The probability of the obtained extreme value of the response exceeding the threshold is calculated, and then the vehicle load effect of the bridge is evaluated. If the failure probability is greater than 5%, it is determined that the vehicle load causes the failure of the bridge structure. Compared with the traditional finite element calculation method, this method greatly shortens the time for calculating the bridge response, and the error at the extreme value of the 95% quantile of the extreme value distribution of the bridge response is controlled below 1%. In addition, this method realizes the selection of the optimal point for the training relationship, thereby improving the efficiency of the model establishment. Fitting curve comparison Figures 9 and 10 shown.

[0116] Figure 9 and Figure 10The results of calculating deflection and stress using the method of the present invention are compared with those of the traditional MCS calculation method (finite element software is used to establish a bridge model, a large number of vehicle samples are input, and then the corresponding response extreme value calculation is performed). It can be seen that the response extreme value distribution curves of the two results are very close, especially in the tail data. Taking deflection as an example, the mean of the bridge response extreme value distribution and the extreme value data corresponding to the 95% quantile are observed. The mean calculated by the finite element method is 0.9710, and the mean calculated by this method is 0.9677, with a difference of only 0.05; the extreme value data corresponding to the 95% quantile calculated by the finite element method is 1.4134, and the extreme value data corresponding to the 95% quantile calculated by this method is 1.4117, with a difference of 0.0017. For the extreme value response distribution of bridges caused by vehicle loads, the tail data, that is, the data with large values, has a very important impact on the bridge, so this method improves calculation efficiency while also ensuring data accuracy.

[0117] For bridges, small deflections or stresses have little impact on the structure; it's the larger data that can damage the structure. Therefore, this method calculates the extreme value distribution of the bridge response. The tail data in an extreme value distribution are the largest of all extreme values, and this data has a significant impact on the bridge. The results of this method overlap well with those of traditional finite element distribution calculations for the tail data, demonstrating the reliability of the results based on improved computational efficiency.

[0118] Example 3

[0119] This embodiment is a vehicle load effect assessment device for a long-span concrete beam bridge, comprising:

[0120] Vehicle Information Collection Unit: This unit, centered around a dynamic weighing system and equipped with high-precision sensors and signal receivers, collects real-time information on axle weights and lane distances of vehicles crossing the bridge. Data is pre-processed using an integrated chip and digital signal processor (DSP), eliminating outliers. The processed data is then stored in a storage module connected to an external interface, ensuring efficient data management and subsequent analysis.

[0121] Random traffic flow generation unit: uses the vehicle parameter information transmitted by the vehicle information acquisition unit to generate a random traffic flow load sample set that takes into account axle weight. This unit uses the processor to perform complex calculation tasks and provides the necessary input data for calculating the extreme values ​​of bridge response.

[0122] Mapping relationship establishment unit: The influence lines of each mid-span section of the bridge are obtained through load testing. Considering the reasonable value range of axle load and lane spacing, a stratified sampling method is used to generate a traffic load sample set within this reasonable value range. The bridge response extreme value corresponding to the traffic load sample set is calculated. The mapping relationship between traffic load parameters and bridge response extreme values ​​is established in the form of a polynomial. The random traffic load sample data generated by the random traffic generation unit, which considers the axle weight, is substituted into the mapping relationship to calculate the bridge response extreme value and obtain the bridge response extreme value distribution.

[0123] Evaluation unit: Set the maximum allowable response value of the bridge as the threshold, find the probability of exceeding the threshold in the extreme value distribution of the bridge response obtained by the mapping relationship, and this probability is the failure probability. The vehicle load effect of the bridge is evaluated based on the failure probability;

[0124] Control Unit: The control unit is responsible for adjusting the input frequency and time nodes of vehicle information, including various settings such as hour, day, month, quarter, and year. Through the external interface of the server terminal, users can adjust the input data in real time to meet different analysis needs and research objectives.

[0125] The pressure exerted by vehicles on bridges is transmitted to the bridge deck through the weight of each axle. To establish a random traffic load sample set, it is necessary to perform probability statistics on the marginal distribution of the axle weight data and to obtain samples by sampling from the marginal distribution. However, each axle weight in an actual vehicle does not exist independently, especially in the case of a multi-axle vehicle with a coupled axle design, which causes the axle weights to influence each other. If only the marginal distribution of each axle weight is considered separately for sampling, the axle weight of the actual vehicle cannot be well reflected, so the correlation of the axle weights needs to be considered. The method of the present invention uses a polynomial function to establish a mapping relationship between traffic load parameters and extreme values ​​of bridge response. It can quickly calculate the extreme values ​​of bridge response caused by vehicle loads, consider the correlation of vehicle axle weights, and improve the accuracy of the random traffic load model.

[0126] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A method for predicting the extreme value of vehicle load effect on a long-span concrete beam bridge, characterized in that: The process of the method is: Step 1: Obtain vehicle data measured by the bridge dynamic weighing system, classify vehicles according to the number of axles, and use the axle weight and lane distance of different vehicle models as traffic load parameters. The number of traffic load parameters is the sum of the axle weights of all vehicle models + the number of lane distances. Use the non-parametric kernel density fitting estimation method to determine the probability density distribution of each traffic load parameter, and then obtain the marginal distribution function F of each traffic load parameter. Considering the correlation of vehicle axle weights, the marginal distribution functions of all axle weights of the same vehicle model are combined according to the following formula to obtain the joint distribution function of axle weight H; H(x 1 ,…,x n )=Φ ρ (Φ -1 (x 1 ),…,Φ -1 (x n ))(F1(x 1 ),…F n (x n )) Where: n is the number of axle loads in a certain type of vehicle, Φ ρ is the distribution function of the multivariate standard normal distribution with the correlation coefficient matrix ρ; Φ -1 Represents the inverse function of the standard normal distribution; x 1 represents the first axle weight sample; x n represents the sample of the nth axle weight; Based on the joint distribution function of axle load and the marginal distribution function of lane distance, a random traffic load sample set considering axle load correlation is established. Step 2: Obtain a reasonable value range for axle load and lane distance, and use stratified sampling method to generate a traffic load sample set within this reasonable value range; Step 3: Obtain the influence line of each span section of the bridge through load testing; Step 4: Load the traffic load sample set from step 2 onto the influence line and calculate the traffic load response extreme value dataset for the bridge. Use these calculated response extreme value datasets and the corresponding traffic load sample set to establish a mapping relationship model between traffic load parameters and bridge response extreme values: Where S is the extreme value of the response; M is the number of polynomials; r m is the coefficient; γ m (X) is a polynomial function; X is the traffic load parameter, corresponding to the axle weight and lane distance of all types of axles; ε is a function with mean 0 and variance σ 2 Normal distribution; For each coefficient r m Introduce the prior distribution, construct the likelihood function, calculate the posterior distribution, and define the coefficient of variation ξ as: Where x new is a new variable point, the axle weight and lane distance of all types of all axles are a traffic load sample, and each traffic load sample is a point; S * 、 are the new variable points x new The mean and variance of the predicted response at ; is the prior variance; μ N is the posterior mean; σ N 2 is the posterior variance; Each time, the first l1 data with the smallest coefficient of variation are selected to update the mapping relationship model until the model converges to obtain a converged mapping relationship model; In step 5, the random traffic load sample set obtained in step 1 considering axle weight is input into the convergence mapping relationship model in step 4, that is, the bridge response extreme value of the current random traffic load sample is obtained, and then the corresponding extreme value distribution is further fitted.

2. The method according to claim 1, characterized in that The method is used to evaluate vehicle load effects on long-span concrete beam bridges: based on national or regional bridge design codes and standards and combined with statistical analysis of historical monitoring data, the maximum allowable response value, the threshold value, is determined; Combined with the extreme value distribution of the response obtained in step 5, the probability of exceeding the threshold is calculated. This probability is the failure probability. The vehicle load effect on the bridge is evaluated based on the failure probability. If the failure probability is greater than 5%, it is determined that the vehicle load causes the bridge structure to fail.

3. The method according to claim 1, characterized in that The traffic load sample set generated in step 2 is defined as A q , select the initial traffic load sample l and the corresponding bridge response extreme value to train the mapping relationship model of traffic load parameters-bridge response extreme value; Where, l is the number of initial traffic load samples; j is the number of random traffic load parameters; Then the remaining traffic load sample A q -l, substitute into In the calculation of S * and Take l1 traffic load samples with the smallest coefficient of variation and add them to the initial traffic load sample l, which is l+l1. Substitute l+l1 into Update the traffic load parameter-bridge response extreme value relationship model; then calculate the remaining traffic load sample A q -l+l1 corresponding to S * and Then take l1 traffic load samples with the smallest coefficient of variation and add them to the initial traffic load sample l, and repeat the above process until the model converges.

4. The method according to claim 1, wherein The condition for model convergence is: ξ is less than or equal to 2.

5. A vehicle load effect evaluation device for a long-span concrete beam bridge, characterized in that: The device adopts the prediction method according to any one of claims 1 to 4, including: Vehicle Information Collection Unit: This unit, with a dynamic weighing system as its core and equipped with high-precision sensors and signal receivers, is responsible for collecting real-time information on axle weights and lane distances of vehicles crossing the bridge. It pre-processes the data using an integrated chip and digital signal processor to eliminate outliers and stores the processed data in a storage module connected to an external interface. Random traffic flow generation unit: uses the vehicle parameter information transmitted by the vehicle information acquisition unit to generate a random traffic flow load sample set considering the axle weight; Mapping relationship establishment unit: The influence lines of each mid-span section of the bridge are obtained through load testing. Considering the reasonable value range of axle load and lane spacing, a stratified sampling method is used to generate a traffic load sample set within this reasonable value range. The bridge response extreme value corresponding to the traffic load sample set is calculated. The mapping relationship between traffic load parameters and bridge response extreme values ​​is established in the form of a polynomial. The random traffic load sample data generated by the random traffic generation unit, which considers the axle weight, is substituted into the mapping relationship to calculate the bridge response extreme value and obtain the bridge response extreme value distribution. Evaluation unit: Set the maximum allowable response value of the bridge as the threshold, find the probability of exceeding the threshold in the extreme value distribution of the bridge response obtained by the mapping relationship, and this probability is the failure probability. The vehicle load effect of the bridge is evaluated based on the failure probability; Control unit: The control unit is responsible for adjusting the input frequency and time nodes of vehicle information, including hour, day, month, quarter and year.

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