Bridge dynamic weighing algorithm based on likelihood estimation

Abstract

The invention relates to the technical field of highway bridge safety monitoring, and discloses a bridge dynamic weighing algorithm based on likelihood estimation. A bridge is used as a carrier for vehicle weighing, an influence line of the bridge is obtained through a calibration test, and an influence line mean vector and an influence line covariance matrix are calculated; an influence line matrix is obtained based on the influence line mean vector, the vehicle speed and the axle distance, and an initial axle load value is calculated through a Moses algorithm; calculating a mean square error diagonal matrix of a measurement error according to the influence line matrix, the bridge load response and the axle load of the previous iteration step, and obtaining a covariance matrix of the bridge load response; calculating an axle load corresponding to the maximum likelihood probability based on the covariance matrix of the bridge load response in combination with the influence line matrix and the bridge load response; and repeating until the difference value between the axle weight updated this time and the axle weight obtained last time is smaller than a preset value, and taking the axle weight updated this time as a final result. According to the invention, the problem of low axle load identification precision of the existing bridge dynamic weighing system is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of highway bridge safety monitoring, and in particular to a bridge dynamic weighing algorithm based on likelihood estimation. Background Art

[0002] A bridge weigh-in-motion (BWIM) system is a system that weighs vehicles using a bridge as a carrier, and has gradually developed into one of the important law enforcement tools for traffic managers to monitor overweight vehicles in real time. The BWIM system can, without interrupting traffic, use sensors installed on the bridge to obtain the load response of the bridge in real time, and thereby calculate information such as vehicle speed, axle spacing, and axle weight.

[0003] Most currently commercial bridge dynamic weighing systems are developed based on the Moses algorithm. This algorithm is based on the influence line at the mid-span position of the bridge, minimizes the sum of the squares of the differences between the measured value and the theoretical value of the load response of the vehicle to the bridge (least squares method), establishes an error function, takes the partial derivative of the axle weight of each axle respectively, and solves for the axle weight. When establishing the error function, the Moses algorithm assumes that the bridge influence line is a fixed value, and the bridge response errors calculated therefrom are independent variables, and the standard deviation of the bridge response at each moment is the same. However, in fact, the bridge influence line is random, and there is a correlation between the influence line values at different positions. In addition, due to the existence of measurement errors, the load response of the bridge under the action of the vehicle follows different numerical distributions at each moment, and there is a correlation between the values. The numerical distribution of the load response is related to factors such as the bridge influence line, measurement error, and vehicle axle weight. For these reasons, the accuracy of the Moses algorithm in the process of axle weight identification is low.

[0004] Although researchers in various countries have modified the Moses algorithm to improve the axle weight identification accuracy of the bridge dynamic weighing system, ultimately the method of establishing the error function is still the least squares method. Therefore, the problem of reduced axle weight identification accuracy caused by the inherent defects of the least squares method has not been solved, and thus the accuracy of the calculated vehicle axle weight will not be improved.

[0005] In summary, how to more efficiently improve the axle weight identification accuracy of the bridge dynamic weighing system has become a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0006] The present invention provides a bridge dynamic weighing algorithm based on likelihood estimation to solve the problem of low axle weight identification accuracy of existing bridge dynamic weighing systems.

[0007] To achieve the above object, the present invention is realized through the following technical solutions: The present invention provides a bridge dynamic weighing algorithm based on likelihood estimation, which includes the following steps: Step 1: Using the bridge as the carrier for vehicle weighing, obtain the influence line of the bridge and the bridge load response through a calibration test , calculate the mean vector of the influence line and the covariance matrix of the influence line , then obtain the vehicle speed and axle spacing, further obtain the influence line matrix I based on the vehicle speed and the mean vector of the influence line corresponding to the axle spacing, and based on the influence line matrix I and the bridge load response , use the Moses algorithm to obtain the axle weight ; Step 2: Calculate the mean square error diagonal matrix of the measurement error according to the influence line matrix I, the bridge load response and the axle weight ; ; Step 3: According to the mean square error diagonal matrix of the measurement error , the covariance matrix of the influence line and the axle weight obtain the covariance matrix of the bridge load response , calculate the likelihood probability of the axle weight corresponding to the bridge response based on the covariance matrix of the bridge load response , and combine the influence line matrix I and the bridge load response calculate the axle weight corresponding to the maximum likelihood probability as the updated axle weight ; Step 4: Repeat Step 2 to Step 3 to iteratively update the axle weight until the difference between the axle weight updated this time and the axle weight obtained last time is less than a preset value, and take the axle weight updated this time as the final result of the bridge dynamic weighing algorithm.

[0008] Further, the method for obtaining the vehicle speed and axle spacing includes: collecting the axle dynamic signals generated when the vehicle to be detected passes through the front and rear two sensors FAD1 and FAD2, calculating the time difference between the peaks of the two axle dynamic signals and the spacing between the sensors, and calculating the speed and axle spacing of the vehicle to be detected based on the time difference and the spacing.

[0009] Further, in Step 1, the covariance matrix of the influence line is calculated according to the correlation of the influence line values between two sampling points on the bridge; The elements in the covariance matrix of the influence line are calculated by the following formula: ; where, represents the covariance between the x th sampling point and the y th sampling point of the bridge influence line;K is the number of influence lines obtained in the calibration test; is the k value of the x th influence line at the th sampling point; x represents the value of the mean of the influence lines at the

[0010] Furthermore, in step 2, first calculate the measurement error based on the influence line matrix I, the bridge load response and the axle weight, and then calculate the mean square error diagonal matrix of the measurement error based on the measurement error; The measurement error is calculated by the following formula: ; where represents the measurement error corresponding to the i th iteration step; represents the bridge load response; I represents the influence line matrix; represents the i th iteration step corresponding axle weight.

[0011] Furthermore, in step 3, the elements in the covariance matrix of the bridge load response are calculated by the following formula: ; where represents the covariance between the bridge load responses at the x th and y th sampling points; represents the covariance between the measurement errors at the x th and y th sampling points; C n represents the number of samples corresponding to the distance between the n th axle and the first axle; A n is the weight of the n th axle, N is the total number of axles; C n is calculated by the following formula: ; where D n represents the distance between the n th axle and the first axle; f is the sampling frequency; v is the vehicle speed.

[0012] Further, the covariance matrix based on the bridge load response The likelihood probability of the axle load corresponding to the bridge response is calculated by the following formula:

[0013] where represents the determinant of the covariance matrix of the bridge load response; R represents the vector of the bridge load response; A represents the axle load.

[0014] Further, when the partial derivative of the likelihood probability with respect to the axle load is zero, the likelihood probability reaches the maximum value, and the corresponding axle load is calculated by the following formula: ; where represents the transpose of the influence line matrix I.

[0015] Further, the difference between the axle load updated this time and the axle load obtained last time is less than the preset value, which is expressed by the following formula: ; where represents the axle load updated this time, represents the preset value.

[0016] Beneficial effects: A bridge dynamic weighing algorithm based on likelihood estimation provided by the present invention believes that the load responses of vehicles to bridges follow different numerical distributions at different times. Considering the influence of the influence line and measurement error, these factors are related through the likelihood probability of the bridge load response, and a vehicle axle load identification formula based on likelihood estimation is obtained. The method of the present invention can reduce the calculation error caused by factors such as measurement error and randomness of the influence line to a certain extent, and effectively improve the accuracy of vehicle axle load identification.

[0017] Specifically, the present invention innovatively introduces the relevant theories and methods of likelihood estimation, and fully considers the measurement error and the correlation of the influence line in the process of axle load identification. Among them, the measurement error is an inevitable factor in the actual measurement process, which will interfere with the axle load identification result; while the correlation of the influence line reflects the internal connection between different measurement points, which is crucial for accurately obtaining the axle load information. In order to more precisely process these complex factors, the present invention introduces the method of likelihood estimation, relates these factors through the likelihood probability of the measured response, and establishes a vehicle axle load identification formula. Compared with the traditional Moses algorithm, the likelihood estimation method adopted by the present invention has significant advantages, considering the influence of measurement error and the correlation of the influence line on axle load identification, and effectively improving the accuracy and robustness of axle load identification. Description of the Drawings

[0018] Figure 1 It is the algorithm flowchart of a bridge dynamic weighing algorithm based on likelihood estimation in Embodiment 1 of the present invention; Figure 2 It is the elevation view of the bridge deck in Embodiment 2 of the present invention; Figure 3 It is the cross-sectional view of the bridge in Embodiment 2 of the present invention; Figure 4 It is the mean value diagram of the influence line of the bridge in Embodiment 2 of the present invention; Figure 5 It is the covariance diagram of the influence line of the bridge in Embodiment 2 of the present invention; Figure 6 It is the schematic diagram of the covariance correlation coefficient of the influence line of the bridge in Embodiment 2 of the present invention; Figure 7 It is the schematic diagram of the bridge dynamic response value in Embodiment 2 of the present invention. Detailed implementation manners

[0019] The technical solutions of the present invention will be described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without any creative work fall within the scope of protection of the present invention.

[0020] Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, the terms such as "a" or "one" do not indicate a quantity limit, but indicate that there is at least one. The terms such as "connected" or "linked" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", "right" are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0021] Embodiment 1 Please refer to Figure 1 , this application embodiment provides a bridge dynamic weighing algorithm based on likelihood estimation, including the following steps: Step 1: Taking the bridge as the carrier for vehicle weighing, obtaining the influence line of the bridge and the bridge load response through a calibration test , calculating the mean vector of the influence line and the covariance matrix of the influence line , then obtain the vehicle speed and axle spacing, and further obtain the influence line matrix I based on the vehicle speed and the mean vector of the influence line. Based on the influence line matrix I and the bridge load response , use the Moses algorithm to obtain the axle weight ; Specifically, through a calibration test, use the weighing sensor set at the mid-span position of the bottom of the bridge main girder to obtain the bridge load response R when the vehicle crosses the bridge * , and select the influence line at the mid-span position of the bridge as the influence line used for vehicle axle weight identification. Conduct multiple calibration tests, obtain a set of influence lines for each calibration test, and perform mathematical statistics to obtain the mean vector of the influence line and the covariance matrix ; While performing the above steps, use the sensors FAD1 and FAD2 on both sides of the weighing sensor set at the bottom of the bridge main girder to obtain the vehicle-bridge dynamic signal when the vehicle crosses the bridge. Calculate the vehicle speed v and the axle spacing D of the vehicle crossing the bridge through the time between the peaks of the vehicle-bridge dynamic signal and the distance between the sensors.

[0022] Specifically, for the influence line covariance matrix , calculate according to the correlation of the influence line values between two sampling points on the bridge; The influence line covariance matrix is calculated by the following formula: ; Among them, represents the covariance between the x th sampling point and the y th sampling point of the bridge influence line; K is the number of influence lines obtained in the calibration test; is the k th influence line at the x th sampling point, represents the value of the influence line mean at the x th sampling point; The following influence line covariance matrix is obtained: ; Among them, S is the number of sampling points of the influence line, calculated by the following formula: ; Among them, L is the bridge length, f is the sampling frequency, v is the vehicle speed.

[0023] Obtain the axle load based on the influence line matrix and the bridge load response combined with the Moses algorithm; ; In the formula, represents the axle load obtained based on the Moses algorithm, represents the transpose of the bridge influence line matrix I, represents the bridge load response.

[0024] Step 2: Calculate the mean square error diagonal matrix of the measurement error according to the influence line matrix I, the bridge load response and the axle load ; Specifically, first calculate the measurement error according to the influence line matrix I, the bridge load response and the axle load, and then calculate the mean square error diagonal matrix of the measurement error based on the measurement error; The measurement error is calculated by the following formula: ; Among them, represents the measurement error corresponding to the i th iteration step, represents the bridge load response, I represents the influence line matrix, represents the axle load corresponding to the i th iteration step, that is, in Step 1; Calculate the standard deviation of the mean square error diagonal matrix based on the measurement error , and obtain the corresponding mean square error diagonal matrix as: .

[0025] Step 3: Obtain the covariance matrix of the bridge load response according to the mean square error diagonal matrix of the measurement error, the influence line covariance matrix and the axle load , calculate the likelihood probability of the axle load corresponding to the bridge response based on the covariance matrix of the bridge load response, and combine the influence line matrix I and the bridge load response to calculate the axle load corresponding to the maximum likelihood probability as the updated axle load ; According to the obtained , and and other variables, calculate the covariance matrix of the bridge response. The covariance matrix of the bridge response is calculated by the following formula: ; Among them, represents the covariance between the influence line of the bridge at the x th sampling point and the y th sampling point; C n represents the number of samples corresponding to the distance between the n th axle and the first axle; A n is the weight of the n th axle; N is the total number of axles; C n is calculated by the following formula: ; Among them, D n represents the distance between the n th axle and the first axle; f is the sampling frequency; v is the vehicle speed.

[0026] The likelihood probability of the axle weight corresponding to the bridge response based on the covariance matrix of the bridge load response is calculated by the following formula: ; Among them, represents the determinant of the covariance matrix of the bridge load response, R represents the vector of the measured response, and A represents the axle weight.

[0027] When the partial derivative of the likelihood probability with respect to the axle weight is zero, the likelihood probability reaches the maximum value, that is: ; After solving the above formula, the calculation formula for the axle weight is obtained: ; Among them, represents the transpose of the influence line matrix I, and R represents the vector of the bridge load response.

[0028] Step 4: Repeat Step 2 to Step 3 to iteratively update the axle weight until the difference between the currently updated axle weight and the previously obtained axle weight is less than a preset value, and use the currently updated axle weight as the final result of the bridge dynamic weighing algorithm.

[0029] Until the difference between the currently updated axle weight and the previously obtained axle weight is less than a preset value is represented by the following formula: ; Among them, represents the currently updated axle weight, represents the preset value.

[0030] Example 2 Take a domestic simply supported beam bridge as an example. The bridge is a simply supported beam bridge composed of ten prefabricated beams, with a main span of 40m, a bridge width of 24m, and four lanes in both directions. Figure 2 shown.

[0031] The axle weight of vehicles crossing the bridge is identified through the following steps: (1) Calibration test is performed on the bridge to obtain the distribution of influence lines. That is, the distribution of influence lines is known and can be used for subsequent calculations. The influence line mean curve is shown in Figure 4 , the variance and correlation coefficient of the influence line are shown in Figure 5 and Figure 6 .

[0032] (2) Carry out vehicle moving load test on the bridge to obtain test measured data. A two-axle vehicle with a total weight of 28.5t was selected as the loading vehicle (front axle 7.4t, rear axle 21.1t, axle spacing 4.7m), and repeatedly drove through lane 3 at a speed of 30km / h. The number of driving times was 10. During the test, axle detection sensors ( Figure 2 FAD1 and FAD2 at a in the figure) obtain information such as the number of vehicle axles, axle spacing and vehicle speed, such as Figure 2 As shown; a dynamic weighing sensor is installed at the bottom of the T-beam in the middle of the bridge to identify the vehicle axle weight, such as Figure 3 The bridge dynamic response value at the mid-span position is shown in Figure 7 As shown, the bridge dynamic response value at the mid-span position of the bridge is the signal of ten load cells ( Figure 3 The sum of the weighing sensor at point b in the figure.

[0033] (3) Use the new algorithm and Moses algorithm to identify the axle weight of the axle dynamic response signal. Solve for the initial axle weight (The axle weight obtained at this time is also used to compare with the results obtained by the new algorithm); the initial axle weight obtained Measurement errors in calculating load responses and the diagonal matrix of the variance of the measurement error The bridge influence line used at this time is the measured bridge influence line, which is the mean influence line and the covariance matrix of the influence line calculated based on the influence line algorithm based on 10 groups of axle dynamic responses of the same loaded vehicle; calculate the new axle weight ; Repeat the above process until the calculated axle weight results converge. The calculation results are shown in Table 1.

[0034] It should be noted here that before the axle load is identified, part of the noise and the coupling response of the axle are eliminated from the dynamic response of the axle by a moving average filter. Considering the influence of the vehicle on the dynamic response of the bridge when getting on and off the bridge, the lengths of the entrance section and the exit section of the vehicle are both taken as 10 m.

[0035] Table 1 Vehicle Axle Load Identification Error Table of Two Algorithms Unit: %

[0036] Note: Error = (Calculated Value - True Value) / True Value × 100%.

[0037] It can be seen from Table 1 that both the mean value and the standard deviation of the axle load error obtained by the new algorithm of 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 0.10%, which is less than 2.06% of the Moses algorithm. Correspondingly, the standard deviation of the error has decreased from 49.04% (Moses algorithm) to 1.52% (new algorithm). This shows that the new algorithm of this application can greatly improve the accuracy of axle load identification.

[0038] Obtaining more accurate vehicle axle loads in highway bridge monitoring can, on the one hand, assist highway bridge management departments in effectively managing overloading and reducing the number of overloaded vehicles crossing the bridge; on the other hand, vehicle information can provide a reliable basis for accurately evaluating the reliability and service life of highway bridges, contribute to the establishment of an intelligent highway bridge management system, and extend the service life of highway bridges.

[0039] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of this application based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A bridge dynamic weighing algorithm based on likelihood estimation, characterized in that, It includes the following steps: Step 1: Use the bridge as the carrier for vehicle weighing, and obtain the influence line of the bridge and the bridge load response through calibration tests , calculate the mean vector of the influence line and the covariance matrix of the influence line , then obtain the vehicle speed and axle spacing, and further obtain the influence line matrix I based on the mean vector of the influence line with respect to the vehicle speed and axle spacing. Based on the influence line matrix I and the bridge load response , use the Moses algorithm to obtain the axle weight; Step 2: According to the influence line matrix I and the bridge load response and the axle weight, calculate the mean square error diagonal matrix of the measurement error ; Step 3: Based on the mean square error diagonal matrix of the measurement error , the influence line covariance matrix , and the covariance matrix of the axle load to obtain the bridge load response , calculate the likelihood probability of the axle load corresponding to the bridge response based on the covariance matrix of the bridge load response . Combine the influence line matrix I and the bridge load response to calculate the axle load corresponding to the maximum likelihood probability as the updated axle load; Step 4: Repeat Step 2 to Step 3 to iteratively update the axle weight until the difference between the axle weight updated this time and the axle weight obtained last time is less than a preset value, and take the axle weight updated this time as the final result of the bridge dynamic weighing algorithm.

2. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1, characterized in that In Step 1, the method for obtaining the vehicle speed and axle spacing includes: collecting the axle dynamic signals generated when the vehicle to be detected passes through the front and rear sensors FAD1 and FAD2, calculating the time difference between the peaks of the two axle dynamic signals and the spacing between the sensors, and calculating the vehicle speed and axle spacing of the vehicle to be detected based on the time difference and the spacing.

3. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1, characterized in that, In Step 1, the influence line covariance matrix is calculated based on the correlation of the influence line values between two sampling points on the bridge; The covariance matrix of the influence line The elements in it are calculated by the following formula: ； Among them, represents the covariance between the influence line of the bridge 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; represents the value of the mean of the influence line at the x -th sampling point.

4. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1, wherein In step 2, first calculate the measurement error according to the influence line matrix I, the bridge load response and the axle load, and then calculate the mean square error diagonal matrix of the measurement error based on the measurement error ; The measurement error is calculated by the following formula: ； Among them, represents the i measurement error corresponding to the th iteration step; represents the bridge load response; I represents the influence line matrix; i represents the axle load corresponding to the 5. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1, characterized in that, In step 3, the elements in the covariance matrix of the bridge load response are calculated by the following formula: ； Among them, represents the covariance of the bridge load response between the x and the y th sampling points; represents the covariance of the measurement error between the x and the y th sampling points; C n represents the sampling quantity corresponding to the distance between the n th axle and the first axle; A n is the weight of the n th axle, N is the total number of axles; C n Calculated by the following formula: ； Among them, D n represents the distance between the n th axle and the first axle; f is the sampling frequency; v is the vehicle speed.

6. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1, characterized in that, The covariance matrix based on bridge load response The likelihood probability of the axle load corresponding to the bridge response is calculated by the following formula: Among them, represents the determinant of the covariance matrix of the bridge load response; R represents the vector of the bridge load response; A represents the axle load.

7. A bridge dynamic weighing algorithm based on likelihood estimation according to claim 6, characterized in that, When the partial derivative of the likelihood probability with respect to the axle weight is zero, the likelihood probability reaches the maximum value, and the corresponding axle weight is calculated by the following formula: ； Among them, represents the transpose of the influence line matrix I.

8. A bridge dynamic weighing algorithm based on likelihood estimation according to claim 1, characterized in that, The condition that the difference between the axle weight updated this time and the axle weight obtained last time is less than a preset value is expressed by the following formula: ； Among them, represents the axle load of this update; represents the preset value.

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