Bridge component extreme effect evaluation method suitable for traffic state change

Abstract

The application relates to a bridge component extreme effect evaluation method suitable for traffic state changes, which comprises the following steps: obtaining extreme value scene characteristics of specific effects according to traffic flow and vehicle data information of a specific place and an effect influence line of a bridge structure; simulating vehicle load extreme value scenes of specific effects of the specific place based on a Monte Carlo method, so as to construct specific effect load models in an experience state; obtaining posterior extreme value scene distribution samples; updating the specific effect load models in the experience state based on the application of particle filtering in a spatial random field, so that the updated models can adjust load levels according to vehicle evolution; and determining bridge component extreme effect evaluation results according to the updated models. Compared with the prior art, the application can accurately simulate complex spatial distribution of traffic load modeling and update according to traffic state changes, so that the bridge component extreme effect can be accurately evaluated in the case of traffic state changes.

Description

Technical Field

[0001] This invention relates to the field of bridge structural performance evaluation technology, and in particular to a method for evaluating the extreme value effect of bridge components under varying traffic conditions. Background Technology

[0002] Bridge structures bear various loads during their long service life, among which traffic loads exhibit significant uncertainty and variability. This uncertainty stems primarily from the constantly evolving traffic conditions at the bridge's location. Traditional design codes do not adequately consider the spatiotemporal variability of vehicle loads, and the traditional traffic load models specified in these codes are mainly designed for bridges with small to medium spans, including D60, US standards, British standards, and European standards. Vehicle load models for small to medium span bridges may not be suitable for direct application to large-span bridges, or at least require periodic updates based on current traffic characteristics before they can be applied to large-span bridges.

[0003] Currently, both domestic and international vehicle load models have limitations in quantitatively representing the complex spatial distribution of traffic loads on bridge decks. Furthermore, traditional location-specific traffic flow simulation methods can only reconstruct traffic flow information, failing to quantitatively represent the complex spatial distribution of traffic loads on bridge decks. In reality, the spatial distribution of vehicles on the bridge deck that triggers the maximum load effect is crucial for assessing bridge safety and understanding bridge performance under vehicle loads. Simultaneously, focusing solely on traffic flow simulation while ignoring traffic scenarios that may lead to extreme response values ​​results in traditional simulation methods being inefficient and computationally intensive in obtaining extreme effects over long time periods.

[0004] It is evident that existing technologies struggle to model the complex spatial distribution of bridge traffic loads under extreme scenarios, and also fail to update traffic load models in a timely manner. Consequently, when assessing extreme effects on bridge components, the technology cannot adapt to real-time changes in traffic conditions, resulting in low accuracy of the assessment results. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method for evaluating the extreme effects of bridge components under changing traffic conditions. By constructing a vehicle spatial distribution model for specific structural effects at a specific location and updating the model based on posterior observation data, it is possible to ensure accurate evaluation of the extreme effects of bridge components under changing traffic conditions.

[0006] The objective of this invention can be achieved through the following technical solution: a method for evaluating the extreme value effect of bridge components under changing traffic conditions, comprising the following steps:

[0007] S1. Based on traffic flow and vehicle data at a specific location and the influence line of specific effects of the bridge structure, obtain the extreme value scenario characteristics of the specific effects, and simulate the extreme value scenario of vehicle load for specific effects at a specific location using the Monte Carlo method.

[0008] S2. Based on the extreme value scenario of vehicle load at a specific location and with specific effects in step S1, construct a specific effect load model under empirical conditions.

[0009] S3. Obtain the posterior extreme value scenario distribution sample, and based on the application of particle filtering in spatial random fields, update the specific effect load model under the empirical state so that the updated model can adjust the load level according to the vehicle evolution.

[0010] S4. Based on the updated model, determine the evaluation results of the extreme value effect of bridge components.

[0011] Furthermore, step S1 specifically includes the following steps:

[0012] S11. Collect WIM (Weigh in Motion) data from specific locations, perform data cleaning operations, and compile corresponding traffic flow and vehicle data information, including but not limited to vehicle total weight, vehicle length, vehicle speed, and vehicle arrival time.

[0013] S12. Construct a finite element model of the bridge structure and obtain the influence lines of the specific effects to be evaluated;

[0014] S13. Based on the total weight and length of the vehicles, filter out the length information of heavy vehicles and determine the length of the bridge deck cell accordingly.

[0015] S14. Based on the influence line of the specific effect of the bridge structure, load the traffic flow data onto the influence line of the specific effect according to the set time step to obtain extreme value scene samples.

[0016] S15. Based on extreme value scenario samples, calculate the Poisson parameters of the distribution location of heavy vehicles in each lane and the Gaussian mixture distribution parameters of the total weight of heavy vehicles in each lane.

[0017] S16. Based on the data obtained in step S15, simulate the position of heavy vehicles based on non-stationary Poisson distribution and simulate the total weight of heavy vehicles based on Nataf transformation to obtain the extreme scenario of load simulation under the current specific effect.

[0018] S17. Repeat steps S12 to S16 to obtain extreme load simulation scenarios under different specific effects at specific locations, so as to simulate the complex spatial distribution of heavy vehicles on the bridge surface.

[0019] Furthermore, in step S13, the heavy vehicle specifically refers to a vehicle with a total weight of 10 tons or more.

[0020] In step S13, the length of the bridge deck cell is greater than the average length of heavy vehicles, and the difference between the two is within a set threshold range.

[0021] Furthermore, step S14 specifically includes the following steps:

[0022] S141. Restore the WIM data to the traffic flow sequence with a set bridge length, then load it onto the influence line of a specific effect, and calculate multiple structural effect values ​​in sequence according to the set time step, which are the obtained samples.

[0023] S142. Select the group of samples with the largest effect value from the multiple groups of samples each day, and use it as the extreme value scenario sample.

[0024] Furthermore, step S15 specifically includes the following steps:

[0025] S151. Based on extreme value scenario samples, extract Poisson distribution parameters from the statistical information of the number of heavy vehicles in each lane:

[0026]

[0027] Where Pr(·) is the probability of the event occurring. Let be the average probability of a cell being occupied by heavy vehicles. For non-stationary events, Change along the lane;

[0028] S152. Based on extreme value scenario samples, extract Gaussian mixture distribution parameters from the total weight statistics of heavy vehicles in each lane:

[0029]

[0030]

[0031] 0≤ ≤1

[0032] in, For and The first and second terms of the mean and covariance matrices k A Gaussian distributed PDF, For the first k The weights of the Gaussian distribution components.

[0033] Furthermore, step S16 specifically includes the following steps:

[0034] S161. A longitudinal non-stationary Poisson distribution method is adopted, and the Poisson distribution parameters are used to simulate the bridge deck position of heavy vehicles under extreme scenarios.

[0035] S162. Based on the Gaussian mixture distribution of the total weight of heavy vehicles, the correlation of the total weight of heavy vehicles along the lane direction is simulated through Nataf transformation.

[0036] Furthermore, the expression for the longitudinal non-stationary Poisson distribution in step S161 is specifically as follows:

[0037]

[0038] in, The average level of occupied cells across the entire lane. This represents the changing pattern of the probability of lane occupancy.

[0039] Furthermore, the specific process of step S2 is as follows: based on the extreme value scenario of vehicle load at a specific location and specific effect in step S1, firstly, the load intensity is obtained by inversion according to the extreme value of the response of the specific effect and the load form, and then a distributed line load with variable intensity is used for modeling to construct a specific effect load model under empirical conditions.

[0040] Furthermore, step S3 specifically involves updating the load form and load intensity in the specific effect load model under empirical conditions.

[0041] Furthermore, the specific process of step S3 is as follows:

[0042] Assume the extreme value scenario load model is a spatial random variable that varies with time, i.e., assume:

[0043] It is a set of random fields, in which, It is a random variable in extreme value scenario samples. n It is the total number of Monte Carlo simulations of extreme scenarios. X It is a time-varying spatial stochastic process used to describe the distribution of vehicle loads on the bridge surface under extreme conditions;

[0044] Extreme value scenario prediction uses a function Represented as:

[0045]

[0046] in, The system error generated during the prediction process is represented by t, which is the time state.

[0047] Considering that traffic flow and composition are constant over a certain period of time, we assume... X It is stable, that is... The linear relationship is then represented, and a particle filtering method is used to update the spatial load model for extreme scenarios using the newly acquired data.

[0048] That is, according to the state-space model method, given a potential state In the case of, assuming the observed values Conditionally independent of each other, The dimension is u , representing the number of observations on the bridge surface used for updating. The dimension is × = n ,in and These represent the number of units in the horizontal and vertical directions, respectively.

[0049] Space observation data and The interrelationships are represented as follows:

[0050]

[0051] in, It is a function matrix, providing a size of u × n Measurement location information, It is observation error. The dimension is also u ;

[0052] Using space observation data Get Random Field The optimal estimate will be the conditional probability. The basic update formula is discretized as follows:

[0053]

[0054] in Sampling is performed with equal probability; if the total number of samples is... α ,but for:

[0055]

[0056] It is the conditional probability density function, which is the observed value. The weights are:

[0057]

[0058]

[0059] in, Based on Each The weights, due to the equation and It is a vector, therefore It is based on observation error It is calculated from the multivariate Gaussian probability density function;

[0060] Therefore, based on the observed spatial data Each can be calculated based on the above equations. The weight ratio is then used to obtain an updated random field through a resampling process based on the weight ratio. This means completing the model update process.

[0061] Compared with the prior art, the present invention has the following advantages:

[0062] First, this invention obtains the extreme value scenario characteristics of specific effects based on traffic flow and vehicle data at specific locations and the influence line of specific effects on bridge structures. Using the Monte Carlo method, it simulates the extreme value scenario of vehicle load under specific effects at specific locations to construct an empirical load model for specific effects. Then, by acquiring posterior extreme value scenario distribution samples and applying particle filtering in spatial random fields, the empirical load model for specific effects is updated. Based on the updated model, the evaluation results of extreme effects on bridge components are determined. Thus, while completing the modeling of complex spatial distribution of traffic loads, the constructed model can be updated based on traffic flow information at specific locations. This model can adjust the load level according to traffic flow evolution, thereby ensuring accurate evaluation of extreme effects on bridge components under changing traffic conditions.

[0063] Second, this invention addresses two aspects. Firstly, it simulates the position of heavy vehicles by employing a non-stationary Poisson process to model the uneven distribution of heavy vehicles on the lanes, assuming they are located within cells on the bridge deck. This accurately simulates the bridge deck positions of heavy vehicles under extreme scenarios. Secondly, it simulates the total weight of heavy vehicles by using a Gaussian mixture distribution to describe and simulate the total weight of heavy vehicles on the bridge deck, and by leveraging Nataf transform to consider the correlation between the total weights of adjacent heavy vehicles. This accurately simulates the total weight of heavy vehicles under extreme scenarios. Thus, it can accurately simulate extreme scenarios of vehicle loads with specific effects, serving as the data foundation for subsequent vehicle load model construction.

[0064] Third, this invention, based on the construction of an extreme vehicle load scenario model, updates the model using posterior observation data. This is achieved by applying a particle filter to spatial observation data collected at discrete locations within the scenario model to update relevant random variables in extreme scenarios. In other words, it periodically assesses and corrects loads after changes in traffic conditions, achieving the goal of updating the model according to changes in traffic status. This enables accurate estimation of the bridge's traffic load response during operation under changing traffic conditions. Attached Figure Description

[0065] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0066] Figure 2 This is a schematic diagram of an extreme scenario for a long-span bridge in the embodiment.

[0067] Figure 3 Comparison of load forms for vehicle load models;

[0068] Figure 4 This is a schematic diagram of a specific effect load model;

[0069] Figure 5 For updating the spatial random field based on observation data, a particle filtering process is used.

[0070] Figure 6 This is a schematic diagram of the resampling process;

[0071] Figure 7 The values ​​represent the probability of heavy vehicles exhibiting different effects in the examples. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0073] Example

[0074] like Figure 1 As shown, a method for evaluating the extreme value effect of bridge components under changing traffic conditions includes the following steps:

[0075] S1. Based on traffic flow and vehicle data at a specific location and the influence line of specific effects of the bridge structure, obtain the extreme value scenario characteristics of the specific effects, and simulate the extreme value scenario of vehicle load for specific effects at a specific location using the Monte Carlo method.

[0076] S2. Based on the extreme value scenario of vehicle load at a specific location and with specific effects in step S1, construct a specific effect load model under empirical conditions.

[0077] S3. Obtain the posterior extreme value scenario distribution sample, and based on the application of particle filtering in spatial random fields, update the specific effect load model under the empirical state so that the updated model can adjust the load level according to the vehicle evolution.

[0078] S4. Based on the updated model, determine the evaluation results of the extreme value effect of bridge components.

[0079] Applying the above technical solutions to practice specifically includes:

[0080] Simulating extreme vehicle load scenarios with specific effects at specific locations using the Monte Carlo method.

[0081] WIM traffic flow data from specific locations is collected, and preliminary data cleaning and other preliminary work are performed. Vehicle data should include information such as total vehicle weight, vehicle length, vehicle speed, and vehicle arrival time. A finite element model of the bridge structure is constructed to obtain the influence line of the effect of interest. In this embodiment, the length information of heavy vehicles weighing over 10 tons is collected to determine the length of the bridge deck cell. The cell length should be slightly longer than the average length of heavy vehicles, mainly to take into account the front and rear trailers of vehicles and necessary driving distances. Based on the influence line of the specific effect, in this embodiment, the time step is 1 second, and the WIM data is restored to the influence line of the traffic flow loading onto the effect. The group with the largest effect among the 86,400 samples per day is selected as the sample of the extreme value scenario.

[0082] Based on the above extreme scenario samples, the Poisson parameters of the heavy vehicle distribution positions in each lane and the Gaussian mixture distribution parameters of the total weight of heavy vehicles in each lane are statistically analyzed. First, a simulation of heavy vehicle positions is performed based on a non-stationary Poisson distribution. Then, based on the statistical information of the heavy vehicle position distribution under specific effects, the Poisson distribution is applied to simulate the bridge deck positions of heavy vehicles in extreme scenarios. The formula for the Poisson distribution is shown below:

[0083]

[0084] In the formula, Pr(·) represents the probability of the event occurring. This represents the average probability of a cell being occupied by a loaded vehicle, for non-stationary events. Change along the lane.

[0085] The non-stationarity of the distribution of loaded vehicles can be expressed by the following formula:

[0086]

[0087] In the formula, This represents the average level of occupied cells across the entire lane. This represents the changing pattern of the probability of occupying a lane.

[0088] Subsequently, a Gaussian mixture distribution simulation of the total vehicle weight was performed based on the Nataf transform. The total vehicle weight is a key variable in vehicle load, exhibiting significant uncertainty and requiring probabilistic simulation methods. Furthermore, the total vehicle weight exhibits a multimodal distribution, which the Gaussian mixture distribution accurately captures. Combining the Nataf transform with the Gaussian mixture distribution allows the correlation of the total vehicle weight to be considered in the simulation. Currently, the Gaussian mixture distribution is widely used in various fields and demonstrates excellent performance in multimodal simulations. (For random variables...) The Gaussian mixture distribution is expressed as:

[0089]

[0090] in Therefore and The PDF of the k-th Gaussian distribution with mean and covariance matrix. The weight of the k-th Gaussian distribution component is given by the following condition: and 0≤ ≤1.

[0091] When applying Gaussian mixture distributions, selecting an appropriate number of components is crucial. Increasing the number of components improves the accuracy of the Gaussian mixture distribution but reduces efficiency. In practice, several entropy criteria can be used to determine the number of components, including the AIC (Akaike Information Criterion) method and the BIC (Bayesian Information Criterion) method.

[0092] Meanwhile, several consecutive heavy vehicles in a lane are a key factor causing extreme load effects, threatening the safety of the bridge structure. Therefore, for extreme scenarios, a correlation is assumed between heavy vehicles in adjacent positions within the same lane. The purpose of setting this parameter is to describe the correlation between adjacent heavy vehicles in the same lane during extreme scenarios, reflected by a correlation function. This embodiment uses the Pearson correlation coefficient to characterize the correlation of the total weight of heavy vehicles, as shown below:

[0093]

[0094] in This represents the correlation coefficient between the total weight of loaded vehicles at adjacent positions j and k. Corresponding to the covariance between adjacent total weights, and ... As distance The correlation weakens as the value increases. Referring to engineering cases in relevant research, an exponential correlation function is used to express this. :

[0095]

[0096] Where D is a parameter representing the relevant length, for distance Take the centroid distance between two adjacent cells.

[0097] The Nataf transformation can be used to convert any random variable into a standard Gaussian distribution, an n-dimensional correlated random vector. The marginal cumulative density function is The correlation coefficient matrix is Through Nataf transformation, Convert to independent standard normal variables .

[0098] The Nataf transformation process is as follows: [Related standard normal variables] By the following formula Transformation:

[0099]

[0100] in It is the marginal cumulative density function of the inverse of the standard Gaussian distribution. The correlation coefficient matrix is ​​assumed to be . and The relationship between them is shown in the following formula:

[0101]

[0102] in The following equations give the mean and standard deviation of the variable, E(∙) and SD(∙), respectively:

[0103]

[0104] in, It can be done The calculation shows that the relationship between the two can be simplified by the following formula:

[0105]

[0106] It can be approximated by a polynomial as follows:

[0107]

[0108] Where parameters to Calculated using the Monte Carlo method. Because... The covariance matrix is ​​positive definite, so it can be decomposed using Cholesky decomposition. It can be decomposed into a lower triangular matrix and an upper triangular matrix, as shown in the following equation:

[0109]

[0110] in It is a lower triangular matrix. Therefore, the variables... It can be represented as With independent standard normal variables The product of is shown in the following formula:

[0111]

[0112] Independent standard normal variables Related variables The relationship can be established as an equation:

[0113]

[0114]

[0115]

[0116]

[0117] Where Φ(∙) is the marginal cumulative density function of the standard Gaussian distribution. Then, the Monte Carlo method is used to analyze the extreme load scenario, where the total weight of the loaded vehicle is simulated according to the following formula:

[0118]

[0119] To obtain sufficient sample data to illustrate the possibility of extreme load responses within the structural design reference period, the Monte Carlo method was employed. Based on multiple simulations, extreme load scenarios under various effects were generated. Possible representative simulation samples include... Figure 2 As shown, the height of the bar chart represents the total weight of each heavy vehicle, and the horizontal and vertical axes represent the cell layout of the bridge structure. The extreme vehicle load scenarios simulating specific effects using the Monte Carlo method serve as the data foundation for the vehicle load model.

[0120] Construction of extreme scenario load model for specific effects

[0121] In this process, it is necessary to consider the load form (the shape of the load: uniform or non-uniform distribution, one or more concentrated loads, etc.) and the load intensity (load value). The updatable part of the constructed load model includes the load form and value. Since the bridge response and traffic parameters are strongly correlated with the distribution of vehicles on the bridge, and different types of effects have different influence line shapes, the load value and form can fully express the changes in traffic flow over time.

[0122] Figure 3 Various possible vehicle load forms are presented, with fidelity decreasing progressively. Load form 1 consists of multiple sets of axle loads, load form 2 includes multiple sets of vehicle loads, and load form 3 is a uniformly linearly distributed vehicle load. Furthermore, vehicle loads can be modeled using distributed line loads with variable intensity (load form 4). Load form 5 represents the most simplified line load form. To achieve a balance between computational efficiency and accuracy, this technical solution selects load form 4 to develop a load model for extreme vehicle scenarios, used for the design and evaluation of long-span bridges. Moreover, the design load values ​​are obtained through inversion based on the extreme values ​​of the response to specific effects and the load form. Figure 4 Example of a specific effect load model constructed.

[0123] Extreme scenario load model update for specific effects

[0124] Traffic load effects are highly correlated with the positional height of vehicles on the bridge deck, especially for long-span bridges. To establish an accurate traffic load model, the vehicle load distribution on the bridge deck should be rationally allocated to obtain the extreme values ​​of the effect. Furthermore, the time-varying load distribution due to changes in traffic flow composition should also be considered. Therefore, when predicting traffic loads, modifications to the traffic environment must be observed and considered periodically. For load models in extreme scenarios, a new method for updating the spatial distribution of vehicle loads is needed. This technical solution assumes that the load model for extreme scenarios is a time-varying spatial random variable.

[0125] Assumption It is a set of random fields, in which is a random variable representing extreme scenario samples, and n is the total number of Monte Carlo simulations of extreme scenario samples. X It is a time-varying spatial stochastic process that describes the distribution of vehicle loads on the bridge surface under extreme conditions. Extreme scenario prediction can be performed using a function... Represented as:

[0126]

[0127] in This represents the systematic error generated during the prediction process, where t is the time state. However, the changes in traffic volume and weight distribution of heavy vehicles are a complex issue related to technological and economic development, especially in the prediction of the spatial distribution of vehicle load under extreme scenarios. Considering that traffic flow and composition can be assumed to be constant over a certain period of time, we assume... X It is stable, that is... This indicates a linear relationship. Subsequently, a particle filtering method is used to update the spatial load model for the extreme scenario using the newly observed data.

[0128] In practice, if the relationship between the random variables in the prediction model and the observed data is non-linear, or if the distribution of the random variables is non-Gaussian, then updating the prediction model using rigorous theoretical methods is usually infeasible. Under these conditions, particle filtering is a flexible technique for updating random variables. According to the state-space model method, given a potential state... In the case of, assuming the observed values They are conditionally independent of each other. The dimension is u , representing the number of units on the bridge surface used for updating observations. The dimension is × = n ,in and These are the number of units in the horizontal and vertical directions, respectively. For space observation data... and The interrelationship can be represented as:

[0129]

[0130] in It is a function matrix, providing a size of u × n Measurement location information. It is observation error. The dimension is also u .

[0131] In order to utilize space observation data Get Random Field The optimal estimate, conditional probability The discrete version of the basic update formula can be written as:

[0132]

[0133] in Samples are taken with equal probability. If the total number of samples is... α ,but It can be written as:

[0134]

[0135] It is the conditional probability density function, which is the observed value. The weights. The weights can be derived from the formula above:

[0136]

[0137] in:

[0138]

[0139] Indicates based on Each The weights. Due to the equation and It is a vector. It is based on observation error It is calculated from the multivariate Gaussian probability density function.

[0140] The update process is as follows Figure 5 As shown: First, based on the observed spatial data Calculate each based on the above equations. The weight ratio. Secondly, the updated random field. This is obtained through a resampling process using weighted ratios, as follows: Figure 6 As shown, random fields with small weights are eliminated. The resampling index is the sequence number of the random field sample, and each index corresponds to a certain weight. Figure 6 In the diagram, horizontal arrows indicate equal divisions to determine which particles are sampled. For example, the particle with index 6 has a weight of... As it is the largest of all the weights, the particle with index 6 was selected 3 times as indicated by the purple arrow, while the particle with index 2 was not selected due to its lower weight.

[0141] To further verify the effectiveness of this technical solution, this embodiment evaluates the extreme value effects of bridge components on a typical six-lane, double-tower, long-span cable-stayed bridge. The bridge's loading length is 2088 m, and the maximum span is 1088 m. The original WIM data is 423 days long and was collected from a six-lane highway. After cleaning, the daily traffic flow is approximately 16,500-50,000 vehicles, totaling 11,055,095 vehicle flow data points (including small and heavy vehicles). The WIM data represents the free-flowing traffic conditions, which forms the basis for extreme value scenario simulation.

[0142] Reconstructing WIM data into a traffic flow sequence across a certain bridge length requires several assumptions: first, that the data monitoring point is located 100m from one side of the bridge; and second, that vehicles maintain a constant speed while crossing the bridge. Based on the arrival time and speed of a vehicle, and the location of the monitoring station (where the arrival time is recorded), the time history of that vehicle crossing the bridge can be obtained. Using the influence line method, the load effect on long-span bridges can be calculated based on the data collected by the WIM system. In this embodiment, the structural effect is calculated once per second for 423 consecutive days. The maximum response from the daily sample of 86,400 seconds is selected as a sample for this model. Figure 2 This shows an example of an extreme value scenario, with a total of 423 samples.

[0143] According to statistics, the average length of large vehicles is 15.13 m, and the peak total wheelbase (i.e., the distance from the first axle to the rear axle) of multi-axle vehicles is 17.5 m. Considering the influence of the front and rear suspensions and the distance between vehicles during travel, the length of each cell should be slightly longer than the wheelbase. Therefore, for the bridge in the case study, each lane is divided into 105 cells, with a cell length of 20 m. The influence lines of the load effect are obtained using the finite element method.

[0144] The Poisson parameters of the non-stationary distribution of the loaded vehicle position under extreme cable force scenarios are shown in Table 1. The Gaussian mixture distribution parameters of the vehicle weight under extreme scenarios are also shown in Table 2. The optimal number of components is determined to be 4 using the AIC method.

[0145] Table 1

[0146]

[0147] Table 2

[0148]

[0149] To obtain sufficient sample data to illustrate the extreme values ​​of the effect within a specific return period, the Monte Carlo method was employed. Based on 10... 5 The simulation generated the simulated extreme scenarios.

[0150] Based on a large number of extreme scenario samples, the probability of heavy vehicles appearing in extreme scenarios of the outer lane under different effects was compiled after averaging. Figure 7 As shown in Table 3, extreme scenario load models for each effect were then established, along with model information updated based on detection information for different flow rates and total weight distributions.

[0151] Table 3

[0152]

[0153] Table 3 presents the load model values ​​for the outer lanes, with the load profile shown as a schematic diagram. This implies that the shape of the load profile differs for different effects on the bridge under study, indicating a non-uniform distribution. The table shows that as the flow rate value of the detected information increases, the posterior model value also increases. This demonstrates that the invention can effectively update the model based on the detected traffic flow information while characterizing the spatial distribution of vehicle loads, and can establish targeted load models for different effects.

[0154] In summary, this technical solution models the spatial distribution of vehicle loads on the bridge deck of long-span bridges, specifically the extreme scenarios that lead to the maximum load effect. It also implements vehicle load modeling for specific stations with different effects and subsequent updates. The data foundation consists of: obtaining the extreme scenario characteristics of the corresponding effects based on WIM data or other traffic flow data at specific bridge sites and the influence line information of specific effects on the bridge structure, and performing Monte Carlo simulations. This simulation data serves as the data basis for constructing the specific effect load model; and collecting WIM information at subsequent bridge sites and obtaining the corresponding extreme scenarios as posterior data required for updates.

[0155] The basic assumptions are: 1) The simulation objects are heavy vehicles with a total weight of more than 10 tons; 2) Based on the statistical information of the length of heavy vehicles, the bridge deck is divided into cells of a specific length, and it is reasonably assumed that the center of gravity of the simulated heavy vehicles is located in the center of the cell.

[0156] In heavy vehicle modeling: Monte Carlo simulations were performed based on the prior extreme scenario distribution. The expanded extreme scenarios were used to construct a specific-effect load model under empirical conditions. This model considered the heavy vehicle distribution in a large number of extreme scenarios, and the load value of each bridge deck cell represented the average level of heavy vehicle occupation in that cell. A good visual model of the bridge deck load distribution for specific effects of extreme vehicle loads was constructed.

[0157] When updating the heavy vehicle model: obtain the posterior extreme value scenario distribution sample, and update the heavy vehicle extreme value scenario model based on the application method of particle filtering in two-dimensional random fields, so that the model can adjust the load level according to the evolution of traffic flow.

[0158] This technical solution considers the continuous evolution of traffic conditions during the service life of bridge structures. To accurately estimate traffic loads, it is essential to periodically assess and correct loads after changes in traffic conditions. This consideration is taken into account when developing the traffic load model. Therefore, this technical solution proposes a spatial distribution model of traffic loads at specific stations applicable to changes in traffic conditions and its updating scheme. It models extreme vehicle load scenarios of the bridge structure and updates the model based on changes in traffic conditions. Specifically, based on the constructed extreme vehicle load scenario model, the model is updated using posterior observation data. Furthermore, a particle filter is applied to spatial observation data collected at discrete locations in the scenario model to update the relevant random variables of the extreme scenarios. This technical solution can accurately estimate the traffic load response of bridges under changing traffic conditions and demonstrates superior performance in describing the complex spatial distribution update problem of traffic load modeling.

Claims

1. A method for evaluating the extreme value effect of bridge components under varying traffic conditions, characterized in that, Includes the following steps: S1. Based on traffic flow and vehicle data at a specific location and the influence line of specific effects of the bridge structure, obtain the extreme value scenario characteristics of the specific effects, and simulate the extreme value scenario of vehicle load for specific effects at a specific location using the Monte Carlo method. S2. Based on the extreme value scenario of vehicle load at a specific location and with specific effects in step S1, construct a specific effect load model under empirical conditions. S3. Obtain the posterior extreme value scenario distribution sample, and based on the application of particle filtering in spatial random fields, update the specific effect load model under the empirical state so that the updated model can adjust the load level according to the vehicle evolution. S4. Based on the updated model, determine the evaluation results of the extreme value effect of bridge components; The specific process of step S3 is as follows: Assume the extreme value scenario load model is a spatial random variable that varies with time, i.e., assume: It is a set of random fields, in which, It is a random variable in extreme value scenario samples. n It is the total number of Monte Carlo simulations of extreme scenarios. X It is a time-varying spatial stochastic process used to describe the distribution of vehicle loads on the bridge surface under extreme conditions; Extreme value scenario prediction uses a function Represented as: in, The system error generated during the prediction process is represented by t, which is the time state. Considering that traffic flow and composition are constant over a certain period of time, we assume... X It is stable, that is... The linear relationship is then represented, and a particle filtering method is used to update the spatial load model for extreme scenarios using the newly acquired data. That is, according to the state-space model method, given a potential state In the case of, assuming the observed values Conditionally independent of each other, The dimension is u , representing the number of observations on the bridge surface used for updating. The dimension is × = n ,in and These represent the number of units in the horizontal and vertical directions, respectively. Space observation data and The interrelationships are represented as follows: in, It is a function matrix, providing a size of u × n Measurement location information, It is observation error. The dimension is also u ; Using space observation data Get Random Field The optimal estimate will be the conditional probability. The basic update formula is discretized as follows: in Sampling is performed with equal probability; if the total number of samples is... α ,but for: It is the conditional probability density function, which is the observed value. The weights are: in, Based on Each The weights, due to the equation and It is a vector, therefore It is based on observation error It is calculated from the multivariate Gaussian probability density function; Therefore, based on the observed spatial data Each can be calculated based on the above equations. The weight ratio is then used to obtain an updated random field through a resampling process based on the weight ratio. This means completing the model update process.

2. The method for evaluating the extreme value effect of bridge components under traffic condition changes according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11. Collect WIM data from specific locations, perform data cleaning operations, and compile corresponding traffic flow and vehicle data information, including but not limited to vehicle total weight, vehicle length, vehicle speed, and vehicle arrival time. S12. Construct a finite element model of the bridge structure and obtain the influence lines of the specific effects to be evaluated; S13. Based on the total weight and length of the vehicles, filter out the length information of heavy vehicles and determine the length of the bridge deck cell accordingly. S14. Based on the influence line of the specific effect of the bridge structure, load the traffic flow data onto the influence line of the specific effect according to the set time step to obtain extreme value scene samples. S15. Based on extreme value scenario samples, calculate the Poisson parameters of the distribution location of heavy vehicles in each lane and the Gaussian mixture distribution parameters of the total weight of heavy vehicles in each lane. S16. Based on the data obtained in step S15, simulate the position of heavy vehicles based on non-stationary Poisson distribution and simulate the total weight of heavy vehicles based on Nataf transformation to obtain the extreme scenario of load simulation under the current specific effect. S17. Repeat steps S12 to S16 to obtain extreme load simulation scenarios under different specific effects at specific locations, so as to simulate the complex spatial distribution of heavy vehicles on the bridge surface.

3. The method for evaluating the extreme value effect of bridge components under traffic condition changes according to claim 2, characterized in that, In step S13, heavy vehicles specifically refer to vehicles with a total weight of 10 tons or more. In step S13, the length of the bridge deck cell is greater than the average length of heavy vehicles, and the difference between the two is within a set threshold range.

4. The method for evaluating the extreme value effect of bridge components under traffic condition changes according to claim 2, characterized in that, Step S14 specifically includes the following steps: S141. Restore the WIM data to the traffic flow sequence with a set bridge length, then load it onto the influence line of a specific effect, and calculate multiple structural effect values ​​in sequence according to the set time step, which are the obtained samples. S142. Select the group of samples with the largest effect value from the multiple groups of samples each day, and use it as the extreme value scenario sample.

5. The method for evaluating the extreme value effect of bridge components under traffic condition changes according to claim 4, characterized in that, Step S15 specifically includes the following steps: S151. Based on extreme value scenario samples, extract Poisson distribution parameters from the statistical information of the number of heavy vehicles in each lane: Where Pr(·) is the probability of the event occurring. Let be the average probability of a cell being occupied by heavy vehicles. For non-stationary events, Change along the lane; S152. Based on extreme value scenario samples, extract Gaussian mixture distribution parameters from the total weight statistics of heavy vehicles in each lane: 0≤ ≤1 in, For and The first and second terms of the mean and covariance matrices k A Gaussian distributed PDF, For the first k The weights of the Gaussian distribution components.

6. The method for evaluating the extreme value effect of bridge components under traffic condition changes according to claim 5, characterized in that, Step S16 specifically includes the following steps: S161. A longitudinal non-stationary Poisson distribution method is adopted, and the Poisson distribution parameters are used to simulate the bridge deck position of heavy vehicles under extreme scenarios. S162. Based on the Gaussian mixture distribution of the total weight of heavy vehicles, the correlation of the total weight of heavy vehicles along the lane direction is simulated through Nataf transformation.

7. The method for evaluating the extreme value effect of bridge components under traffic condition changes according to claim 1, characterized in that, The specific process of step S2 is as follows: Based on the extreme value scenario of vehicle load at a specific location and specific effect in step S1, the load intensity is first obtained by inversion according to the extreme value of the response of the specific effect and the load form. Then, a distributed line load with variable intensity is used for modeling to construct a specific effect load model under empirical conditions.

8. The method for evaluating the extreme value effect of bridge components under traffic condition changes according to claim 7, characterized in that, Step S3 specifically involves updating the load form and load intensity in the specific effect load model under empirical conditions.

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