High-precision bridge moving load identification method

Abstract

The invention relates to the technical field, and discloses a high-precision bridge moving load identification method. The method comprises the following steps: calibrating a bridge to obtain influence line distribution of the bridge; obtaining a load response to the bridge when the monitoring vehicle passes through the bridge, and carrying out axle load recognition through a Moses algorithm to obtain an initial value of the axle load; obtaining a contribution degree diagonal matrix of the load response based on the influence line distribution, a noise signal in the load response and the axle load, and obtaining the updated axle load according to the contribution degree diagonal matrix in combination with the load response and the influence line distribution; the previous step is repeatedly executed until the difference value between the axle load obtained this time and the axle load obtained last time is lower than a preset threshold value, the axle load obtained this time serves as the axle load of the monitoring vehicle, and the problem that the axle load recognition precision of an existing bridge moving load recognition system is low is solved.

Description

Technical Field

[0001] The 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 is a system that uses the bridge as a carrier to weigh vehicles. It has gradually developed into one of the important monitoring tools for traffic managers to monitor vehicle overweight in real time. The bridge moving load identification system can obtain the load response of the vehicle to the bridge in real time without interrupting traffic, using sensors installed on the bridge, and then calculate the vehicle speed, wheelbase, axle weight and other information. At present, most commercial bridge moving load identification systems are developed based on the Moses algorithm. Based on the influence line at the mid-span position of the bridge, the algorithm minimizes the sum of the squares of the difference between the test value and the theoretical value of the vehicle load response to the bridge, establishes an error function, and calculates the partial derivative of each axle weight to solve the axle weight. When the least squares method is used to minimize the error function, the errors of the load response at each moment are independent of each other and have the same standard deviation, which leads to the same impact of the load response at each moment on the axle weight identification result. However, in reality, the error of 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 has the same contribution to axle weight identification, which is inconsistent with the actual situation, resulting in low axle weight identification accuracy.

[0003] Later, although the Moses algorithm was modified to improve the axle weight recognition accuracy of the bridge moving load recognition system, most studies only considered the impact of measurement errors on axle weight recognition accuracy, assuming that the bridge influence line is a constant value, and ignoring the impact of the influence line distribution on axle weight recognition accuracy, it is difficult to effectively improve the recognition accuracy of vehicle axle weight. Summary of the invention

[0004] The invention provides a high-precision bridge moving load identification method to solve the problem of low axle weight identification accuracy of the existing bridge moving load identification system.

[0005] In order to achieve the above object, the present invention is implemented by the following technical solutions: The present invention provides a high-precision bridge moving load identification method, comprising the following steps: Step 1: Calibrate the bridge and obtain the influence line distribution of the bridge; Step 2: Obtain the load response of the bridge when the monitoring vehicle passes through the bridge, and obtain the initial value of the axle weight by performing axle weight identification through the Moses algorithm; Step 3: Obtain the noise signal generated by the bridge when there is no vehicle running, 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 the error function based on the contribution diagonal matrix, axle weight, load response and influence line distribution, and update the axle weight based on the error function and the axle weight corresponding to the current iteration step; 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.

[0006] Specifically, the algorithm of the present invention can establish a response-weight adaptive matching mechanism: based on the difference in the contribution of load response to axle weight identification, the algorithm automatically assigns a larger weight to a high response and a smaller weight to a low response. For example, in the vehicle on-bridge section and the vehicle off-bridge section, in these two driving sections, since the vehicle does not directly act on the bridge, the dynamic response of the vehicle-bridge at this time basically comes from factors such as residual vibration and noise of vehicle-bridge coupling. When performing axle weight identification, it is necessary to reduce the impact of this part on the accuracy of the result to improve the accuracy of the result, so a smaller weight coefficient should be assigned; when the vehicle is fully on the bridge, the response of the vehicle load to the bridge is large, and a larger weight coefficient needs to be assigned.

[0007] Furthermore, the influence line distribution At each moment, it follows a Gaussian distribution: ; in, for t The influence line mean at time , for t The variance of the influence line at time .

[0008] Furthermore, the method also includes step 5: acquiring 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 acquiring the vehicle power signal.

[0009] According to the above operation, the speed and wheelbase of the monitored vehicle can be measured while measuring the axle weight.

[0010] Further, the step of obtaining a contribution diagonal matrix of the load response based on the influence line distribution, the noise signal in the load response, and the axle weight includes: calculating a variance vector according to the noise signal in the load response, obtaining the variance vector of the noise signal in the load response, and obtaining a contribution diagonal matrix of the load response based on the variance vector of the noise signal in the load response combined with the influence line distribution and the axle weight; The noise signal in the load response is a signal collected by the weighing sensor when there is no vehicle running on the bridge.

[0011] Further, 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 weight includes: obtaining a variance vector of the load response 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 weight square vector obtained based on the axle weight; obtaining a square vector of the 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 weight vector; constructing a diagonal matrix of contribution to the load response based on the square vector of the 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, Indicates that the data in the matrix are calculated separately; The square vector of the coefficient of variation is expressed by the following formula: ; ; ; Among them, 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 weight square vector, V represents the mean influence line matrix constructed based on the influence line distribution; A represents the axle weight vector; Represents element-wise exponentiation.

[0012] Further, constructing the error function according to the contribution diagonal matrix, the axle weight, the load response and the influence line distribution includes: constructing the 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 n axle weight of each axle; Indicates n Axles in t The bridge influence line value corresponding to the loading position at the time; Indicated in t The load response of the measured bridge at time Indicated in t The contribution of the load response at the time.

[0013] Further, 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.

[0014] Furthermore, the partial derivative of each axle weight according to the error function is expressed by the following formula: ; in, Indicates j axle weight of each axle; Indicates j Axles in t The influence line value corresponding to the loading position at the moment.

[0015] Furthermore, the difference between the axle weight obtained this time and the axle weight obtained last time is lower than the predetermined threshold value by the following formula: ; in, Indicates the axle weight before updating, Indicates a predetermined threshold.

[0016] Beneficial effects: 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 accuracy of axle weight identification to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of a high-precision bridge moving load identification method according to Embodiment 1 of the present invention; Figure 2 Schematic diagram of the influence line mean curve in Example 1 of the present invention; Figure 3 Schematic diagram of the variance curve of the influence line of Example 1 of the present invention; Figure 4 This is a schematic elevation diagram of a measuring bridge according to Embodiment 2 of the present invention, wherein A represents a FAD sensor and B represents a weighing sensor; Figure 5 This is a schematic cross-sectional view of a measuring bridge according to Embodiment 2 of the present invention, wherein A represents a FAD sensor and B represents a weighing sensor; Figure 6 This is a diagram of the axle dynamic response signal of Example 2 of the present invention. DETAILED DESCRIPTION

[0018] The technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, "one" or "one" and other similar words do not indicate quantity restrictions, but indicate the existence of at least one. "Connect" or "connected" and other similar words 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 described object changes, the relative positional relationship also changes accordingly.

[0020] Example 1 See also Figure 1 The embodiment of the present invention provides a high-precision bridge moving load identification method, comprising the following steps: Step 1: Calibrate the bridge and obtain the influence line distribution of the bridge; See also Figure 2-3 , the influence line distribution follows the Gaussian distribution: ; in, is the influence line mean at time t, is 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 obtain the axle weight by performing axle weight identification using the Moses algorithm; Specifically, a load cell installed at the mid-span of the bottom of the bridge main beam is used to obtain the bridge load response when the vehicle passes the bridge, and the influence line at the mid-span of the bridge is selected as the influence line distribution used for vehicle axle weight identification. The bridge influence line matrix is ​​constructed according to the influence line distribution, and the partial derivative of the error function for each axle weight is calculated in combination with the principle of least squares method. The minimum value of the error function when the partial derivative is zero is taken as the axle weight; First, establish the error function corresponding to the Moses algorithm: ; in, t Indicates the vehicle motion moment, T represents the total time the vehicle moves on the bridge, N Indicates the number of axles; Indicated in t The load response of the measured bridge at time Indicates n Axles in t The bridge influence line value corresponding to the loading position at time , Indicates n axle weight of each axle; represents the load response vector, I represents the bridge influence line matrix, and A represents the axle load vector; The error function is established according to the least squares method, and the partial derivative of the error function is calculated for each axle weight. When the partial derivative of the error function for each axle weight is zero, the error function takes the minimum value. By solving the calculation, the initial axle weight of the vehicle traveling on the bridge is obtained, and its expression is: ; 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.

[0021] Step 3: Obtain the noise signal in the load response of the bridge when there is no vehicle running, 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 the error function based on the contribution diagonal matrix, axle weight, load response and influence line distribution, and update the axle weight based on the error function and the axle weight corresponding to the current iteration step; Specifically, a load cell is used to collect a signal of the bridge when no vehicle is running as a noise signal in the load response, and a variance vector R of the noise is calculated.

[0022] Specifically, the variance vector of the load response measurement error is obtained according to the influence line distribution, the noise signal in the load response and the axle weight, 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 weight square vector obtained based on the axle weight; 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 weight vector; the contribution diagonal matrix of the load response is constructed based on the square vector of the coefficient of variation, and the updated axle weight is obtained according to the contribution diagonal matrix combined with the load response and the bridge influence line matrix constructed based on the influence line distribution, including the following steps: Step 301: Calculate the square vector of the coefficient of variation, multiply the bridge influence line variance matrix by the initial axle load square vector, and then 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, and 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: ; ; ; Among them, S (i) represents the load response variance vector; M (i) represents the theoretical load response vector; Variance vector representing the measurement error of the load response; 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.

[0023] Step 302: Normalize the response variance vector to obtain the initial contribution diagonal matrix of the bridge response: , the expression is: ; 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 ; 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 calculated according to the error function to obtain the axle weight expression when the partial derivative is zero. Substitute the axle weight expression when the partial derivative value is zero and obtain the updated axle weight based on the axle weight expression; 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 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. , its error function is as follows: ; Among them, in the formula, Indicates t The contribution of the load response at time t, and ; Calculate the partial derivative of the error function for each axle weight: ; in, n and j Respectively represent n and j axles; Indicates n Axles in t The bridge influence line value corresponding to the loading position at the time; Indicates j Axles in t The influence line value corresponding to the loading position at the moment.

[0024] Let the partial derivative be zero, and we get the axle weight expression at this time: ; Where the contribution diagonal matrix of the load response is determined by the variance of the axle weight, influence line variance, and measurement error; 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 the axle weight obtained this time is used as the axle weight of the monitored vehicle; Specifically, repeat steps 301 to 303 in step 3 until the calculated axle weight results converge, and the two iterations before and after Step and The axle weight difference of the step is less than the preset threshold , whose expression is: ; In summary, a high-precision bridge moving load identification method 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. Therefore, the contribution of the load response value at each moment to the axle weight identification is considered in the calculation process, so as to distinguish the contribution of different load responses to the axle weight identification, and effectively improve the axle weight identification accuracy. Example 2 Take a domestic simply supported beam bridge as an example. The bridge is a simply supported beam bridge composed of ten prefabricated beams, with a main span of 40m, a bridge width of 24m, and four lanes in both directions.

[0025] The axle weight of vehicles crossing the bridge is identified through the following steps: (1) Carry out vehicle moving load test on the bridge and obtain test measured data. A two-axle vehicle with a total weight of 28.5 tons (7.4 tons on the front axle, 21.1 tons on the rear axle, and 4.7 meters between the axles) was selected as the loading vehicle in the test. 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; a dynamic weighing sensor is installed at the bottom of the T-beam in the middle of the bridge to identify the vehicle axle weight, such as Figure 5 The bridge dynamic response value at the mid-span position is shown in Figure 6 As shown, the bridge dynamic response value at the mid-span position of the bridge is the sum of the signals of ten load cells ( Figure 5 The bridge bottom sensor at B in the figure).

[0026] (2) The signal of the bridge when there is no vehicle passing by is collected by the weighing sensor as the noise signal in the load response, and the variance vector R of the noise signal is calculated.

[0027] (3) The algorithm of the present invention and the Moses algorithm are used to identify the axle weight of the axle dynamic response signal. The initial axle weight is calculated 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 the current iteration step is calculated 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 according to the 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 ; Repeat the above process until the calculated axle weight results converge. The calculation results are shown in Table 1.

[0028] It should be pointed out here that before identifying the axle load, the dynamic response of the vehicle bridge is partly eliminated by the moving average filter to eliminate the noise and vehicle bridge coupling response. Considering the impact of the vehicle on the dynamic response of the bridge when going up and down the bridge, the length of the vehicle entering and leaving the bridge is 10 m.

[0029] Table 1 Vehicle axle weight recognition error table of two algorithms Unit: %

[0030] Note: Error = (calculated value - true value) / true value × 100% It can be seen from Table 1 that the mean and standard deviation of the axle weight error obtained by a high-precision bridge moving load identification method are lower than the error 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 2.06% of the Moses algorithm. Correspondingly, the error standard deviation dropped from 49.04% (Moses algorithm) to 37.43% (present invention). This shows that the high-precision bridge moving load identification method provided by the present invention can improve the accuracy of axle weight identification to a certain extent.

[0031] Obtaining more accurate vehicle axle weights during 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 accurate assessment of highway bridge reliability and lifespan, help establish an intelligent highway bridge management system, and extend the service life of highway bridges.

[0032] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined 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; Step 2: Obtain the load response of the bridge when the monitoring vehicle passes through the bridge, and obtain the initial value of the axle weight by performing axle weight identification through the Moses algorithm; Step 3: Obtain the noise signal in the load response of the bridge when there is no vehicle running, 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 the error function based on the contribution diagonal matrix, axle weight, load response and influence line distribution, and update the axle weight based on the error function and the axle weight corresponding to the current iteration step; 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 influence line distribution At each moment, it follows a Gaussian distribution: ； in, for t The influence line mean at time , for t The variance of the influence line at time .

3. The high-precision bridge moving load identification method according to claim 1 is characterized in that: The method also includes step 5: acquiring 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 acquiring the vehicle power signal.

4. The high-precision bridge moving load identification method according to claim 1 is characterized in that: The step of 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 load comprises: calculating the variance vector according to the noise signal in the load response, obtaining the variance vector of the noise signal in the load response, and obtaining the contribution diagonal matrix of 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 a signal collected by the weighing sensor when there is no vehicle running on the bridge.

5. The high-precision bridge moving load identification method according to claim 4 is characterized in that: The method of obtaining a contribution diagonal matrix of 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 weight includes: 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 weight square vector obtained based on the axle weight; 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 weight vector; and constructing a contribution diagonal matrix of 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, Indicates that the data in the matrix are calculated separately; The square vector of the coefficient of variation is expressed by the following formula: ； ； ； Among them, 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 weight square vector, V represents the mean influence line matrix constructed based on the influence line distribution; A represents the axle weight vector; Represents element-wise exponentiation.

6. The high-precision bridge moving load identification method according to claim 5 is characterized in that: The constructing the error function according to the contribution diagonal matrix, the axle weight, the load response and the influence line distribution includes: constructing the 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 n axle weight of each axle; Indicates n Axles in t The bridge influence line value corresponding to the loading position at the time; Indicated in t The load response of the measured bridge at time Indicated in t The contribution of the load response at the time.

7. The high-precision bridge moving load identification method according to claim 6 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.

8. The high-precision bridge moving load identification method according to claim 7 is characterized in that: The partial derivative of each axle weight according to the error function is expressed by the following formula: ； in, Indicates j axle weight of each axle; Indicates j Axles in t The influence line value corresponding to the loading position at the moment.

9. The high-precision bridge moving load identification method according to claim 8 is characterized in that: 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: ； in, Indicates the axle weight before updating, Indicates a predetermined threshold.

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