Disaster loss bridge traffic feasibility fast decision method and system based on flexibility identification

Abstract

The application provides a kind of disaster loss bridge traffic feasibility fast decision method and system based on flexibility identification, belongs to the bridge engineering maintenance monitoring technical field based on signal data processing, obtains excitation force signal and bridge response signal;Modal parameters of bridge are identified by using complex modal indicator function method, and full displacement flexibility matrix is reconstructed, and is disassembled and reorganized into measuring point displacement loading matrix, and full displacement loading matrix is obtained through curve fitting and interpolation, the static deflection of bridge or the dynamic deflection when vehicle passes through bridge at low speed is predicted, and the traffic decision scheme is determined according to the design limit of cross section deflection.This application is driven based on response data, simple operation, short test time, high environmental adaptability, can control prediction accuracy by itself, overcome the strict condition that traditional flexibility identification method needs to ensure that load acting position and measuring point position coincide, one point one algorithm is realized in matrix disassembly process, storage space is saved, prediction efficiency is improved, vehicle can be flexibly loaded when bridge dynamic and static deflection is predicted.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering maintenance and monitoring technology based on signal data processing, specifically to a method and system for rapid decision-making on the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification. Background Technology

[0002] Prefabricated simply supported beam bridges account for a large proportion of highway bridges due to their advantages such as convenient construction, simple prefabrication process, and low cost. Existing research on highway bridge assessment mainly relies on static load testing methods, which are complex, time-consuming, costly, and highly subjective, failing to meet the practical needs of rapid assessment of damaged bridges. Rapid assessment methods and technologies based on impact vibration can solve the industry problem that traditional visual inspection and load testing methods are unsuitable for rapid assessment of the load-bearing capacity of damaged bridges. However, existing impact vibration methods involve dense sensor deployment and lengthy data cable installation, only enabling prediction of static load deflection, and requiring the loading location and measuring point to coincide. Load testing often requires graded loading, and it is impossible to guarantee that all loading points are at the measuring point during each stage. Bridges are crucial components and key nodes in transportation networks, acting as bottlenecks in traffic routes. If it is not possible to quickly determine whether a bridge is dangerous and whether it can be opened to traffic, choosing to open a new route will only prolong the time required for emergency repairs. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for rapid decision-making on the feasibility of opening a damaged bridge to traffic based on flexibility identification, which can predict the dynamic deflection of a bridge when vehicles pass at low speeds and the static deflection at any loading position, and can solve at least one of the technical problems existing in the background art.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] In a first aspect, the present invention provides a method for rapid decision-making on the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification, comprising:

[0006] Obtain bridge response and excitation force signals from multiple impact vibration tests on prefabricated beam bridges;

[0007] The bridge displacement frequency response function is calculated based on the obtained bridge response and excitation force signals.

[0008] The modal parameters of a bridge are identified based on the complex modal indicator function method, and the full displacement compliance matrix is ​​calculated.

[0009] The full displacement compliance matrix is ​​decomposed and recombined into a displacement loading matrix, and the full displacement loading matrix is ​​obtained by using an interpolation function;

[0010] By determining the wheel load and the position of the wheel or the vehicle's trajectory, and based on the full displacement loading matrix, the static and dynamic deflection of the bridge can be predicted.

[0011] Optionally, impact tests can be performed sequentially at different mid-span locations of the main beam, with at least two excitation points selected. Sensors should be placed at the bottom of the beam at critical sections of the bridge to collect excitation force signals and bridge response signals for each test, and perform data preprocessing.

[0012] Optionally, the complex modal indicator function method is used to identify the basic modal parameters of the bridge, including natural frequency, mode shape, damping ratio, and deep modal parameters, including modal scaling factor and system poles; the displacement frequency response function matrix is ​​decomposed into singular values, the natural frequency of the structure is determined by the singular value curve, and the displacement frequency response function matrix is ​​weighted by left and right weighting vectors to obtain the enhanced displacement frequency response function.

[0013] Optionally, after obtaining the enhanced frequency response function, at least five discrete frequency points near each natural frequency of the enhanced frequency response function are selected to obtain the polynomial coefficient vector; the concept of state-space equations is introduced to reduce the order of the second-order equation system and simplify the calculation to obtain the system pole expression; the modal parameters obtained by identification are substituted into the expression, and the modal scaling factor is calculated using the least squares method; the full displacement compliance matrix of the bridge structure is obtained by combining the first three system poles, mode shapes, and modal scaling factors.

[0014] Optionally, all elements in the m rows of the full displacement compliance matrix are reorganized according to the actual position of the measuring point on the bridge to obtain the displacement loading matrix corresponding to the numbered measuring point m. Curve fitting and surface interpolation are performed on the displacement loading matrix, and the interpolation accuracy is selected according to the actual requirements to obtain the full displacement loading matrix of measuring point m.

[0015] Optionally, the magnitude of the static load on the bridge and the wheel contact point of each wheel are determined to obtain the vehicle loading matrix. The displacement loading compliance coefficient of the actual wheel position is multiplied and superimposed with the wheel force to obtain the static deflection at measuring point m. The static displacement of all measuring points is calculated in sequence to realize the prediction of static deflection of the vehicle under any working condition when it is parked on the bridge. For low-speed vehicles, the feasibility condition for vehicle passage requires that any measuring point can satisfy the following at any time: the dynamic displacement at measuring point m is not greater than the maximum calculated effect value of the deflection of the control section at measuring point m.

[0016] Secondly, the present invention provides a rapid decision-making system for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility recognition, comprising:

[0017] The acquisition module is used to acquire bridge response and excitation force signals from multiple impact vibration tests on prefabricated beam bridges.

[0018] The first calculation module is used to calculate the bridge displacement frequency response function based on the acquired bridge response and excitation force signal;

[0019] The second calculation module is used to calculate the full displacement compliance matrix based on the modal parameters of the bridge identified by the complex modal indicator function method.

[0020] The disassembly module is used to disassemble the full displacement compliance matrix and reassemble it into a displacement loading matrix, and to obtain the full displacement loading matrix using an interpolation function;

[0021] The prediction module is used to determine the wheel load and the position of the wheel or the vehicle's movement trajectory, and predicts the static and dynamic deflection of the bridge based on the full displacement loading matrix.

[0022] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification as described in the first aspect.

[0023] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification as described in the first aspect.

[0024] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification as described in the first aspect.

[0025] The beneficial effects of this invention are: it is based on response data-driven, does not rely on finite element models, is simple to operate, has short testing time, high environmental adaptability, and can control the prediction accuracy itself. In particular, it overcomes the strict condition that traditional bridge deflection prediction methods require the load application location to coincide with the measurement point location. The matrix decomposition process realizes point-to-point calculation, saves computer cache calls, improves prediction efficiency, and allows for flexible vehicle loading when predicting bridge dynamic and static deflection.

[0026] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the process for a rapid decision-making method on the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification, as described in an embodiment of the present invention.

[0029] Figure 2 This is a schematic diagram of the on-site layout and sensor numbering sequence as described in an embodiment of the present invention.

[0030] Figure 3 This is a schematic diagram illustrating the identification of inherent frequencies using different singularity curves according to an embodiment of the present invention.

[0031] Figure 4 A schematic diagram of the displacement loading matrix transformation process described in an embodiment of the present invention.

[0032] Figure 5 This is a schematic diagram illustrating the selection of frequency points for solving the polynomial coefficients of the enhanced frequency response function according to an embodiment of the present invention. Detailed Implementation

[0033] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0034] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0035] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0036] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0037] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0038] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments, and the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0039] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0040] This invention provides a rapid decision-making method for the feasibility of opening a damaged bridge to traffic based on flexibility identification. The method includes: installing sensors on key sections of the main girder of a prefabricated beam bridge, conducting impact vibration tests in stages to obtain excitation force signals and bridge response signals; using the complex modal indicator function method to identify the bridge's modal parameters and reconstruct the full displacement flexibility matrix; further decomposing and recombining the full displacement flexibility matrix into a measurement point displacement loading matrix, and obtaining the full displacement loading matrix through curve fitting and interpolation; then predicting the bridge's static deflection or the dynamic deflection when vehicles pass over the bridge at low speeds, and determining the traffic opening decision scheme based on the section deflection design limit. This invention's method is response data-driven, does not rely on a finite element model, is simple to operate, has short testing time, high environmental adaptability, and allows for self-control of prediction accuracy. In particular, it overcomes the stringent condition of traditional flexibility identification methods requiring the load application location to coincide with the measurement point location. The matrix decomposition process achieves point-to-point calculation, saving computer cache calls, improving prediction efficiency, and allowing for flexible vehicle loading during bridge dynamic and static deflection prediction.

[0041] Example 1

[0042] In this embodiment 1, a rapid decision-making system for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification is first provided, including: an acquisition module for acquiring the bridge response and excitation force signals from multiple impact vibration tests on the prefabricated beam bridge; a first calculation module for calculating the bridge displacement frequency response function based on the acquired bridge response and excitation force signals; a second calculation module for calculating the full displacement flexibility matrix based on the modal parameters of the bridge identified by the complex modal indicator function method; a disassembly module for disassembling the full displacement flexibility matrix and reassembling it into a displacement loading matrix, and obtaining the full displacement loading matrix using an interpolation function; and a prediction module for determining the wheel load and the wheel's position or vehicle trajectory, and predicting the bridge's static deflection and dynamic deflection based on the full displacement loading matrix.

[0043] In this embodiment 1, based on the above system, a rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification is realized, including: acquiring the bridge response and excitation force signals from multiple impact vibration tests on the prefabricated beam bridge; calculating the bridge displacement frequency response function based on the acquired bridge response and excitation force signals; identifying the modal parameters of the bridge based on the complex modal indicator function method and calculating the full displacement flexibility matrix; disassembling the full displacement flexibility matrix and recombining it into a displacement loading matrix, and using an interpolation function to obtain the full displacement loading matrix; determining the wheel load and the wheel's position or vehicle trajectory, and predicting the bridge's static deflection and dynamic deflection based on the full displacement loading matrix.

[0044] Impact tests were conducted sequentially at different mid-span locations of the main beams, with at least two excitation points selected. Sensors were placed at the bottom of the beams at critical sections of the bridge to collect excitation force signals and bridge response signals for each test, and the data was preprocessed.

[0045] The complex modal indicator function method is used to identify the basic modal parameters of the bridge, including natural frequency, mode shape, and damping ratio, as well as the deep modal parameters, including modal scaling factor and system poles. The displacement frequency response function matrix is ​​decomposed into singular values, and the natural frequency of the structure is determined by the singular value curve. The displacement frequency response function matrix is ​​then weighted by left and right weighting vectors to obtain the enhanced displacement frequency response function.

[0046] After obtaining the enhanced frequency response function, at least five discrete frequency points near each natural frequency of the enhanced frequency response function are selected to obtain the polynomial coefficient vector. The concept of state-space equations is introduced to reduce the order of the second-order equation system and simplify the calculation to obtain the system pole expression. The modal parameters obtained by identification are substituted into the modal parameters, including the system poles, mode shapes and enhanced frequency response functions of each order. The modal scaling factor is calculated by the least squares method. Combined with the first three system poles, mode shapes and modal scaling factors, the full displacement compliance matrix of the bridge structure is obtained.

[0047] The elements of all m rows of the full displacement compliance matrix are reorganized according to the actual position of the measuring point on the bridge to obtain the displacement loading matrix corresponding to the numbered measuring point m. Curve fitting and surface interpolation are performed on the displacement loading matrix, and the interpolation accuracy is selected according to the actual needs, so as to obtain the full displacement loading matrix of measuring point m.

[0048] The static load magnitude and wheel contact point of each wheel acting on the bridge are determined to obtain the vehicle loading matrix. The displacement loading compliance coefficient of the actual wheel position is multiplied and superimposed with the wheel force to obtain the static deflection at measuring point m. By calculating the static displacement of all measuring points in sequence, the static deflection prediction of the vehicle parked on the bridge under any working condition can be realized. For low-speed vehicles, the vehicle passage feasibility condition requires that any measuring point can satisfy the following at any time: the dynamic displacement at measuring point m is not greater than the maximum calculated effect value of the deflection of the control section at measuring point m.

[0049] Example 2

[0050] In this embodiment 2, a method for quickly determining the feasibility of opening a disaster-damaged bridge to traffic is proposed. This method obtains bridge condition information in a timely manner, shortens bridge inspection time, and provides a technical decision-making solution for whether emergency rescue vehicles can carry equipment and materials across the disaster-damaged bridge.

[0051] A rapid decision-making method for the feasibility of opening disaster-damaged bridges to traffic based on flexibility identification includes the following steps:

[0052] Step 1: Conduct multiple impact vibration tests on the prefabricated beam bridge, collect bridge response and excitation force signals, and calculate the bridge displacement frequency response function.

[0053] Step 2: Calculate the full displacement compliance matrix by identifying the modal parameters of the bridge based on the complex modal indicator function method.

[0054] Step 3: Decompose the full displacement compliance matrix and reassemble it into a displacement loading matrix, then use an interpolation function to obtain the full displacement loading matrix.

[0055] Step 4: Determine the wheel weight and the position of the wheel or the vehicle's trajectory to predict the bridge's static and dynamic deflection.

[0056] In step one, impact tests are performed sequentially at different mid-span positions of the main beam. At least two excitation points are selected, and sensors are placed at the bottom of the beam at the critical section of the bridge to collect the excitation force signal and bridge response signal for each test, and the data is preprocessed.

[0057] In step two, the complex modal indicator function method is used to identify the basic modal parameters of the bridge, including natural frequencies, mode shapes, and damping ratios, as well as deeper modal parameters, including modal scaling factors and system poles. First, the displacement frequency response function matrix is ​​decomposed into singular values, and the natural frequencies of the structure are determined through the singular value curves. Then, the displacement frequency response function matrix is ​​weighted using left and right weighting vectors to obtain the enhanced displacement frequency response function.

[0058]

[0059] Wherein: H d (ω) is the displacement frequency response function; {u r} is the first left singular vector of order r. is{u r A vector consisting of the coefficients at each impact point;

[0060] After obtaining the enhanced frequency response function, at least five discrete frequency points near each natural frequency of the enhanced frequency response function are selected to obtain the polynomial coefficient vector:

[0061]

[0062] Where: the + in the upper right corner of the matrix indicates a pseudo-inverse operation, and each mode corresponds to a set of polynomial coefficients, all of which are complex numbers.

[0063] By introducing the concept of state-space equations, the second-order equation system is reduced in order and simplified, resulting in the following expression for the system poles:

[0064]

[0065] Substituting the obtained modal parameters, including the system poles, mode shapes, and enhanced frequency response functions for each order, the modal scaling factor is calculated using the least squares method. Its expression is as follows:

[0066]

[0067] Where: {φ r} is the vector of the r-th modal complex vibration mode of the structure, which is approximately the first left singular value vector;

[0068] Combining the poles, mode shapes, and modal scaling factors of the first three system orders, the full displacement compliance matrix of the bridge structure is obtained, and its expression is:

[0069]

[0070] Where: * represents the conjugate of the complex number; [F d [ is an N0×N0 square matrix, where N0 represents the number of measurement points, and can be expanded as follows:]

[0071]

[0072] In step three, all elements of row m of the full displacement compliance matrix are reorganized according to the actual positions of the measuring points on the bridge to obtain the displacement loading matrix corresponding to the numbered measuring point m, which can be expressed as:

[0073]

[0074] Wherein: the displacement loading matrix is ​​an n-row, 5-column matrix, where the number of rows n represents the number of main beam segments of the prefabricated beam bridge; the 5 columns represent the displacement loading compliance coefficients at the corresponding positions of the support, L / 4, L / 2, 3L / 4, and support, respectively.

[0075] Curve fitting and surface interpolation are performed on the displacement loading matrix, with the interpolation accuracy selected according to actual requirements, to obtain the full displacement loading matrix [F] of the measuring point m. L ] m .

[0076] In step four, the magnitude of the static load on the bridge exerted by each wheel and the wheel contact point are determined to obtain the vehicle loading matrix, which can be represented as:

[0077]

[0078] Where: w represents the number of wheels; x represents the coordinate of the contact point in the longitudinal direction of the bridge; y represents the coordinate of the contact point in the transverse direction of the bridge; the coordinate axis directions are as follows: Figure 2 As shown; f is the wheel weight;

[0079] The static deflection at measuring point m is obtained by multiplying the displacement compliance coefficient at the actual position of wheel application with the wheel force and then superimposing the results. It can be expressed as:

[0080]

[0081] Where: s x s y These represent the interpolation intervals in the longitudinal and transverse directions of the bridge in step (4), respectively, in meters.

[0082] By calculating the static displacement of all measuring points in sequence, the static deflection of a vehicle parked on a bridge under any working condition can be predicted. For a low-speed vehicle, the dynamic displacement at measuring point m can be expressed as:

[0083]

[0084] Where: t is time;

[0085] The feasibility of vehicle passage requires that any measuring point can satisfy the following relationship at any time:

[0086] d m (t)≤[δ m ]

[0087] Where: [δ m [ ] represents the maximum calculated effect value of the deflection at the control section of measuring point m.

[0088] Example 3

[0089] Addressing existing engineering challenges such as long inspection times for damaged bridges, incomplete vehicle traffic rules, and reliance on engineers' experience for judgment, such as... Figures 1 to 5 This embodiment provides a rapid decision-making method for the feasibility of opening a damaged bridge to traffic. It aims to provide quantitative decision-making suggestions on whether emergency rescue vehicles can pass through the damaged beam bridge when the safety status of the bridge is unknown. It provides technical support for emergency rescue vehicles to carry materials and equipment to the disaster area as soon as possible, make full use of the 72-hour golden time for rapid rescue, and promote and strengthen the post-disaster event mitigation and emergency response strategies of the transportation system.

[0090] Figure 1 This is a flowchart of the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification, as described in this embodiment. Figure 1 The method for quickly deciding on the feasibility of opening damaged bridges to traffic includes the following steps:

[0091] Step 1: Conduct impact vibration tests on the prefabricated beam bridge. First, conduct impact tests at different mid-span locations of the main beams, selecting at least two excitation points. Accelerometers should be placed at the bottom of the beams at sections L / 4, L / 2, and 3L / 4 of each main beam, numbered sequentially as follows: Figure 2 As shown. During the impact, ensure the hammer head makes perpendicular contact with the bridge deck as much as possible. Hold the hammer firmly when it bounces back for the first time after the first impact to avoid secondary impact. After signal acquisition, preprocess the data to remove secondary impact forces and corresponding response data, and use window function filtering for noise reduction and smooth the response curve. The processed acceleration response signal is converted into a displacement time history signal through integral transform and Fourier transform, and the displacement frequency response function is calculated for dissimilarity checking. The expression for the displacement frequency response function is as follows:

[0092]

[0093] Where: ω is the angular frequency; A(ω) represents the acceleration response spectrum; A(ω) represents the displacement response spectrum; F(ω) represents the excitation force spectrum; since the excitation force signal is different each time, the displacement frequency response function needs to be calculated separately and then combined when constructing the displacement frequency response function matrix.

[0094] Step 2: Identify modal parameters and calculate the full displacement compliance matrix. The complex modal indicator function method is a frequency domain-based parameter identification method that uses singular value decomposition (SVD) to identify the modal parameters of a structure, including natural frequencies, mode shapes, damping ratios, system poles, and modal scaling factors. First, the displacement frequency response function matrix is ​​obtained through singular value decomposition:

[0095]

[0096] Where: U(ω), S(ω), and V(ω) are the left singular matrix, singular value matrix, and right singular matrix with respect to frequency ω, respectively; h in the upper right corner of the matrix represents the self-conjugate matrix; the number of excitation force points is N. i The number of measurement points is N0;

[0097] The largest singular value in the singular matrix is ​​the first singular value, and the first column of the corresponding left singular matrix is ​​the first left singular vector. A singular value curve is plotted with frequency on the x-axis and the logarithm of each order of singular value on the y-axis, as shown below. Figure 3 As shown. The first three natural frequencies of the structure are extracted based on the peak abscissa of the first singular value curve. The enhanced displacement frequency response function is then obtained by weighting the displacement frequency response function matrix using left and right weighting vectors.

[0098]

[0099] Wherein: H d (ω) is the displacement frequency response function; {u r} is the first left singular vector of order r. is{u r A vector consisting of the coefficients at each impact point;

[0100] To further identify the system poles, a second-order uniform matrix polynomial model is constructed, which can be represented as:

[0101] [(jω) 2 α2+(jω)α1+α0]EH(ω)=(jω) 2 β2+(jω)β1+β0

[0102] The coefficients of the polynomial are the unknowns to be solved. Let the highest-order coefficient α2 be 1. At least five discrete frequency points near the natural frequency of each order of the enhanced frequency response function are selected to obtain the polynomial coefficient vector:

[0103]

[0104] Where: the + in the upper right corner of the matrix indicates a pseudo-inverse operation, and each mode corresponds to a set of polynomial coefficients, all of which are complex numbers.

[0105] Introducing the concept of state-space equations simplifies the second-order system of equations to obtain the characteristic equation:

[0106]

[0107] Substituting the coefficient vectors α1 and α0, the system pole expression is obtained using the generalized eigenvalue solution method.

[0108] Substituting the form of the displacement frequency response function in the complex mode into the definition of the enhancement frequency response function, we obtain the relationship between the enhancement frequency response function and the modal scaling factor:

[0109]

[0110] Where: {φ r} is the vector of the r-th modal complex vibration mode of the structure, which is approximately the first left singular value vector;

[0111] Combining the obtained system nodes, mode shapes, and enhanced frequency response functions of each order, the modal scaling factor is calculated using the least squares method, and the expression is:

[0112]

[0113] Since the displacement compliance matrix is ​​a special case of the displacement frequency response function matrix at frequency 0, combined with the poles λ of the first three order systems... r , mode shape {φ r Modal scaling factor Q r Letting ω = 0, we obtain the complex modal full displacement compliance matrix of the bridge structure, which is expressed as:

[0114]

[0115] Where: * represents the conjugate of the complex number; [F d [ is an N0×N0 square matrix, where N0 represents the number of measurement points, and can be expanded as follows:]

[0116]

[0117] Step 3: Reconstruct the full displacement loading matrix. Since each main girder has 3 measuring points, the displacement loading matrix corresponding to measuring point m is a new matrix consisting of n rows and 5 columns, where n represents the number of main girder segments in the prefabricated beam bridge, and the 5 columns represent the displacement compliance coefficients at the corresponding positions of the supports, L / 4, L / 2, 3L / 4, and the supports, respectively. Therefore, the displacement loading matrix for measuring point m can be expressed as:

[0118]

[0119] The bridge's total displacement loading matrix is ​​obtained using a suitable interpolation function. First, a cubic spline curve is used to perform curve fitting and extrapolation on the column vector data of the displacement loading matrix to obtain the compliance coefficient of the blank area between the edge beam sensor and the longitudinal edge of the bridge. Finally, the entire displacement loading matrix is ​​interpolated onto the surface, with the interpolation accuracy selected according to actual requirements, thus obtaining the total displacement loading matrix [F] of measuring point m. L ] mThe matrix has a total of OK Column, where s x s y L and W represent the interpolation intervals in the longitudinal and transverse directions of the bridge, respectively; L and W represent the bridge span and bridge width, respectively.

[0120] Step 4: Predicting the dynamic and static deflection of the bridge. Determine the magnitude of the static load exerted on the bridge by each wheel and the wheel contact point to obtain the vehicle loading matrix, which can be represented as:

[0121]

[0122] Where: w represents the number of wheels; x represents the longitudinal coordinate of the contact point on the bridge; y represents the transverse coordinate of the contact point on the bridge; f is the wheel weight;

[0123] Based on the actual position of the wheel, the compliance coefficient at the corresponding position in the complete displacement loading matrix is ​​found. The compliance coefficient is then multiplied and superimposed with the static load by indexing the matrix elements. Therefore, the static displacement at measuring point m can be expressed as:

[0124]

[0125] By calculating the static displacement of all measuring points in sequence, the static deflection of a vehicle parked on a bridge under any working condition can be predicted. For a low-speed vehicle, the dynamic displacement of measuring point m as a function of time t can be expressed as:

[0126]

[0127] Calculate the dynamic deflection of all points sequentially during vehicle movement. The feasibility of vehicle passage requires that any measuring point can satisfy the following relationship at any time:

[0128] d m (t)≤[δ m ]

[0129] Where: [δ m [ ] represents the maximum calculated effect value of the deflection at the control section of measuring point m.

[0130] Example 4

[0131] This embodiment 4 provides a non-transitory computer-readable storage medium for storing computer instructions. When these computer instructions are executed by a processor, they implement the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification, as described above. The method includes:

[0132] The bridge response and excitation force signals from multiple impact vibration tests on the prefabricated beam bridge are obtained; the bridge displacement frequency response function is calculated based on the obtained bridge response and excitation force signals; the modal parameters of the bridge are identified based on the complex modal indicator function method, and the full displacement compliance matrix is ​​calculated; the full displacement compliance matrix is ​​decomposed and recombined into a displacement loading matrix, and the full displacement loading matrix is ​​obtained using an interpolation function; the wheel load and wheel position or vehicle trajectory are determined, and the static and dynamic deflection of the bridge is predicted based on the full displacement loading matrix.

[0133] Example 5

[0134] This embodiment 5 provides a computer device, including a memory and a processor. The processor and the memory communicate with each other. The memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification, as described above. The method includes:

[0135] The bridge response and excitation force signals from multiple impact vibration tests on the prefabricated beam bridge are obtained; the bridge displacement frequency response function is calculated based on the obtained bridge response and excitation force signals; the modal parameters of the bridge are identified based on the complex modal indicator function method, and the full displacement compliance matrix is ​​calculated; the full displacement compliance matrix is ​​decomposed and recombined into a displacement loading matrix, and the full displacement loading matrix is ​​obtained using an interpolation function; the wheel load and wheel position or vehicle trajectory are determined, and the static and dynamic deflection of the bridge is predicted based on the full displacement loading matrix.

[0136] Example 6

[0137] This embodiment 6 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the above-described method for rapid decision-making on the feasibility of opening disaster-damaged bridges to traffic, the method including:

[0138] The bridge response and excitation force signals from multiple impact vibration tests on the prefabricated beam bridge are obtained; the bridge displacement frequency response function is calculated based on the obtained bridge response and excitation force signals; the modal parameters of the bridge are identified based on the complex modal indicator function method, and the full displacement compliance matrix is ​​calculated; the full displacement compliance matrix is ​​decomposed and recombined into a displacement loading matrix, and the full displacement loading matrix is ​​obtained using an interpolation function; the wheel load and wheel position or vehicle trajectory are determined, and the static and dynamic deflection of the bridge is predicted based on the full displacement loading matrix.

[0139] In summary, the rapid decision-making method for the feasibility of opening a damaged bridge to traffic based on flexibility identification, as described in this invention, is data-driven by the bridge's output response and does not rely on a finite element model, thus remaining unaffected by the accuracy of model construction. By identifying the bridge's displacement flexibility matrix and converting it into a displacement loading matrix for surface interpolation, the testing accuracy can be quantitatively controlled. The method uses the displacement loading matrix to predict the bridge's static and dynamic deflection vectors, overcoming the practical application bottleneck of traditional flexibility identification methods that require the loading point to coincide with the measuring point. It can simulate the graded loading process of load tests and achieve deflection prediction at any vehicle loading position. By decomposing the displacement flexibility matrix containing all measuring point flexibility information into a displacement loading matrix for each measuring point, a point-by-point calculation is achieved, reducing computer cache calls during the prediction stage and significantly accelerating prediction efficiency. Therefore, it can be used to predict the dynamic deflection of each measuring point on the bridge during low-speed vehicle passage. In practical applications, it has the advantages of simple operation, high environmental adaptability, and short testing time. It not only has a broad prospect of replacing load tests for rapid assessment of bearing capacity, but also meets the urgent need for rapid assessment of whether heavy rescue machinery and transport vehicles can safely pass on damaged bridges in road emergency rescue and clearance tasks.

[0140] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0141] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0142] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a processFigure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0143] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0144] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A rapid decision-making method for the feasibility of opening disaster-damaged bridges to traffic based on flexibility identification, characterized in that, include: Obtain bridge response and excitation force signals from multiple impact vibration tests on prefabricated beam bridges; The bridge displacement frequency response function is calculated based on the obtained bridge response and excitation force signals. The complex modal indicator function method is used to identify the basic modal parameters of the bridge, including natural frequency, mode shape, and damping ratio, as well as the deep modal parameters, including modal scaling factor and system poles. The displacement frequency response function matrix is ​​decomposed into singular values, and the natural frequency of the structure is determined by the singular value curve. The enhanced displacement frequency response function is obtained by weighting the displacement frequency response function matrix using left and right weighting vectors. The modal parameters of a bridge are identified using the complex modal indicator function method, and the full displacement compliance matrix is ​​calculated. Specifically, after obtaining the enhanced displacement frequency response function, at least five discrete frequency points near each natural frequency of the enhanced displacement frequency response function are selected to obtain the polynomial coefficient vector. The concept of state-space equations is introduced to simplify the second-order equation system, yielding the system pole expression. Substituting the identified modal parameters, including system poles, mode shapes, and enhanced displacement frequency response functions, into the expression, the modal scaling coefficients are calculated using the least squares method. Combined with the first three system poles, mode shapes, and modal scaling coefficients, the full displacement compliance matrix of the bridge structure is obtained. The full displacement compliance matrix is ​​decomposed and recombined into a displacement loading matrix, and the full displacement loading matrix is ​​obtained by using an interpolation function. Specifically, all elements in the m rows of the full displacement compliance matrix are recombined according to the actual position of the measuring point on the bridge to obtain the displacement loading matrix corresponding to the numbered measuring point m. Curve fitting and surface interpolation are performed on the displacement loading matrix, and the interpolation accuracy is selected according to the actual requirements to obtain the full displacement loading matrix of measuring point m. By determining the wheel load and the wheel's position or vehicle trajectory, and based on the full displacement loading matrix, the static and dynamic deflection of the bridge is predicted. Specifically, the static load magnitude and wheel contact point of each wheel acting on the bridge are determined to obtain the vehicle loading matrix. The displacement loading compliance coefficient of the actual wheel position is multiplied and superimposed with the wheel force to obtain the static deflection at measuring point m. By calculating the static displacement of all measuring points in sequence, the static deflection prediction of the vehicle parked on the bridge under any working condition can be realized. For low-speed vehicles, the feasibility condition for vehicle passage requires that any measuring point can satisfy the following at any time: the dynamic displacement at measuring point m is not greater than the maximum calculated effect value of the deflection of the control section at measuring point m.

2. The rapid decision-making method for the feasibility of opening disaster-damaged bridges to traffic based on flexibility identification as described in claim 1, characterized in that, Impact tests were conducted sequentially at different mid-span locations of the main beams, with at least two excitation points selected. Sensors were placed at the bottom of the beams at critical sections of the bridge to collect excitation force signals and bridge response signals for each test, and the data was preprocessed.

3. A rapid decision-making system for the feasibility of opening disaster-damaged bridges to traffic based on flexibility recognition, characterized in that, include: The acquisition module is used to acquire bridge response and excitation force signals from multiple impact vibration tests on prefabricated beam bridges. The first calculation module is used to calculate the bridge displacement frequency response function based on the acquired bridge response and excitation force signals. It employs the complex modal indicator function method to identify the bridge's basic modal parameters, including natural frequencies, mode shapes, and damping ratios, as well as deeper modal parameters, including modal scaling factors and system poles. The module then performs singular value decomposition on the displacement frequency response function matrix, determines the structure's natural frequencies through singular value curves, and uses left and right weighted vectors to perform weighted calculations on the displacement frequency response function matrix to obtain the enhanced displacement frequency response function. The second calculation module is used to calculate the full displacement compliance matrix based on the modal parameters of the bridge identified by the complex modal indicator function method. Specifically, after obtaining the enhanced displacement frequency response function, at least five discrete frequency points near each natural frequency of the enhanced displacement frequency response function are selected to obtain the polynomial coefficient vector. The concept of state-space equations is introduced to simplify the second-order equations, obtaining the system pole expression. Substituting the identified modal parameters, including the system poles, mode shapes, and enhanced displacement frequency response function, the modal scaling coefficients are calculated using the least squares method. Combined with the first three system poles, mode shapes, and modal scaling coefficients, the full displacement compliance matrix of the bridge structure is obtained. The disassembly module is used to disassemble the full displacement compliance matrix and reassemble it into a displacement loading matrix. The full displacement loading matrix is ​​obtained by using an interpolation function. Specifically, all elements in the m rows of the full displacement compliance matrix are reassembled according to the actual position of the measuring point on the bridge to obtain the displacement loading matrix corresponding to the numbered measuring point m. The displacement loading matrix is ​​then subjected to curve fitting and surface interpolation. The interpolation accuracy is selected according to the actual requirements to obtain the full displacement loading matrix of measuring point m. The prediction module is used to determine the wheel load and the wheel's position or vehicle trajectory. Based on the full displacement loading matrix, it predicts the static and dynamic deflection of the bridge. Specifically, it determines the magnitude of the static load and the wheel contact point of each wheel on the bridge to obtain the vehicle loading matrix. The displacement loading compliance coefficient of the actual wheel position is multiplied and superimposed with the wheel force to obtain the static deflection at measuring point m. By calculating the static displacement of all measuring points in sequence, the static deflection prediction can be achieved under any working condition when the vehicle is parked on the bridge. For low-speed vehicles, the feasibility condition for vehicle passage requires that any measuring point can satisfy the following at any time: the dynamic displacement at measuring point m is not greater than the maximum calculated effect value of the deflection of the control section at measuring point m.

4. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification as described in claim 1 or 2.

5. A computer device, characterized in that, The system includes a memory and a processor, which communicate with each other. The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification as described in claim 1 or 2.

6. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the rapid decision-making method for the feasibility of opening a disaster-damaged bridge to traffic based on flexibility identification as described in claim 1 or 2.

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