Bridge dynamic weighing algorithm based on Bayesian maximum posterior probability

Abstract

The invention relates to the technical field of highway bridge safety monitoring, in particular to a bridge dynamic weighing algorithm based on Bayesian maximum posterior probability. Obtaining influence lines through a bridge calibration test, and calculating an influence line matrix, a mean value and a covariance; using a Moses algorithm to obtain the vehicle axle load as the axle load of the initial main cycle i = 0; initial axle load distribution is set, the covariance of load response is obtained through the influence line covariance, the measurement noise and the axle load of the main cycle, and an axle load mean vector and a stable value of the covariance are iterated together with the influence line matrix, the initial axle load distribution and the load response to serve as the axle load distribution of the main cycle; according to the axle load distribution, the influence line matrix, the load response and the covariance thereof, the posterior probability of the axle load is obtained, and the axle load when the probability is the maximum serves as the axle load corresponding to the (i + 1) th main cycle; and repeating until the axle load update difference value is smaller than the preset value, and outputting the axle load result, thereby solving the problem of low axle load identification precision of the existing bridge dynamic weighing system.

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 the difference between the test value and the theoretical value of the load response of the vehicle to the bridge based on the influence line at the bridge midspan (least square method), establishes an error function, and respectively calculates the partial derivative 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, without considering 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 correspondingly, 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 acting on the bridge by each axle of the vehicle fluctuates around the static value during the driving process, 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 precision of the Moses algorithm in the axle load identification process is low.

[0004] Although researchers in various countries have made corrections to the Moses algorithm, the axle load identification precision 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, without considering the influence of the coupling dynamic effect of the vehicle and the bridge and the fluctuation of the axle load on the axle load identification. The results show that the applicability of these corrected methods is not strong, and the vehicle axle load precision will not be 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 a 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: The application provides a bridge dynamic weighing algorithm based on a Bayesian maximum posterior probability, comprising the following steps: 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, as the initial main loop axle load value; 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.

[0008] The axle load is obtained by the Moses algorithm, as the initial main loop axle load i =0. The axle load is calculated by the following formula: A (i=0) =(I T I) T I T R * ; Wherein: A (i=0) represents the initial main loop axle load i =0, 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.

[0009] Step 2: obtain the axle load mean vector and axle load covariance matrix, then obtain the measurement noise standard deviation, combine the influence line covariance matrix and 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. Step 3: The mean vector of the axle load and the covariance matrix of the axle load are iteratively updated by repeating the sub-cycle of step 2 until the difference between the mean vector of the axle load of this update and the mean vector of the axle load of the last update is less than a preset value, and the mean vector of the axle load and the covariance matrix of the axle load corresponding to this main cycle are taken as the mean vector of the axle load and the covariance matrix of the axle load of the next main cycle; Step 4: The prior probability of the axle load is calculated according to the axle load, the updated mean vector of the axle load and the updated covariance matrix of the axle load, the likelihood probability of the load response is calculated according to the influence line matrix, the axle load, the load response and the covariance matrix of the updated load response, the posterior probability of the axle load is obtained according to the prior probability of the axle load and the likelihood probability of the load response, and the axle load corresponding to the maximum posterior probability of the axle load is taken as the updated axle load; Step 5: The axle load is iteratively updated by repeating the main cycle of steps 2 to 4 until the difference between the axle load of this update and the axle load obtained last time is less than a preset value, and the axle load of this update is taken as the final result of the bridge dynamic weighing algorithm.

[0010] 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 advantages that the most credible estimation solution under the current information can be provided on the basis of considering 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 calculation efficiency, and is suitable for engineering implementation of real-time dynamic weighing system.

[0011] Further, the influence line covariance matrix is calculated according to the correlation between the influence line values between two sampling points; The elements in the influence line covariance matrix are calculated by the following formula: ; Wherein, represents the covariance between the bridge influence line at the x th sampling point and the y th sampling point; K is the number of influence lines obtained in the calibration test; is the value of the k th influence line at the x th sampling point; is the value of the k th influence line at the y th sampling point; represents the value of the mean value of the influence line at the x th sampling point.

[0012] Furthermore, the acquisition of the axle weight mean vector and the axle weight covariance matrix includes: the axle weight mean vector and the axle weight covariance matrix acquired in the first main loop and the i +1 main loop to obtain the axle weight mean vector and axle weight covariance matrix; The axle weight mean vector obtained in the first main loop is the axle weight value calculated by the Moses algorithm in step 1. The axle weight covariance matrix obtained for the first time is obtained based on preset conditions, which include that the standard deviation of each axle weight is 1 kN and the correlation coefficient is 0. The said i +1 main loop obtains the axle weight mean vector and axle weight covariance matrix based on the data saved in the previous main loop.

[0013] Furthermore, 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 sampling points and The covariance between the sampling points; Indicates the total number of axles; Indicates the n The average axle weight of each axle; Indicates the n The influence line corresponding to the axle is in g The sampling point and j The covariance between the sampling points; C n Indicates the n The number of samples corresponding to the distance between the first axle and the second axle; represents the standard deviation of measurement noise; C n Calculated by the following formula: ; in, D n Indicates the n The distance between the first axle and the second axle; f is the sampling frequency; v is the vehicle speed.

[0014] Furthermore, in step 2, updating the axle load covariance matrix based on the covariance matrix of the load response includes: obtaining an updated axle load covariance matrix according to the covariance matrix of the load response, the influence line matrix, and the axle load covariance matrix; The axle load covariance matrix is ​​calculated by the following formula: ; in, and Respectively represent h +1 sub-loop iteration and h The axis-weight covariance matrix of the second sub-cycle iteration; represents the influence line matrix; T represents the transpose operation; is the covariance matrix of the load response.

[0015] Furthermore, in step 2, updating the axle load mean vector based on the updated axle load covariance matrix includes: obtaining an updated axle load mean vector based on the updated axle load covariance matrix, the influence line matrix, the covariance matrix of the load response, the load response, and the axle load mean vector; The axle weight mean vector is calculated by the following formula: ; in, is the load response; and Respectively represent h +1 sub-loop iteration and h The axis weight mean vector of the second sub-loop iteration; and Respectively represent h +1 sub-loop iteration and h The axis-weight covariance matrix of the second sub-cycle iteration; represents the influence line matrix; is the covariance matrix of the load response.

[0016] Furthermore, in step 4, the posterior estimated probability of the axle weight is calculated using the following formula: ; in, represents the posterior probability of axle weight; represents the prior probability of axle weight; represents the likelihood probability of the load response; represents the axis weight vector; represents the influence line matrix; T represents the transpose operation; represents the load response vector; represents the axle weight covariance matrix; represents the mean vector of axle weights; Represents the covariance matrix of the load response.

[0017] Furthermore, the a priori probability of the axle load is calculated by the following formula: ; wherein, denotes the axle load vector; The likelihood probability of the load response is calculated by the following formula: ; wherein, Z denotes the total number of samples of the load response.

[0018] Further, in step 4, the axle load corresponding to the maximum axle load posterior probability is calculated by the following formula: ; wherein, A (i+1) denotes the axle load corresponding to the i-th main cycle; i denotes the axle load corresponding to the i-th main cycle; denotes the axle load covariance matrix; denotes the influence line matrix; T denotes the transpose operation; denotes the covariance matrix of the load response; denotes the covariance matrix of the load response; denotes the axle load mean vector; denotes the load response vector.

[0019] Further, the difference between the axle load until the current update and the axle load obtained last time is less than a preset value, which is represented by the following formula: ; wherein, denotes the axle load corresponding to the i-th main cycle; i denotes the axle load corresponding to the i-th main cycle; denotes the axle load corresponding to the i-th main cycle; i denotes the axle load corresponding to the i-th main cycle; denotes the preset value.

[0020] Beneficial effects: The bridge dynamic weighing algorithm based on the Bayesian maximum posterior probability provided by the application considers that the load response of the vehicle to the bridge obeys different numerical distributions at different times, and has correlation between different measuring points, considers the dynamic effect of the influence line and the axle load and the influence of the measurement noise, obtains the posterior probability of the vehicle axle load through the prior probability of the vehicle axle load and the likelihood probability of the load response, associates these factors, and obtains the vehicle axle load identification formula based on the Bayesian maximum posterior probability. The method of the application considers the influence of the vehicle-bridge coupling dynamic effect on the axle load identification, can reduce the calculation error caused by the dynamic effect of the influence line and the axle load and the measurement noise and the like to a certain extent, and effectively improves the precision of the vehicle axle load identification.

[0021] The application introduces the related theory and method of Bayesian algorithm, and fully considers the influence of the influence line and the dynamic effect of the axle load and the influence of the measurement noise and other factors in the axle load identification process. The measurement noise is an inevitable factor in the actual measurement link, which will interfere with the axle load identification result; the dynamic effect of the influence line and the axle load is considered to more accurately fit the dynamic load response of the vehicle to the bridge, which is crucial for accurately obtaining the axle load information. In order to more accurately process these complex factors, the application introduces the method of Bayesian maximum posterior probability, and the factors are associated through the posterior probability of the vehicle axle load to establish the vehicle axle load identification formula. Compared with the traditional Moses algorithm, the Bayesian maximum posterior probability method used in the application has obvious advantages, considers the influence of the measurement noise, the dynamic effect of the influence line and the axle load on the axle load identification, and effectively improves the accuracy and robustness of the axle load identification. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 A flow chart of a bridge dynamic weighing algorithm based on Bayesian maximum posterior probability of a preferred embodiment of the application; Figure 2 A bridge elevation schematic diagram of embodiment 2 of the application, wherein a represents a FAD sensor for measuring the vehicle-bridge dynamic signal, the left side represents FAD1, and the right side represents FAD2, b represents a weighing sensor; Figure 3 A bridge cross-sectional schematic diagram of embodiment 2 of the application, wherein a represents a FAD sensor for measuring the vehicle-bridge dynamic signal, and b represents a weighing sensor; Figure 4 An influence line mean value schematic diagram of the bridge influence line of embodiment 2 of the application; Figure 5 A covariance schematic diagram of the bridge influence line of embodiment 2 of the application; Figure 6 A schematic diagram of the covariance correlation coefficient of the bridge influence line of embodiment 2 of the application; Figure 7 An axle load mean value iteration schematic diagram of embodiment 2 of the application; Figure 8 A bridge dynamic response value schematic diagram of embodiment 2 of the application. DETAILED DESCRIPTION

[0023] The technical solutions of the application will be described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the application, not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0024] Unless otherwise defined, technical terms or scientific terms used in the present application shall have the ordinary meanings to those skilled in the art to which the present application pertains. The terms "first", "second", and similar terms are used herein merely to distinguish one element from another, and are not intended to imply any order or sequence, or any importance. Similarly, the terms "one" or "a" or "an" are used herein to mean "at least one", and are not intended to limit the number of elements to a single element. The terms "connected" or "coupled" or similar terms are used herein to mean either a direct connection or an indirect connection, and are not limited to a direct physical or mechanical connection or a direct electrical connection. The terms "upper", "lower", "left", "right", and the like are used herein merely to indicate relative positions, and are not intended to limit the absolute positions of the described objects.

[0025] Embodiment 1 Please refer to Figure 1 The embodiment of the present application provides a bridge dynamic weighing algorithm based on Bayesian maximum posterior probability, comprising the following steps: Step 1: calibration test to obtain the influence line of the bridge, and then measure the noise and load response , calculate the influence line mean vector and the influence line mean square deviation matrix , obtain the vehicle speed and the axle spacing, calculate the influence line matrix based on the vehicle speed, the axle spacing and the influence line mean vector, and calculate the axle load by the Moses algorithm according to the influence line matrix and the load response, as the axle load value of the initial main loop; Specifically, through the calibration test, the load response R * of the vehicle passing through the bridge is obtained by using the weighing sensor arranged at the mid-span position of the main girder of the bridge, and the influence line at the mid-span position of the bridge is selected as the influence line used for vehicle axle load identification, a plurality of calibration tests are performed, a group of influence lines are obtained each time, mathematical statistics is performed, the influence line mean vector and the covariance matrix are obtained; at the same time of performing the above steps, the vehicle-bridge dynamic signals of the vehicle passing through the bridge are obtained by using the FAD sensor 1 and the FAD sensor 2 arranged at the front and back sides of the weighing sensor arranged at the bottom of the main girder of the bridge, the vehicle speed v and the axle spacing D of the vehicle passing through the bridge are calculated according to the time between the peaks of the vehicle-bridge dynamic signals and the spacing between the two FAD sensors. Regarding the influence line covariance matrix, the elements in the influence line covariance matrix are calculated according to the correlation between the influence line values at the two sampling points, and are calculated by the following formula: ; Wherein, represents the influence line of the bridge at the i th sampling point and the j th sampling point x . ycovariance between two sampling points; K the number of influence lines acquired in the calibration test; the value of the i-th influence line at the j-th sampling point; k the value of the i-th influence line at the j-th sampling point; x the value of the i-th influence line at the j-th sampling point; the value of the i-th influence line at the j-th sampling point; k the value of the i-th influence line at the j-th sampling point; y the value of the i-th influence line at the j-th sampling point. the value of the i-th influence line at the j-th sampling point. x

[0026] The influence line covariance matrix is represented as follows: ; wherein, t is the number of sampling points of the influence line, which is calculated by the following formula: ; wherein, L is the bridge length, f is the sampling frequency, v is the vehicle speed.

[0027] At the end of step 1, the axle load is acquired based on the influence line matrix and the load response combined with the Moses algorithm; ; wherein, represents the axle load acquired based on the Moses algorithm, represents the transpose of the bridge influence line matrix I, represents the load response.

[0028] Step 2: Acquire the axle load mean vector and the axle load covariance matrix , and acquire the measurement noise standard deviation Combine the influence line covariance matrix with 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 ; For the first acquired axle load mean vector and the axle load covariance matrix , wherein the axle load mean vector is set as the axle load value calculated by the Moses algorithm, and the axle load covariance matrix ​Based on the preset standard deviation of each axle load of 1 kN, the correlation coefficient is 0, the covariance matrix of the axle load is calculated and the measurement noise standard deviation Both are prior art, this place does not make superfluous, for subsequent execution calculation axle load mean vector and axle load covariance matrix are based on the data obtained by the last main loop iteration saved.

[0029] The elements of the covariance matrix of the load response are calculated by the following formula: ; Wherein, denotes the covariance of the load response between the th sampling point and the th sampling point; denotes the total number of axles; denotes the mean value of the axle load of the n th axle; denotes the covariance of the influence line corresponding to the n th axle between the g th sampling point and the j th sampling point; C n denotes the sampling number corresponding to the distance between the n th axle and the first axle; denotes the measurement noise standard deviation; C n It is calculated by the following formula: ; Wherein, D n denotes the distance between the n th axle and the first axle; f is the sampling frequency; v is the vehicle speed; According to the covariance matrix of the load response , the influence line matrix I and the axle load covariance matrix The axle load covariance matrix is updated, based on the updated axle load covariance matrix , the influence line matrix I, the covariance matrix of the load response , the load response and the axle load mean vector The axle load mean vector is updated and obtained; The updated axle load covariance matrix is calculated by the following formula: ; Wherein, and the axis weight covariance matrix of the (i+1)th iteration, respectively; and the axis weight covariance matrix of the (i+1)th iteration, respectively; h and the axis weight covariance matrix of the (i+1)th iteration, respectively; h and the axis weight covariance matrix of the (i+1)th iteration, respectively; denotes the influence line matrix; T denotes the transpose operation; is the covariance matrix of the load response.

[0030] the updated axis weight mean vector is calculated by the following formula: ; wherein, is the load response matrix; and the axis weight mean vector of the (i+1)th iteration, respectively; and the axis weight mean vector of the (i+1)th iteration, respectively; h and the axis weight mean vector of the (i+1)th iteration, respectively; h and the axis weight mean vector of the (i+1)th iteration, respectively.

[0031] Step 3: iteratively update the axis weight mean vector and the axis weight covariance matrix in the sub-loop of Step 2 until the difference between the axis weight mean vector of this update and the axis weight mean vector of the last update is less than a preset value, and the axis weight mean vector and the axis weight covariance matrix corresponding to this main loop are taken as the updated axis weight mean vector and the updated axis weight covariance matrix; is specifically represented by the following formula: ; wherein, denotes the axis weight mean vector updated in this sub-loop; denotes the axis weight mean vector updated in the last sub-loop; denotes a preset value.

[0032] Step 4: calculate the prior probability of the axis weight A according to the updated axis weight mean vector and the updated axis weight covariance matrix , calculate the likelihood probability of the load response according to the influence line matrix I, the axis weight A, the load response and the updated covariance matrix of the load response , and obtain the posterior probability of the axis weight according to the prior probability of the axis weight and the likelihood probability of the load response, and take the axis weight corresponding to the maximum axis weight posterior probability as the updated axis weight; The prior probability of the axis weight is calculated by the following formula: ; wherein, denotes the axis weight vector; The likelihood probability of the load response is calculated by the following formula: ; wherein, ZThe total number of samples representing the load response.

[0033] The posterior probability of the axle load is calculated by the following formula: ; Wherein, represents the posterior probability of the axle load; represents the prior probability of the axle load; represents the likelihood probability of the load response; represents the axle load covariance matrix; represents the mean vector of the axle load.

[0034] The axle load corresponding to the maximum posterior probability of the axle load is calculated by the following formula: ; Wherein, A (i+1) represents the axle load corresponding to the main loop of the i th time; represents the axle load covariance matrix; represents the influence line matrix; represents the covariance matrix of the load response; represents the mean vector of the axle load; represents the load response vector.

[0035] Step 5: Repeat the main loop of steps 2 to 4 to iteratively update the axle load until the difference between the updated axle load and the axle load obtained last time is less than a preset value, and the updated axle load is taken as the final result of the bridge dynamic weighing algorithm.

[0036] The difference between the updated axle load and the axle load obtained last time is less than a preset value, which is represented by the following formula: ; Wherein, represents the updated axle load of the main loop; represents the preset value.

[0037] Example 2 Taking a simply supported beam bridge in China as an example. The bridge is a simply supported beam bridge composed of ten precast beams, with a main span of 40 m, a bridge width of 24 m, and four lanes in both directions, as shown in Figure 2 and Figure 3 .

[0038] The axle load of the vehicle passing through the bridge is identified by the following steps: (1) Calibration test is carried out on the bridge to obtain the distribution of the influence line, i.e. the distribution of the influence line is known and can be used for subsequent calculation. The influence line mean curve is shown in Figure 4 , and the variance and correlation coefficient of the influence line are shown in Figure 5 and Figure 6 .

[0039] (2) Vehicle moving load test is conducted on the bridge to obtain the test measured data. A two-axle vehicle with a total weight of 28.5 t is selected as the loading vehicle (7.4 t for the front axle, 21.1 t for the rear axle, and 4.7 m for the axle spacing), which repeatedly travels at a speed of 30 km / h from lane three. The vehicle runs 10 times. In the test process, axle detection sensors are installed under the flange plates on both sides of the mid-span section of the bridge to obtain the information such as the number of vehicle axles, the axle spacing, and the vehicle speed, as shown in FIG. 2; dynamic weighing sensors are installed at the mid-span beam bottom of the bridge to identify the vehicle axle weight, as shown in FIG. 3. The obtained bridge dynamic response values at the mid-span position of the bridge are shown in FIG. 4, where the bridge dynamic response values at the mid-span position of the bridge are the sum of the signals of the ten weighing sensors (the weighing sensors in FIG. 2b). Figure 2 FAD1 and FAD2 at a in the middle, Figure 6 representing the coefficient relationship between the sampling points of the sensors) to obtain the information such as the number of vehicle axles, the axle spacing, and the vehicle speed, as shown in FIG. 2; dynamic weighing sensors are installed at the mid-span beam bottom of the bridge to identify the vehicle axle weight, as shown in FIG. 3. The obtained bridge dynamic response values at the mid-span position of the bridge are shown in FIG. 4, where the bridge dynamic response values at the mid-span position of the bridge are the sum of the signals of the ten weighing sensors (the weighing sensors in FIG. 2b). Figure 2 Figure 7 Figure 8 Figure 3

[0040] (3) The axle weight is identified by using the new algorithm and the Moses algorithm on the vehicle-bridge dynamic response signal. The initial axle weight (the axle weight obtained at this time is also used for comparison with the result obtained by the new algorithm); the initial axle weight mean vector is , and the initial axle weight covariance matrix is the unit matrix (the closer the initial axle weight covariance matrix is to the true axle weight covariance, the faster the iteration speed of the algorithm); the covariance matrix of the load response is obtained according to the influence line covariance matrix, the measurement noise variance, and the initial axle weight mean vector, where the bridge influence line used at this time is the measured influence line of the bridge, which is the mean influence line and the influence line covariance matrix calculated based on the influence line algorithm according to 10 groups of vehicle-bridge dynamic responses of the same loading vehicle; the axle weight mean vector and the axle weight covariance matrix are updated based on the influence line matrix, the covariance matrix of the load response, the load response, the initial influence line mean vector, and the initial influence line covariance matrix, and the above process is repeated until the axle weight mean converges; the new axle weight is calculated; the above process is repeatedly performed until the axle weight result converges. The calculation result is shown in Table 1.

[0041] It should be noted that before identifying the axle weight, the vehicle-bridge dynamic response is filtered by a moving average filter to eliminate a part of the noise and the vehicle-bridge coupling response. Considering that the vehicle has an impact on the dynamic response of the bridge when it is on the bridge and off the bridge, the lengths of the entry and exit sections of the vehicle on the bridge are both taken as 10 m.

[0042] Table 1: Vehicle axle weight identification error table of two algorithms (unit: %) ​​​​

[0043] Note: Error = (calculated value - true value) / true value x 100%.

[0044] As can be seen from Table 1, in addition to the total weight error mean being similar, the rest of the axle weight error mean and standard deviation obtained by the new algorithm are lower than the error of Moses algorithm. Taking the front axle as an example, the mean error of the new algorithm is 1.07%, which is less than 2.06% of Moses algorithm. Correspondingly, the error standard deviation is reduced from 49.04% (Moses algorithm) to 1.90% (new algorithm). This shows that the new algorithm can greatly improve the accuracy of axle weight identification.

[0045] In highway bridge monitoring, obtaining more accurate vehicle axle weight can help highway bridge management departments efficiently manage overload phenomenon and reduce the number of overloaded vehicles passing through the bridge. On the other hand, vehicle information can provide a reliable basis for accurate assessment of highway bridge reliability and life, help to establish an intelligent highway bridge management system, and prolong the service life of highway bridges.

[0046] The above describes the preferred embodiments of the present application in detail. It should be understood that those skilled in the art can make many modifications and changes without creative labor based on the concept of the present application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment based on the existing technology according to the concept of the present application shall be within the protection scope defined by the claims.

Claims

1. A bridge dynamic weighing algorithm based on Bayesian maximum a posteriori probability, characterized in that, The method comprises the following steps: Step 1: calibrating a test to obtain an influence line of a bridge, then measuring noise and collecting load response of the bridge caused by a vehicle passing through the bridge, calculating an influence line mean vector and an influence line covariance matrix, obtaining a vehicle speed and an axle spacing of the vehicle passing through the bridge, calculating an influence line matrix based on the vehicle speed, the axle spacing and the influence line mean vector, and calculating axle weights by a Moses algorithm according to the influence line matrix and the load response, as initial axle weight values of a main loop; Step 2: obtaining an axle weight mean vector and an axle weight covariance matrix, then obtaining a measurement noise standard deviation, combining the influence line covariance matrix and the axle weight mean vector to calculate a covariance matrix of the load response, updating the axle weight covariance matrix based on the covariance matrix of the load response, and updating the axle weight mean vector based on the updated axle weight covariance matrix; Step 3: iteratively updating the axle weight mean vector and the axle weight covariance matrix by repeating the sub-loop of Step 2 until a difference between the axle weight mean vector of this update and the axle weight mean vector of the last update is less than a preset value, and the axle weight mean vector and the axle weight covariance matrix corresponding to this main loop are taken as the axle weight mean vector and the axle weight covariance matrix of this main loop; Step 4: calculating an axle weight prior probability according to the axle weight, the updated axle weight mean vector and the updated axle weight covariance matrix, calculating a load response likelihood probability according to the influence line matrix, the axle weight, the covariance matrix of the load response and the updated load response, and obtaining an axle weight posterior probability according to the axle weight prior probability and the load response likelihood probability, and taking the axle weight corresponding to the maximum axle weight posterior probability as the updated axle weight; Step 5: iteratively updating the axle weight by repeating the main loop of Steps 2 to 4 until a difference between the axle weight of this update and the axle weight obtained last time is less than a preset value, and taking the axle weight of this update as a final result of the bridge dynamic weighing algorithm.

2. The Bayesian maximum a posteriori based algorithm for bridge dynamic weighing according to claim 1, characterized in that, The influence line covariance matrix is calculated according to the correlation between influence line values at two sampling points; An element in the influence line covariance matrix is calculated by the following formula: ； wherein, denotes the covariance of the bridge influence line between the x th sampling point and the y th sampling point; K is the number of influence lines obtained in the calibration test; is the value of the k th influence line at the x th sampling point; is the value of the k th influence line at the y th sampling point; denotes the value of the influence line mean at the x th sampling point.

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

4. The Bayesian maximum a posteriori based algorithm for bridge dynamic weighing according to claim 1, characterized in that, In Step 2, an element of the covariance matrix of the load response is calculated by the following formula: ； wherein, denotes the covariance of the load response between the th sampling point and the th sampling point; denotes the total number of axles; denotes the mean axle load of the n th axle; denotes the covariance of the influence line corresponding to the n th axle between the g th sampling point and the j th sampling point; C n denotes the number of samples corresponding to the distance between the n th axle and the first axle; denotes the standard deviation of the measurement noise; C n By the formula: ； wherein, D n denotes the distance between the first n axle and the second axle; f is the sampling frequency; v is the vehicle speed.

5. The Bayesian maximum a posteriori based algorithm for bridge dynamic weighing according to claim 1, characterized in that, In Step 2, the updating of the axle weight covariance matrix based on the covariance matrix of the load response includes obtaining an updated axle weight covariance matrix according to the covariance matrix of the load response, the influence line matrix and the axle weight covariance matrix; The axle weight covariance matrix is calculated by the following formula: ； wherein, with denoting the axis weight covariance matrix of the h +1th sub-cycle iteration and the h th sub-cycle iteration, respectively; denoting the influence line matrix; T denotes the transpose operation; is the covariance matrix of the load response.

6. The Bayesian maximum a posteriori based algorithm for bridge dynamic weighing according to claim 1, characterized in that, In Step 2, the updating of the axle weight mean vector based on the updated axle weight covariance matrix includes obtaining an updated axle weight mean vector based on the updated axle weight covariance matrix, the influence line matrix, the covariance matrix of the load response, the load response and the axle weight mean vector; The axle weight mean vector is calculated by the following formula: ； wherein, is the load response; and denote the mean vector of the axle load of the h +1th sub-cycle iteration and the h th sub-cycle iteration, respectively; and denote the covariance matrix of the axle load of the h +1th sub-cycle iteration and the h th sub-cycle iteration, respectively; denotes the influence line matrix; is the covariance matrix of the load response.

7. The bridge dynamic weighing algorithm based on Bayesian maximum posterior probability according to claim 1, characterized in that, In Step 4, the axle weight posterior probability is calculated by the following formula: ； wherein, represents a posterior probability of axle load; represents a prior probability of axle load; represents a likelihood probability of load response; represents a vector of axle loads; represents an influence line matrix; T represents a transpose operation; represents a vector of load responses; represents a covariance matrix of axle loads; represents a mean vector of axle loads; represents a covariance matrix of load responses.

8. The bridge dynamic weighing algorithm based on Bayesian maximum posterior probability according to claim 7, characterized in that, The axle weight prior probability is calculated by the following formula: ； wherein represents the axle load vector; The load response likelihood probability is calculated by the following formula: ； wherein, Z represents the total number of samples of the load response.

9. The bridge dynamic weighing algorithm based on Bayesian maximum posterior probability according to claim 1, characterized in that, In step 4, the corresponding axle load when the axle load posterior probability is maximum is calculated by the following formula: ； where A (i+1) represents the i represents the axle load corresponding to the main cycle of order +1 ; represents the axle load covariance matrix; represents the influence line matrix; T represents the transpose operation; represents the covariance matrix of the load response; represents the axle load mean vector; represents the load response vector.

10. The bridge dynamic weighing algorithm based on Bayesian maximum posterior probability according to claim 1, characterized in that, The difference between the axle load until the current update and the axle load acquired last time is less than a preset value, which is represented by the following formula: ； wherein, represents the axle load corresponding to the first i +1 main cycle; represents the axle load corresponding to the first i +1 main cycle; represents a preset value.

Images