A bridge weigh-in-motion algorithm based on likelihood estimation

Abstract

The present invention relates to the technical field of highway bridge safety monitoring, and discloses a bridge dynamic weighing algorithm based on likelihood estimation. With the bridge as the carrier for vehicle weighing, a calibration test is performed to obtain the influence line of the bridge, and the influence line mean vector and influence line covariance matrix are calculated; the influence line matrix is ​​obtained based on the influence line mean vector, vehicle speed and axle spacing, and the initial axle weight is calculated using the Moses algorithm; the mean square error diagonal matrix of the measurement error is calculated based on the influence line matrix, the bridge load response and the axle weight of the previous iteration step, and the covariance matrix of the bridge load response is obtained; the axle weight corresponding to the maximum likelihood probability is calculated based on the covariance matrix of the bridge load response combined with the influence line matrix and the bridge load response; this process is repeated until the difference between the updated axle weight and the last obtained axle weight is less than a preset value, and the updated axle weight is used as the final result. The present invention solves the problem of low axle weight recognition accuracy of the existing bridge dynamic weighing system.

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] Bridge Weigh-in-Motion (BWIM) systems, which use bridges as a vehicle platform for weighing vehicles, have become a key enforcement tool for traffic managers, enabling them to monitor overweight vehicles in real time. Without interrupting traffic, BWIM uses sensors installed on the bridge to obtain real-time load responses, thereby inferring information such as vehicle speed, axle spacing, and axle weight.

[0003] Currently, most commercial bridge weigh-in-motion systems are developed based on the Moses algorithm. This algorithm uses the influence line at the bridge's midspan as its basis. It minimizes the sum of the squares of the differences between the measured and theoretical values ​​of the vehicle's load response to the bridge (using the least squares method). This algorithm then establishes an error function, taking the partial derivative of each axle load to determine the axle weight. When developing this error function, the Moses algorithm assumes that the bridge's influence line is fixed. The resulting bridge response errors are independent variables, and the standard deviation of the bridge response is the same at every moment. However, in reality, bridge influence lines are random, and influence line values ​​at different locations are correlated. Furthermore, due to measurement errors, the bridge's load response to vehicles exhibits different distributions at each moment, and these values ​​are correlated. The distribution of the load response depends on factors such as the bridge's influence line, measurement errors, and vehicle axle loads. For these reasons, the Moses algorithm suffers from low accuracy in axle load identification.

[0004] Although researchers from various countries have since modified the Moses algorithm to improve the axle weight identification accuracy of the bridge dynamic weighing system, the method used to establish the error function is still the least squares method. Therefore, the problem that the least squares method itself has defects that lead to reduced axle weight identification accuracy has not been solved, and the calculated vehicle axle weight accuracy 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 technical personnel in this field urgently need to solve. 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 recognition accuracy of the existing bridge dynamic weighing system.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0008] The present invention provides a bridge dynamic weighing algorithm based on likelihood estimation, comprising the following steps:

[0009] Step 1: Using the bridge as the vehicle weighing carrier, obtain the bridge influence line and bridge load response through calibration test , calculate the influence line mean vector and influence line covariance matrix , and then obtain the vehicle speed and axle distance, and further obtain the influence line matrix I according to the vehicle speed, axle distance and the influence line mean vector. Based on the influence line matrix I and the bridge load response , use Moses algorithm to obtain axle weight ;

[0010] Step 2: Based on the influence line matrix I, bridge load response and axle load Calculate the mean square error diagonal matrix of measurement errors ;

[0011] Step 3: Based on the mean square error diagonal matrix of measurement error , influence line covariance matrix and axle load Obtaining the covariance matrix of the bridge load response , based on the covariance matrix of the bridge load response Calculate the likelihood probability of the bridge response corresponding to the axle load, combining the influence line matrix I with the bridge load response The axle weight corresponding to the maximum likelihood probability is calculated as the updated axle weight ;

[0012] The covariance matrix of the bridge load response is The elements in are calculated using the following formula:

[0013] ;

[0014] in, The bridge load response is x Hedi y The covariance between the sampling points; The measurement error is x Hedi y 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; For the n The weight of each axle, N is the total number of axles;

[0015] Cn Calculated by the following formula:

[0016] ;

[0017] 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;

[0018] The covariance matrix based on the bridge load response The likelihood probability of the bridge response corresponding to the axle load is calculated using the following formula:

[0019] ;

[0020] in, The determinant of the covariance matrix representing the bridge load response; A is the vector representing the load response of the bridge; A is the axle load;

[0021] Step 4: Repeat steps 2 to 3 to iteratively update the axle weight until the difference between the updated axle weight and the last obtained axle weight is less than a preset value, and use the updated axle weight as the final result of the bridge dynamic weighing algorithm.

[0022] Furthermore, the method for obtaining the vehicle speed and axle distance includes: collecting the axle power signal generated when the vehicle to be detected passes through the front and rear sensors FAD1 and FAD2, and calculating the time difference between the peak values ​​of the two axle power signals and the distance between the sensors, and calculating the speed and axle distance of the vehicle to be detected based on the time difference and distance.

[0023] Furthermore, in step 1, the influence line covariance matrix Calculated based on the correlation between the influence line values ​​between any two sampling points on the bridge;

[0024] The influence line covariance matrix The elements in are calculated using the following formula:

[0025] ;

[0026] in, Indicates the bridge influence line at x The sampling point and y The covariance between the sampling points; K is the number of influence lines obtained in the calibration test; For the k The influence line is x The value at each sampling point; Indicates the influence line mean at x The value at each sampling point.

[0027] Furthermore, in step 2, firstly according to the influence line matrix I and the bridge load response And the axle weight calculation measurement error, and then calculate the mean square error diagonal matrix of the measurement error based on the measurement error ;

[0028] The measurement error is calculated by the following formula:

[0029] ;

[0030] in, Indicates the i The measurement error corresponding to the iteration step; represents the bridge load response; I represents the influence line matrix; Indicates the i The axle weight corresponding to the iteration step.

[0031] Furthermore, when the partial derivative of the likelihood probability with respect to the axle weight is zero, the likelihood probability reaches its maximum value, and its corresponding axle weight is calculated by the following formula:

[0032] ;

[0033] in, represents the transpose of the influence line matrix I.

[0034] Furthermore, the difference between the axle weight currently updated and the axle weight last obtained is less than the preset value, which is expressed by the following formula:

[0035] ;

[0036] in, Indicates the axle weight of this update. Indicates the preset value.

[0037] Beneficial effects:

[0038] This invention provides a bridge weigh-in-motion algorithm based on likelihood estimation. This algorithm assumes that the load response of a vehicle to a bridge follows different numerical distributions at different times. It considers the effects of influence lines and measurement errors, and correlates these factors through the likelihood probability of the bridge load response to derive a vehicle axle load identification formula based on likelihood estimation. This method can, to a certain extent, reduce calculation errors caused by factors such as measurement errors and the randomness of influence lines, effectively improving the accuracy of vehicle axle load identification.

[0039] Specifically, the present invention innovatively introduces theories and methods related to likelihood estimation, and fully considers the measurement error and the correlation of the influence line in the axle weight identification process. Among them, the measurement error is an inevitable factor in the actual measurement link, which will interfere with the axle weight identification result; and the correlation of the influence line reflects the intrinsic connection between different measurement points, which is crucial for accurately obtaining axle weight information. In order to more accurately handle these complex factors, the present invention introduces a likelihood estimation method, which associates these factors through the likelihood probability of the measured response and establishes a vehicle axle weight identification formula. Compared with the traditional Moses algorithm, the likelihood estimation method adopted by the present invention has significant advantages. It takes into account the impact of the measurement error and the correlation of the influence line on axle weight identification, and effectively improves the accuracy and robustness of axle weight identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is an algorithm flow chart of a bridge dynamic weighing algorithm based on likelihood estimation according to Example 1 of the present invention;

[0041] Figure 2 is a schematic diagram of the bridge deck elevation according to embodiment 2 of the present invention;

[0042] Figure 3 is a schematic cross-sectional view of a bridge according to embodiment 2 of the present invention;

[0043] Figure 4 1 is a schematic diagram of the influence line mean value of the bridge influence line according to embodiment 2 of the present invention;

[0044] Figure 5 is a covariance diagram of the bridge influence line according to Example 2 of the present invention;

[0045] Figure 6 Schematic diagram of the covariance correlation coefficient of the bridge influence line according to Example 2 of the present invention;

[0046] Figure 7 Schematic diagram of the bridge dynamic response value of Example 2 of the present invention. DETAILED DESCRIPTION

[0047] The following is a clear and complete description of the technical solutions of the present invention. It should be understood that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0048] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "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, words such as "one" or "a" do not indicate a quantity limitation, but rather indicate the existence of at least one. Words such as "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0049] Example 1

[0050] See Figure 1 The embodiment of the present application provides a bridge dynamic weighing algorithm based on likelihood estimation, comprising the following steps:

[0051] Step 1: Using the bridge as the vehicle weighing carrier, obtain the bridge influence line and bridge load response through calibration test , calculate the influence line mean vector and influence line covariance matrix , and then obtain the vehicle speed and axle distance, and further obtain the influence line matrix I according to the vehicle speed, axle distance and the influence line mean vector. Based on the influence line matrix I and the bridge load response , use Moses algorithm to obtain axle weight ;

[0052] Specifically, through calibration tests, the load cell installed at the bottom mid-span of the bridge main beam is used to obtain the bridge load response R when the vehicle passes the bridge. * The influence line at the mid-span of the bridge is selected as the influence line used for vehicle axle load identification. Multiple calibration tests are carried out. Each calibration test obtains a set of influence lines. Mathematical statistics are performed to obtain the influence line mean vector and covariance matrix While executing the above steps, the load cell sensors FAD1 and FAD2 at the front and rear sides of the load cell at the bottom of the bridge main beam are used to obtain the axle power signal of the vehicle when it passes the bridge. The speed of the vehicle passing the bridge is calculated by the time between the peaks of the axle power signal and the distance between the sensors. v and axle spacing D .

[0053] Specifically, for the influence line covariance matrix , calculated based on the correlation of the influence line values ​​between any two sampling points on the bridge;

[0054] The influence line covariance matrix is ​​calculated as follows:

[0055] ;

[0056] in, Indicates the bridge influence line at x The sampling point and y The covariance between the sampling points; K is the number of influence lines obtained in the calibration test; For the k The influence line is x The value at each sampling point, Indicates the influence line mean at x The value at each sampling point;

[0057] The following influence line covariance matrix is ​​obtained:

[0058] ;

[0059] in, S is the number of sampling points of the influence line, which is calculated by the following formula:

[0060] ;

[0061] in, L For the bridge chief, f is the sampling frequency, v is the vehicle speed.

[0062] The axle load is obtained based on the influence line matrix and the bridge load response combined with the Moses algorithm;

[0063] ;

[0064] Where, Indicates the axle weight obtained based on the Moses algorithm, represents the transpose of the bridge influence line matrix I, represents the bridge load response.

[0065] Step 2: Based on the influence line matrix I, bridge load response and axle load Calculate the mean square error diagonal matrix of measurement errors ;

[0066] Specifically, first according to the influence line matrix I, bridge load response And the axle weight calculation measurement error, and then calculate the mean square error diagonal matrix of the measurement error based on the measurement error ;

[0067] The measurement error is calculated using the following formula:

[0068] ;

[0069] in, Indicates the i The measurement error corresponding to the iteration step is, represents the bridge load response, I represents the influence line matrix, Indicates the i The axle weight corresponding to the iteration step is the axle weight in step 1. ;

[0070] 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:

[0071] .

[0072] Step 3: Based on the mean square error diagonal matrix of measurement error , influence line covariance matrix and axle load Obtaining the covariance matrix of the bridge load response , based on the covariance matrix of the bridge load response Calculate the likelihood probability of the bridge response corresponding to the axle load, combining the influence line matrix I with the bridge load response The axle weight corresponding to the maximum likelihood probability is calculated as the updated axle weight ;

[0073] According to the obtained 、 and Equivariate calculation of the covariance matrix of the bridge response , the covariance matrix of the bridge response is calculated as follows:

[0074] ;

[0075] in, Indicates the bridge influence line at x The sampling point and y 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; For the n The weight of each axle; N is the total number of axles;

[0076] C n Calculated by the following formula:

[0077] ;

[0078] 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.

[0079] The likelihood probability of the axle load corresponding to the bridge response is calculated based on the covariance matrix of the bridge load response using the following formula:

[0080] ;

[0081] in, The determinant of the covariance matrix representing the bridge load response, is the vector representing the measured response, and A is the axle load.

[0082] When the partial derivative of the likelihood probability with respect to the axle weight is zero, the likelihood probability reaches its maximum value, that is:

[0083] ;

[0084] After solving the above formula, we get the axle weight The calculation formula is:

[0085] ;

[0086] in, represents the transpose of the influence line matrix I, and R represents the vector of bridge load responses.

[0087] Step 4: Repeat steps 2 to 3 to iteratively update the axle weight until the difference between the updated axle weight and the last obtained axle weight is less than the preset value, and use the updated axle weight as the final result of the bridge dynamic weighing algorithm.

[0088] Until the difference between the axle weight of this update and the axle weight of the last acquisition is less than the preset value, it is expressed by the following formula:

[0089] ;

[0090] in, Indicates the axle weight of this update. Indicates the preset value.

[0091] Example 2

[0092] 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.

[0093] Perform the following steps to identify the axle weight of vehicles crossing the bridge:

[0094] (1) Calibration test is carried out 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 .

[0095] (2) Carry out vehicle moving load test on the bridge and obtain the 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, wheelbase 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) obtain information such as the number of vehicle axles, axle spacing and vehicle speed, such as Figure 2 As shown; dynamic weighing sensors are installed at the bottom of the T-beam in the middle of the bridge to identify the vehicle axle weight, as shown Figure 3 The bridge dynamic response value at the mid-span position is shown as Figure 7 As shown, the bridge dynamic response value at the mid-span position is the signal of ten load cells ( Figure 3 The sum of the weighing sensor at point b).

[0096] (3) Use the new algorithm and Moses algorithm to identify the axle load of the axle dynamic response signal. Solve the initial axle load (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 calculated load responses and the diagonal matrix of the variance of the measurement error The bridge influence line used at this time is the measured influence line of the bridge, which is the mean influence line and the covariance matrix of the influence line calculated based on the influence line algorithm based on the 10 groups of vehicle-bridge dynamic responses of the same loaded vehicle; calculate the new axle weight The above process is repeated until the calculated axle load converges. The calculation results are shown in Table 1.

[0097] It's important to note that before axle load identification, the vehicle-bridge dynamic response is filtered through a moving average filter to eliminate some noise and vehicle-bridge coupling. Considering the impact of vehicles on the bridge's dynamic response when entering and exiting the bridge, the vehicle entry and exit sections are both 10 meters long.

[0098] Table 1 Vehicle axle weight recognition error table of two algorithms Unit: %

[0099]

[0100] Note: Error = (calculated value - true value) / true value × 100%.

[0101] Table 1 shows that the mean and standard deviation of axle weight errors obtained by our new algorithm are both lower than those of the Moses algorithm. For the front axle, for example, the new algorithm's mean error is 0.10%, less than the Moses algorithm's 2.06%. Correspondingly, the standard deviation of the error decreases from 49.04% (Moses algorithm) to 1.52% (new algorithm). This demonstrates that our new algorithm can significantly improve axle weight identification accuracy.

[0102] Obtaining more accurate vehicle axle weights during 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 bridges. On the other hand, vehicle information can provide a reliable basis for accurate assessments of highway bridge reliability and lifespan, contributing to the establishment of an intelligent highway bridge management system and extending the service life of highway bridges.

[0103] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A bridge dynamic weighing algorithm based on likelihood estimation, characterized in that: The steps include: Step 1: Using the bridge as the vehicle weighing carrier, obtain the bridge influence line and bridge load response through calibration test , calculate the influence line mean vector and influence line covariance matrix , and then obtain the vehicle speed and axle distance, and further obtain the influence line matrix I according to the vehicle speed, axle distance and the influence line mean vector. Based on the influence line matrix I and the bridge load response , use Moses algorithm to obtain axle weight; Step 2: Based on the influence line matrix I, bridge load response And the mean square error diagonal matrix of the axle weight calculation measurement error ; Step 3: Based on the mean square error diagonal matrix of measurement error , influence line covariance matrix The covariance matrix of the bridge load response is obtained by combining the axle load , based on the covariance matrix of the bridge load response Calculate the likelihood probability of the bridge response corresponding to the axle load, combining the influence line matrix I with the bridge load response The axle weight corresponding to the maximum likelihood probability is calculated as the updated axle weight; The covariance matrix of the bridge load response is The elements in are calculated using the following formula: ； in, The bridge load response is x Hedi y The covariance between the sampling points; The measurement error is x Hedi y 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; For the n The weight of each axle, N is the total number of axles; 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; The covariance matrix based on the bridge load response The likelihood probability of the bridge response corresponding to the axle load is calculated using the following formula: ； in, The determinant of the covariance matrix representing the bridge load response; A is the vector representing the load response of the bridge; A is the axle load; Step 4: Repeat steps 2 to 3 to iteratively update the axle weight until the difference between the updated axle weight and the last obtained axle weight is less than a preset value, and use the updated axle weight as the final result of the bridge dynamic weighing algorithm.

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

3. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1 is characterized in that: In step 1, the influence line covariance matrix Calculated based on the correlation between the influence line values ​​between any two sampling points on the bridge; The influence line covariance matrix The elements in are calculated using the following formula: ； in, Indicates the bridge influence line at x The sampling point and y The covariance between the sampling points; K is the number of influence lines obtained in the calibration test; For the k The influence line is x The value at each sampling point; Indicates the influence line mean at x The value at each sampling point.

4. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1 is characterized in that: In step 2, firstly according to the influence line matrix I and bridge load response And the axle weight calculation measurement error, 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: ； in, Indicates the i The measurement error corresponding to the iteration step; represents the bridge load response; I represents the influence line matrix; Indicates the i The axle weight corresponding to the iteration step.

5. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1 is characterized in that: When the partial derivative of the likelihood probability with respect to the axle weight is zero, the likelihood probability reaches its maximum value, and its corresponding axle weight is calculated by the following formula: ； in, represents the transpose of the influence line matrix I.

6. The bridge dynamic weighing algorithm based on likelihood estimation according to claim 1 is characterized in that: The difference between the axle weight currently updated and the axle weight last obtained is less than the preset value is expressed by the following formula: ； in, Indicates the axle weight of this update; Indicates the preset value.

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