A bridge bearing capacity virtual evaluation method based on reconstructed flexibility matrix

Abstract

The application discloses a bridge bearing capacity virtual evaluation method based on a reconstructed flexibility matrix and belongs to the technical field of bridge bearing capacity evaluation.The application constructs a full-bridge flexibility matrix through a proportional factor and a transformation matrix based on deflection influence lines of partial measuring points, does not need to depend on high-order modal information, reduces the calculation complexity and the number of measuring point arrangement, and improves engineering applicability; virtual static load loading is carried out through the reconstructed flexibility matrix, the structural response under multiple load working conditions can be simulated, the "overloading" damage risk caused by actual loading is avoided, and the safety of the detection process is improved.Combining the virtual static load response with the theoretical calculation value, a virtual calculation checking coefficient is obtained, scientific evaluation of the bridge bearing capacity is realized, the evaluation result is highly consistent with the traditional static load test, and good engineering feasibility and reliability are achieved.

Description

Technical Field

[0001] This invention relates to the field of bridge bearing capacity assessment technology, and specifically to a virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix. Background Technology

[0002] As a core component of transportation infrastructure, the load-bearing capacity of bridges directly affects traffic safety and the continuity of socio-economic activities. With the increase of service time, bridges will experience a gradual degradation in structural performance due to factors such as repeated vehicle loads, environmental erosion (such as carbonization and chloride ion intrusion), material aging (such as concrete cracking and steel corrosion), and accidental damage (such as impacts and earthquakes). Therefore, it is necessary to periodically assess their load-bearing capacity to determine whether they meet design requirements and traffic safety standards.

[0003] The current core technology system for bridge load-bearing capacity assessment revolves around the "load-response" relationship, mainly divided into three categories: static load testing, dynamic load testing, and derivative methods based on the combination of signal processing and structural mechanics. At the practical level, traditional load testing suffers from efficiency and economic bottlenecks: long traffic disruption times, high equipment and labor costs, and poor on-site adaptability. At the technical level, traditional signal processing and structural characteristic identification have accuracy limitations: inaccurate removal of dynamic components, unresolved multi-axis effects and ill-posedness in influence line identification, complex and redundant high-order modal calculations for flexibility matrix construction, and a lack of "virtual loading" in verification coefficient calculation.

[0004] To address this, a virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix is ​​proposed. Summary of the Invention

[0005] The technical problem to be solved by this invention is: how to solve the efficiency and economic bottlenecks and accuracy shortcomings of the existing technology, and to provide a virtual evaluation method for bridge bearing capacity based on the reconstructed flexibility matrix.

[0006] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0007] S1: Conduct on-site surveys and organize basic data for the bridge to determine the test load efficiency and the optimal number of deflection measurement points.

[0008] S2: Conduct on-site testing, using a test vehicle to apply uniform loading and extracting deflection time history response data from each deflection measurement point;

[0009] S3: Preprocess the extracted deflection time history response data, remove the vehicle-induced response dynamic components, construct the vehicle information matrix, solve the deflection influence line, and then reconstruct the full bridge flexibility matrix.

[0010] S4: Based on the vehicle loading position under static load conditions, perform virtual loading based on the full bridge flexibility matrix to obtain the bridge's virtual static load response value and calculate the bridge's virtual evaluation verification coefficient. This allows for the assessment of the bridge's load-bearing capacity.

[0011] Furthermore, in step S3, the specific process of separating the vehicle-induced response dynamic components is as follows:

[0012] S301: Use VMD to decompose the deflection time history response data obtained in step S2 into K finite bandwidth IMF components;

[0013] S302: The deflection time history response data decomposed by VMD is used to obtain the main frequency of each IMF component through FFT;

[0014] S303: The IMF components with a main frequency greater than the fundamental frequency of the bridge structure are treated as dynamic components and removed. The remaining IMF components are reconstructed, and the reconstructed signal is the measured quasi-static time history response of the bridge.

[0015] Furthermore, in step S303, to avoid over-decomposition or incomplete decomposition of the deflection time history response data, values ​​are gradually selected starting from K=2, and when IMF... (K-1) When the main frequency is lower than the fundamental frequency of the bridge structure, for the IMF (K-1) and IMF (K) Perform signal reconstruction.

[0016] Furthermore, in step S3, the specific process of identifying the deflection influence line is as follows:

[0017] S311: Assuming that the bridge responses caused by each axle of the vehicle are independent of each other, that is, the measured bridge response is the superposition result of the bridge responses caused by each axle of the vehicle, the measured bridge response is as follows:

[0018] ;

[0019] Where R(c) is the measured bridge response; N is the number of vehicle axles; A i The axle load of the vehicle's i-axis; The influence coefficient of the vehicle's i-axis; The dynamic response generated by the vehicle's i-axis; G i This is the distance between the vehicle's front axle and the i-axis.

[0020] S312: The influence line identification model is established as follows:

[0021] ;

[0022] in, This is the quasi-static time history response vector of the bridge; For vehicle information matrix; The influence line coefficient for bridges;

[0023] S313: Using the front axle upper bridge and the rear axle lower bridge as the start and end points of timing, construct the vehicle information matrix as follows:

[0024] ;

[0025] Where L is the vehicle information matrix;

[0026] S314: Introducing an error term to correct the influence line identification model:

[0027] ;

[0028] in, R represents the error; R is the corrected influence line identification model.

[0029] S315: Based on L2 regularization, the least squares expression is constrained by the L2 penalty function to establish the influence line solution expression. Its regularization expression is:

[0030] ;

[0031] in, As a penalty factor;

[0032] S316: Regularize the matrix Substituting the regularization expression, taking its derivative, and setting the derivative to 0, we obtain the expression for solving the influence line:

[0033] ;

[0034] in, The penalty factor is selected using the L-curve method.

[0035] Furthermore, in step S315, the regularization matrix... as follows:

[0036] .

[0037] Furthermore, in step S3, the specific process of reconstructing the full-bridge compliance matrix is ​​as follows:

[0038] S321: Assemble the deflection influence lines of each node of the bridge into a full-bridge flexibility matrix. :

[0039] ;

[0040] in, For degrees of freedom, Indicates the first Influence line of nodal deflection;

[0041] S322: The bridge is simplified as a multi-degree-of-freedom system, and its flexibility matrix is ​​calculated as follows:

[0042] ;

[0043] in, The mode shape matrix is ​​normalized to its mass. It is a diagonal matrix formed by the squares of the natural frequencies of each order; The extracted mode shape order; For the first First natural frequency; For the first Mode shape vector; This represents the number of nodes extracted from the mode shape.

[0044] S323: In step S322, As can be seen from steps S321 and S322, Then, the transformation matrix of the flexibility matrix is ​​constructed. :

[0045] ;

[0046] Obtain the transformation matrix The value of each element in the array is:

[0047] ;

[0048] in, The extracted mode shape order; For the first First natural frequency; For the first Mode shape vector; This represents the number of nodes extracted from the mode shape.

[0049] S324: Considering only the first-order vibration mode, the compliance matrix is ​​constructed and simplified to:

[0050] ;

[0051] S325: Selecting bridge sections Each node, along with its corresponding deflection influence line, constructs a new compliance matrix. :

[0052] ;

[0053] For the same location on the bridge deck:

[0054] ;

[0055] S326: Using a matrix Constructing the transformation matrix as follows:

[0056] ;

[0057] For the case of R=1, the transformation matrix middle The value is:

[0058] ;

[0059] and The ratio is a constant, and , Regardless of the value of , this ratio is defined as a scaling factor. ,but and The mathematical relationship is as follows:

[0060] ;

[0061] S327: Based on the acquired deflection influence line data and the constructed compliance matrix It can calculate the compliance matrix containing the scaling factor. There is a one-to-one correspondence between the row vectors and the deflection influence lines. The corresponding scaling factor is calculated using the acquired deflection influence line data. :

[0062] ;

[0063] in: Indicates the bridge at the The deflection affects the first line. The value of the point, Representation matrix The Middle The deflection affects the first line. The value of the point, Indicates the number of deflection influence lines. Indicates the number of influence coefficients in the deflection influence line;

[0064] S328: Further calculations yielded:

[0065] ;

[0066] Based on the above solution , The square root is the flexibility matrix. .

[0067] Furthermore, in step S4, the bridge virtual evaluation verification coefficients are... The calculation formula is as follows:

[0068] S41: The obtained compliance matrix Given the load vector, the static deflection of any bridge node can be calculated using the following formula:

[0069] ;

[0070] in: For the first One load vector value; Indicates the bridge is in The first on the flexibility matrix The amplitude at that point; The total number of loads loaded; For bridges Calculate deflection under static load;

[0071] S42: Calculate the virtual evaluation verification coefficient for the bridge. :

[0072] .

[0073] Furthermore, in step S4, when When the actual load-bearing capacity of the bridge meets the design requirements, the structural safety reserve is sufficient; when This indicates that the actual load-bearing capacity of the bridge does not meet the design requirements and that the structural safety reserve is insufficient.

[0074] The present invention has the following advantages over the prior art:

[0075] 1. By combining single-vehicle mobile loading with virtual static load assessment, traditional large-scale static load tests are eliminated, significantly reducing on-site testing time and traffic interruption time, lowering manpower and equipment costs, and improving bridge inspection efficiency.

[0076] 2. By combining variational mode decomposition (VMD) with virtual Fourier transform (FFT), the vehicle-induced dynamic response components can be accurately identified and eliminated, and high-quality quasi-static deflection time history data can be obtained, providing reliable input for subsequent influence line identification.

[0077] 3. Based on the deflection influence lines of some measuring points, the full bridge flexibility matrix is ​​constructed through scaling factors and transformation matrices. This eliminates the need to rely on high-order modal information, reduces computational complexity and the number of measuring points, and improves engineering applicability.

[0078] 4. By performing virtual static load loading through the reconstructed flexibility matrix, the structural response under various load conditions can be simulated, avoiding the risk of "overloading" damage that may be caused by actual loading and improving the safety of the detection process.

[0079] 5. By combining the virtual static load response with the theoretical calculation value, and virtually calculating the verification coefficient, a scientific assessment of the bridge's load-bearing capacity can be achieved. The assessment results show a high degree of agreement with traditional static load tests, demonstrating good engineering feasibility and reliability. Attached Figure Description

[0080] Figure 1 This is a flowchart illustrating the virtual evaluation method for bridge bearing capacity based on the reconstructed flexibility matrix in an embodiment of the present invention.

[0081] Figure 2 This is a flowchart illustrating the virtual assessment process for bridge bearing capacity in an embodiment of the present invention.

[0082] Figure 3 This is a schematic diagram of a damaged simply supported beam bridge model in an embodiment of the present invention;

[0083] Figure 4(a) is a graph showing the results of VMD removal of dynamic components in an embodiment of the present invention;

[0084] Figure 4(b) is a graph showing the results of VMD removal of dynamic components in an embodiment of the present invention;

[0085] Figure 5 This is a three-dimensional schematic diagram of the full-bridge compliance matrix in an embodiment of the present invention;

[0086] Figure 6 This is a schematic diagram of the test condition layout in an embodiment of the present invention;

[0087] Figure 7 This is a schematic diagram comparing the actual and predicted deflection in a static load experiment according to an embodiment of the present invention. Detailed Implementation

[0088] 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.

[0089] Example 1

[0090] like Figure 1 As shown, this embodiment provides a technical solution: a virtual evaluation method for bridge bearing capacity based on a reconstructed flexibility matrix, comprising the following steps:

[0091] Step 1: Conduct on-site surveys and organize basic data for the bridge, develop a virtual assessment plan for the bridge's load-bearing capacity, and determine the testing load efficiency and the optimal number of deflection measurement points.

[0092] Step 2: Conduct on-site testing. Based on the optimal number of deflection measurement points determined in the test plan, use the test vehicle to apply uniform load and extract the deflection time history response data of each deflection measurement point.

[0093] Step 3: Preprocess the measured deflection time history response data, remove the vehicle-induced response dynamic components, construct the vehicle information matrix, solve the deflection influence line, and then reconstruct the full bridge flexibility matrix.

[0094] Step 4: Based on the vehicle loading position under static load conditions, perform virtual loading based on the full bridge flexibility matrix to obtain the bridge's virtual static load response value and calculate the bridge's virtual evaluation verification coefficient. This allows for the assessment of the bridge's load-bearing capacity.

[0095] The theoretical methods used in the above steps will be explained in more detail below.

[0096] 1.1 Principle of Deflection Influence Line Identification

[0097] 1.1.1 Removal of vehicle-induced response dynamic components

[0098] Variational mode decomposition (VMD) decomposes the original signal (deflection time history response data) into K intrinsic mode functions (IMFs) with finite bandwidths, and iteratively searches for the optimal solution of the variational modes. Assuming that each IMF component has a certain center frequency, the VMD iteratively searches for K modes, with the constraint that the sum of all modes equals the original signal, minimizing the sum of the estimated bandwidths of each mode. Its constrained variational expression is as follows:

[0099] (1)

[0100] in, This represents the k-th IMF component; Let f(t) represent the center frequency of the k-th IMF component; f(t) represents the original signal. The unit impact function.

[0101] To find the optimal solution to the constrained variational problem, the Lagrange multiplication operator λ(t) and the quadratic penalty factor α are used to transform the constrained variational problem into an unconstrained variational problem. The Lagrange multiplication operator λ(t) ensures the strictness of the constraints, while the quadratic penalty factor α ensures the accuracy of signal reconstruction under Gaussian noise. The extended Lagrange expression is:

[0102] (2)

[0103] The Alternating Direction Method of Multipliers (ADMM) is used to continuously update each IMF component and its center frequency to solve for the "saddle point" in the Lagrange expression. This is done through a cyclical update process. , , The value is updated using the following formula:

[0104] (3)

[0105] (4)

[0106] (5)

[0107] Repeat steps (3) to (5) until the loop termination condition is met. The termination condition formula is:

[0108] (6)

[0109] The deflection time history response after VMD decomposition was processed using a Virtual Fourier Transform (FFT) to obtain the dominant frequencies of each IMF component. IMF components with dominant frequencies higher than the bridge structure's fundamental frequency were discarded as dynamic components. To avoid over-decomposition or incomplete decomposition of the original signal, values ​​were gradually selected starting from K=2. When the IMF... (K-1) When the main frequency is lower than the structural fundamental frequency, for the IMF (K-1) and IMF (K) The signal is reconstructed, and the reconstructed signal is the measured quasi-static time history response of the bridge.

[0110] 1.1.2 Establishment of Influence Line Identification Method

[0111] The quasi-static time history response of each lane of the bridge, preprocessed using VMD, exhibits vehicle multi-axle effects. An influence line identification model is established using L2 regularization to eliminate these effects. It is assumed that the bridge responses caused by each axle are independent, meaning the measured bridge response is the sum of the responses caused by each axle. The measured bridge response is shown in the equation:

[0112] (7)

[0113] Where: R(c) is the measured bridge response; N is the number of vehicle axles; A i The axle load of the vehicle's i-axis; The influence coefficient of the vehicle's i-axis; The dynamic response generated by the vehicle's i-axis; G i The distance from the front axle to the i-axis is [i-axis distance]. The influence line recognition model is as follows:

[0114] (8)

[0115] in: This is the quasi-static time history response vector of the bridge; For vehicle information matrix; This represents the influence line coefficient for bridges.

[0116] The vehicle information matrix is ​​shown below, with the front axle upper bridge and the rear axle lower bridge as the start and end points of timing:

[0117] (9)

[0118] Where L is the vehicle information matrix;

[0119] There is an error between the quasi-static time history response of each lane of the bridge after VMD preprocessing and the actual static time history response of the bridge. An error term is introduced to correct the influence line identification matrix model, as shown in the following formula:

[0120] (10)

[0121] in: For error; This is the corrected influence line identification model.

[0122] Introducing an error term can cause ill-posed problems in the influence line identification matrix. Since L2 regularization can constrain the least squares expression through the L2 penalty function, this method is used to establish the influence line solution expression, whose regularization expression is:

[0123] (11)

[0124] in, As a penalty factor;

[0125] Regularization matrix Usually:

[0126] (12)

[0127] Regularize the matrix Substituting into equation (11), taking the derivative and setting it to 0, we obtain the expression for solving the influence line:

[0128] (13)

[0129] in: The penalty factor is selected using the L-curve method.

[0130] 1.2 Principle of Influence Line Compliance Matrix Identification

[0131] The bridge flexibility matrix, as an important tool in structural mechanics for describing the deformation characteristics of bridges under load, is actually a systematic integration of the deflection influence lines of various nodes of the bridge. The study identifies the overall bridge flexibility matrix by establishing the physical relationship between the flexibility matrix and the deflection influence lines of some measuring points.

[0132] The deflection influence lines of each node of the bridge form the overall bridge flexibility matrix. :

[0133] (14)

[0134] in: For degrees of freedom, Indicates the first Influence line of nodal deflection.

[0135] According to the flexibility matrix theory constructed by Pandey et al., a bridge can be simplified into a multi-degree-of-freedom system. The formula for calculating its flexibility matrix is ​​shown in the following equation (15):

[0136] (15)

[0137] in: The mode shape matrix is ​​normalized to its mass. It is a diagonal matrix formed by the squares of the natural frequencies of each order; The extracted mode shape order; For the first First natural frequency; For the first Mode shape vector; This represents the number of nodes extracted from the mode shape.

[0138] In equation (15), From equations (14) and (15), it can be seen that... Then, the transformation matrix of the flexibility matrix is ​​constructed. :

[0139] (16)

[0140] Substituting equation (15) into equation (16), we obtain the transformation matrix. The value of each element in the array is:

[0141] (17)

[0142] in: The extracted mode shape order; For the first First natural frequency; For the first Mode shape vector; This represents the number of nodes extracted from the mode shape.

[0143] From equation (15), it can be seen that the influence of higher-order modal information on the compliance matrix is ​​limited. Therefore, to simplify the calculation, only the first-order vibration mode is considered to construct the compliance matrix. Then equation (17) can be simplified to:

[0144] (18)

[0145] Selecting bridges Each node, along with its corresponding deflection influence line, constructs a new compliance matrix. :

[0146] (19)

[0147] For the same location on the bridge deck:

[0148] (20)

[0149] Using matrix Construct the same transformation matrix as in equation (11) :

[0150] (twenty one)

[0151] For the case of R=1, the transformation matrix middle The value is:

[0152] (twenty two)

[0153] and The ratio is:

[0154] (twenty four)

[0155] visible and The ratio is a constant, and , Regardless of the value of , this ratio is defined as a scaling factor. ,but and The mathematical relationship is as follows:

[0156] (25)

[0157] Based on the obtained deflection influence line data and the constructed compliance matrix The compliance matrix containing the scaling factor can be calculated according to equation (25). Given the matrix... There is a one-to-one correspondence between the row vectors and the deflection influence lines, so the corresponding scaling factor can be calculated using the acquired deflection influence line data. :

[0158] (26)

[0159] in: Indicates the bridge at the The deflection affects the first line. The value of the point, Representation matrix The Middle The deflection affects the first line. The value of the point, Indicates the number of deflection influence lines. This indicates the number of influence coefficients in the deflection influence line.

[0160] According to equations (25) and (26), we can obtain:

[0161] (27)

[0162] The solution can be obtained from equation (26). , The square root is the flexibility matrix. .

[0163] 1.3 Virtual Assessment Method for Bridge Bearing Capacity

[0164] Based on the influence line compliance matrix of the identification Given the load vector, the static deflection (static load response value) of any bridge node can be calculated using the following formula:

[0165] (28)

[0166] in: For the first One load vector value; Indicates the bridge is in On the influence line compliance matrix, the first The amplitude at that point; The total number of loads loaded; For bridges Calculate deflection under static load;

[0167] According to the "Specifications for Load Testing of Highway Bridges", the structural verification coefficient... This refers to the measured deflection value at the control section measuring point during bridge load testing. (or strain value) and theoretically calculated deflection value The ratio of (or strain value) is evaluated according to the following criteria: when When the actual load-bearing capacity of the bridge meets the design requirements, the structural safety reserve is sufficient; when This indicates that the actual load-bearing capacity of the bridge does not meet the design requirements and that the structural safety reserve is insufficient.

[0168] To address the problems of long static time, traffic obstruction, and high cost associated with conventional load testing, this invention proposes a virtual evaluation and verification coefficient for bridges based on the influence line flexibility matrix. This enables the assessment of bridge conditions.

[0169] (29)

[0170] To enhance the practicality and operability of the proposed bridge bearing capacity assessment method based on influence line-reconstructed flexibility matrix, the following virtual assessment implementation process for bridge bearing capacity is formulated. The virtual assessment process for bridge bearing capacity is as follows: Figure 2 As shown.

[0171] Step 1: Conduct on-site surveys and organize basic data for the bridge, develop a virtual assessment plan for the bridge's bearing capacity, and determine the testing load efficiency and the optimal number of deflection measurement points.

[0172] Step 2: Conduct on-site testing, determine the optimal number of deflection measurement points according to the test plan, use the test vehicle to perform uniform loading and extract the deflection time history response of each deflection measurement point;

[0173] Step 3: Preprocess the measured deflection time history response data, remove the vehicle-induced response dynamic components, construct the vehicle information matrix, solve the deflection influence line, and then reconstruct the full bridge flexibility matrix.

[0174] Step 4: Referring to the "Specifications for Load Testing of Highway Bridges" (JTG / TJ21-01-2015), calculate the theoretical response value of the bridge model under static load test conditions. Based on the vehicle loading position under static load conditions, perform virtual loading based on the influence line flexibility matrix to obtain the virtual static load response value of the bridge and calculate the virtual evaluation verification coefficient of the bridge. Step 5: According to the "Specifications for Testing and Evaluation of Bearing Capacity of Highway Bridges" (JTG / TJ21-2011), evaluate the bearing capacity of the bridge structure through the calculation results of the virtual evaluation verification coefficient of the bridge, and then issue a virtual evaluation report on bearing capacity.

[0175] By reconstructing the full bridge flexibility matrix using the deflection influence lines identified from a small number of measuring points, and then virtually loading the full bridge flexibility matrix, the measured response values ​​under the corresponding static load conditions can be obtained by relying solely on the moving loading 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 for loading.

[0176] The numerical simulation results are as follows:

[0177] Numerical Examples of Simply Supported Beams

[0178] 1. Establishment of numerical examples

[0179] The test vehicle was loaded at a constant speed of 20 km / h along the bridge's centerline. To simulate the bridge's actual operational state after stiffness performance degradation, a damaged bridge model was established by reducing the elastic modulus of the mid-span region (5-15m) by 15%, as shown below. Figure 2 As shown. Since noise is unavoidable during actual bridge testing, 5% Gaussian white noise was added to the extracted deflection response. The control sections were selected at the quarter points of the bridge span, and deflection response data were extracted for each control section, as shown below. Figure 3 As shown. At this time, the fundamental frequency of the example structure is 5.784Hz.

[0180] Depend on Figure 3 Analysis shows that when a vehicle crosses the bridge at a speed of 20 km / h, the bridge deflection response exhibits significant fluctuations. To obtain the quasi-static deflection response of the bridge, the VMD preprocessing method is used. Using the bridge's fundamental frequency as a threshold, IMF components with frequencies higher than the bridge's fundamental frequency are removed, eliminating vehicle-induced dynamic components and test noise. The quasi-static deflection time history response at each control section of the bridge is obtained, as shown in Figure 4(a). After VMD processing, the bridge's quasi-static response contains multi-axle effect interference from vehicles. To further eliminate axle effect interference, a vehicle information matrix is ​​constructed, and the influence line identification equation is solved using the Tikhonov regularization method. The multi-axle vehicle moving load is transformed into a deflection influence line under a unit concentrated load, as shown in Figure 4(b).

[0181] Based on the above deflection influence line identification method, the matrix of deflection influence lines at the control sections of the bridge span quarter points is obtained. Based on known deflection influence lines and matrices [ ]; Calculate the scaling factor c, and then reconstruct the full-bridge flexibility matrix, see below. Figure 5 As shown.

[0182] 2. Operating Condition Settings

[0183] Based on the "Specifications for Load Testing of Highway Bridges," a standard load test scheme for bridges was designed. Two 34t three-axle loading vehicles were selected, with axle loads of 60kN, 140kN, and 140kN respectively. The bridge was subjected to medium-load loading, and the static load test loading efficiency was calculated to determine the arrangement of the test vehicles. The static load test loading efficiency should ideally be between 0.85 and 1.05. The test vehicle arrangement is detailed below. Figure 6 As shown, the loading efficiency at this time =0.89, which meets the test requirements.

[0184] 3. Prediction of Virtual Static Load Deflection of Simply Supported Beams

[0185] The static deflection under virtual loading was calculated using the influence line compliance matrix from the main beam test. The calculation required equivalent nodal distribution of the vehicle load, allocating wheel forces to the calculation nodes of the compliance matrix according to the equivalent load distribution principle. A comparison of the actual deflection and predicted deflection under medium load conditions is shown below. Figure 7 As shown.

[0186] Depend on Figure 7 Analysis shows that for this simply supported beam bridge under static load conditions in the mid-span, the predicted deflection calculated using the influence line flexibility matrix under virtual loading matches well with the static deflection under actual load. This indicates that the predicted deflection based on the virtual static load using the flexibility matrix can effectively replace the static deflection value under actual static load test conditions, demonstrating certain engineering feasibility.

[0187] 4. Virtual assessment of the load-bearing capacity of simply supported beams

[0188] The influence line flexibility matrix was calculated to determine the deflection verification coefficients of each control section under virtual loading conditions, thus verifying the feasibility of the virtual static load test method based on the flexibility matrix in bridge bearing capacity assessment. The deflection verification coefficients of each control section in the mid-span of the bridge are shown in Table 1.

[0189] As shown in Table 1, the verification coefficients for the static load test of the mid-span under actual loading are between 1.12 and 1.14, and the verification coefficients for the virtual evaluation under virtual loading are between 1.09 and 1.15. The maximum relative error of the verification coefficients is 2.68%. The deflection verification coefficients calculated by both methods are greater than 1, indicating that the bearing capacity of the damaged bridge does not meet the design requirements.

[0190] Table 1 Verification of calibration coefficients under static load test

[0191]

[0192] In summary, the method of this invention can obtain relatively accurate static deflection values, which can effectively replace the static deflection values ​​under actual static load test conditions, and calculate virtual evaluation verification coefficients. Furthermore, combined with bridge specifications, it can be used to evaluate the load-bearing capacity of bridges.

[0193] 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 virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix, characterized in that, Includes the following steps: S1: Conduct on-site surveys and organize basic data for the bridge to determine the test load efficiency and the optimal number of deflection measurement points. S2: Conduct on-site testing, using a test vehicle to apply uniform loading and extracting deflection time history response data from each deflection measurement point; S3: Preprocess the extracted deflection time history response data, remove the vehicle-induced response dynamic components, construct the vehicle information matrix, solve the deflection influence line, and then reconstruct the full bridge flexibility matrix. S4: Based on the vehicle loading position under static load conditions, perform virtual loading based on the full bridge flexibility matrix to obtain the bridge's virtual static load response value and calculate the bridge's virtual evaluation verification coefficient. This allows for the assessment of the bridge's load-bearing capacity.

2. The virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix according to claim 1, characterized in that, In step S3, the specific process of separating the vehicle-induced response dynamic components is as follows: S301: Use VMD to decompose the deflection time history response data obtained in step S2 into K finite bandwidth IMF components; S302: The deflection time history response data decomposed by VMD is used to obtain the main frequency of each IMF component through FFT; S303: The IMF components with a main frequency greater than the fundamental frequency of the bridge structure are treated as dynamic components and removed. The remaining IMF components are reconstructed, and the reconstructed signal is the measured quasi-static time history response of the bridge.

3. The virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix according to claim 2, characterized in that, In step S303, to avoid over-decomposition or incomplete decomposition of the deflection time history response data, values ​​are gradually selected starting from K=2, and when IMF... (K-1) When the main frequency is lower than the fundamental frequency of the bridge structure, for the IMF (K-1) and IMF (K) Perform signal reconstruction.

4. The virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix according to claim 2, characterized in that, In step S3, the specific process of deflection influence line identification is as follows: S311: Assuming that the bridge responses caused by each axle of the vehicle are independent of each other, that is, the measured bridge response is the superposition result of the bridge responses caused by each axle of the vehicle, the measured bridge response is as follows: ； Where R(c) is the measured bridge response; N is the number of vehicle axles; A i The axle load of the vehicle's i-axis; The influence coefficient of the vehicle's i-axis; The dynamic response generated by the vehicle's i-axis; G i This is the distance between the vehicle's front axle and the i-axis. S312: The influence line identification model is established as follows: ； in, This is the quasi-static time history response vector of the bridge; For vehicle information matrix; The influence line coefficient for bridges; S313: Using the front axle upper bridge and the rear axle lower bridge as the start and end points of timing, construct the vehicle information matrix as follows: ； Where L is the vehicle information matrix; S314: Introducing an error term to correct the influence line identification model: ； in, R represents the error; R is the corrected influence line identification model. S315: Based on L2 regularization, the least squares expression is constrained by the L2 penalty function to establish the influence line solution expression. Its regularization expression is: ； in, As a penalty factor; S316: Regularize the matrix Substituting the regularization expression, taking its derivative, and setting the derivative to 0, we obtain the expression for solving the influence line: ； in, The penalty factor is selected using the L-curve method.

5. The virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix according to claim 4, characterized in that, In step S315, the regularization matrix as follows: 。 6. The virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix according to claim 4, characterized in that, In step S3, the specific process of reconstructing the full-bridge compliance matrix is ​​as follows: S321: Assemble the deflection influence lines of each node of the bridge into a full-bridge flexibility matrix. : ； in, For degrees of freedom, Indicates the first Influence line of nodal deflection; S322: The bridge is simplified as a multi-degree-of-freedom system, and its flexibility matrix is ​​calculated as follows: ； in, The mode shape matrix is ​​normalized to its mass. It is a diagonal matrix formed by the squares of the natural frequencies of each order; The extracted mode shape order; For the first First natural frequency; For the first Mode shape vector; This represents the number of nodes extracted from the mode shape. S323: In step S322, As can be seen from steps S321 and S322, Then, the transformation matrix of the flexibility matrix is ​​constructed. : ； Obtain the transformation matrix The value of each element in the array is: ； in, The extracted mode shape order; For the first First natural frequency; For the first Mode shape vector; This represents the number of nodes extracted from the mode shape. S324: Considering only the first-order vibration mode, the compliance matrix is ​​constructed and simplified to: ； S325: Selecting bridge sections Each node, along with its corresponding deflection influence line, constructs a new compliance matrix. : ； For the same location on the bridge deck: ； S326: Using a matrix Constructing the transformation matrix as follows: ； For the case of R=1, the transformation matrix middle The value is: ； and The ratio is a constant, and , Regardless of the value of , this ratio is defined as a scaling factor. ,but and The mathematical relationship is as follows: ； S327: Based on the acquired deflection influence line data and the constructed compliance matrix It can calculate the compliance matrix containing the scaling factor. There is a one-to-one correspondence between the row vectors and the deflection influence lines. The corresponding scaling factor is calculated using the acquired deflection influence line data. : ； in: Indicates the bridge at the The deflection affects the first line. The value of the point, Representation matrix The Middle The deflection affects the first line. The value of the point, Indicates the number of deflection influence lines. Indicates the number of influence coefficients in the deflection influence line; S328: Further calculations yielded: ； Based on the above solution , The square root is the flexibility matrix. .

7. The virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix according to claim 6, characterized in that, In step S4, the bridge virtual evaluation verification coefficients are... The calculation formula is as follows: S41: The obtained compliance matrix Given the load vector, the static deflection of any bridge node can be calculated using the following formula: ； in: For the first One load vector value; Indicates the bridge is in The first on the flexibility matrix The amplitude at that point; The total number of loads loaded; For bridges Calculate deflection under static load; S42: Calculate the virtual evaluation verification coefficient for the bridge. : 。 8. The virtual assessment method for bridge bearing capacity based on a reconstructed flexibility matrix according to claim 7, characterized in that, In step S4, when When the actual load-bearing capacity of the bridge meets the design requirements, the structural safety reserve is sufficient; when This indicates that the actual load-bearing capacity of the bridge does not meet the design requirements and that the structural safety reserve is insufficient.

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