Bridge dynamic weighing algorithm based on maximum entropy regularization

Abstract

This application provides a bridge dynamic weighing algorithm based on maximum entropy regularization. The steps include: First, obtain the measured response M of the bridge when the vehicle crosses the bridge m and the influence line matrix IL; Second, use M m and IL to calculate the initial value A of the axle weight 0 , and define the initial value r of the regularization parameter i=1 , where i represents the number of times of the main loop; Third, enter the sub-loop, substitute r i and A 0 into the iterative formula of the non-linear conjugate gradient method for calculation until the axle weight converges, and the absolute value of the difference between the axle weights obtained from the previous and the current iterations is less than e, that is: |A i k - A i k‑1 | < e. Assign the axle weight A i k at the k-th iteration after the convergence of the sub-loop to A i ; Fourth, substitute A i into the Regińska formula to obtain the parameter V, and calculate the next regularization parameter r i+1 ; Fifth, judge whether i is greater than 10. If not, substitute r i=i+1 into step three, and repeat the calculation process of steps three to five; If so, draw the r-V curve; Sixth, observe whether there is a minimum value in the curve. If not, substitute r i=i+1 into step three, and repeat the calculation process of steps three to five; If there is, output the axle weight corresponding to the minimum value and use it as the axle weight identification result.

Description

Technical Field

[0001] This invention belongs to the technical field of bridge health monitoring systems and overweight vehicle identification, and in particular relates to a bridge dynamic weighing algorithm based on maximum entropy regularization. Background Technology

[0002] In recent years, with the rapid development of the national economy, the demand for road freight transportation has been continuously rising, thus stimulating the further development of my country's transportation industry. Overloading of vehicles not only causes irreversible structural damage to bridges but also reduces their service life, and in severe cases, can directly lead to bridge collapse. Therefore, effectively obtaining vehicle load information and strictly controlling overloaded vehicles have become urgent problems to be solved.

[0003] Currently, there are two main types of systems for identifying the axle load of overloaded vehicles: (1) Static weighing system. This system directly uses a weighbridge to obtain the static axle load of the vehicle, but its weighing efficiency is low; (2) Dynamic weighing system. Sensors are installed on the road surface to obtain the axle load information of the vehicle while it is in motion. Because this method is convenient and fast, it has been extended to the monitoring of overloaded vehicles on bridges and named Bridge Weigh-in-motion (BWIM). The BWIM system uses the bridge as a weighing carrier to dynamically weigh vehicles crossing the bridge. That is, it uses weighing sensors installed on the bridge to obtain the response information of the vehicle when crossing the bridge (such as strain, deflection, etc.), and then calculates the axle load of the vehicle crossing the bridge using the Moses algorithm (least squares method). However, the Moses algorithm does not consider the impact of measurement error on the accuracy of the result when identifying axle load, resulting in low accuracy of axle load (especially single axle load) identification.

[0004] This invention proposes a bridge dynamic weighing algorithm based on maximum entropy regularization. By introducing an entropy regularization term, the algorithm suppresses the influence of measurement errors and improves the accuracy of axle load identification results. Summary of the Invention

[0005] The purpose of this invention is to provide a bridge dynamic weighing algorithm based on maximum entropy regularization, so as to improve the accuracy of axle load identification in actual bridges by the bridge dynamic weighing system.

[0006] To solve the above problems, the technical solution adopted in this invention is a bridge dynamic weighing algorithm based on maximum entropy regularization, comprising the following steps:

[0007] A. Obtain the bridge load response M when a vehicle crosses the bridge. m And the influence line matrix IL.

[0008] B. According to the formula, the initial value A of the axle load is obtained. 0 The calculation formula is:

[0009] A 0 = (||M m || 2 / ||IL|| 1 )I

[0010] Where, I is the N unit vector of row 1 and column 1, N is the number of axle shafts; ||M m || 2 is the 2-norm of the bridge load response; ||IL|| 1 is the 1-norm of the influence line matrix.

[0011] C. Define the initial value r i=1 of the regularization parameter r, and i represents the i-th main loop.

[0012] D. Calculate the vehicle axle weight A i corresponding to the regularization parameter r i . Enter the sub-loop, substitute the regularization parameter r i and the initial value A 0 of the axle weight into the iteration formula of the nonlinear conjugate gradient method for calculation (except for the first iteration), and obtain the axle weight A i k corresponding to the k-th iteration. Iterate repeatedly until convergence, and the absolute value of the difference between the axle weights obtained from the previous and subsequent iterations is less than the threshold e = 0.01 kN, that is: |A i k - A i k-1 | < e, and output A i k . Assign A i k to A i , and A i is used as the vehicle axle weight corresponding to the i-th main loop. The iteration formula of the nonlinear conjugate gradient method is:

[0013] grad E (A i k-1 ) = 2IL'(M m - ILA i k-1 ) + r i 2 [I + log(A i k-1 )]

[0014] β i k-2 = {[grad E (A i k-1 ) - gradE (A i k-2 )]'grad E (A i k-1 )} / ||grad E (A i k-1 )|| 2

[0015] p i k-1 =-grad E (A i k-1 )+β i k-2 p i k-2

[0016] A i k =A i k-1 +α i k-1 p i k-1

[0017] In the formula: p i k-1 For regularization parameter r i The corresponding axis weight search direction in the k-th iteration is initially set to p. i 0 =-grad E( A 0 );α i k-1 For regularization parameter r i The corresponding step size along the search direction in the k-th iteration is determined by the inaccurate line search method, and its expression is: α i k-1 =arg min E (A) i k-1 +α i p i k-1 ); IL' represents the transpose of the influence line matrix IL.

[0018] E. The axle load value A obtained in step D. i Substituting into the Regińska formula, we obtain the parameter V. The Regińska formula is:

[0019] V= E norm · F norm3

[0020] In the formula, E norm The 2-norm of the measurement error, F norm It is the 2-norm of the weighted regularization.

[0021] F. Calculate the next regularization parameter r according to the calculation formula. i+1 The calculation formula is:

[0022] r i+1 =r i +Δ

[0023] In the formula, Δ is the calculation step size of the regularization parameter, expressed as: Δ = 0.1r i=1 r i=1 The initial value for the defined regularization parameter.

[0024] G. Determine if i is greater than 10. If not, let i = i + 1 and repeat the calculation process from step D to step G. If yes, plot the rV curve.

[0025] H. Determine if the rV curve has a minimum value. If it does not have a minimum value, let i = i + 1 and repeat the calculation process from step D to step H. If it has a minimum value, the axle load corresponding to the minimum value is the desired value.

[0026] I. Output the axle load corresponding to the minimum value in step H as the axle load identification result.

[0027] Preferably, in step A, the influence line matrix IL is constructed from the influence line vectors obtained by calibration tests on a calibrated vehicle with a known axle load.

[0028] Preferably, in step C, the initial value of the defined regularization parameter r is... i=1 Greater than 0.

[0029] Preferably, in step D, grad E (A i k-1 ) is the error function E (A) in A i k-1 The gradient at the point. Error function. E (A) The expression is:

[0030] E (A)=||M m -ILA|| 2 +r 2 A'log (A)

[0031] In the formula, A' represents the transpose of the axis weight vector.

[0032] Preferably, in step D, A is used. 0 During the first iteration, let p i 0 =-grad E( A 0 ), then p i 0 Substitute A 0 +α i 0 p i 0 To obtain the axle load A for the next step i 1 , where α i 0 The expression is: α i 0 =arg min E (A) 0 +α i p i 0 The subsequent calculations are performed according to the formula in step D.

[0033] Preferably, in step D, expression α i k-1 =arg min E (A) i k-1 +α i p i k-1 The meaning is: return the value of α that minimizes the error function. i The value of .

[0034] Preferably, in step D, A must always be ensured. i k-1 +α i k-1 p i k-1 Greater than 0.

[0035] Preferably, the Regińska formula in step E contains the following two parametric expressions:

[0036] E norm =||M m -ILA i || 2

[0037] F norm =||A i || 2

[0038] In the formula, A i The regularization solution for axle load is the axle load value obtained after substituting the regularization parameter.

[0039] The beneficial effects of this invention are: a bridge dynamic weighing algorithm based on maximum entropy regularization, which takes into account the influence of measurement error on axle load identification results, and improves the accuracy of axle load identification results by introducing an entropy regularization term to suppress the influence of measurement error.

[0040] Specifically, this invention improves the accuracy of axle load identification by introducing an entropy regularization term to suppress the influence of measurement errors. For example, as bridges age, road conditions deteriorate, leading to an increase in measurement errors in the dynamic response of vehicles crossing the bridge. Since the Moses algorithm for axle load identification does not consider the impact of measurement errors, the accuracy of axle load identification continuously deteriorates. To improve axle load identification accuracy, this invention introduces an entropy regularization term to reduce the impact of measurement errors on the results, thereby improving the accuracy of axle load identification. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is the flowchart of the maximum entropy algorithm.

[0043] Figure 2 This is a sensor layout diagram.

[0044] Figure 3 This is a schematic diagram of the bridge's cross-section.

[0045] Figure 4 It is the dynamic strain response signal at the mid-span of the bridge.

[0046] Figure 5 It is the measured influence line at the mid-span of the bridge.

[0047] Figure 6 This is the rV curve corresponding to the 7th set of data. Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.

[0049] This paper proposes a dynamic weighing algorithm for bridges based on maximum entropy regularization, the flowchart of which is shown below. Figure 1 The algorithm includes the following steps:

[0050] Step 1: Obtain the bridge load response M when a vehicle crosses the bridge using a weighing sensor installed at the bottom of the main girder at mid-span. m The influence line vector of the bridge mid-span position is obtained through calibration tests using a calibrated vehicle with a known axle load, and then the influence line matrix IL is obtained. The vehicle-bridge dynamic signal when the vehicle crosses the bridge is obtained by using sensors FAD1 and FAD2 set at the bottom of the main beam flange. The vehicle speed and wheelbase of the vehicle crossing the bridge are calculated by the time difference between the peak values ​​of the vehicle-bridge dynamic signal and the distance between the two sensors. The bridge load response with time as the abscissa is transformed into the bridge load response with the vehicle driving position as the abscissa.

[0051] Step 2: Obtain the initial value A of the axle load according to the formula. 0 The calculation formula is:

[0052] A 0 =(||M m || 2 / ||IL|| 1 )I (1)

[0053] In the formula, I is N A unit vector in row 1 and column 1. N For the number of axles; ||M m || 2 The 2-norm of the bridge load response; ||IL|| 1 Let be the 1-norm of the influence line matrix.

[0054] Step 3: Define the initial value of the regularization parameter r. i=1 , where i represents the i-th main loop.

[0055] Step 4: Calculate the regularization parameter r i Corresponding vehicle axle load A i Enter the sub-loop and set the regularization parameter r. i and initial value of axle load A 0 Substituting the values ​​into the iterative formula of the nonlinear conjugate gradient method (except for the first iteration), we obtain the axle load A corresponding to the k-th iteration.i k Iterate repeatedly until convergence, and the absolute value of the difference in axle weights obtained from two consecutive iterations is less than the threshold e = 0.01 kN, i.e.: |A i k - A i k-1 | < e, and output A i k Assign A i k to A i as the axle weight of the vehicle corresponding to the i-th main loop. The iteration formula of the nonlinear conjugate gradient method is: i As the axle weight of the vehicle corresponding to the i-th main loop. The iteration formula of the nonlinear conjugate gradient method is:

[0056] grad E (A i k-1 ) = 2IL'(M m - ILA i k-1 ) + r i 2 [I + log(A i k-1 )] (2)

[0057] β i k-2 = {[grad E (A i k-1 ) - grad E (A i k-2 )]' grad E (A i k-1 )} / ||grad E (A i k-1 )|| 2 (3)

[0058] p i k-1 = - grad E (A i k-1 ) + β i k-2 p i k-2 (4)

[0059] A i k = A i k-1 + α i k-1 p i k-1(5)

[0060] In the formula: p i k-1 For regularization parameter r i The corresponding axis weight search direction in the k-th iteration is initially set to p. i 0 =-grad E( A 0 );α i k-1 For regularization parameter r i The corresponding step size along the search direction in the k-th iteration is determined by the inaccurate line search method, and its expression is: α i k-1 =arg min E (A) i k-1 +α i p i k-1 ); IL' represents the transpose of the influence line matrix IL.

[0061] Step 5: Calculate the axle load A obtained in Step 4. i Substituting into the Regińska formula, we obtain the parameter V. The Regińska formula is:

[0062] V= E norm · F norm 3 (6)

[0063] In the formula, E norm The 2-norm of the measurement error, F norm It is the 2-norm of the weighted regularization.

[0064] Step 6: Calculate the next regularization parameter r according to the calculation formula. i+1 The calculation formula is:

[0065] r i+1 =r i +Δ (7)

[0066] In the formula, Δ is the calculation step size of the regularization parameter, expressed as: Δ = 0.1r i=1 r i=1 The initial value for the defined regularization parameter.

[0067] Step 7: Determine if i is greater than 10. If not, let i = i + 1 and repeat the calculation process from Step 4 to Step 7. If yes, plot the rV curve.

[0068] Step 8: Determine if the rV curve has a minimum value. If it does not have a minimum value, let i = i + 1 and repeat the calculation process from Step 4 to Step 8. If it has a minimum value, the axle load corresponding to the minimum value is the desired value.

[0069] Step 9: Output the axle load corresponding to the minimum value in Step 8 as the axle load identification result.

[0070] In summary, this invention improves the accuracy of axle load identification by introducing an entropy regularization term to suppress the influence of measurement errors on axle load identification results. Specific implementation examples:

[0072] Take the approach bridge of a simply supported beam bridge in China as an example. The bridge consists of 10 T-beams with a span of 40m and a width of 24m. It has four lanes in both directions, with non-motorized vehicle lanes and pedestrian walkways on both sides.

[0073] The axle load of vehicles crossing the bridge is identified through the following steps:

[0074] (1) A vehicle test was conducted on the bridge to obtain measured data. A two-axle vehicle was selected as the loading vehicle, with a total weight of 28.5t (7.4t for the front axle and 21.1t for the rear axle) and an axle spacing of 4.7m. The vehicle repeatedly drove through lane three 10 times at a speed of 30km / h. Axle detection sensors installed under the flanges on both sides of the mid-span section of the bridge were used. Figure 2 The peak values ​​of the dynamic response signals measured by FAD1 and FAD2 in the bridge are used to obtain information such as the number of axles, wheelbase, and vehicle speed; the weighing sensors installed at the bottom of the T-beams in the middle of the bridge span are used to obtain information such as the number of axles, wheelbase, and vehicle speed. Figure 2 The dynamic strain response of a vehicle crossing the bridge is obtained for axle load identification. The obtained dynamic response at the mid-span of the bridge is shown below. Figure 4 As shown in the figure, the dynamic strain response at the mid-span of the bridge is the sum of the signals from ten weighing sensors (B1~B10).

[0075] (2) Axle load identification is performed on the dynamic strain response of the vehicle-bridge using the maximum entropy algorithm. (a) Obtain the bridge dynamic load response M when the vehicle crosses the bridge. m (a) Obtain the initial value A of the axle load according to formula (1) and the influence line matrix IL; (b) Obtain the initial value A of the axle load according to formula (1). 0 (c) Define the initial value of the regularization parameter r. i=1 (d) Calculate the regularization parameter r. i Corresponding vehicle axle load A i Enter the sub-loop and set the regularization parameter r. i and initial value of axle load A 0 Substituting the values ​​into the iterative formula of the nonlinear conjugate gradient method (except for the first iteration), we obtain the axle load A corresponding to the k-th iteration. i kIterate repeatedly until convergence, and the absolute value of the difference in axle weights obtained from two consecutive iterations is less than the threshold e = 0.01 kN, that is: |A i k - A i k-1 | < e, and output A i k . Assign A i k to A i as the axle weight corresponding to the i-th main loop. (e) Substitute the axle weight A i calculated in step d into formula (6) to obtain the parameter V; (f) Calculate the value of the next regularization parameter r i according to formula (7); (g) Determine whether i is greater than 10. If not, let i = i + 1 and repeat the calculation process from step d to step g; if so, plot the r-V curve; (h) Determine whether there is a minimum value in the r-V curve. If there is no minimum value, let i = i + 1 and repeat the calculation process from step d to step h; if there is a minimum value, the axle weight corresponding to the minimum value is the required one; (i) Output the axle weight corresponding to the minimum value in step h as the axle weight recognition result. The calculation results are shown in Table 1. i+1

[0076] It should be noted here that the influence line here is the measured influence line at the mid-span position of the bridge, which is obtained through calibration tests with calibration vehicles of known axle weights. Additionally, considering the influence of the dynamic strain responses of the upper and lower bridge sections on the axle weight recognition accuracy, the lengths of the measured influence line in the upper and lower bridge sections are both taken as 10 m here, and the total length of the influence line is 60 m, as Figure 5 shown.

[0077] Table 1 Comparison statistical table of axle weight recognition result errors of two algorithms (unit: %)

[0078]

[0079] Table 1 shows the axle weight recognition results of the two algorithms. It can be seen from the table that the accuracy of the single-axle recognition results of the maximum entropy algorithm is better than that of the Moses algorithm. Taking the first set of results as an example, the errors of the front axle and the rear axle of the maximum entropy algorithm are -40.2% and 9.0% respectively, both lower than the results of the Moses algorithm (front axle: -47.8%, rear axle: 15.3%). It can be seen that compared with the Moses algorithm, using the maximum entropy algorithm for axle weight recognition can improve the result accuracy and can be better applied to the overload monitoring of actual bridges.

[0080] ​Road transportation is an indispensable part of rapid socio-economic development. However, the presence of overloaded vehicles can severely damage bridges, resulting in significant waste of economic resources. Therefore, better monitoring of overloaded vehicles and protecting bridges from damage can greatly reduce this waste.

[0081] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

Claims

1. A bridge dynamic weighing algorithm based on maximum entropy regularization, characterized by including the following steps: A. Obtain the bridge load response when vehicles cross the bridge. and influence line matrix ; B. Obtain the initial value of the axle load according to the formula. The calculation formula is: In the formula, I is a unit vector. N This refers to the number of axles. || represents the 2-norm of the bridge load response; The 1-norm of the influence line matrix; C. Define regularization parameters initial value , i Indicates the first i Secondary main loop; D. Calculate the regularization parameter Corresponding vehicle axle load Enter the sub-loop and set the regularization parameter. and initial value of axle load Substituting the values ​​into the iterative formula of the nonlinear conjugate gradient method for calculation, except for the first iteration, we obtain the... k The axis weight corresponding to the next iteration Repeat the iterations until convergence, and the absolute value of the difference in axle weight between two consecutive iterations is less than the threshold. ,Right now: Output ,Will Assigned , As the first i The iterative formula for the nonlinear conjugate gradient method for the vehicle axle load corresponding to the secondary main loop is: In the formula: Regularization parameter The corresponding number k The initial value of the axle weight search direction in the next iteration is set as follows: ; Regularization parameter The corresponding number k The step size along the search direction in the next iteration is determined by the non-precise line search method, and its expression is: ; Influence line matrix Transpose of; E. The axle load calculated in step D Substituting into the Regińska formula, we obtain the parameters. The Regińska formula is: In the formula, The 2-norm of the measurement error, For the 2-norm of the axial weight canonical solution; F. Calculate the next regularization parameter according to the calculation formula. The calculation formula is: In the formula, The step size for calculating the regularization parameter is expressed as: , The initial values ​​for the defined regularization parameters; G. Judgment i Is it greater than 10? If not, then let Repeat steps D through G; if so, draw the graph. curve; H. Judgment Does the curve have a local minimum? If it does not have a local minimum, let... Repeat steps D to H; if a minimum value exists, the axle load corresponding to the minimum value is the desired value. I. Output the axle load corresponding to the minimum value in step H as the axle load identification result.

2. The bridge dynamic weighing algorithm based on maximum entropy regularization according to claim 1, characterized in that, In step A, the influence line matrix It is constructed from the influence line vectors obtained from calibration tests of calibrated vehicles with known axle loads.

3. The bridge dynamic weighing algorithm based on maximum entropy regularization according to claim 1, characterized in that, In step C, the initial value of the defined regularization parameter is... Greater than 0.

4. The bridge dynamic weighing algorithm based on maximum entropy regularization according to claim 1, characterized in that, In step D, Error function exist gradient at point, error function The expression is: In the formula, This represents the transpose of the axis-weighted vector.

5. The bridge dynamic weighing algorithm based on maximum entropy regularization according to claim 1, characterized in that, In step D, using the initial axle load value During the first iteration, let Then Substitution The next step is to obtain the axle load. ,in The expression is: The subsequent calculations are performed according to the formula in step D.

6. The bridge dynamic weighing algorithm based on maximum entropy regularization according to claim 1, characterized in that, In step D, the expression The meaning is: return the time when the error function is minimized. The value of .

7. The bridge dynamic weighing algorithm based on maximum entropy regularization according to claim 1, characterized in that, In step D, it is essential to always ensure Greater than 0.

8. The bridge dynamic weighing algorithm based on maximum entropy regularization according to claim 1, characterized in that, The Regińska formula in step E contains the following two parametric expressions: In the formula, The regularization solution for axle load is the axle load obtained after substituting the regularization parameters.

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