A dynamic weighing algorithm for bridges based on regularization.

Abstract

This invention relates to the field of highway bridge safety monitoring technology and discloses a bridge dynamic weighing algorithm based on a regularization algorithm. The invention obtains an axle load calculation formula with a regularization matrix by adding a penalty term to the error function. The regularization matrix is ​​determined by the axle load covariance matrix and the load response covariance matrix. Specifically, the process involves: obtaining the influence line distribution through calibration tests; obtaining the initial axle load given an initial regularization matrix; calculating the load response covariance matrix based on the influence line distribution, the initial axle load, and measurement noise, and iterating a stable axle load covariance matrix by combining it with the preset initial axle load covariance matrix; generating a regularization matrix based on the load response covariance matrix and the updated axle load covariance matrix, and calculating a new axle load; repeating the above iterative process until the axle load update difference is less than a preset value, and finally outputting the axle load result. This invention effectively improves the axle load identification accuracy of the bridge dynamic weighing system.

Description

Technical Field

[0001] This invention relates to the field of highway bridge safety monitoring technology, and in particular to a bridge dynamic weighing algorithm based on regularization. Background Technology

[0002] Bridge Weigh-in-Motion (BWIM) is an intelligent monitoring system that uses bridges as a carrier to dynamically weigh vehicles. It is widely used in practical traffic engineering because it can quickly identify the weight information of passing vehicles without interrupting traffic.

[0003] Most commercially available bridge dynamic weighing systems are based on the Moses algorithm, which calculates the weight of moving loads on the bridge by analyzing strain information at specific locations. While effective under ideal conditions, the Moses algorithm suffers from significant overfitting in practical applications, especially under conditions of noise interference, uneven road surfaces, or large bridge spans. Overfitting in the Moses algorithm manifests in several ways: the impact of data noise (road surface roughness, measurement errors, and vehicle-bridge dynamic effects, etc.) often significantly affects the model, causing it to fit the noise and reducing its generalization ability on new data; and instability in the inversion algorithm itself, as the core equation of the Moses algorithm is an ill-conditioned inverse problem, leading to instability of the solution and sensitivity to small disturbances. Traditional Tikhonov regularization algorithms, by adding a penalty term to the loss function to control model complexity, can mitigate overfitting to some extent, but selecting the appropriate regularization parameter is difficult. The L-curve method is often used to select the optimal regularization parameter. This method requires plotting the logarithmic curve of the fitting error and the regularization error, and taking the inflection point of the curve as the optimal parameter. Not only is the computational efficiency low and the inflection point sometimes not obvious, but the L-curve method usually selects a globally fixed regularization parameter, which lacks adaptability and is difficult to cope with changes under different noise levels.

[0004] In summary, how to efficiently and accurately handle the overfitting problem in order to improve the axle load identification accuracy of bridge dynamic weighing systems has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This invention provides a bridge dynamic weighing algorithm based on regularization. This algorithm is a method suitable for dealing with uncertainty and model overfitting. It can effectively alleviate the overfitting problem and improve the accuracy and stability of axle load identification, thereby solving the problem of low axle load identification accuracy in existing bridge dynamic weighing systems.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] This invention provides a dynamic weighing algorithm for bridges based on a regularization algorithm, comprising the following steps:

[0008] Step 1: Using multiple sets of bridge response data obtained from calibration tests, extract a set of bridge influence lines for each response set. Statistically analyze the set of bridge influence lines to obtain the mean vector and covariance matrix of the influence lines. Using the bridge as the vehicle weighing carrier, record the bridge load response, and then obtain the vehicle speed and axle spacing. Calculate the influence line matrix based on the vehicle speed, axle spacing, and mean vector of the influence lines. Calculate the axle load based on the influence line matrix and the bridge load response combined with a given regularization matrix, using this as the axle load for the main loop.

[0009] In the first iteration of the main loop, the given regularization matrix is ​​set to 0.

[0010] Step 2: Obtain the axle load covariance matrix. Calculate the load response covariance matrix based on the influence line covariance matrix, the measurement noise standard deviation, and the axle load covariance matrix obtained in the previous step. Update the axle load covariance matrix based on the load response covariance matrix.

[0011] Step 3: Repeat the sub-loop of Step 2 to update the axle weight covariance matrix until the predetermined number of times is reached, and save the updated axle weight covariance matrix.

[0012] Step 4: Update the regularization matrix based on the covariance matrix of the load response and the saved axle load covariance matrix, and then update the axle load based on the influence line matrix, the bridge load response and the updated regularization matrix.

[0013] The regularization matrix is ​​updated based on the covariance matrix of the load response and the stored axle load covariance matrix, using the following formula:

[0014] ;

[0015] in, Indicates the process The regularization matrix of the secondary main loop iteration; Indicates the process The axis weight covariance matrix of the secondary loop iteration;

[0016] Step 5: Repeat the main loop from Step 2 to Step 4 to update the axle load until the difference between the updated axle load and the previously obtained axle load is less than a preset value, and take the updated axle load as the final result of the bridge dynamic weighing algorithm.

[0017] Through the above operations, the regularization matrix during the update process is determined by the covariance matrix of the load response and the covariance matrix of the axle load. This regularization matrix, based on fully utilizing observed data, can automatically optimize for data with different noise levels through adaptive iterative updates, thus more comprehensively reflecting the influence of factors such as vehicle-bridge dynamic effects. Compared with traditional regularization algorithms, this algorithm exhibits stronger stability under noise interference, more effectively alleviates the data overfitting problem, and has higher computational efficiency, making it suitable for engineering applications in real-time dynamic weighing systems.

[0018] Furthermore, in step 1, the influence line covariance matrix is ​​obtained by calculating the correlation between the influence lines between each pair of sampling points set on the bridge.

[0019] The elements in the influence line covariance matrix are calculated using the following formula:

[0020] ;

[0021] in, Indicates the bridge's influence line at the 1st x The sampling point and the first y Covariance between sampling points; K To determine the number of influence lines obtained in the calibration experiment; For the first k The influence line is at the 1st x The values ​​at each sampling point; For the first k The influence line is at the 1st y The values ​​at each sampling point; This indicates the influence line mean at the th x The values ​​at each sampling point; This indicates the influence line mean at the th y The values ​​at each sampling point.

[0022] Furthermore, in step 2, obtaining the axle load covariance matrix includes: the axle load covariance matrix obtained in the first main loop and the... i+ The axis weight covariance matrix obtained in the first main loop;

[0023] The axle load covariance matrix obtained in the first main loop is based on preset conditions, including that the standard deviation of the axle load of each axle is 1kN and the correlation coefficient is 0.

[0024] The first i The axle load covariance matrix obtained in the +1st main loop is based on the... i Data is retrieved from the secondary main loop.

[0025] Furthermore, in step 2, the elements of the covariance matrix of the bridge load response are calculated using the following formula:

[0026] ;

[0027] in, Indicates the load response at the 1st The sampling point and the first Covariance between sampling points; Indicates the total number of axles; This represents the average axle load. This indicates that the influence line corresponding to the nth axle is at the th position. The covariance between the j-th sampling point and the j-th sampling point; Cn represents the number of samples corresponding to the distance between the n-th axle and the first axle; Indicates the standard deviation of measurement noise;

[0028] C n Calculated using the following formula:

[0029] ;

[0030] in, D n Indicates the first n The distance between each axle and the first axle; f The sampling frequency; v For vehicle speed.

[0031] Furthermore, in step 2, updating the axle load covariance matrix based on the load response covariance matrix includes: obtaining the updated axle load covariance matrix based on the load response covariance matrix, the influence line matrix, and the axle load covariance matrix.

[0032] The covariance matrix of the axle load is calculated using the following formula:

[0033] ;

[0034] in, and They represent the first h+ 1st subloop iteration and the 1st iteration h The axis weight covariance matrix of the secondary loop iteration; T represents the transpose operation; I represents the influence line matrix.

[0035] Furthermore, the axle load is calculated based on the influence line matrix and the bridge load response combined with the regularized matrix, expressed by the following formula:

[0036] ;

[0037] in, Indicates the first i The axle weight is obtained by +1 main loop iterations; Indicates the first The regularization matrix obtained from the secondary main loop iteration is in The time-regularized matrix is ​​set to 0; T represents the transpose operation; This indicates the bridge load response.

[0038] Furthermore, the condition that the difference between the axle load updated in this update and the previously obtained axle load is less than a preset value is expressed by the following formula:

[0039] ;

[0040] in, Indicates the first i The axle weight is obtained by +1 main loop iterations; This indicates the preset value.

[0041] Beneficial effects:

[0042] This invention provides a dynamic weighing algorithm for bridges based on regularization. By adding a penalty term to the error function, a formula for calculating axle load containing a regularization matrix is ​​obtained. The regularization matrix is ​​determined by the axle load covariance matrix and the load response covariance matrix. Compared to traditional regularization methods that rely on the L-curve method to determine a single regularization parameter, the new algorithm can adaptively iteratively solve for the global regularization parameter, which not only improves computational efficiency but also significantly reduces the risk of data overfitting.

[0043] The new algorithm considers the impact of vehicle-bridge dynamics on overfitting, assuming that the bridge influence line, axle load, and vehicle load response to the bridge follow different numerical distributions at different times, and that there are correlations between the measurement points. Therefore, this invention can effectively mitigate the calculation errors caused by vehicle-bridge dynamics, thereby improving the accuracy and stability of axle load identification.

[0044] Specifically, this invention, combining relevant theories of regularization algorithms, fully considers the influence of factors such as the dynamic effects of the influence line and axle load, as well as measurement noise, during axle load identification. Since measurement noise is unavoidable, it directly affects the identification results. Considering the dynamic effects of the influence line and axle load helps to more accurately fit the dynamic load response, thereby mitigating overfitting caused by the dynamic effects of the vehicle and axle, becoming a key factor in improving identification accuracy. By introducing a regularization algorithm and adding a penalty term to the error function, this invention, through iterative adaptive updating of the regularization matrix, can more accurately handle the influence of noise factors, enhancing the model's data adaptability and the reliability of the calculation results. Attached Figure Description

[0045] Figure 1 This is a flowchart of a bridge dynamic weighing algorithm based on a regularization algorithm according to Embodiment 1 of the present invention.

[0046] Figure 2 This is a schematic diagram of the bridge deck elevation of Embodiment 2 of the present invention;

[0047] Figure 3 This is a schematic diagram of the bridge cross-section in Embodiment 2 of the present invention;

[0048] Figure 4 This is a schematic diagram of the mean value of the bridge influence line in Embodiment 2 of the present invention;

[0049] Figure 5 This is a schematic diagram of the variance of the bridge influence line in Embodiment 2 of the present invention;

[0050] Figure 6 This is a schematic diagram of the covariance correlation coefficient of the bridge influence line in Embodiment 2 of the present invention;

[0051] Figure 7 This is a schematic diagram of the bridge dynamic response values ​​in Embodiment 2 of the present invention. Detailed Implementation

[0052] The technical solution of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms "an" or "a" and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms "connected" or "linked" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up," "down," "left," "right," etc., are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship also changes accordingly.

[0054] Example 1

[0055] Please see Figure 1 This application provides a bridge dynamic weighing algorithm based on a regularization algorithm, including the following steps:

[0056] Step 1: Using multiple sets of bridge response data obtained from calibration tests, extract a set of bridge influence lines from each set of responses. Statistically analyze the set of bridge influence lines to obtain the mean vector of the influence lines. Covariance matrix of influence lines Using bridges as the weighing platform for vehicles, the bridge load response is recorded. Next, obtain the vehicle speed and axle spacing. Calculate the influence line matrix I based on the vehicle speed, axle spacing, and the mean vector of the influence lines. Then, use the influence line matrix I and the bridge load response... Combined with a given regularization matrix Calculate axle load As the axis of the main cycle ;

[0057] Specifically, the influence line at the mid-span of the bridge was selected as the influence line used for vehicle axle load identification. Calibration tests were conducted to obtain multiple sets of bridge response data. For each set of response data, an influence line was obtained. Mathematical statistics were performed to obtain the mean vector of the influence lines. Covariance Matrix .

[0058] The bridge load response R when a vehicle crosses the bridge is obtained by using a weighing sensor installed at the mid-span of the bottom of the main beam of the bridge. * The vehicle speed is calculated by using sensors FAD1 and FAD2, located on either side of the weighing sensor at the bottom of the main beam of the bridge, to acquire the vehicle-bridge dynamic signal when a vehicle crosses the bridge. The dynamic signal is measured by the time interval between the peak values ​​of the vehicle-bridge dynamic signal and the distance between the two FAD sensors. v and axle spacing D .

[0059] Based on this, the influence line covariance matrix is ​​obtained by calculating the correlation between the influence lines between each pair of sampling points set on the bridge. The elements in the influence line covariance matrix are calculated using the following formula:

[0060] ;

[0061] in, Indicates the bridge's influence line at the 1st x The sampling point and the first y Covariance between sampling points; K To determine the number of influence lines obtained in the calibration experiment; For the first k The influence line is at the 1st x The values ​​at each sampling point; For the first k The influence line is at the 1st y The values ​​at each sampling point; This indicates the influence line mean at the th x The values ​​at each sampling point; This indicates the influence line mean at the th y The values ​​at each sampling point.

[0062] The following influence line covariance matrix is ​​obtained from the above:

[0063] ;

[0064] in, X The number of sampling points for the influence line is calculated using the following formula:

[0065] ;

[0066] in, L For the bridge length, f Sampling frequency, v For vehicle speed.

[0067] Step 2: Obtain the axle weight covariance matrix According to the influence line covariance matrix The standard deviation of the noise and the covariance matrix of the load response obtained in the previous step are measured, and the axle load covariance matrix is ​​updated based on the covariance matrix of the load response.

[0068] The acquisition of the standard deviation of the measurement noise is an existing technology and will not be elaborated on here.

[0069] When initially acquiring the axle load covariance matrix, it was obtained based on preset conditions, including a standard deviation of 1 kN for the axle load of each vehicle axle and a correlation coefficient of 0. The axle load covariance matrix was calculated using the standard deviation of measurement noise. All of these are existing technologies and will not be elaborated here. The subsequent calculations of the axle load mean vector and axle load covariance matrix are based on the data saved from the previous main loop iteration.

[0070] Specifically, the elements of the covariance matrix of the bridge load response are calculated using the following formula:

[0071] ;

[0072] in, Indicates the load response at the 1st The sampling point and the first Covariance between sampling points; Indicates the total number of axles; This represents the average axle load. This indicates that the influence line corresponding to the nth axle is at the th position. The covariance between the j-th sampling point and the j-th sampling point; Cn represents the number of samples corresponding to the distance between the n-th axle and the first axle; Indicates the standard deviation of measurement noise;

[0073] C n Calculated using the following formula:

[0074] ;

[0075] in, D n Indicates the first n The distance between each axle and the first axle; f The sampling frequency; v For vehicle speed.

[0076] For updating the axle load covariance matrix, based on the load response covariance matrix... Influence line matrix I and axis weight covariance matrix Obtain the updated axle weight covariance matrix ;

[0077] Covariance matrix of axle load Calculated using the following formula:

[0078] ;

[0079] in, and They represent the first h+ 1st subloop iteration and the 1st iteration h The axis weight covariance matrix of the secondary loop iteration; T represents the transpose operation.

[0080] Step 3: Repeat the sub-loop of Step 2 to iteratively update the axle weight covariance matrix until the predetermined number of iterations is reached, and save the updated axle weight covariance matrix.

[0081] In this embodiment, the axle weight covariance matrix is ​​updated 10 times. In other embodiments, the number of iterations of the axle weight covariance matrix can be adjusted based on the axle weight recognition accuracy requirements.

[0082] Step 4: Based on the covariance matrix of the load response The saved axis weight covariance matrix For regularized matrix Update, then based on influence line matrix I and bridge load response With the updated regularization matrix Update axle load;

[0083] Based on the covariance matrix of the load response The saved axis weight covariance matrix For regularized matrix An update is represented by the following formula:

[0084] ;

[0085] in, Indicates the first The regularization matrix obtained from the secondary main loop iteration; Indicates the process The axis weight covariance matrix of the secondary loop iteration.

[0086] The axle load is calculated based on the influence line matrix and the bridge load response combined with the regularization matrix, and is expressed by the following formula:

[0087] ;

[0088] in, Indicates the first The axle weight obtained from the secondary main loop iteration; Indicates the first The regularization matrix obtained from the second main loop iteration; T represents the transpose operation.

[0089] Step 5: Repeat the main loop from Step 2 to Step 4 to update the axle load until the difference between the updated axle load and the previously obtained axle load is less than a preset value, and take the updated axle load as the final result of the bridge dynamic weighing algorithm.

[0090] The difference between the axle load in this update and the previously obtained axle load will be less than a preset value, as expressed by the following formula:

[0091] ;

[0092] in, Indicates the first i The axle weight is obtained by +1 main loop iterations; This indicates the preset value.

[0093] Example 2

[0094] Take a simply supported beam bridge in China as an example. This bridge is a simply supported beam bridge composed of ten precast beams, with a main span of 40m, a bridge width of 24m, and four lanes in both directions. Figure 2 As shown.

[0095] The axle load of vehicles crossing the bridge is identified through the following steps:

[0096] (1) A calibration test was conducted on the bridge to obtain the distribution of the influence lines. Since the distribution of the influence lines is known, it can be used for subsequent calculations. The mean curve of the influence lines is shown in [reference needed]. Figure 4 The variance and correlation coefficient of the influence line are shown in the following figures. Figure 5 and Figure 6 .

[0097] (2) A vehicle moving load test was conducted on the bridge to obtain the measured test data. A two-axle vehicle with a total weight of 28.5t was selected as the loading vehicle (7.4t for the front axle, 21.1t for the rear axle, and a wheelbase of 4.7m), and it repeatedly drove across lane three at a speed of 30km / h. The number of vehicle runs was 10. During the test, axle detection sensors were installed under the flange plates on both sides of the mid-span section of the bridge. Figure 2 At point a, FAD1 and FAD2 are used to obtain information such as the number of vehicle axles, axle spacing, and vehicle speed. Figure 2 As shown; dynamic weighing sensors are installed at the bottom of the T-beams at the mid-span of the bridge to identify vehicle axle loads, such as... Figure 3 As shown. The obtained dynamic response values ​​of the bridge at the mid-span are as follows. Figure 7 As shown, the bridge dynamic response value at the mid-span of the bridge is the signal from ten weighing sensors. Figure 3 The sum of the load cells at point b.

[0098] (3) Axle load identification is performed on the axle dynamic response signal using a new algorithm. Given an initial regularization matrix... (Given an initial regularization matrix of 0) Solve for the initial axle load. The initial axle load covariance matrix is ​​set as an identity matrix (the closer the initial axle load covariance matrix is ​​to the true axle load covariance, the faster the algorithm iteration speed); the covariance matrix of the bridge load response is obtained based on the influence line covariance matrix, the measurement noise variance, and the initial axle load. 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 of 10 sets of vehicle-bridge dynamic responses of the same loaded vehicle; the axle load covariance matrix is ​​iteratively updated based on the influence line matrix and the load response covariance matrix; the regularization matrix is ​​calculated based on the axle load and load response covariance matrices. ; Calculate the new axle load Repeat the above process until the calculated axle load result converges. The calculation results are shown in Table 1.

[0099] It should be noted that before identifying axle load, the vehicle-axle dynamic response was filtered using a moving average filter to eliminate some noise and vehicle-axle coupling response. Considering the impact of vehicles on the bridge's dynamic response when entering and exiting the bridge, the lengths of both the vehicle's entry and exit sections were set to 10m.

[0100] Table 1: Vehicle axle load identification error table for the two algorithms.

[0101]

[0102] Note: Error = (Calculated value - Actual value) / Actual value × 100%, Unit: %.

[0103] As shown in Table 1, the mean and standard deviation of the axle load error obtained by the new algorithm in this application are both lower than those of the Tikhonov regularization algorithm. Taking the front axle as an example, the mean error of the new algorithm is 2.20%, which is less than the 5.32% of the traditional Tikhonov regularization algorithm. Correspondingly, the standard deviation of the error decreased from 45.98% (Tikhonov regularization algorithm) to 3.64%. This indicates that the bridge dynamic weighing algorithm based on regularization algorithm proposed in this application can significantly improve the accuracy of axle load identification and also improve the ability to resist overfitting.

[0104] Obtaining more accurate vehicle axle loads through highway bridge monitoring can, on the one hand, assist highway bridge management departments in efficiently managing overloading and reducing the number of overloaded vehicles crossing bridges; on the other hand, vehicle information can provide a reliable basis for accurately assessing the reliability and lifespan of highway bridges, contributing to the establishment of an intelligent highway bridge management system and extending the service life of highway bridges.

[0105] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A bridge dynamic weighing algorithm based on a regularization algorithm, characterized in that, The method comprises the following steps: Step 1: obtaining a plurality of groups of bridge response data through calibration tests, extracting a group of bridge influence lines from each group of responses, performing statistics on the set of bridge influence lines, obtaining an influence line mean vector and an influence line covariance matrix, taking the bridge as a carrier for vehicle weighing, recording the bridge load response, obtaining the vehicle speed and the axle spacing, calculating an influence line matrix according to the vehicle speed, the axle spacing and the influence line mean vector, and calculating the axle weight based on the influence line matrix, the bridge load response and a given regularization matrix, which is taken as the axle weight in the main loop; Step 2: obtaining an axle weight covariance matrix, calculating the covariance matrix of the load response according to the influence line covariance matrix, the measurement noise standard deviation and the axle weight obtained in the previous step, and updating the axle weight covariance matrix based on the covariance matrix of the load response; Step 3: repeating the sub-loop of step 2 to update the axle weight covariance matrix until a predetermined number of times is reached, and saving the updated axle weight covariance matrix; Step 4: updating the regularization matrix according to the covariance matrix of the load response and the saved axle weight covariance matrix, and updating the axle weight according to the influence line matrix, the bridge load response and the updated regularization matrix; The updating of the regularization matrix according to the covariance matrix of the load response and the saved axle weight covariance matrix is represented by the following formula: ； wherein, denotes the regularization matrix after the main loop iteration; denotes the regularization matrix after the sub loop iteration; The calculation of the axle weight based on the influence line matrix, the bridge load response and the regularization matrix is represented by the following formula: ； in, This represents the axle weight obtained in the (i+1)th iteration of the main loop; Indicates the first The regularization matrix obtained from the secondary main loop iteration is in The time-regularized matrix is ​​set to 0; T represents the transpose operation; Indicates the bridge load response; Step 5: repeating the main loop of steps 2 to 4 to update the axle weight until the difference between the updated axle weight and the axle weight obtained last time is less than a preset value, and taking the updated axle weight as the final result of the bridge dynamic weighing algorithm.

2. The bridge dynamic weighing algorithm based on regularization algorithm according to claim 1, characterized in that, In step 1, the influence line covariance matrix is obtained by calculating the correlation between the influence lines of two sampling points arranged on the bridge; The elements in the influence line covariance matrix are 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; denotes the value of the influence line mean at the y th sampling point.

3. The bridge dynamic weighing algorithm based on regularization algorithm of claim 1, wherein, In step 2, the obtaining the axle load covariance matrix comprises: the axle load covariance matrix obtained by the first main loop and the axle load covariance matrix obtained by the first i+ 1 main loop The axle weight covariance matrix obtained in the first main loop is obtained based on a preset condition, and the preset condition includes that the standard deviation of each axle weight is 1kN and the correlation coefficient is 0; The first i The axle load covariance matrix obtained in the first i Data saved in the first main loop acquisition.

4. The bridge dynamic weighing algorithm based on regularization algorithm of claim 1, wherein, In step 2, the elements of the covariance matrix of the bridge 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 axle load; denotes the covariance of the influence line corresponding to the th axle between the th sampling point and the th sampling point; Cn denotes the number of samples corresponding to the distance between the 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 f is the sampling frequency; v is the vehicle speed.​ 5. The bridge dynamic weighing algorithm based on regularization algorithm of claim 1, wherein, In step 2, the updating of the axle weight covariance matrix based on the covariance matrix of the load response comprises: obtaining the updated axle weight covariance matrix based on 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 Ri and R2denote the axial covariance matrix of the first h+ 1stsub-cycle iteration and the second h sub-cycle iteration, respectively; T denotes the transpose operation; and I denotes the influence line matrix.

6. The bridge dynamic weighing algorithm based on regularization algorithm of claim 1, wherein, The condition that the difference between the updated axle weight and the axle weight obtained last time is less than a preset value is represented by the following formula: ； wherein, represents the axis weight obtained in the first i +1 main loop iteration; represents a preset value.

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