A small and medium-sized bridge bearing capacity evaluation method based on vehicle moving loading

Abstract

The application discloses a kind of based on vehicle movement loading small and medium-sized bridge bearing capacity evaluation method, belong to bridge bearing capacity evaluation technical field, comprising the following steps: S1: time history response acquisition;S2: time history response preprocessing;S3: influence line identification;S4: bearing capacity evaluation.The application utilizes single heavy vehicle movement loading to obtain bridge time history response;Then the structural dynamic component in bridge time history response is stripped using variational mode decomposition, and then a bridge influence line identification mathematical model is constructed according to sampling frequency and vehicle wheelbase, so as to eliminate the vehicle multi-axle effect in bridge time history response;And the stable solution of bridge influence line is solved using Tikhonov regularization method;Then by carrying out virtual loading on bridge influence line, reconstructing bridge virtual static response, and using traditional check coefficient method to evaluate bridge bearing capacity, the bridge bearing capacity evaluation rate is effectively improved, and the bridge structure damage caused by high loading efficiency is avoided.

Description

Technical Field

[0001] This invention relates to the field of bridge load-bearing capacity assessment technology, and specifically to a method for assessing the load-bearing capacity of small and medium-sized bridges based on vehicle-driven loading. Background Technology

[0002] The deterioration of existing bridge performance leads to a degradation in load-bearing capacity. Static load testing is widely used for bridge performance evaluation. Static load testing observes the static response of a bridge under stationary vehicle loads, thereby evaluating its load-bearing capacity. However, static load testing requires traffic interruption, resulting in high time costs for personnel and vehicles, significant disruption to daily traffic, and the high load efficiency specified in the test can easily cause new damage to in-service bridges. Furthermore, current research on the applicability of this method for rapid load-bearing capacity assessment of more complex steel-concrete composite continuous beam bridges is still lacking. Therefore, this paper proposes a method for assessing the load-bearing capacity of small and medium-sized bridges based on vehicle-driven loading. Summary of the Invention

[0003] The technical problem to be solved by this invention is: how to solve the problems of heavy load static placement and traffic obstruction in the static load test process of bridges. It provides a method for evaluating the load-bearing capacity of small and medium-sized bridges based on vehicle moving load. This method effectively improves the bridge load-bearing capacity evaluation rate and avoids damage to the bridge structure caused by high loading efficiency.

[0004] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0005] S1: Time-Schedule Response Acquisition

[0006] The bridge time history response, including bridge influence line information, structural dynamic components, and vehicle multi-axle effects, was obtained by using vehicle-moving loading.

[0007] S2: Time-history response preprocessing

[0008] Variational mode decomposition is used to remove the structural dynamic components from the time history response of the bridge to obtain the quasi-static time history response of the bridge;

[0009] S3: Influence Line Identification

[0010] A vehicle information matrix is ​​constructed and an influence line identification model is established. An error term is introduced and the Tikhonov regularization method is used to optimize the influence line identification model. The optimized influence line identification model is then used to solve for the bridge influence line.

[0011] S4: Load-bearing capacity assessment

[0012] Virtual loading is performed on the bridge influence line obtained in step S3 to reconstruct the bridge's virtual static response, and the bridge's load-bearing capacity is evaluated using the evaluation verification coefficient method.

[0013] Furthermore, in step S2, the specific processing procedure of the VMD method is as follows:

[0014] S21: By iteratively searching for K modes, and setting the sum of all modes equal to the original signal as a constraint, the variational constraint problem is described as follows:

[0015]

[0016] in, For the partial derivative with respect to time t, u k For the Kth IMF component, ω k Let f(t) be the frequency of the Kth IMF component, δ(t) be the Reichstag distribution function, and f(t) be the input signal.

[0017] S22: By introducing a quadratic penalty factor α and the Lagrange multiplication operator λ(t), the variational constrained problem is transformed into an unconstrained variational problem. The unconstrained lagrange function is as follows:

[0018]

[0019] S23: Use the Lagrange multiplication operator to obtain the saddle point in the unconstrained lagrange function, and update u through iteration. k n+1 ω k n+1 , λ k n+1 ;

[0020] S24: Initialize {ω k 1}、{u k 1}、λ 1 n, iteratively update u k The iteration continues until the tolerance error ε is met, at which point the iteration stops and K IMF components are output.

[0021] Furthermore, in step S23, the update formula is defined as follows:

[0022]

[0023]

[0024]

[0025] Where ^ represents the Fourier transform operation, and τ is the time step. Equivalent to the current remaining amount Wiener filtering, This is the centroid of the power spectrum of the current mode function.

[0026] Furthermore, in step S24, the tolerance error discriminant is as follows:

[0027]

[0028] Furthermore, in step S2, after processing with the VMD method, the bridge time history response is decomposed into K IMF components. The dominant frequency of each IMF component is obtained through Fast Fourier Transform. IMF components with a dominant frequency greater than the fundamental frequency of the bridge structure are considered as structural dynamic components and are eliminated. K starts from 2 and takes values ​​sequentially. (K-1) The main frequency is lower than the fundamental frequency of the bridge structure, for IMF (K-1) IMF (K) The signal is reconstructed, and the reconstructed signal is the quasi-static time history response of the bridge structure measuring points, or the quasi-static time history response of the bridge.

[0029] Furthermore, in step S2, the expression for the quasi-static time history response of the bridge is as follows:

[0030]

[0031] Where Y(k) is the measured bridge response, S is the number of vehicle axles, and M is the number of axles. i For vehicle axle load, η is the influence line coefficient corresponding to the i-th axis. i Q is the structural dynamic component coefficient. i The sampling difference between each axis and the first axis is an integer, and its specific expression is:

[0032] Q i =C i f / v

[0033] Among them, C i Let f be the distance between the i-th axis and the first axis, f be the sampling frequency, and v be the vehicle speed.

[0034] Furthermore, in step S3, the influence line recognition model is as follows:

[0035] Y s =LΦ

[0036] Among them, Y S For the quasi-static response of the bridge, Φ is the influence line coefficient of the bridge node, and L is the vehicle information matrix;

[0037] With the front axle entering the bridge and the rear axle exiting the bridge as the start and end points of timing, the vehicle information matrix is ​​as follows:

[0038]

[0039] Furthermore, in step S3, the influence line identification model is corrected by introducing an error e. The corrected influence line identification model is as follows:

[0040] Y s =LΦ+e;

[0041] The Tikhonov regularization method is used to restrict the least squares expression by using the L2 norm as a penalty function, resulting in the following regularized expression for the influence line solution:

[0042]

[0043] Wherein, the regularization matrix T is:

[0044]

[0045] Substituting the regularization matrix into the regularization expression for the influence line solution and taking the derivative, then setting the derivative to 0, the optimized influence line identification model is as follows:

[0046] Φ=(L T L+λ 2 T T T) -1 L T Y S

[0047] Where λ is the regularization coefficient, the optimal value of λ is determined by the L-curve method to minimize the sum of the norms of the two terms in the regularization expression of the influence line solution;

[0048] The bridge influence line can be solved by substituting the optimal value of λ into the optimized influence line identification model expression. The optimal value of λ is located at the point of maximum curvature of the L curve.

[0049] Furthermore, in step S4, the influence line coefficient θ of bridge section i is used... i The corresponding load M at this location i By adding the products, the virtual static response of the bridge can be reconstructed, the virtual loading of the bridge influence line can be realized, and then the evaluation verification coefficient can be constructed. The bearing capacity of the bridge can be evaluated based on the calculated evaluation verification coefficient results.

[0050] Furthermore, in step S4, the formula for calculating the evaluation verification coefficient is as follows:

[0051]

[0052] Where G is the number of lanes, θ i ξ is the influence line coefficient corresponding to the position of section i at the measuring point, and ξ is the evaluation and verification coefficient.

[0053] Compared with existing technologies, this invention has the following advantages: This method for assessing the load-bearing capacity of small and medium-sized bridges based on vehicle-driven loading obtains the bridge time-history response, which includes bridge influence line information, structural dynamic components, and vehicle multi-axle effects, by using single-vehicle-driven loading. Then, variational mode decomposition is used to remove the structural dynamic components from the bridge time-history response. A mathematical model for identifying the bridge influence line is then constructed based on the sampling frequency and vehicle wheelbase, thereby eliminating the vehicle multi-axle effects in the bridge time-history response. The stable solution of the bridge influence line is obtained using the Tikhonov regularization method. Finally, virtual loading is carried out on the bridge influence line to reconstruct the bridge's virtual static response, and the traditional verification coefficient method is used to evaluate the bridge's load-bearing capacity. This effectively improves the bridge load-bearing capacity assessment rate and avoids damage to the bridge structure caused by high loading efficiency. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the rapid assessment method for the bearing capacity of small and medium-sized bridges based on vehicle-driven loading in Embodiment 1 of the present invention.

[0055] Figure 2 This is a schematic diagram of the L-curve method in Embodiment 1 of the present invention;

[0056] Figure 3(a) is a schematic diagram of the bridge structure in Embodiment 2 of the present invention (unit: mm);

[0057] Figure 3(b) is a schematic diagram of the bridge cross-section arrangement in Embodiment 2 of the present invention (unit: mm);

[0058] Figure 4 This is a schematic diagram of the loading vehicle type in Embodiment 2 of the present invention (unit: m);

[0059] Figure 5(a) is a schematic diagram of the mid-span static load test condition 1 in Embodiment 2 of the present invention (unit: m);

[0060] Figure 5(b) is a schematic diagram of the mid-span static load test condition 2 in Embodiment 2 of the present invention (unit: m);

[0061] Figure 6 This is a diagram showing the time history curve of bridge deflection and the VMD preprocessing results in Embodiment 2 of the present invention;

[0062] Figure 7 This is a diagram showing the bridge strain time history curve and VMD preprocessing results in Embodiment 2 of the present invention;

[0063] Figure 8 This is the measured influence line of bridge deflection in Embodiment 2 of the present invention;

[0064] Figure 9 This is the measured bridge strain influence line in Embodiment 2 of the present invention. Detailed Implementation

[0065] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0066] Example 1

[0067] like Figure 1 As shown, this embodiment provides a technical solution: a rapid assessment method for the bearing capacity of small and medium-sized bridges based on vehicle moving load. This method primarily employs Variational Mode Decomposition (VMD) to remove the structural dynamic components from the bridge's time-history response, thereby obtaining the bridge's quasi-static time-history response. Then, a vehicle information matrix is ​​constructed based on the vehicle wheelbase and sampling frequency. The ill-conditioned equations in the bridge influence line identification model are solved using the Tikhonov regularization method to identify the bridge influence lines. Virtual loading is then applied along the identified bridge influence lines to reconstruct the bridge's virtual static load test conditions, obtaining the bridge's static virtual response. Comparison with the static response results obtained from actual static load tests demonstrates the feasibility and effectiveness of the rapid assessment method for bridge bearing capacity based on measured influence lines.

[0068] The present invention specifically includes the following steps:

[0069] I. Time-History Response Preprocessing

[0070] The VMD method iteratively decomposes the time-domain signal into K finite-bandwidth IMFs ranging from high to low frequencies to search for the optimal solution of variational modes. Assuming that each finite-bandwidth IMF perturbs around its respective center frequency, the method iteratively searches for K modes, with the constraint that the sum of the modes equals the original signal. The goal is to minimize the estimated bandwidth of each mode. The variational constraint problem is described as follows:

[0071]

[0072] in: For the partial derivative with respect to time t, u k For the Kth IMF component, ω k Let f(t) be the frequency of the Kth IMF component, δ(t) be the Reichstag distribution function, and f(t) be the input signal.

[0073] To find the optimal solution to the above constrained variational problem, a quadratic penalty factor α and a Lagrange multiplication operator λ(t) are introduced, transforming equation (1) into an unconstrained variational problem. The expression for the unconstrained lagrange function is as follows:

[0074]

[0075] Where α is the quadratic penalty factor and λ(t) is the Lagrange multiplier operator.

[0076] The "saddle point" in equation (2) is obtained by using the alternating multiplication operator, and u is updated iteratively. k n+1 ω k n+1 , λ k n+1 The update formula is defined as follows:

[0077]

[0078]

[0079]

[0080] Where: ^ represents the Fourier transform operation, and τ is the time step. Equivalent to the current remaining amount Wiener filtering, This is the centroid of the power spectrum of the current mode function.

[0081] Initialize {ω k 1}、{u k 1}、λ 1 n, iteratively update u k , ε, λ, until the allowable error ε (ε = 10) is met. -7 The iteration stops, and K IMF components are output. The tolerance error is judged by equation (6):

[0082]

[0083] To prevent over-decomposition or incomplete decomposition of the original signal, K is selected sequentially starting from 2. When IMF (K-1) The dominant frequency is less than the structural fundamental frequency, for IMF (K-1) IMF (K) The signal is reconstructed, and the reconstructed signal is the quasi-static time history response of the bridge as measured in the experiment, i.e., the quasi-static time history response of the bridge.

[0084] II. Establishment of Influence Line Identification Model

[0085] Assuming that the bridge structural responses caused by each axle of the vehicle are independent, i.e., the measured bridge response is the result of the superposition of the bridge responses caused by each axle of the vehicle, the continuous influence lines can be discretized and simplified into influence line coefficients on a finite number of nodes in the structure. For each sampling point k, the bridge response is expressed as follows:

[0086]

[0087] Where Y(k) is the measured bridge response, i.e., S is the number of vehicle axles, M i For vehicle axle load, η is the influence line coefficient corresponding to the i-th axis. i Q is the structural dynamic component coefficient. i Let Q be the sampling difference between each axis and the first axis, and Q i It must be an integer, and the specific expression is:

[0088] Q i =C i f / v (8)

[0089] Among them, C i Let f be the distance between the i-th axis and the first axis, f be the sampling frequency, and v be the vehicle speed.

[0090] The mathematical model for influence line identification is:

[0091] Y s =LΦ (9)

[0092] Where: Y s Let Φ be the quasi-static response of the bridge, Φ be the influence line coefficient of the bridge node, and L be the vehicle information matrix.

[0093] The vehicle information matrix is ​​determined by parameters such as sampling frequency, vehicle axle load, number of axles, wheelbase, and vehicle speed. Vehicle speed and sampling frequency determine the number of columns in the vehicle information matrix, while sensor sampling frequency determines the number of rows. Taking the front axle entering the bridge and the rear axle exiting the bridge as the starting and ending points of timing, the vehicle information matrix is ​​expressed as shown in equation (10):

[0094]

[0095] III. Identification of Bridge Influence Lines

[0096] Substituting the quasi-static time history response of the bridge after VMD preprocessing into equation (9) to solve for the influence line, however, there may still be insufficient stripping of dynamic components after time history response preprocessing. Therefore, the error e correction formula (9) is introduced, and the corrected influence line identification model is shown in equation (11):

[0097] Y s =LΦ+e (11)

[0098] Since the error term in equation (11) causes the mathematical equation of the influence line identification model to become ill-conditioned, the Tikhonov regularization method can use the L2 norm as a penalty function to restrict the least squares expression, thereby effectively solving the ill-posed problem caused by the error term. The regularization equation for solving the influence line is shown in equation (12):

[0099]

[0100] The regularization empirical matrix T is:

[0101]

[0102] Substituting the empirical matrix into equation (12) and differentiating it, setting the derivative to 0, the expression for solving the influence line (the optimized influence line identification model) is as follows:

[0103] Φ=(L T L+λ 2 T T T) -1 L T Y S (14)

[0104] Where λ is the regularization coefficient, the optimal value of λ is determined by the L-curve method to minimize the sum of the norms of the two terms in the regularization expression of the influence line solution;

[0105] Introducing the L2 norm as a penalty function can make the ill-posed problem fluctuate within a small range and satisfy certain smoothness properties. In equation (14), λ is the regularization coefficient. The L-curve method is used to determine λ so that the sum of the norms of the two terms in equation (12) is minimized. Since (log||Y-LΦ||, log||TΦ||) is roughly L-shaped, the optimal value of λ is located at the point of maximum curvature of the L-curve, see Figure 1 Substituting the optimal value of λ into equation (14) will yield the bridge influence line.

[0106] IV. Rapid Assessment of Bridge Load-Bearing Capacity

[0107] To quickly assess the load-bearing capacity of a bridge through a single-vehicle loading test, it is first necessary to calculate the internal forces, stresses, or deformation effects of the control sections under the design load, and then calculate the corresponding internal forces, stresses, or deformation effects of the control sections during the loading test. The bridge load test, as a technical means of assessing its load-bearing capacity, is not a verification test. Under the premise of ensuring sufficient stress and elastic deformation of the structure in the elastic stage, the lower load efficiency used in the test loading is selected within the range of [0.30, 0.60] to ensure that the rapid passage of a single heavy vehicle can achieve "lightweight" loading, which can basically cover the load requirements under normal bridge use. The rapid assessment of the test load efficiency can be calculated using the following formula (15):

[0108] η q=S s / [S(1+μ)] (15)

[0109] Where, η q To quickly evaluate the efficiency of the test load, S s S represents the maximum calculated effect value of the control section under the load during the loading test, S represents the corresponding most unfavorable effect value of the control section under the control load, and μ represents the impact coefficient taken according to the specification.

[0110] To ensure the efficiency of vehicle-driven loading, and to facilitate comparison of the rationality and accuracy of the proposed method, a single-vehicle heavy-load loading condition was designed for the bridge, incorporating static load test design conditions. A single heavy-load vehicle was loaded in the lane designated for static load testing. The time history response of each control section of the bridge was obtained. Using the aforementioned influence line identification method, the bridge time history response was reconstructed into the bridge influence line. The influence line coefficient θ of section i of the bridge was then used to... i The corresponding load M at this location i By adding the products, the static response of the bridge during the static load test can be reconstructed, realizing the virtual loading of the bridge influence line, and then constructing the verification coefficient for rapid evaluation of the bridge's bearing capacity, as shown in equation (16):

[0111]

[0112] Where G is the number of lanes, θ i ξ is the influence line coefficient corresponding to the position of section i at the measuring point, and ξ is the rapid evaluation and verification coefficient.

[0113] To further improve the practicality and operability of the proposed method, a suggested procedure for rapid assessment of bridge load-bearing capacity is provided:

[0114] (1) Conduct on-site investigation and basic data collection of bridges, formulate a rapid assessment test plan for bridge bearing capacity, determine the control section and measurement point layout of the bridge to be measured, select a single heavy vehicle to calculate the load efficiency, and design the loading conditions.

[0115] (2) Conduct on-site testing, install sensors according to the test plan, use the idling speed of the loading vehicle to achieve rapid loading, repeat loading three times, take the average value of the measured time history response data of the bridge, test the fundamental frequency of the bridge structure, and observe and record the abnormal response of the bridge.

[0116] (3) Preprocess the time history response data, remove the dynamic components in the time history response, construct the vehicle information matrix, solve the influence line identification model, convert the bridge time history response into the spatial response under the bridge longitudinal axis coordinate, and obtain the measured influence line of the bridge structure.

[0117] (4) Refer to the "Specifications for Load Testing of Highway Bridges" (JTG / T J21-01-2015) to calculate the theoretical response value of the bridge model under static load test conditions. Based on the vehicle loading position under static load conditions, virtual loading is performed on the bridge based on the measured influence line to obtain the virtual static load response value of the bridge and calculate the bridge rapid evaluation verification coefficient.

[0118] (5) According to the "Specification for Testing and Evaluation of Bearing Capacity of Highway Bridges" (JTG / T J21-2011), the bearing capacity of the bridge structure is evaluated by the calculation results of the bridge rapid evaluation verification coefficient, and a rapid evaluation report of bearing capacity is issued.

[0119] Virtual loading is achieved by using the bridge influence line, which can realize multiple static load conditions in the corresponding lane by relying on the movement of a single heavy vehicle. Therefore, this method can not only greatly improve the shortcomings of traditional static load tests such as long-term traffic interruption, but also greatly reduce the risk of new damage to the bridge due to "overloading" by using only a single heavy vehicle.

[0120] Example 2

[0121] To further investigate the accuracy and reliability of the rapid bridge load-bearing capacity assessment method in Example 1, a single two-axle loading vehicle was used to conduct a rapid load-bearing capacity assessment of a three-span steel-concrete composite beam bridge under low-speed loading. This example test selected a three-span continuous steel-concrete composite beam bridge. The bridge is a symmetrically arranged double-span bridge running north-south, with the east and west sides separated in the middle. The span combination is 35m+35m+35m. The bridge is orthogonally arranged, with a bridge deck width of 3m (pedestrian walkway) + 9m (driving road). The western half of the bridge was used as the research object. The measured fundamental frequency of the bridge structure was 2.718Hz. The bridge deflection and strain time history response measurement points were selected at the bottom of beam #1 in the middle of the middle span. The bridge structure and cross-sectional dimensions are shown in Figures 3(a) and (b).

[0122] Operating Condition Arrangement Instructions

[0123] The working condition layout is shown in Table 1, and the loading vehicle type is shown in Table 2. Figure 4 Under the premise of meeting the test load efficiency, the bridge was loaded according to the static load test conditions. The maximum load efficiency of the rapid evaluation test was calculated to be 0.36, and the maximum static load test efficiency was calculated to be 0.47.

[0124] Table 1 Loading Vehicle Quality Information

[0125] vehicle Front axle weight / kN Rear axle weight / kN Total weight / kN Car #1 87.8 296.2 384.0 Car #2 83.7 292.8 376.5

[0126] The mid-span section of the bridge was selected as the test section. Under the moving loading condition, a heavy vehicle No. 1 slowly and uniformly passed over the bridge deck along lane 1 and lane 2 at a speed of 3051.7 m / h. The loading lanes are shown in Figures 5(a) and (b). The deflection and strain time history response curves of the test section were tested. The timing start and end points were the front axle of the loaded vehicle going onto the bridge and the rear axle going off the bridge. To explore the reliability of the proposed method, a static load test of the bridge was also carried out, and the verification coefficient of the corresponding section of the bridge under the static load test was analyzed. The mid-span loading conditions 1 and 2 of the bridge static load test are shown in Figures 5(a) and (b).

[0127] Identify the influence line

[0128] Based on the VMD preprocessing method, using the bridge's fundamental frequency of 2.718Hz as the threshold for IMF decomposition, IMF components with a dominant frequency greater than the bridge's fundamental frequency were stripped to obtain the bridge's quasi-static deflection and strain time history response. (See...) Figure 6 , Figure 7 The spatial density of the influence line coefficients is expanded using linear interpolation, making the sampling difference in equation (8) an integer. This allows for the construction of a vehicle information matrix to establish an influence line identification model. Tikhonov regularization is then used to identify bridge influence lines. The identification results are shown in [the table below]. Figure 8 , Figure 9 As shown.

[0129] Rapid assessment results of load-bearing capacity

[0130] According to the virtual loading method, the virtual response in the static load test condition of the bridge is reconstructed on the identified deflection and strain influence lines. The bridge bearing capacity rapid assessment verification coefficient is calculated according to Equation (16). The results are compared with the bridge static load test deflection and strain results. The specific results are shown in Tables 2 and 3.

[0131] Table 2 Comparison of Bridge Rapid Assessment and Static Load Test Deflection Assessment Results

[0132]

[0133] Table 3 Comparison of Bridge Rapid Assessment and Static Load Test Strain Assessment Results

[0134]

[0135]

[0136] Rapid loading tests were conducted on the bridge control sections based on measured influence lines. Comparison of the static load test results with Tables 2 and 3, and analysis of the deflection and strain effects, revealed that the trends and patterns of the test results from both methods are largely consistent. This indicates that the rapid loading test results using influence lines can be used to assess the bridge's load-bearing capacity under lower load efficiencies. Compared to the static load tests, the verification coefficients obtained from the rapid assessment of the bridge's load-bearing capacity are generally lower, with the deflection effect verification coefficient being up to 10.77% lower and the strain effect verification coefficient being up to 11.90% lower.

[0137] Analysis shows that due to the short holding time and insufficient stress response of the bridge structure under rapid loading, the bridge effect values ​​obtained from the rapid loading test are too small. However, the vehicle-driven loading effect is closer to the actual moving load borne by the bridge, and the test results using moving vehicle loading are still within the reliable range for rapid load capacity assessment. Combined with the continuous beam bridge test study, it is shown that the bridge has good load capacity. The verification coefficient of the control section effect increases with the increase of static load test load efficiency, but the rapid load capacity assessment results do not show this trend. This is because the bridge holding time is short during rapid loading, and the "peak-shaving" phenomenon exists in the VMD bridge time history response preprocessing method during the process of stripping the bridge dynamic components. As a result, the virtual static response reconstructed based on the measured influence line of the bridge is smaller than the static response of the corresponding static load test condition, and the verification coefficient of the control section also shows a relatively consistent pattern.

[0138] The proposed rapid bridge load-bearing capacity assessment method serves as a supplement to static load testing. Its testing process and methods are scientific, reasonable, and highly practical. It can reduce the operating cost of static load testing under lower load efficiency, avoid new structural damage, and provide effective and reliable bridge load-bearing capacity assessment results. It is recommended for rapid screening of the load-bearing capacity of bridges in good technical condition.

[0139] In summary, the above-described method for assessing the load-bearing capacity of small and medium-sized bridges based on vehicle-driven loading, using a three-span steel-concrete composite beam bridge as the research object, conducted static load tests and rapid assessment tests to verify the practicality and operability of the rapid bridge load-bearing capacity assessment method based on measured influence lines. By reconstructing the static virtual response of the bridge under static load test conditions through virtual loading on the identified influence lines, a comparison of the verification coefficients of the two test methods revealed that the maximum error in the deflection verification coefficient was 10.77%, and the maximum error in the strain verification coefficient was 11.90%. This is because the vehicle-driven loading of the bridge has a short holding time, and the method is based on VMD and Tikhon... The OV regularized influence line identification method suffers from "peak shaving" and other issues, resulting in the verification coefficients of rapid load-bearing capacity assessment methods being lower than those of static load tests. The rapid load-bearing capacity assessment method based on measured influence lines is scientifically sound, practical, and operable, and can serve as a supplement to static load tests. According to the proposed implementation process, bridges in good technical condition can be rapidly screened for load-bearing capacity, effectively improving the assessment rate. Furthermore, this method avoids structural damage caused by high loading efficiency, providing methodological support and case studies for "lightweight" rapid screening of bridge load-bearing capacity.

[0140] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for assessing the bearing capacity of small and medium-sized bridges based on vehicle-driven loading, characterized in that, Includes the following steps: S1: Time-Schedule Response Acquisition The bridge time history response, including bridge influence line information, structural dynamic components, and vehicle multi-axle effects, was obtained by using vehicle-moving loading. S2: Time-history response preprocessing The VMD method was used to remove the structural dynamic components from the time history response of the bridge to obtain the quasi-static time history response of the bridge. S3: Influence Line Identification A vehicle information matrix is ​​constructed and an influence line identification model is established. An error term is introduced and the Tikhonov regularization method is used to optimize the influence line identification model. The optimized influence line identification model is then used to solve for the bridge influence line. S4: Load-bearing capacity assessment Virtual loading is performed on the bridge influence line obtained in step S3 to reconstruct the bridge's virtual static response, and the bridge's bearing capacity is evaluated using the evaluation verification coefficient method. In step S2, after processing with the VMD method, the bridge time history response is decomposed into K IMF components. The principal frequency of each IMF component is obtained through Fast Fourier Transform. IMF components with a principal frequency greater than the fundamental frequency of the bridge structure are considered as structural dynamic components and are eliminated. K starts from 2 and takes values ​​sequentially. (K-1) The main frequency is lower than the fundamental frequency of the bridge structure, for IMF (K-1) IMF (K) The signal is reconstructed, and the reconstructed signal is the quasi-static time history response of the bridge structure measuring points, which is also the quasi-static time history response of the bridge. In step S3, the influence line identification model is as follows: AND s =LΦ Among them, Y S For the quasi-static response of the bridge, Φ is the influence line coefficient of the bridge node, and L is the vehicle information matrix; With the front axle entering the bridge and the rear axle exiting the bridge as the start and end points of timing, the vehicle information matrix is ​​as follows: In step S4, the influence line coefficient θ of bridge section i is used... i The corresponding load M at this location i By adding the products, the virtual static response of the bridge can be reconstructed, the virtual loading of the bridge influence line can be realized, and then the evaluation verification coefficient can be constructed. The bridge bearing capacity can be evaluated based on the calculated evaluation verification coefficient results. In step S4, the formula for calculating the evaluation verification coefficient is as follows: Where G is the number of lanes, θ i ξ is the influence line coefficient at the location corresponding to section i of the measuring point, and ξ is the evaluation and verification coefficient; M i S represents the vehicle axle load at the corresponding location of bridge section i; s This represents the maximum calculated effect value of the load control section during the loading test.

2. The method for evaluating the bearing capacity of small and medium-sized bridges based on vehicle-driven loading according to claim 1, characterized in that: In step S2, the specific processing procedure of the VMD method is as follows: S21: By iteratively searching for K modes, and setting the sum of all modes equal to the original signal as a constraint, the variational constraint problem is described as follows: in, For the partial derivative with respect to time t, u k For the Kth IMF component, ω k Let f(t) be the frequency of the Kth IMF component, δ(t) be the Reichstag distribution function, and f(t) be the input signal. S22: By introducing a quadratic penalty factor α and the Lagrange multiplication operator λ(t), the variational constrained problem is transformed into an unconstrained variational problem. The unconstrained lagrange function is as follows: S23: Use the Lagrange multiplication operator to obtain the saddle point in the unconstrained lagrange function, and update u through iteration. k n+1 ω k n+1 , λ k n+1 ; S24: Initialize {ω k 1 }、{u k 1 }、λ 1 n, iteratively update u k The iteration continues until the tolerance error ε is met, at which point the iteration stops and K IMF components are output.

3. The method for evaluating the bearing capacity of small and medium-sized bridges based on vehicle-driven loading according to claim 2, characterized in that: In step S23, the update formula is defined as follows: Where ^ represents the Fourier transform operation, and τ is the time step. Equivalent to the current remaining amount Wiener filtering, This is the centroid of the power spectrum of the current mode function.

4. The method for evaluating the bearing capacity of small and medium-sized bridges based on vehicle-driven loading according to claim 2, characterized in that: In step S24, the tolerance error discriminant is as follows:

5. The method for evaluating the bearing capacity of small and medium-sized bridges based on vehicle-driven loading according to claim 4, characterized in that: In step S2, the expression for the quasi-static time history response of the bridge is as follows: Where Y(k) is the measured bridge response, S is the number of vehicle axles, and M is the number of axles. i For vehicle axle load, η is the influence line coefficient corresponding to the i-th axis. i Q is the structural dynamic component coefficient. i The sampling difference between each axis and the first axis is an integer, and its specific expression is: Q i =C i f / v Among them, C i Let f be the distance between the i-th axis and the first axis, f be the sampling frequency, and v be the vehicle speed.

6. The method for evaluating the bearing capacity of small and medium-sized bridges based on vehicle-driven loading according to claim 5, characterized in that: In step S3, the influence line identification model is corrected by introducing an error e. The corrected influence line identification model is as follows: Y s < LΦ+e; The Tikhonov regularization method is used to restrict the least squares expression by using the L2 norm as a penalty function, resulting in the following regularized expression for the influence line solution: Wherein, the regularization matrix T is: Substituting the regularization matrix into the regularization expression for the influence line solution and taking the derivative, then setting the derivative to 0, the optimized influence line identification model is as follows: Φ=(L T L+λ 2 T T T) -1 L T Y S Where λ is the regularization coefficient, the optimal value of λ is determined by the L-curve method to minimize the sum of the norms of the two terms in the regularization expression of the influence line solution; The bridge influence line can be solved by substituting the optimal value of λ into the optimized influence line identification model expression. The optimal value of λ is located at the point of maximum curvature of the L curve.

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