A bridge bending stiffness identification method and device based on multi-angle influence lines

Abstract

A method and device for identifying the bending stiffness of a bridge based on multi-angle influence lines. The angle influence lines are extracted by testing the bridge angle response; a variety of distribution functions are introduced to simulate the distribution of the bridge bending stiffness, and the parameters of the distribution functions are optimized with the multi-angle influence lines as the target to achieve bending stiffness identification. The specific implementation steps are: A. Carry out a bridge moving load test to extract the angle influence lines of the bridge support section; B. Establish the relationship between the bridge bending stiffness and the multi-angle influence lines; C. Select a suitable distribution function to simulate the bridge bending stiffness distribution; D. Introduce an optimization algorithm, with the measured multi-angle influence lines as the target, and estimate the parameters of the distribution function. The present invention uses the bridge angle as the test object, accurately obtains the bridge bending stiffness distribution from multiple angle influence lines, and provides a new idea for bridge detection and status assessment.

Description

Technical Field

[0001] This invention relates to a method for identifying the distribution of bending stiffness in bridges, specifically a method and apparatus for identifying the bending stiffness of small-to-medium span bridges with stiffness degradation based on multi-turn influence line information, belonging to the field of bridge inspection. Background Technology

[0002] During their service life, bridge structures inevitably experience stiffness degradation and reduced structural load-bearing capacity due to various factors such as environmental corrosion and material aging, which can lead to safety hazards in severe cases. Bridge bending stiffness encompasses geometric and physical parameters, directly reflecting the bridge's health status. Therefore, effectively and accurately identifying the distribution of bridge bending stiffness is crucial for safe bridge operation and maintenance, and has become a popular research area in recent years.

[0003] Traditional methods for identifying bridge flexural stiffness degradation primarily rely on dynamic or static testing. While dynamic testing is favored due to its convenience, dynamic responses are susceptible to environmental changes. Compared to dynamic responses, static responses exhibit a higher signal-to-noise ratio; however, static load tests require multiple loading vehicles for extended periods, leading to limitations in economy and timeliness. Recently, researchers have proposed a novel loading method based on moving vehicles crossing the bridge, employing influence lines to assess bridge flexural stiffness degradation. Deflection influence lines are the most widely used, sensitive to stiffness degradation, and readily available extraction methods from moving load tests.

[0004] In deflection testing, contact measurements offer high accuracy, but require a working surface near the measurement point to fix the sensor. However, the maximum deflection of a bridge typically occurs at mid-span, making it difficult to provide a suitable working space for deflection testing, thus limiting its application in bridge evaluation. Similar to deflection response, bridge rotation response is another form of structural deformation, also reflecting the degradation of flexural stiffness. In recent years, many scholars have used bridge rotation influence lines to identify bridge flexural stiffness. It should be noted that the rotation near the supports is usually larger than at other sections, making it an ideal parameter for identifying bridge flexural stiffness. Furthermore, sections near the supports are located above the piers, providing a suitable working platform for measurement. Compared to mid-span deflection, the rotation response of the support sections offers significant advantages in terms of measurement convenience. Summary of the Invention

[0005] To address the shortcomings of existing bridge stiffness identification methods, this invention proposes a bridge bending stiffness identification method and device based on multi-turn influence lines.

[0006] This invention introduces multiple stiffness distribution functions to simulate the distribution of bending stiffness, and uses the multi-rotation influence line as the target to estimate the parameters in the function, thereby realizing the identification of the bending stiffness distribution of bridges.

[0007] The first aspect of this invention relates to a method for identifying the flexural stiffness of bridges based on multi-turn influence lines, comprising the following steps:

[0008] A. Conduct bridge moving load tests and extract the influence line of the rotation angle of the bridge bearing section;

[0009] A1. Conduct bridge moving load tests to measure the bridge's rotation response. A test vehicle with known axle load, wheelbase, and number of axles can be used. The vehicle should be controlled to travel at a uniform, slow speed across the bridge, based on actual conditions. Throughout the test, the rotation response at the bridge supports should be collected at an appropriate sampling frequency.

[0010] A2. The influence line of bridge rotation is extracted from the bridge's moving load response as the basic data for identifying the bridge's bending stiffness. The patent (patent number: 201510212858.9) proposes a damage detection method based on influence lines, in which the influence line extraction step employs a "multi-segment basis function fitting method" to accurately describe and extract the bridge's influence line information.

[0011] B. Establish the relationship between bridge bending stiffness and influence lines of multiple rotation angles;

[0012] B1. Solve the computational model of a general beam. The boundary conditions of a general beam can be simplified to constraint springs with rotational stiffness. For continuous beams, the constraint springs can be considered as constraints on other simplified beam segments, and the spring stiffness can be calculated by applying a unit couple at the beam ends:

[0013]

[0014] In the formula, k ij It is the rotational stiffness of each span; θ i This is the rotation angle at the i-th support section. The stiffness of the constraint spring can be calculated from the end rotation angle:

[0015]

[0016] In the formula, K is the stiffness of the constraint spring; θ1 is the rotation angle of the first support section.

[0017] B2. Based on the bridge's bending stiffness, derive the influence line of rotation for general bridge structures. According to the unit load theorem, structural displacement can be obtained through the bending moment M(x,X) under actual load and the bridge bending moment under virtual load. It is calculated using the bending stiffness EI(X). The influence line of the rotation angle can be expressed as:

[0018]

[0019] In the formula, M(x,X) is the bending moment at section X of the beam when a unit force is applied at position x, which can be expressed as:

[0020]

[0021] In the formula, L b M1 is the span length; M2 and M1 are the spring constraint moments, which can be calculated using the force method.

[0022]

[0023] In numerical calculations, the relationship between the influence line of the rotation angle and the bending stiffness of the bridge can be represented in matrix form:

[0024]

[0025] In the formula, R i The rotation influence line vector of measuring point i; M is the load bending moment matrix; It is the bending moment matrix of the virtual force; e is a vector related to the bending stiffness of the bridge; N i It is the transformation matrix of the bending stiffness and the influence line of the rotation angle at measuring point i.

[0026] C. Select an appropriate distribution function to simulate the flexural stiffness distribution of the bridge;

[0027] C1. Introduce a distribution function to simulate the bending stiffness of the bridge and establish the relationship between the parameters of the distribution function and the influence line of the bridge rotation angle. The vector e related to the bending stiffness of the bridge can be described by the distribution function:

[0028]

[0029] In the formula, φ is the distribution function; Y is the parameter to be estimated in the distribution function.

[0030] C2. Select a suitable bending stiffness distribution function. Depending on the bridge type and damage mode, the following functions can be used for simulation.

[0031] The most commonly used forms are uniform stiffness and uniform reduction, which can be expressed as:

[0032]

[0033] In the formula, a k b is the reduced bending stiffness. k Location of the injury center; l d d represents the damaged area; d represents the undamaged bending stiffness.

[0034] The distribution function for stiffness degradation caused by a single crack can be expressed as:

[0035]

[0036] In the formula, a k The peak value of the curve corresponds to the degree of damage; b k Location of the peak center; c k Control the extent of the damage.

[0037] For more complex forms, a parameter r can be introduced:

[0038]

[0039] In the formula, a k b represents the peak value of the curve, corresponding to the degree of damage; c represents the position of the peak center, indicating the location of the damage; k Controlling the extent of the damage; r k Control the slope of the curves on both sides of the peak.

[0040] For beams with variable cross-sections, shape functions are added to the distribution function. Taking a three-span bridge as an example, the distribution function can be expressed as:

[0041]

[0042] In the formula, α1, α2, and α3 are parameters that control the cross-sectional changes; l1, l2, l3, and l4 are parameters related to the bridge span.

[0043] When the damage is unknown, φ3 can more comprehensively describe the bending stiffness of the bridge and is applicable to most types of damage. If the damage type determined in the preliminary investigation conforms to the φ1 or φ2 function, using the φ1 or φ2 function with fewer parameters can simplify the calculation. For beams with variable cross-sections, the φ4 function is used.

[0044] D. Introduce an optimization algorithm to estimate the parameters of the distribution function, using the measured multi-turn influence line as the target.

[0045] D1. Establish a least-squares optimization problem to find the optimal parameters that make the predicted influence line of the turning angle match the measured influence line of the turning angle. Using the measured multi-turn influence line as the objective value and the predicted influence line as a vector related to the stiffness distribution function, this is represented as a least-squares optimization problem:

[0046]

[0047] R pi =N i e(Y)(12b)

[0048] In the formula, It is a 2-norm; R ai and R pi These are the predicted angle influence line and the measured angle influence line, respectively.

[0049] D2. The LM optimization algorithm is used to estimate the model parameters. The residual between the measured multi-influence line and the predicted multi-influence line is:

[0050]

[0051] In the formula, δ(Y) is the residual. When the parameter produces an increment step of ΔY, the residual can be expressed as...

[0052]

[0053] In the formula, ΔY is the increment step size; J is the Jacobian matrix of e(Y), used to obtain the gradient of the function. To obtain the increment step size ΔY, let the derivative of δ(Y+ΔY) with respect to ΔY be 0. The increment step can be solved as:

[0054]

[0055] In the formula, I is the identity matrix and λ is the control coefficient.

[0056] The iteration stops when the residuals of two consecutive iterations fall below a predetermined threshold. The termination criterion is defined as follows:

[0057] δ j -δ j-1 ≤ε (16)

[0058] D3. Substitute the model parameters into the distribution function to obtain the bridge's flexural stiffness distribution curve. The process of identifying the bridge's flexural stiffness is as follows: Figure 2 As shown. During the iteration process, N i It changes with the bending stiffness, and should be updated according to Y in each iteration.

[0059] A second aspect of the present invention relates to a bridge bending stiffness identification device based on multi-angle influence lines, comprising a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement a bridge bending stiffness identification method based on multi-angle influence lines of the present invention.

[0060] A third aspect of the invention relates to a computer-readable storage medium having a program stored thereon that, when executed by a processor, implements a method for identifying the bending stiffness of a bridge based on multi-angle influence lines.

[0061] Compared with existing methods, this method has the following advantages:

[0062] (1) This method uses the influence line of bridge rotation angle as a parameter to identify the bending stiffness of the bridge. The rotation angle response at the bridge support is larger than that at other sections, making it sensitive to the degradation of bridge stiffness. At the same time, it is located above the pier, providing a suitable working platform, which has the advantage of convenience compared to deflection testing.

[0063] (2) This method provides different distribution functions for various types of bridges and bending stiffness distributions to match their stiffness distribution characteristics. This method is applicable to the stiffness identification of most small and medium span beams and continuous beams, and has wide adaptability.

[0064] (3) This method uses an optimization algorithm to estimate stiffness parameters based on the influence lines of multiple turning angles. Compared with the single-point method, this method combines data from multiple measurement points and has a high-precision advantage in identifying the bending stiffness distribution of bridges. Attached Figure Description

[0065] Figure 1 This is a flowchart of the bridge bending stiffness distribution identification process of the present invention;

[0066] Figure 2 This is a flowchart of the parameter estimation algorithm of the present invention;

[0067] Figure 3 This is a numerical simulation vehicle-bridge coupling diagram of the present invention;

[0068] Figure 4 This is the bridge rotation response diagram of the present invention;

[0069] Figure 5 This is the bridge corner influence line diagram of the present invention;

[0070] Figure 6 shows the identification results of bridge bending stiffness distribution under working conditions 1 to 4 of the present invention, where (a) is working condition 1, (b) is working condition 2, (c) is working condition 3, and (d) is working condition 4.

[0071] Figure 7 This is a diagram showing the stiffness distribution of the bridge with variable cross-section under working condition 5 of the present invention.

[0072] Figure 8 This is a diagram showing the identification results of bridge bending stiffness distribution under working condition 5 of the present invention; Detailed Implementation

[0073] The following is a detailed description of the bridge bending stiffness identification method based on multi-turn angle influence lines according to the present invention, with reference to the accompanying drawings.

[0074] Example 1

[0075] This embodiment relates to a method for identifying the bending stiffness of bridges based on multi-turn influence lines, such as... Figure 1 As shown, the specific steps include:

[0076] A. Conduct bridge moving load tests and extract the influence line of the rotation angle of the bridge bearing section;

[0077] A1. Conduct numerical simulations of vehicles crossing the bridge to obtain the bridge's rotational response. The vehicle-bridge coupling model is as follows: Figure 3 As shown. A three-span continuous beam bridge is selected for calculation. The span arrangement is 30m + 30m + 30m, and the mass per unit length is 5.207 × 10⁻⁶ m. 4 kg / m, flexural stiffness EI=10.63×10 10 N·m 2 A seven-DOF vehicle model was selected, with the tractor mass m1 = 3930 kg and the trailer mass m2 = 15700 kg. Quasi-static loading was simulated, with a vehicle speed of v = 1 m / s and a road surface roughness of ISO A. Angle measurement points (R1, R2, R3, R4) were set near each support. A uniform reduction model was used to simulate the degradation of the bridge's bending stiffness, with five damage scenarios set, as shown in Table 1.

[0078] Table 1. Bridge Damage Conditions

[0079]

[0080] The Wilson-θ method was used to calculate the rotational response of the bridge in the vehicle-bridge coupled system. The rotational responses under various working conditions are as follows: Figure 4 As shown.

[0081] A2. The influence line of bridge rotation angle was extracted from the bridge moving load response using a multi-segment basis function iterative fitting method. A 50-segment piecewise function was used to extract the initial influence line, followed by iterative fitting using a 16-segment piecewise function to obtain the accurate influence line of bridge rotation angle. The extracted influence lines for each load case are shown below. Figure 5 As shown.

[0082] B. Establish the relationship between bridge bending stiffness and influence lines of multiple rotation angles;

[0083] B1. Solve the computational model of a general beam. The boundary conditions of a general beam can be simplified to constraint springs with rotational stiffness. For continuous beams, the constraint springs can be considered as constraints on other simplified beam segments, and the spring stiffness can be calculated by applying a unit couple at the beam ends:

[0084]

[0085] In the formula, k ij It is the rotational stiffness of each bridge span; θ i This is the rotation angle at the i-th support section. The stiffness of the constraint spring can be calculated from the end rotation angle:

[0086]

[0087] In the formula, K is the stiffness of the constraint spring; θ1 is the rotation angle of the first support section.

[0088] B2. Based on the bending stiffness of bridges, derive the influence line of rotation for general bridge structures. Based on the unit load theorem in structural mechanics, the bending moment M(x,X) of the bridge under actual load and the bending moment M under virtual load can be derived. i The rotation of the portion near the support is calculated using the bending stiffness EI(X). The influence line of the rotation angle can be represented as:

[0089]

[0090] In the formula, M(x,X) is the bending moment at section X of the beam when a unit force is applied at position x, which can be expressed as:

[0091]

[0092] In the formula, L b M1 is the span length; M2 and M1 are the spring constraint moments, which can be calculated using the force method.

[0093]

[0094] In numerical calculations, the influence lines of the corners at different locations can be represented in matrix form:

[0095]

[0096] In the formula, R i M is the influence line vector of the rotation angle at the i-th measuring point; M is the load bending moment matrix. It is the bending moment matrix of the virtual force; e is a vector related to the bending stiffness of the bridge; N i It is the transformation matrix of the bending stiffness and the influence line of the rotation angle at the i-th measuring point.

[0097] C. Select an appropriate distribution function to simulate the flexural stiffness distribution of the bridge;

[0098] C1. Introduce a distribution function to simulate the bending stiffness of the bridge and establish the relationship between the parameters of the distribution function and the influence line of the bridge rotation angle. The vector e related to the bending stiffness of the bridge can be described by the distribution function:

[0099]

[0100] In the formula, φ is the distribution function; Y is the parameter to be estimated in the distribution function.

[0101] C2. Select a suitable bending stiffness distribution function. Depending on the bridge type and damage mode, the following functions can be used for simulation.

[0102] Assuming the damage mode is unknown, the φ3 distribution function, which has broad applicability, is selected for working conditions 1-4:

[0103]

[0104] In the formula, a k b represents the peak value of the curve, corresponding to the degree of damage; c represents the position of the peak center, indicating the location of the damage; k Controlling the extent of the damage; r k Control the slope of the curves on both sides of the peak.

[0105] For the variable cross-section beam in load case 5, select the φ4 distribution function:

[0106]

[0107] In the formula, α1, α2, and α3 are parameters that control the cross-sectional changes; l1, l2, l3, and l4 are parameters related to the bridge span.

[0108] D. Introduce an optimization algorithm to estimate the parameters of the distribution function, using the measured multi-turn influence line as the target.

[0109] D1. Establish a least-squares optimization problem to find the optimal parameters that make the predicted influence line of the turning angle match the measured influence line of the turning angle. Using the measured multi-turn influence line as the objective value and the predicted influence line as a vector related to the stiffness distribution function, this is represented as a least-squares optimization problem:

[0110]

[0111] R pi =N i e(Y)(12b)

[0112] In the formula, It is a 2-norm; R ai and R pi These are the predicted angle influence line and the measured angle influence line, respectively.

[0113] D2. The LM optimization algorithm is used to estimate the model parameters. The residual between the measured multi-influence line and the predicted multi-influence line is:

[0114]

[0115] In the formula, δ(Y) is the residual. When the parameter produces an increment step of ΔY, the residual can be expressed as...

[0116]

[0117] In the formula, ΔY is the increment step size; J is the Jacobian matrix of e(Y), used to obtain the gradient of the function. To obtain the increment step size ΔY, let the derivative of δ(Y+ΔY) with respect to ΔY be 0. The increment step can be solved as:

[0118]

[0119] In the formula, I is the identity matrix and λ is the control coefficient.

[0120] The iteration stops when the residuals of two consecutive iterations fall below a predetermined threshold. The termination criterion is defined as follows:

[0121] δ j -δ j-1 ≤ε (16)

[0122] D3. Substitute the estimated parameters to obtain the bridge stiffness distribution curve. The bridge flexural stiffness identification results for load cases 1-4 are shown in Figure 6. The variable cross-section form of the bridge in load case 5 is shown below. Figure 7 As shown, the bending stiffness identification results are as follows: Figure 8 As shown, the identified curve and the actual bending stiffness curve show good consistency under various working conditions, verifying the applicability and feasibility of this invention.

[0123] Example 2

[0124] This embodiment relates to a bridge bending stiffness identification device based on multi-angle influence lines, including a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement a bridge bending stiffness identification method based on multi-angle influence lines according to Embodiment 1.

[0125] Example 3

[0126] This embodiment relates to a computer-readable storage medium storing a program that, when executed by a processor, implements a bridge bending stiffness identification method based on multi-angle influence lines as described in Embodiment 1.

[0127] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A bridge bending stiffness identification method based on multi-angle influence lines, characterized in that: The following steps are involved: A. Carry out bridge moving load test and extract the rotation influence line of bridge support section; B. Establish the relationship between the bridge bending stiffness and the multi-angle influence line; Step B specifically includes: B1. Solve the calculation model of a general beam; the boundary conditions of a general beam can be simplified to a constraint spring with rotational stiffness; for a continuous beam, the constraint spring can be considered as the constraint of other spans on the simplified beam segment, and the spring stiffness can be calculated by applying a unit couple at the beam end: In the formula, k ij is the rotational stiffness of each span; θ i is the rotation angle of the i-th support section; the stiffness of the restraint spring can be calculated from the end rotation angle: Where K is the stiffness of the restraining spring; θ1 is the rotation angle of the first support section; B2. Based on the bending stiffness of the bridge, the rotation influence line of the general bridge structure is derived; the relationship between the rotation influence line and the bending stiffness of the bridge can be expressed in matrix form: In the formula, R i is the rotation influence line vector of measuring point i; M is the external load bending moment matrix; is the fictitious force-moment matrix; e is a vector related to the bending stiffness of the bridge; N i is the transformation matrix of the bending stiffness and the rotational influence line of the i measuring point; C. Select appropriate distribution function to simulate the distribution of bridge bending stiffness; D. Introduce an optimization algorithm to estimate the parameters of the distribution function with the measured multi-angle influence lines as the target.

2. The method for identifying the bending stiffness of a bridge based on multi-angle influence lines according to claim 1, characterized in that: Step A specifically includes: A1. Carry out bridge moving load test to test the rotational response at the bridge support; A2. Extract the bridge rotation influence line from the rotation response as the basic data for identifying the bridge bending stiffness.

3. The method for identifying the bending stiffness of a bridge based on multi-angle influence lines according to claim 1 is characterized in that: Step C specifically includes: C1. Introduce distribution function to simulate the bending stiffness of bridges, and establish the relationship between distribution function parameters and bridge rotation influence line; the vector e related to the bending stiffness of bridges is described by distribution function: Where φ is the distribution function; Y is the parameter to be estimated in the distribution function; C2. Select an appropriate bending stiffness distribution function; according to the bridge type and damage form, use uniform stiffness and uniform reduction, expressed as: In the formula, a k is the reduced bending stiffness; b k is the location of the injury center; l d is the damaged area; d is the undamaged bending stiffness; For the stiffness degradation caused by a single crack, the distribution function can be expressed as: In the formula, a k Indicates the peak value of the curve, corresponding to the degree of damage; b k The location of the peak center; c k Control the scope of damage; For a more complex form, we introduce the parameter r: In the formula, a k a represents the peak value of the curve, corresponding to the degree of damage; b represents the position of the center of the peak value, representing the damage location; c k Control the scope of damage; k Control the slope of the curve on both sides of the peak; For variable cross-section beams, the shape function is added to the distribution function. Taking a three-span bridge as an example, the distribution function is expressed as: Where α1, α2, α3 are the parameters controlling the cross-section change; l1, l2, l3, l4 are the parameters related to the bridge span; When the damage is unknown, φ3 can more comprehensively describe the flexural stiffness of the bridge and is applicable to most types of damage. If the damage type determined in the preliminary investigation conforms to the φ1 or φ2 function, the φ1 or φ2 function with fewer parameters can simplify the calculation. For variable-section beams, the φ4 function is used.

4. The method for identifying the bending stiffness of a bridge based on multi-angle influence lines according to claim 1, characterized in that: Step D specifically includes: D1. Establish a least squares optimization problem, which aims to find the best parameters to make the predicted corner influence line consistent with the measured corner influence line; take the measured multi-corner influence line as the target value, and the predicted influence line as the vector related to the stiffness distribution function, which is expressed as a least squares optimization problem: R pi =N i e(Y)(9b) In the formula, is the 2 norm; R ai and R pi They are the predicted corner influence line and the measured corner influence line respectively; D2. The LM optimization algorithm is used to estimate the model parameters. The optimal solution obtained by this optimization algorithm is: Where I is the unit matrix, λ is the control coefficient, and J is the Jacobian matrix of e(Y); D3. Substitute the model parameters into the distribution function to obtain the bridge bending stiffness distribution curve.

5. A bridge bending stiffness identification device based on multi-angle influence lines, characterized in that: It comprises a memory and one or more processors, wherein the memory stores executable codes, and when the one or more processors execute the executable codes, they are used to implement a bridge bending stiffness identification method based on multi-angle influence lines as described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that: A program is stored thereon, and when the program is executed by a processor, a bridge bending stiffness identification method based on multi-angle influence lines as described in any one of claims 1 to 4 is implemented.

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