A high-precision bridge moving load identification method

Abstract

The present invention relates to the technical field and discloses a high-precision bridge moving load identification method. The method comprises: calibrating the bridge to obtain the influence line distribution of the bridge; obtaining the load response generated by the monitoring vehicle when passing the bridge, and performing axle weight identification using the Moses algorithm to obtain the initial value of the axle weight; obtaining the contribution diagonal matrix of the load response based on the influence line distribution, the noise signal in the load response, and the axle weight, and obtaining the updated axle weight according to the contribution diagonal matrix combined with the load response and the influence line distribution; repeating the previous step until the difference between the axle weight obtained this time and the axle weight obtained previously is lower than a predetermined threshold, and using the axle weight obtained this time as the axle weight of the monitoring vehicle, thereby solving the problem of low axle weight identification accuracy of existing bridge moving load identification systems.

Description

Technical Field

[0001] The present invention relates to the technical field of highway bridge monitoring, and in particular to a high-precision bridge moving load identification method. Background Art

[0002] The Bridge Moving Load Identification System, which uses bridges as a carrier to weigh vehicles, has become a crucial monitoring tool for traffic managers, enabling them to monitor vehicle overweights in real time. Without interrupting traffic, the Bridge Moving Load Identification System uses sensors installed on the bridge to capture the load response of vehicles on the bridge in real time, thereby inverting information such as vehicle speed, wheelbase, and axle weight.

[0003] Currently, most commercial bridge moving load identification systems are developed based on the Moses algorithm. Based on the influence line at the bridge's midspan, this algorithm minimizes the sum of the squares of the differences between the measured and theoretical values of the vehicle's load response to the bridge, establishing an error function. The partial derivative of each axle load is then taken to determine the axle weight. When the least squares method is used to minimize the error function, the errors in the load response at each moment are independent and have the same standard deviation, resulting in the load response at each moment having the same impact on the axle weight identification result. However, in reality, the error in the load response is determined by factors such as the vehicle axle weight, the distribution of the influence line, and noise, and is not a fixed value. Therefore, the Moses algorithm assumes that each load response value contributes equally to axle weight identification, which is inconsistent with reality and results in low axle weight identification accuracy.

[0004] Although the Moses algorithm has been modified to improve the axle load identification accuracy of bridge moving load identification systems, most studies only consider the impact of measurement errors on axle load identification accuracy, assuming that the bridge influence line is a constant value and ignoring the impact of the influence line distribution on axle load identification accuracy. This makes it difficult to effectively improve vehicle axle load identification accuracy. Summary of the Invention

[0005] The present invention provides a high-precision bridge moving load identification method to solve the problem of low axle load identification accuracy of the existing bridge moving load identification system.

[0006] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0007] The present invention provides a high-precision bridge moving load identification method, comprising the following steps:

[0008] Step 1: Calibrate the bridge and obtain the influence line distribution of the bridge;

[0009] Step 2: Obtain the load response of the bridge when the monitoring vehicle passes through the bridge, and use the Moses algorithm to identify the axle weight to obtain the initial value of the axle weight;

[0010] Step 3: Obtain the noise signal generated by the bridge when there is no vehicle traveling. Obtain the contribution diagonal matrix of the load response based on the influence line distribution, the noise signal in the load response, and the axle weight. Construct an error function based on the contribution diagonal matrix, axle weight, load response, and influence line distribution. Update the axle weight based on the error function and the axle weight corresponding to the current iteration step.

[0011] The step of obtaining a diagonal matrix of contribution to the load response based on the influence line distribution, the noise signal in the load response, and the axle load comprises: calculating a variance vector based on the noise signal in the load response, obtaining the variance vector of the noise signal in the load response, and obtaining a diagonal matrix of contribution to the load response based on the variance vector of the noise signal in the load response in combination with the influence line distribution and the axle load;

[0012] The noise signal in the load response is the signal collected by the load cell when there is no vehicle running on the bridge;

[0013] The method of obtaining a diagonal matrix of contribution to the load response based on the variance vector of the noise signal in the load response in combination with the influence line distribution and the axle load comprises: obtaining a load response variance vector based on the variance vector of the noise signal in the load response in combination with the influence line variance matrix constructed based on the influence line distribution and the axle load square vector obtained based on the axle load; obtaining a square vector of coefficient of variation based on the load response variance vector in combination with the mean influence line matrix constructed based on the influence line distribution and the axle load vector; and constructing a diagonal matrix of contribution to the load response based on the square vector of coefficient of variation;

[0014] The contribution diagonal matrix W is expressed by the following formula:

[0015] ;

[0016] Where C represents the square vector of the coefficient of variation, Represents element-by-element division operation in a matrix;

[0017] The square vector of the coefficient of variation is expressed by the following formula:

[0018] ;

[0019] ;

[0020] ;

[0021] Where S represents the load response variance vector; M represents the theoretical response vector; R represents the variance vector of the load response measurement error; L represents the influence line variance matrix constructed based on the influence line distribution; G represents the vehicle axle load square vector, V represents the mean influence line matrix constructed based on the influence line distribution; A represents the axle load vector; Represents element-wise exponentiation;

[0022] Step 4: Repeat step 3 until the difference between the axle weight obtained this time and the axle weight obtained last time is lower than a predetermined threshold, and use the axle weight obtained this time as the axle weight of the monitored vehicle.

[0023] Specifically, the algorithm of the present invention establishes an adaptive response-weight matching mechanism: based on the differences in the contribution of load responses to axle load identification, the algorithm automatically assigns greater weights to high responses and lesser weights to low responses. For example, during sections of travel such as when a vehicle is approaching or exiting a bridge, since the vehicle does not directly impact the bridge, the axle dynamic response primarily comes from factors such as residual vibration and noise from vehicle-bridge coupling. To improve the accuracy of axle load identification, it is important to reduce this impact, thus assigning a smaller weight coefficient. On the other hand, when the vehicle is fully on the bridge, the vehicle load has a greater response to the bridge, requiring a larger weight coefficient.

[0024] Furthermore, the influence line distribution At each moment, it obeys the Gaussian distribution:

[0025] ;

[0026] in, for t The influence line mean at time , for t The variance of the influence line at time .

[0027] Furthermore, the method further includes step 5: obtaining the axle power signal of the vehicle, and calculating the speed and wheelbase values of the monitored vehicle based on the time difference between the peak values of the axle power signal and the distance between the sensors for obtaining the vehicle power signal.

[0028] According to the above operation, the speed and wheelbase of the monitored vehicle can be measured while measuring the axle weight.

[0029] Furthermore, constructing the error function according to the contribution diagonal matrix, the axle weight, the load response, and the influence line distribution includes: constructing an error function under the influence of the axle weight and the influence line distribution according to the contribution diagonal matrix, the axle weight, the load response, and the influence line distribution;

[0030] The error function under the influence of axle load and influence line distribution is expressed by the following formula:

[0031] ;

[0032] in, represents the error function, N is the total number of axles, T is the total time the vehicle moves on the bridge, Indicates the n axle load of each axle; Indicates the n Axles in t The bridge influence line value corresponding to the loading position at the time; Indicates t The load response of the measured bridge at time Indicates t The contribution of the load response at the time.

[0033] Furthermore, the axle weight corresponding to the current iteration step based on the error function includes: calculating a partial derivative of each axle weight according to the error function, obtaining an axle weight expression when the partial derivative is zero, and obtaining the axle weight corresponding to the current iteration step based on the axle weight expression;

[0034] The axle weight corresponding to the current iteration step is calculated by the following formula:

[0035] ;

[0036] in, represents the updated axle load; I represents the bridge influence line matrix, represents the transpose of the bridge influence line matrix; i represents the iteration step; represents the load response vector.

[0037] Furthermore, the partial derivative of each axle weight according to the error function is expressed by the following formula:

[0038] ;

[0039] in, Indicates the j axle load of each axle; Indicates the j Axles in t The influence line value corresponding to the loading position at the moment.

[0040] Furthermore, the difference between the axle weight obtained this time and the axle weight obtained last time is lower than the predetermined threshold value, which is expressed by the following formula:

[0041] ;

[0042] in, Indicates the axle weight before updating, Indicates a predetermined threshold.

[0043] Beneficial effects:

[0044] The present invention provides a high-precision bridge moving load identification method, which takes into account that the bridge influence line obeys different numerical distributions at different times, and combines factors such as the bridge influence line distribution, vehicle axle weight and noise to obtain the coefficient of variation of the load response at each moment. In the vehicle load identification process, the coefficient of variation of the load response at each moment is introduced into the axle weight solution formula in the form of axle weight identification contribution. The greater the contribution of the load response, the greater its contribution to axle weight identification, and vice versa. Distinguishing the contribution of different load responses to axle weight identification can improve the axle weight identification accuracy to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of a high-precision bridge moving load identification method according to Example 1 of the present invention;

[0046] Figure 2 Schematic diagram of the influence line mean curve in Example 1 of the present invention;

[0047] Figure 3 Schematic diagram of the variance curve of the influence line of Example 1 of the present invention;

[0048] Figure 4 This is a schematic elevation diagram of a measurement bridge according to Example 2 of the present invention, wherein A represents a FAD sensor and B represents a weighing sensor;

[0049] Figure 5 This is a schematic cross-sectional view of a measurement bridge according to Example 2 of the present invention, wherein A represents a FAD sensor and B represents a weighing sensor;

[0050] Figure 6 This is a diagram of the axle dynamic response signal of Example 2 of the present invention. DETAILED DESCRIPTION

[0051] 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.

[0052] 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.

[0053] Example 1

[0054] See Figure 1 The embodiment of the present invention provides a high-precision bridge moving load identification method, comprising the following steps:

[0055] Step 1: Calibrate the bridge and obtain the influence line distribution of the bridge;

[0056] See Figure 2-3 , the influence line distribution obeys the Gaussian distribution:

[0057] ;

[0058] in, is the mean value of the influence line at time t, is the variance of the influence line at time t;

[0059] Step 2: Obtain the load response of the bridge when the monitoring vehicle passes through the bridge, and obtain the axle weight through axle weight identification using the Moses algorithm;

[0060] Specifically, a load cell installed at the mid-span of the bridge's main beam bottom is used to obtain the bridge load response when a vehicle passes through the bridge. The influence line at the mid-span of the bridge is selected as the influence line distribution used for vehicle axle load identification. Based on the influence line distribution, a bridge influence line matrix is constructed. Combined with the principle of least squares, the partial derivative of the error function with respect to each axle load is calculated. The minimum value of the error function when the partial derivative is zero is taken as the axle weight.

[0061] First, establish the error function corresponding to the Moses algorithm:

[0062] ;

[0063] in, t Indicates the vehicle's motion moment, T represents the total time the vehicle moves on the bridge, N Indicates the number of axles; Indicates t The load response of the measured bridge at time Indicates the n Axles in t The bridge influence line value corresponding to the loading position at the time, Indicates the n axle load of each axle; represents the load response vector, I represents the bridge influence line matrix, and A represents the axle load vector;

[0064] The error function is established using the least squares method, and the partial derivative of the error function with respect to each axle weight is calculated. When the partial derivative of the error function with respect to each axle weight is zero, the error function takes its minimum value. By solving the calculation, the initial axle weight of the vehicle traveling on the bridge is obtained, which is expressed as:

[0065] ;

[0066] in, Indicates the axle weight obtained by the Moses algorithm, represents the load response, I represents the influence line matrix based on the bridge, Represents the transpose of the bridge influence line matrix.

[0067] Step 3: Obtain the noise signal in the load response of the bridge when there is no vehicle traveling. Obtain the contribution diagonal matrix of the load response based on the influence line distribution, the noise signal in the load response, and the axle weight. Construct an error function based on the contribution diagonal matrix, axle weight, load response, and influence line distribution. Update the axle weight based on the error function and the axle weight corresponding to the current iteration step.

[0068] Specifically, a load cell is used to collect signals of the bridge when no vehicle is traveling on it as noise signals in the load response, and the variance vector R of the noise is calculated.

[0069] Specifically, the variance vector of the load response measurement error is obtained based on the influence line distribution, the noise signal in the load response, and the axle load, and the load response variance vector is obtained by combining the influence line variance matrix constructed based on the influence line distribution and the axle load square vector obtained based on the axle load; based on the load response variance vector, the square vector of the coefficient of variation is obtained by combining the mean influence line matrix constructed based on the influence line distribution and the axle load vector; based on the square vector of the coefficient of variation, a contribution diagonal matrix of the load response is constructed, and the updated axle load is obtained based on the contribution diagonal matrix, the load response, and the bridge influence line matrix constructed based on the influence line distribution, including the following steps:

[0070] Step 301: Calculate the square vector of the coefficient of variation. Multiply the bridge influence line variance matrix by the square vector of the initial axle load and add the result to the variance vector of the response measurement error to obtain the response variance vector. Multiply the bridge mean influence line matrix by the axle load vector to obtain the theoretical response vector. Divide the response variance vector by the square of each element of the theoretical response vector to obtain the square vector of the coefficient of variation. The expression is:

[0071] ;

[0072] ;

[0073] ;

[0074] Among them, S (i) represents the load response variance vector; M (i) represents the theoretical load response vector; The variance vector representing the load response measurement error; represents the influence line variance matrix constructed based on the influence line distribution; represents the square vector of vehicle axle weight, and V represents the mean influence line matrix constructed based on the influence line distribution.

[0075] Step 302: Obtain the initial contribution diagonal matrix of the bridge response , the expression is:

[0076] ;

[0077] Step 303: Diagonal matrix of contribution Substitute the axle weight expression when the partial derivative value is zero to obtain the updated axle weight , calculate the corresponding measurement error variance vector ;

[0078] Specifically, the error function under the influence of axle weight and influence line distribution is constructed according to the contribution diagonal matrix, axle weight, load response and influence line distribution. The partial derivative of each axle weight is obtained according to the error function, and the axle weight expression when the partial derivative is zero is obtained. Substitute the axle weight expression when the partial derivative value is zero and obtain the updated axle weight based on the axle weight expression;

[0079] Regarding the error function, the error of the vehicle load response to the bridge obeys different numerical distributions at different times and is related to factors such as the influence line distribution, axle weight and measurement error. That is, the error of the load response has heteroscedasticity, so the contribution diagonal matrix of the load response is introduced into the constructed error function. , and its error function is as follows:

[0080] ;

[0081] Among them, Indicates the t The contribution of the load response at time t, and ;

[0082] Calculate the partial derivative of the error function with respect to each axle load:

[0083] ;

[0084] in, n and j Respectively represent n Hedi j axles; Indicates the n Axles in t The bridge influence line value corresponding to the loading position at the time; Indicates the j Axles in t The influence line value corresponding to the loading position at the moment.

[0085] Let the partial derivative be zero, and we can get the axle weight expression at this time:

[0086] ;

[0087] Wherein, the contribution diagonal matrix of load response is determined by the variance of axle load, influence line variance and measurement error;

[0088] Step 4: Repeat step 3 until the difference between the axle weight obtained this time and the axle weight obtained last time is lower than a predetermined threshold, and use the axle weight obtained this time as the axle weight of the monitored vehicle;

[0089] Specifically, repeat steps 301 to 303 in step 3 until the calculated axle weight results converge, and the two iterations before and after Buhe The axle weight difference of the step is less than the predetermined threshold , whose expression is:

[0090] ;

[0091] In summary, a high-precision bridge moving load identification method considers the different numerical distributions of the bridge influence line at different times. This method, combined with factors such as the bridge influence line distribution, vehicle axle load, and noise, derives the coefficient of variation of the load response at each moment. During the vehicle load identification process, the coefficient of variation of the load response at each moment is incorporated into the axle load solution formula as a contribution to axle load identification. Therefore, the contribution of the load response value at each moment to axle load identification is considered during the calculation process. This allows the contribution of different load responses to axle load identification to be differentiated, effectively improving axle load identification accuracy.

[0092] Example 2

[0093] Take a domestic simply supported beam bridge as an example. The bridge is composed of ten precast beams, with a main span of 40m, a width of 24m, and four lanes in both directions.

[0094] Perform the following steps to identify the axle weight of vehicles crossing the bridge:

[0095] (1) Carry out vehicle moving load test on the bridge and obtain the test measured data. The test selected a two-axle vehicle with a total weight of 28.5 tons as the loading vehicle (front axle 7.4 tons, rear axle 21.1 tons, and axle spacing of 4.7 meters). The vehicle was repeatedly driven through lane 3 at a speed of 30 km / h. The number of driving times was 10. During the test, axle detection sensors ( Figure 4 FAD1 and FAD2 at A in the figure) obtain information such as the number of vehicle axles, wheelbase and speed, such as Figure 4 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 5 The bridge dynamic response value at the mid-span position is shown as Figure 6 As shown, the bridge dynamic response value at the mid-span position is the sum of the ten load cell signals ( Figure 5 Bridge bottom sensor at B in the figure).

[0096] (2) The load cell is used to collect the signal of the bridge when there is no vehicle passing through it as the noise signal in the load response, and the variance vector R of the noise signal is calculated.

[0097] (3) The axle weight is identified by the axle weight calculation formula of the Moses algorithm using the algorithm of the present invention and the Moses algorithm. The initial axle weight is solved using the axle weight calculation formula of the Moses algorithm. (The axle weight obtained at this time is also used to compare with the results obtained by the algorithm of the present invention); combined with the axle weight obtained , the variance vector R of the noise signal in the load response and the variance matrix of the influence line, and calculate the current iteration step i The corresponding load response variance vector The variance of the bridge influence line used at this time is the variance of 10 groups of influence lines calculated based on the influence line algorithm based on 10 groups of vehicle-bridge dynamic responses of the same loaded vehicle; the inverse vector of the response variance is normalized, and the initial contribution diagonal matrix of the bridge response is calculated using the contribution diagonal matrix formula ; The contribution diagonal matrix of the bridge response will be obtained Substitute into the axle weight expression to get the new axle weight The above process is repeated until the calculated axle load converges. The calculation results are shown in Table 1.

[0098] It is 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 length of both the vehicle entry and exit sections is set to 10 meters.

[0099] Table 1 Vehicle axle weight recognition error table of two algorithms Unit: %

[0100]

[0101] Note: Error = (calculated value - true value) / true value × 100%

[0102] Table 1 shows that the axle load error mean and standard deviation obtained by a high-precision bridge moving load identification method are both lower than those of the Moses algorithm. Taking the front axle as an example, the mean error of the present invention is 0.56%, which is less than the 2.06% of the Moses algorithm. Correspondingly, the standard deviation of the error is reduced from 49.04% (Moses algorithm) to 37.43% (present invention). This demonstrates that the high-precision bridge moving load identification method provided by the present invention can improve the accuracy of axle load identification to a certain extent.

[0103] 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.

[0104] 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 high-precision bridge moving load identification method, characterized in that: The steps include: Step 1: Calibrate the bridge and obtain the influence line distribution of the bridge; The influence line distribution At each moment, it obeys the Gaussian distribution: ； in, for t The influence line mean at time , for t The variance of the influence line at time t; Step 2: Obtain the load response of the bridge when the monitoring vehicle passes through the bridge, and use the Moses algorithm to identify the axle weight to obtain the initial value of the axle weight; Step 3: Obtain the noise signal in the load response of the bridge when there is no vehicle traveling. Obtain the contribution diagonal matrix of the load response based on the influence line distribution, the noise signal in the load response, and the axle weight. Construct an error function based on the contribution diagonal matrix, axle weight, load response, and influence line distribution. Update the axle weight based on the error function and the axle weight corresponding to the current iteration step. The step of obtaining a diagonal matrix of contribution to the load response based on the influence line distribution, the noise signal in the load response, and the axle load comprises: calculating a variance vector based on the noise signal in the load response, obtaining the variance vector of the noise signal in the load response, and obtaining a diagonal matrix of contribution to the load response based on the variance vector of the noise signal in the load response in combination with the influence line distribution and the axle load; The noise signal in the load response is the signal collected by the load cell when there is no vehicle running on the bridge; The method of obtaining a diagonal matrix of contribution to the load response based on the variance vector of the noise signal in the load response in combination with the influence line distribution and the axle load comprises: obtaining a load response variance vector based on the variance vector of the noise signal in the load response in combination with the influence line variance matrix constructed based on the influence line distribution and the axle load square vector obtained based on the axle load; obtaining a square vector of coefficient of variation based on the load response variance vector in combination with the mean influence line matrix constructed based on the influence line distribution and the axle load vector; and constructing a diagonal matrix of contribution to the load response based on the square vector of coefficient of variation; The contribution diagonal matrix W is expressed by the following formula: ； Where C represents the square vector of the coefficient of variation, Represents element-by-element division operation in a matrix; The square vector of the coefficient of variation is expressed by the following formula: ； ； ； Where S represents the load response variance vector; M represents the theoretical response vector; R represents the variance vector of the noise signal in the load response; L represents the influence line variance matrix constructed based on the influence line distribution; G represents the vehicle axle load square vector, V represents the mean influence line matrix constructed based on the influence line distribution; A represents the axle load vector; Represents element-wise exponentiation; Step 4: Repeat step 3 until the difference between the axle weight obtained this time and the axle weight obtained last time is lower than a predetermined threshold, and use the axle weight obtained this time as the axle weight of the monitored vehicle.

2. The high-precision bridge moving load identification method according to claim 1 is characterized in that: The method further includes step 5: obtaining the axle power signal of the vehicle, and calculating the speed and wheelbase values of the monitored vehicle according to the time difference between the peak values of the axle power signal and the distance between the sensors for obtaining the vehicle power signal.

3. The high-precision bridge moving load identification method according to claim 1 is characterized in that: The constructing of the error function according to the contribution diagonal matrix, the axle weight, the load response and the influence line distribution includes: constructing an error function under the influence of the axle weight and the influence line distribution according to the contribution diagonal matrix, the axle weight, the load response and the influence line distribution; The error function under the influence of axle load and influence line distribution is expressed by the following formula: ； in, represents the error function, N is the total number of axles, T is the total time the vehicle moves on the bridge, Indicates the n axle load of each axle; Indicates the n Axles in t The bridge influence line value corresponding to the loading position at the time; Indicates t The load response of the measured bridge at time Indicates t The contribution of the load response at the time.

4. The high-precision bridge moving load identification method according to claim 3 is characterized in that: The axle weight corresponding to the current iteration step based on the error function includes: calculating a partial derivative of each axle weight according to the error function, obtaining an axle weight expression when the partial derivative is zero, and obtaining the axle weight corresponding to the current iteration step based on the axle weight expression; The axle weight corresponding to the current iteration step is calculated by the following formula: ； in, represents the updated axle load; I represents the bridge influence line matrix, represents the transpose of the bridge influence line matrix; i represents the iteration step; represents the load response vector.

5. The high-precision bridge moving load identification method according to claim 4 is characterized in that: The partial derivative of each axle weight according to the error function is expressed by the following formula: ； in, Indicates the j axle load of each axle; Indicates the j Axles in t The influence line value corresponding to the loading position at the moment.

6. The high-precision bridge moving load identification method according to claim 5 is characterized in that: The difference between the axle weight obtained this time and the axle weight obtained previously is lower than the predetermined threshold value is expressed by the following formula: ； in, Indicates the axle weight before updating, Indicates a predetermined threshold.

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