A bridge dynamic weighing algorithm based on bayesian maximum posterior probability

Abstract

The application relates to the technical field of highway bridge safety monitoring, in particular to a bridge dynamic weighing algorithm based on a Bayesian maximum posterior probability. i An influence line is obtained through a bridge calibration test, an influence line matrix, a mean value and a covariance are calculated, a vehicle axle load is obtained through a Moses algorithm, the axle load is taken as the axle load of a first main loop i =0; an initial axle load distribution is set, a covariance of a load response is obtained from the influence line covariance, measurement noise and the axle load of the main loop, and the axle load response, the influence line matrix, the initial axle load distribution and the load response are iterated to obtain a stable value of an axle load mean vector and covariance, which is taken as the axle load distribution of the main loop; the axle load distribution, the influence line matrix, the load response and the covariance thereof are used to obtain a posterior probability of the axle load, and the axle load corresponding to a maximum value of the probability is taken as the axle load corresponding to a second main loop; the process is repeated until an axle load updating difference value is less than a preset value, and an axle load result is output, so that the problem of low axle load recognition precision of an existing bridge dynamic weighing system is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of highway bridge safety monitoring, and particularly relates to a bridge dynamic weighing algorithm based on a Bayesian maximum posterior probability. BACKGROUND

[0002] A bridge dynamic weighing system (Bridge Weigh-in-Motion, BWIM) is an intelligent monitoring system for realizing vehicle dynamic weighing based on a bridge structure, and has become one of important law enforcement means for real-time monitoring of overloaded vehicles by a traffic management department. The system realizes real-time collection of bridge dynamic response data under the condition of not affecting normal traffic operation through a sensor array installed on the bridge, and inversely calculates key parameters such as vehicle driving speed, wheelbase and axle load by using an algorithm.

[0003] At present, most of the commercially available bridge dynamic weighing systems are developed based on the Moses algorithm. The algorithm minimizes the sum of squares of differences between test values and theoretical values of load responses of a vehicle to a bridge based on the influence line at the bridge midspan (least square method), establishes an error function, and respectively calculates partial derivatives of each axle load to solve the axle weight. When the error function is established, the Moses algorithm assumes that the bridge influence line is a fixed value, and does not consider the coupling dynamic effect of the vehicle and the bridge. The bridge response error calculated by the Moses algorithm is a variable independent of each other, and the standard deviation of the bridge response at each time is the same, and the axle weight at each time is also constant. In fact, the dynamic response error of the bridge caused by the vehicle mainly includes the fluctuation part of the coupling dynamic effect of the vehicle and the bridge and the interference caused by the measurement noise, so the influence line used in the identification of the vehicle axle load needs to consider the coupling dynamic effect of the vehicle and the bridge. In addition, due to the influence of factors such as road roughness and vehicle-bridge coupling, the force of each axle acting on the bridge fluctuates around the static value during the driving of the vehicle, that is, the axle load also includes a dynamic effect, and the axle loads are subject to different numerical distributions and have correlation between each other. In summary, due to the interference of the measurement noise, the dynamic effect of the bridge influence line and the vehicle axle load, the load response of the bridge under the action of the vehicle is subject to different numerical distributions at each time, and there is correlation between the numerical values. The numerical distribution of the load response is related to factors such as the bridge influence line, the measurement noise and the vehicle axle load. For these reasons, the Moses algorithm has low accuracy in the process of axle load identification.

[0004] Although researchers in various countries have made corrections to the Moses algorithm, the axle load identification accuracy of the bridge dynamic weighing system can be improved to a certain extent, however, most of the methods are still the basic least square method, and the influence of the coupling dynamic effect of the vehicle and the bridge and the fluctuation of the axle force on the axle load identification is not considered. The results show that the applicability of these corrected methods is not strong, and the vehicle axle load accuracy is not significantly improved.

[0005] Therefore, how to more efficiently improve the axle load identification accuracy of the bridge dynamic weighing system has become a technical problem that needs to be solved by those skilled in the art. SUMMARY

[0006] The application provides a bridge dynamic weighing algorithm based on Bayesian maximum posterior probability to solve the problem that the existing bridge dynamic weighing system algorithm cannot effectively and accurately measure the axle load.

[0007] To achieve the above-mentioned purpose, the application realizes the technical scheme as follows:

[0008] The application provides a bridge dynamic weighing algorithm based on Bayesian maximum posterior probability, comprising the following steps:

[0009] Step 1: calibrate the influence line of the bridge, then measure the noise and load response, calculate the influence line mean vector and influence line mean square deviation matrix, obtain the vehicle speed and axle spacing, calculate the influence line matrix based on the vehicle speed, axle spacing and influence line mean vector, and calculate the axle load by the Moses algorithm according to the influence line matrix and load response, which is the initial main loop axle load value.

[0010] The method for obtaining the vehicle speed and axle spacing comprises collecting the vehicle-bridge dynamic signals generated when the vehicle to be detected passes through the front and rear sensors, calculating the time difference between the peak values of the two groups of vehicle-bridge dynamic signals and the spacing of the sensors, and calculating the speed and axle spacing of the vehicle to be detected based on the time difference and the spacing.

[0011] The axle load is obtained by the Moses algorithm, which is the initial main loop i =0 axle load.

[0012] The axle load is calculated by the following formula:

[0013] A (i=0) =(I T I) T I T R * ;

[0014] Wherein: A (i=0) represents the initial main loop i =0 axle load, I represents the bridge influence line matrix, I T represents the transpose of the bridge influence line matrix, and R * represents the load response generated by the vehicle during driving on the bridge.

[0015] Step 2: Obtain the axle load mean vector and the axle load covariance matrix, and then obtain the measurement noise standard deviation to combine the influence line covariance matrix and the axle load mean vector to calculate the covariance matrix of the load response, update the axle load covariance matrix based on the covariance matrix of the load response, and update the axle load mean vector based on the updated axle load covariance matrix;

[0016] Step 3: Repeat the sub-loop of step 2 to iteratively update the axle load mean vector and the axle load covariance matrix until the difference between the current updated axle load mean vector and the last updated axle load mean vector is less than a preset value, and the axle load mean vector and the axle load covariance matrix corresponding to the current main loop are taken as the axle load mean vector and the axle load covariance matrix of the current main loop;

[0017] Step 4: Calculate the prior probability of the axle load based on the axle load, the updated axle load mean vector and the updated axle load covariance matrix, calculate the likelihood probability of the load response based on the influence line matrix, the axle load, the load response and the updated covariance matrix of the load response, and obtain the posterior probability of the axle load based on the prior probability of the axle load and the likelihood probability of the load response, and take the axle load corresponding to the maximum axle load posterior probability as the updated axle load;

[0018] Step 5: Repeat the main loop of steps 2 to 4 to iteratively update the axle load until the difference between the current updated axle load and the last obtained axle load is less than a preset value, and take the current updated axle load as the final result of the bridge dynamic weighing algorithm.

[0019] Through the above design, not only the influence of measurement noise, axle load and influence line distribution on load response is considered, but also the influence of dynamic effect of influence line and axle load is considered. At the same time, the related content of Bayesian algorithm is introduced into bridge dynamic weighing, the posterior probability of axle load is obtained based on the prior probability of axle load and the likelihood probability of load response, in the algorithm, the axle load with the maximum posterior probability is taken as the final identification result, which has the advantage of providing the most credible estimation solution under the current information based on the consideration of the likelihood estimation of observation data and prior knowledge. Compared with the traditional least square method, the algorithm has stronger stability under noise interference, and has higher efficiency in calculation, and is suitable for engineering implementation of real-time dynamic weighing system.

[0020] Further, the influence line covariance matrix is calculated according to the correlation between the influence line values at two sampling points;

[0021] The elements in the influence line covariance matrix are calculated by the following formula:

[0022] ;

[0023] Wherein, represents the bridge influence line at the first x sampling point and the first yCovariance between sampling points; K To determine the number of influence lines obtained in the calibration experiment; For the first k The influence line is at the 1st x The values ​​at each sampling point; For the first k The influence line is at the 1st y The values ​​at each sampling point; This indicates the influence line mean at the th x The values ​​at each sampling point.

[0024] Furthermore, obtaining the axle load mean vector and axle load covariance matrix includes: the axle load mean vector and axle load covariance matrix obtained in the first main loop and the... i +1 main loop to obtain the axle weight mean vector and axle weight covariance matrix;

[0025] The axle load mean vector obtained in the first main loop is the axle load value calculated by the Moses algorithm in step 1. The axle load covariance matrix obtained in the first loop is based on preset conditions, including that the standard deviation of the axle load of each axle is 1kN and the correlation coefficient is 0.

[0026] The first i +1 main loop to obtain the axle weight mean vector and axle weight covariance matrix based on the data saved in the previous main loop.

[0027] Furthermore, in step 2, the elements of the covariance matrix of the load response are calculated using the following formula:

[0028] ;

[0029] in, Indicates the load response at the 1st The sampling point and the first Covariance between sampling points; Indicates the total number of axles; Indicates the first n The average axle load of each axle; Indicates the first n The influence line corresponding to each axle is at the [number]th [location]. g The sampling point and the first j Covariance between sampling points; C n Indicates the first n The number of samples corresponding to the distance between each axle and the first axle; Indicates the standard deviation of measurement noise;

[0030] C n Calculated using the following formula:

[0031] ;

[0032] in, D n Indicates the first n The distance between each axle and the first axle; f The sampling frequency; v For vehicle speed.

[0033] Furthermore, in step 2, updating the axle load covariance matrix based on the load response covariance matrix includes: obtaining the updated axle load covariance matrix based on the load response covariance matrix, the influence line matrix, and the axle load covariance matrix.

[0034] The axle load covariance matrix is ​​calculated using the following formula:

[0035] ;

[0036] in, and They represent the first h +1 sub-loop iterations and the... h The axis weight covariance matrix of the secondary loop iteration; Indicates the influence line matrix; T indicates the transpose operation; Let be the covariance matrix of the load response.

[0037] Furthermore, in step 2, updating the axle load mean vector based on the updated axle load covariance matrix includes: obtaining the updated axle load mean vector based on the updated axle load covariance matrix, influence line matrix, load response covariance matrix, load response, and axle load mean vector.

[0038] The axle load mean vector is calculated using the following formula:

[0039] ;

[0040] in, For load response; and They represent the first h +1 sub-loop iterations and the... h The average vector of axis weights in the second iteration of the sub-loop; and They represent the first h +1 sub-loop iterations and the... h The axis weight covariance matrix of the secondary loop iteration; Represents the influence line matrix; Let be the covariance matrix of the load response.

[0041] Furthermore, in step 4, the posterior probability estimate of the axle load is calculated using the following formula:

[0042] ;

[0043] in, This represents the posterior probability of axle load. This represents the prior probability of axle load; This represents the likelihood probability of the load response; Represents the axis weight vector; Indicates the influence line matrix; T indicates the transpose operation; Represents the load response vector; Represents the axle weight covariance matrix; The vector representing the mean of the axle load; This represents the covariance matrix of the load response.

[0044] Furthermore, the prior probability of the axle load is calculated using the following formula:

[0045] ;

[0046] in, Represents the axis weight vector;

[0047] The likelihood probability of the load response is calculated using the following formula:

[0048] ;

[0049] in, Z This represents the total number of samples taken for the load response.

[0050] Furthermore, in step 4, the axle load corresponding to the maximum posterior probability is calculated using the following formula:

[0051] ;

[0052] Among them, A (i+1) Indicates the first i +1 main loop corresponding to the axis weight; Represents the axle weight covariance matrix; Indicates the influence line matrix; T indicates the transpose operation; The covariance matrix represents the load response; The covariance matrix represents the load response; Represents the axle load mean vector; This represents the load response vector.

[0053] Furthermore, the condition that the difference between the axle load updated in this update and the previously obtained axle load is less than a preset value is expressed by the following formula:

[0054] ;

[0055] in, Indicates the first i +1 main loop corresponding to the axis weight; Indicates the first i The axis weight corresponding to the secondary main cycle; This indicates the preset value.

[0056] Beneficial effects:

[0057] This invention provides a dynamic bridge weighing algorithm based on Bayesian maximum a posteriori probability. It assumes that the vehicle's load response to the bridge follows different numerical distributions at different times, and that different measuring points are correlated. Considering the influence of influence lines, the dynamic effects of axle load, and measurement noise, the posterior probability of the vehicle axle load is obtained through the prior probability of the axle load and the likelihood probability of the load response. These factors are then correlated to derive a vehicle axle load identification formula based on Bayesian maximum a posteriori probability. This method considers the impact of vehicle-bridge coupled dynamic effects on axle load identification, which can reduce calculation errors caused by influence lines, the dynamic effects of axle load, and measurement noise to a certain extent, effectively improving the accuracy of vehicle axle load identification.

[0058] This invention introduces Bayesian algorithm theory and methods, and fully considers the influence of factors such as influence lines, the dynamic effects of axle load, and measurement noise during axle load identification. Measurement noise is an unavoidable factor in actual measurement, interfering with axle load identification results. Considering the dynamic effects of influence lines and axle load is crucial for accurately fitting the vehicle's dynamic load response to the bridge and for accurately obtaining axle load information. To handle these complex factors more precisely, this invention introduces the Bayesian maximum a posteriori probability method, linking these factors through the posterior probability of vehicle axle load to establish a vehicle axle load identification formula. Compared to the traditional Moses algorithm, the Bayesian maximum a posteriori probability method used in this invention has significant advantages, considering the impact of measurement noise, influence lines, and the dynamic effects of axle load on axle load identification, effectively improving the accuracy and robustness of axle load identification. Attached Figure Description

[0059] Figure 1 This is a flowchart of a bridge dynamic weighing algorithm based on Bayesian maximum posterior probability, according to a preferred embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram of the bridge deck elevation of Embodiment 2 of the present invention, where a represents the FAD sensor for measuring the vehicle-axle dynamic signal, the left side represents FAD1, the right side represents FAD2, and b represents the weighing sensor;

[0061] Figure 3This is a schematic diagram of the bridge cross section of Embodiment 2 of the present invention, where a represents the FAD sensor for measuring the vehicle axle dynamic signal and b represents the weighing sensor;

[0062] Figure 4 This is a schematic diagram of the mean value of the bridge influence line in Embodiment 2 of the present invention;

[0063] Figure 5 This is a schematic diagram of the covariance of the bridge influence line in Embodiment 2 of the present invention;

[0064] Figure 6 This is a schematic diagram of the covariance correlation coefficient of the bridge influence line in Embodiment 2 of the present invention;

[0065] Figure 7 This is a schematic diagram of the axle load mean iteration in Embodiment 2 of the present invention;

[0066] Figure 8 This is a schematic diagram of the bridge dynamic response values ​​in Embodiment 2 of the present invention. Detailed Implementation

[0067] The technical solution of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms "an" or "a" and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms "connected" or "linked" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up," "down," "left," "right," etc., are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship also changes accordingly.

[0069] Example 1

[0070] Please see Figure 1 This application provides a bridge dynamic weighing algorithm based on Bayesian maximum posterior probability, including the following steps:

[0071] Step 1: Obtain the influence line of the bridge through calibration tests, and then measure the noise and load response. Calculate the mean vector of the influence lines. With influence line mean square matrix The system obtains vehicle speed and axle spacing, calculates influence line matrix based on vehicle speed, axle spacing and influence line mean vector, and calculates axle load using Moses algorithm based on influence line matrix and load response, which is used as the axle load value for the initial main loop.

[0072] Specifically, through calibration tests, the load response R of a vehicle crossing the bridge is obtained using a weighing sensor installed at the mid-span of the bottom of the main beam. * The influence line at the mid-span of the bridge was selected as the influence line for vehicle axle load identification. Multiple calibration tests were conducted, and a set of influence lines was obtained from each calibration test. Mathematical statistics were performed to obtain the mean vector of the influence lines. Covariance Matrix While performing the above steps, FAD sensors 1 and 2, located on either side of the weighing sensor at the bottom of the main beam of the bridge, are used to acquire the vehicle-bridge dynamic signal when the vehicle crosses the bridge. The speed of the vehicle crossing the bridge is calculated by using the time between the peak values ​​of the vehicle-bridge dynamic signal and the distance between the two FAD sensors. v and axle spacing D ;

[0073] Regarding the influence line covariance matrix, it is calculated based on the correlation between the influence line values ​​at pairwise sampling points. The elements in the influence line covariance matrix are calculated using the following formula:

[0074] ;

[0075] in, Indicates the bridge's influence line at the 1st x The sampling point and the first y Covariance between sampling points; K To determine the number of influence lines obtained in the calibration experiment; For the first k The influence line is at the 1st x The values ​​at each sampling point; For the first k The influence line is at the 1st y The values ​​at each sampling point; This indicates the influence line mean at the th x The values ​​at each sampling point.

[0076] The influence line covariance matrix is ​​represented as follows:

[0077] ;

[0078] in, t The number of sampling points for the influence line is calculated using the following formula:

[0079] ;

[0080] In the formula, L For the bridge length, f Sampling frequency, v For vehicle speed.

[0081] At the end of step 1, the axle load is obtained based on the influence line matrix and the load response combined with the Moses algorithm;

[0082] ;

[0083] In the formula, This indicates the axle load obtained based on the Moses algorithm. This represents the transpose of the bridge influence line matrix I. This indicates the load response.

[0084] Step 2: Obtain the axle load mean vector And axis weight covariance matrix Then obtain the standard deviation of the measurement noise. Combining the influence line covariance matrix The covariance matrix of the load response is calculated using the axle load mean vector. Based on the covariance matrix of load response The covariance matrix of the axis The update is performed based on the updated axle weight covariance matrix. For the axle weight mean vector Update;

[0085] For the first obtained axle load mean vector And axis weight covariance matrix , where the axle weight mean vector Set as the axle load value calculated by the Moses algorithm, axle load covariance matrix Based on a preset standard deviation of 1 kN for the axle load of each axle and a correlation coefficient of 0, the axle load covariance matrix was calculated, and the measurement noise standard deviation was used to determine the axle load covariance matrix. All of these are existing technologies and will not be elaborated here. The subsequent calculations of the axle load mean vector and axle load covariance matrix are based on the data saved from the previous main loop iteration.

[0086] Covariance matrix of load response The elements are calculated using the following formula:

[0087] ;

[0088] in, Indicates the load response at the 1st The sampling point and the first Covariance between sampling points; Indicates the total number of axles; Indicates the first n The average axle load of each axle; Indicates the first n The influence line corresponding to each axle is at the [number]th [location]. g The sampling point and the first j Covariance between sampling points; C n Indicates the first n The number of samples corresponding to the distance between each axle and the first axle; Indicates the standard deviation of measurement noise;

[0089] C n Calculated using the following formula:

[0090] ;

[0091] in, D n Indicates the first n The distance between each axle and the first axle; f The sampling frequency; v For vehicle speed;

[0092] Based on the covariance matrix of the load response Influence line matrix I and axis weight covariance matrix Update axis weight covariance matrix Based on the updated axle weight covariance matrix Influence line matrix I, covariance matrix of load response Load response and the axle load mean vector Update the axle load mean vector ;

[0093] Updated axle weight covariance matrix Calculated using the following formula:

[0094] ;

[0095] in, and They represent the first h +1 iterations and the h The axis weight covariance matrix of the next iteration; Indicates the influence line matrix; T indicates the transpose operation; Let be the covariance matrix of the load response.

[0096] Updated axle load mean vector Calculated using the following formula:

[0097] ;

[0098] in, This is the load response matrix; and They represent the first h +1 iterations and the h The mean vector of axis weights for each iteration.

[0099] Step 3: Repeat the sub-loop of Step 2 to iteratively update the axle weight mean vector and axle weight covariance matrix until the difference between the updated axle weight mean vector and the previously updated axle weight mean vector is less than a preset value, and use it as the axle weight mean vector and axle weight covariance matrix corresponding to the current main loop.

[0100] Specifically, this can be expressed by the following formula:

[0101] ;

[0102] in, This represents the average axis weight vector updated in this sub-loop; This represents the average axis weight vector updated in the previous sub-loop; This indicates the preset value.

[0103] Step 4: Based on axle load A and the updated axle load mean vector and the updated axle weight covariance matrix Calculate the prior probability of axle load based on the influence line matrix I, axle load A, and load response. and the covariance matrix of the updated load response Calculate the likelihood probability of the load response, obtain the posterior probability of the axle load based on the prior probability of the axle load and the likelihood probability of the load response, and take the axle load corresponding to the maximum posterior probability of the axle load as the updated axle load.

[0104] The prior probability of axle load is calculated using the following formula:

[0105] ;

[0106] in, Represents the axis weight vector;

[0107] The likelihood probability of the load response is calculated using the following formula:

[0108] ;

[0109] in, Z This represents the total number of samples taken for the load response.

[0110] The posterior probability estimate of axle load is calculated using the following formula:

[0111] ;

[0112] in, This represents the posterior probability of axle load. This represents the prior probability of axle load; This represents the likelihood probability of the load response; Represents the axle weight covariance matrix; This represents the mean vector of axle loads.

[0113] The axle load corresponding to the maximum posterior probability of axle load is calculated using the following formula:

[0114] ;

[0115] Among them, A (i+1) Indicates the first i +1 main loop corresponding to the axis weight; Represents the axle weight covariance matrix; Represents the influence line matrix; The covariance matrix represents the load response; Represents the axle load mean vector; This represents the load response vector.

[0116] Step 5: Repeat the main loop from Step 2 to Step 4 to iteratively update the axle load until the difference between the updated axle load and the previously obtained axle load is less than a preset value, and take the updated axle load as the final result of the bridge dynamic weighing algorithm.

[0117] The difference between the axle load in this update and the previously obtained axle load will be less than a preset value, as expressed by the following formula:

[0118] ;

[0119] in, This indicates the axis weight updated in this main loop; This indicates the preset value.

[0120] Example 2

[0121] Take a simply supported beam bridge in China as an example. This bridge is a simply supported beam bridge composed of ten precast beams, with a main span of 40m, a bridge width of 24m, and four lanes in both directions. Figure 2 and Figure 3 As shown.

[0122] The axle load of vehicles crossing the bridge is identified through the following steps:

[0123] (1) A calibration test was conducted on the bridge to obtain the distribution of the influence lines. Since the distribution of the influence lines is known, it can be used for subsequent calculations. The mean curve of the influence lines is shown in [reference needed]. Figure 4The variance and correlation coefficient of the influence line are shown in the figure below. Figure 5 and Figure 6 .

[0124] (2) A vehicle moving load test was conducted on the bridge to obtain the measured test data. A two-axle vehicle with a total weight of 28.5t was selected as the loading vehicle (7.4t for the front axle, 21.1t for the rear axle, and a wheelbase of 4.7m), and it repeatedly drove across lane three at a speed of 30km / h. The number of vehicle runs was 10. During the test, axle detection sensors were installed under the flange plates on both sides of the mid-span section of the bridge. Figure 2 FAD1 and FAD2 at point a Figure 6 (This represents the coefficient relationship between the sensor's sampling points) to obtain information such as the number of vehicle axles, axle spacing, and vehicle speed. Figure 2 As shown; dynamic weighing sensors are installed at the bottom of the beams at mid-span of the bridge to identify vehicle axle loads, such as... Figure 7 As shown. The obtained dynamic response values ​​of the bridge at the mid-span are as follows. Figure 8 As shown, the bridge dynamic response value at the mid-span of the bridge is the signal from ten weighing sensors. Figure 3 The sum of the load cells at point b.

[0125] (3) Axle load identification is performed on the axle dynamic response signal using the new algorithm and the Moses algorithm. The initial axle load is then calculated. (The axle load obtained at this point is also used for comparison with the results obtained by the new algorithm); the initial axle load mean vector is set as follows: The initial axle load covariance matrix is ​​an identity matrix (the closer the initial axle load covariance matrix is ​​to the true axle load covariance, the faster the algorithm iteration speed). The load response covariance matrix is ​​obtained based on the influence line covariance matrix, the measurement noise variance, and the initial axle load mean vector. The bridge influence line used here is the measured bridge influence line, calculated based on the mean influence line and its covariance matrix using the influence line algorithm from 10 sets of vehicle-bridge dynamic responses of the same loaded vehicle. The axle load mean vector and axle load covariance matrix are updated based on the influence line matrix, the load response covariance matrix, the load response, the initial influence line mean vector, and the initial influence line covariance matrix. This process is repeated until the axle load mean converges. The new axle load is then calculated. Repeat the above process until the calculated axle load result converges. The calculation results are shown in Table 1.

[0126] It should be noted that before identifying axle load, the vehicle-axle dynamic response was filtered using a moving average filter to eliminate some noise and vehicle-axle coupling response. Considering the impact of vehicles on the bridge's dynamic response when entering and exiting the bridge, the lengths of both the vehicle's entry and exit sections were set to 10m.

[0127] Table 1: Vehicle axle load identification error for the two algorithms (unit: %)

[0128]

[0129] Note: Error = (Calculated value - Actual value) / Actual value × 100%.

[0130] As shown in Table 1, except for the total weight error, the mean and standard deviation of the axle weight error obtained by the new algorithm in this application are lower than those of the Moses algorithm. Taking the front axle as an example, the mean error of the new algorithm is 1.07%, which is less than the 2.06% of the Moses algorithm. Correspondingly, the standard deviation of the error decreased from 49.04% (Moses algorithm) to 1.90% (new algorithm). This demonstrates that the new algorithm in this application can significantly improve the accuracy of axle weight identification.

[0131] Obtaining more accurate vehicle axle loads through highway bridge monitoring can, on the one hand, assist highway bridge management departments in efficiently managing overloading and reducing the number of overloaded vehicles crossing bridges; on the other hand, vehicle information can provide a reliable basis for accurately assessing the reliability and lifespan of highway bridges, contributing to the establishment of an intelligent highway bridge management system and extending the service life of highway bridges.

[0132] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A dynamic weighing algorithm for bridges based on Bayesian maximum a posteriori probability, characterized in that, Includes the following steps: Step 1: Obtain the influence line of the bridge through calibration test, then measure the noise and collect the load response of vehicles crossing the bridge, calculate the mean vector and covariance matrix of the influence line, obtain the vehicle speed and axle spacing of the vehicles crossing the bridge, calculate the influence line matrix based on the vehicle speed, axle spacing and the mean vector of the influence line, and calculate the axle load using the Moses algorithm based on the influence line matrix and the load response, which is used as the axle load value of the initial main loop; Step 2: Obtain the axle load mean vector and axle load covariance matrix. Then, obtain the measurement noise standard deviation and calculate the load response covariance matrix by combining the influence line covariance matrix and the axle load mean vector. Update the axle load covariance matrix based on the load response covariance matrix, and update the axle load mean vector based on the updated axle load covariance matrix. The update of the axle load covariance matrix based on the load response covariance matrix includes: obtaining the updated axle load covariance matrix according to the load response covariance matrix, the influence line matrix, and the axle load covariance matrix; The axle load covariance matrix is ​​calculated using the following formula: ； in, and They represent the first h +1 sub-loop iterations and the... h The axis weight covariance matrix of the secondary loop iteration; Indicates the influence line matrix; T indicates the transpose operation; Let be the covariance matrix of the load response; The step of updating the axle load mean vector based on the updated axle load covariance matrix includes: obtaining the updated axle load mean vector based on the updated axle load covariance matrix, influence line matrix, load response covariance matrix, load response, and axle load mean vector. The axle load mean vector is calculated using the following formula: ； in, For load response; and They represent the first h +1 sub-loop iterations and the... h The average vector of axis weights in the second iteration of the sub-loop; and They represent the first h +1 sub-loop iterations and the... h The axis weight covariance matrix of the secondary loop iteration; Represents the influence line matrix; Let be the covariance matrix of the load response; Step 3: Repeat the sub-loop of Step 2 to iteratively update the axle weight mean vector and axle weight covariance matrix until the difference between the updated axle weight mean vector and the previously updated axle weight mean vector is less than a preset value, and use it as the axle weight mean vector and axle weight covariance matrix corresponding to the current main loop. Step 4: Calculate the prior probability of axle load based on axle load, updated axle load mean vector, and updated axle load covariance matrix. Calculate the likelihood probability of load response based on influence line matrix, axle load, load response, and updated load response covariance matrix. Obtain the posterior probability of axle load based on the prior probability and the likelihood probability of load response. Use the axle load with the maximum posterior probability as the updated axle load. The posterior probability of the axle load is calculated using the following formula: ； in, This represents the posterior probability of axle load. This represents the prior probability of axle load; This represents the likelihood probability of the load response; Represents the axis weight vector; Indicates the influence line matrix; T indicates the transpose operation; Represents the load response vector; Represents the axle weight covariance matrix; The vector representing the mean of the axle load; The covariance matrix represents the load response; The axle load corresponding to the maximum posterior probability of the axle load is calculated using the following formula: ； Among them, A (i+1) Indicates the first i +1 main loop corresponding to the axis weight; Represents the axle weight covariance matrix; Indicates the influence line matrix; T indicates the transpose operation; The covariance matrix represents the load response; Represents the axle load mean vector; Represents the load response vector; Step 5: Repeat the main loop from Step 2 to Step 4 to iteratively update the axle load until the difference between the updated axle load and the previously obtained axle load is less than a preset value, and take the updated axle load as the final result of the bridge dynamic weighing algorithm.

2. The bridge dynamic weighing algorithm based on Bayesian maximum a posteriori probability according to claim 1, characterized in that, The influence line covariance matrix is ​​calculated based on the correlation between the influence line values ​​at each pair of sampling points. The elements in the influence line covariance matrix are calculated using the following formula: ； in, Indicates the bridge's influence line at the 1st x The sampling point and the first y Covariance between sampling points; K To determine the number of influence lines obtained in the calibration experiment; For the first k The influence line is at the 1st x The values ​​at each sampling point; For the first k The influence line is at the 1st y The values ​​at each sampling point; This indicates the influence line mean at the th x The values ​​at each sampling point.

3. The bridge dynamic weighing algorithm based on Bayesian maximum a posteriori probability according to claim 1, characterized in that, The process of obtaining the axle load mean vector and axle load covariance matrix includes: the axle load mean vector and axle load covariance matrix obtained in the first main loop and the... i+ The axle weight mean vector and axle weight covariance matrix obtained in the first main loop; The axle load mean vector obtained in the first main loop is the axle load value calculated by the Moses algorithm in step 1. The axle load covariance matrix obtained in the first loop is based on preset conditions, including that the standard deviation of the axle load of each axle is 1kN and the correlation coefficient is 0. The first i +1 main loop to obtain the axle weight mean vector and axle weight covariance matrix based on the data saved in the previous main loop.

4. The bridge dynamic weighing algorithm based on Bayesian maximum a posteriori probability according to claim 1, characterized in that, In step 2, the elements of the covariance matrix of the load response are calculated using the following formula: ； in, Indicates the load response at the 1st The sampling point and the first Covariance between sampling points; Indicates the total number of axles; Indicates the first n The average axle load of each axle; Indicates the first n The influence line corresponding to each axle is at the [number]th [location]. g The sampling point and the first j Covariance between sampling points; C n Indicates the first n The number of samples corresponding to the distance between each axle and the first axle; Indicates the standard deviation of measurement noise; C n Calculated using the following formula: ； in, D n Indicates the first n The distance between each axle and the first axle; f The sampling frequency; v For vehicle speed.

5. The bridge dynamic weighing algorithm based on Bayesian maximum a posteriori probability according to claim 1, characterized in that, The prior probability of the axle load is calculated using the following formula: ； in, Represents the axis weight vector; The likelihood probability of the load response is calculated using the following formula: ； in, Z This represents the total number of samples taken for the load response.

6. The bridge dynamic weighing algorithm based on Bayesian maximum a posteriori probability according to claim 1, characterized in that, The difference between the axle load updated this time and the axle load obtained last time is less than a preset value, which is expressed by the following formula: ； in, Indicates the first i +1 main loop corresponding to the axis weight; Indicates the first i The axis weight corresponding to the secondary main cycle; This indicates the preset value.

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