A simply supported beam bridge bearing stiffness rapid test and evaluation method based on local mode shape

Abstract

The application belongs to the field of bridge structure vibration test and safety detection and evaluation, and particularly relates to a simply supported beam bridge bearing stiffness rapid test and evaluation method based on local vibration mode. A small number of acceleration sensors are arranged in the cross-bridge direction of the mid-span section of the simply supported beam bridge during the test. The first three orders of frequencies of the environment excitation bridge and the local vibration mode of the main beam are tested under the condition that the bridge traffic is not interrupted. The shape of the first three orders of local vibration modes is usually characterized by "one flat, two inclined and three curved" in the cross-bridge direction. Then, the displacement flexibility matrix of the main beam structure is calculated and identified in combination with the finite element model, the actual modal deflection of the mid-span measuring point of the bridge under the equivalent load of the static load test is predicted, the deflection checking coefficient of the main beam is calculated according to the actual modal deflection value of the mid-span measuring point of the bridge and the theoretical design deflection value, and whether the actual bearing state of the bridge structure meets the design requirements is judged. The method has the advantages that the detection and evaluation rate of the bearing state of the bridge is improved, the detection cost is reduced, and the bridge traffic does not need to be interrupted.

Description

Technical Field

[0001] This application belongs to the field of bridge structure vibration testing and safety assessment, specifically involving a rapid testing method for the bearing stiffness of a simply supported beam bridge based on local vibration modes under conditions that do not interrupt traffic. Background Technology

[0002] Bridges, as a crucial component of national urban infrastructure and key hubs connecting highway transportation routes, play a vital role in improving the efficiency of the transportation system and ensuring the sustained and stable development of the national economy. From the perspective of the entire life cycle of bridge structures, the combined effects of material aging, environmental erosion, long-term load effects, and fatigue effects inevitably lead to the accumulation of structural damage, significantly reducing the bridge's load-bearing capacity and seriously threatening its safe operation. Rapid and reliable testing of the load-bearing status of bridges in service, and determining the actual safety reserve of the bridge structure, can effectively prevent catastrophic consequences during operation and is of great significance for ensuring the safe operation of transportation routes.

[0003] Load testing is the most accurate and objective method for assessing bridge load-bearing capacity, playing a crucial role in bridge safety maintenance. However, due to its large scale and the need for prolonged traffic interruption, it is relatively uneconomical and unsuitable for large-scale static load testing of numerous small and medium-sized bridges. Modal testing based on environmental excitation is currently the most commonly used method for health monitoring. It relies on external environmental conditions or natural conditions such as normal vehicle traffic, offering advantages in simplicity and speed. However, environmental excitation can only output basic modal parameters of the structure, such as frequency, mode shape, and damping, failing to obtain deeper structural parameters. Furthermore, basic modal parameters cannot be directly linked to the load-bearing stiffness that describes bridge performance.

[0004] Therefore, how to quickly and reliably detect the actual load-bearing stiffness of bridges in service and ensure the safe operation of existing bridges is an urgent problem to be solved. Summary of the Invention

[0005] To address the aforementioned deficiencies in existing technologies, this invention provides a rapid testing method for the load-bearing stiffness of simply supported beam bridges based on local vibration modes. The testing is convenient and fast, requiring only a small number of acceleration sensors placed at the bottom of the mid-span section of the bridge. Under normal traffic excitation conditions, the actual load-bearing stiffness of the simply supported beam bridge can be quickly and effectively tested and evaluated. The technical solution is as follows:

[0006] A rapid testing and evaluation method for the load-bearing stiffness of a simply supported beam bridge based on local vibration modes includes the following steps:

[0007] S1. Select the bridge span to be tested as the evaluation object, establish a three-dimensional finite element model of the simply supported beam bridge, and use beam elements for the main beam, solid crossbeam, virtual crossbeam, and crash barrier. Use shell elements for the bridge deck concrete leveling layer, and simplify the asphalt layer to a concentrated mass incorporated into the main body of the bridge. Use spring elements to simulate the vertical support of the beam end supports. Based on the three-dimensional finite element model of the main beam of the simply supported beam bridge, analyze and calculate the theoretical modal parameters of the structure. Extract the theoretical vibration modes of local measuring points at the mid-span section from the theoretical vibration modes of the simply supported beam bridge finite element model, calculate the correlation coefficient between the theoretical vibration modes of the local measuring points and the theoretical vibration modes of the finite element model, and select the first r orders of the least effective vibration modes with a correlation coefficient greater than 0.98. Usually, r is the 3rd order.

[0008] S2. A small number of vibration acceleration sensors are deployed transversely at the mid-span section of a simply supported beam bridge. Without interrupting traffic on the bridge deck, the acceleration time-history response data of the main beam's mid-span measuring points under environmental excitation are collected. Modal parameter identification methods are used to identify the first three measured frequencies and measured local vibration modes of the simply supported beam bridge. The measured first three local vibration modes typically exhibit a "one horizontal, two oblique, three curved" characteristic in the transverse direction. The measured local vibration modes differ from the overall vibration modes. The overall vibration modes are measured at numerous measuring points covering the entire bridge deck of the simply supported beam bridge and are structurally... The local vibration mode is a comprehensive representation of the dynamic characteristics, while the local vibration mode is a vibration mode measured at a small number of mid-span measuring points of a simply supported beam bridge. It is a local measuring point diagram of a certain order of the overall vibration mode diagram of the bridge structure. The local vibration mode can be a few orders of the entire vibration mode order of the bridge structure. The local vibration mode of a simply supported beam bridge may not be able to fully represent all the dynamic characteristics of the bridge structure, but it has fully represented the vertical vibration characteristics of the mid-span section of the bridge. In this invention, the deflection of the mid-span section of a simply supported beam bridge obtained by the identification and prediction of the local vibration mode is basically equal to the deflection of the mid-span section obtained by the identification and prediction of the overall vibration mode of the whole bridge.

[0009] The main innovation of this invention lies in the fact that the vertical deflection of the main beam mid-span section, which meets engineering accuracy requirements, can be tested and identified using only a few measuring points on the local vibration mode of the main beam mid-span section of a simply supported beam bridge. Highway and urban road simply supported beam bridges are typically wide, and the main beam in the transverse direction consists of many prefabricated hollow slabs, T-beams, or small box girders, making the entire main beam bridge deck a large rectangular plane with both considerable length and width. To test the overall modal vibration mode of the main beam structure, conventional bridge modal testing requires the deployment of more than 50 sensors on the bridge deck. To illustrate the complex and time-consuming testing process of obtaining the overall vibration mode of the entire bridge in conventional modal testing of simply supported beam bridges, the following example uses a common prefabricated simply supported T-beam highway bridge:

[0010] A highway simply supported beam bridge is a 25m span simply supported T-beam bridge. The bridge deck is divided into two sections, each consisting of seven precast prestressed concrete T-beams in the transverse direction. The supports are ordinary plate rubber bearings. The substructure consists of column piers, gravity U-shaped abutments, and bored pile foundations. The cross-section of the simply supported T-beam bridge is shown in the attached figure. Figure 2 As shown.

[0011] To test the overall vibration modes of this simply supported beam bridge, an environmental random excitation testing method was adopted. High-sensitivity accelerometers were placed at eight-eighths of the span of each main girder. A reference point was fixed, and other measuring points were moved. Modal synthesis technology was used to test the overall vibration modes of the bridge. To fully obtain the vibration response of the bridge structure, the sampling time for each batch was 30 minutes, and vibration data was collected in a total of 8 batches. The layout of the measuring points for the entire bridge is shown in the attached figure. Figure 3 As shown, a total of 63 vibration measurement points were set up on the bridge deck. It would take more than 5 hours to complete all the tests. In particular, the sensor wires were prone to getting tangled and messy during the movement of the measurement points, which wasted a lot of time during the test.

[0012] After collecting vibration acceleration data from all measuring points on the bridge, the modal parameters of the simply supported T-beam bridge were identified using time-domain or frequency-domain modal identification methods. The first three identified vibration modes of the bridge are shown in the attached figure. Figure 4 - Appendix Figure 6 As shown. The overall displacement compliance matrix of the simply supported beam bridge is calculated from the first three overall vibration modes of the bridge. This compliance matrix is ​​a high-dimensional matrix of order 63*63.

[0013] Therefore, due to the large span of simply supported beam bridges, the main beam deck is similar to a large square plate. The testing process for the overall vibration mode of the entire bridge is complex, tedious, time-consuming, and labor-intensive. The large number of measuring points increases the probability of errors and mistakes during the testing process. The large number of measuring points may directly lead to a large identification error in the actual testing process. Moreover, if the data quality of individual measuring points is poor, it will seriously affect the identification accuracy of the overall vibration mode of the bridge.

[0014] If the local mode shape testing method of this invention is used, only one sensor needs to be installed on each of the seven T-beams at the mid-span section of the simply supported beam bridge, resulting in a total of seven measuring points at the mid-span section. This number of measuring points is only 1 / 9 of the number of measuring points required for conventional overall mode shape testing. Local mode shapes of the simply supported beam bridge can be tested and identified without interrupting traffic on the bridge deck. This allows for the calculation of the 7*7 displacement compliance matrix at the mid-span measuring points, and then accurate prediction of the modal deflection at the mid-span measuring points under vertical loads. Compared to the overall mode shape testing of the entire bridge, local mode shape testing is faster, more convenient, saves time and effort, and has a lower error rate.

[0015] Modal parameter identification methods can employ the highly accurate Random Subspace Identification (SSI) method. Based on a discrete-time state-space model, the SSI directly processes the time series of test data. Common algorithms can be divided into two categories: covariance-driven SSI and data-driven SSI. The basic principle is based on the minimum realization theory of linear systems, utilizing the special relationship between the Hankel matrix and the system's observability and controllability matrices to obtain the system matrix and output matrix, thereby identifying the system's modal parameters in the state space. The covariance-driven SSI method uses the covariance of the measured response signals to form a Hankel matrix. Then, singular value decomposition of the Hankel matrix is ​​used to eliminate noise and determine the order, thus identifying the structure's modal parameters.

[0016] S3. Based on the measured frequency ω of the bridge Ei Compared with the measured local vibration mode φ Ei =[φ E1 ,φ E2 ,...,φ En ], select the theoretical modal shape φ of the simply supported beam bridge finite element model that matches it. Ai =[φ A1 ,φ A2 ,...,φ An ], in φ Ai Extract the mode shape data corresponding to the measurement points to form the theoretical modal local mode shape φ * Ai =[φ * A1 ,φ * A2 ,...,φ * An ];

[0017] φ, a local vibration mode measured from a simply supported beam bridge Ei =[φ E1 ,φ E2 ,...,φ En ] and finite element theory modal local vibration modes φ * Ai =[φ * A1 ,φ * A2 ,...,φ * An Calculate m respectively Ei and m Ai ,in:

[0018]

[0019]

[0020] In the formula M * This is the mass matrix of a simply supported beam bridge.

[0021] Calculate the measured local vibration modes φ of each order of a simply supported beam bridge. Ei The corresponding normalization factor a i The measured local vibration modes were normalized to obtain the normalized local vibration modes of the bridge structure. Then calculate the final measured displacement compliance matrix F of the simply supported beam bridge. d .

[0022]

[0023]

[0024]

[0025] S4. According to the "Specifications for Load Testing of Highway Bridges", the equivalent concentrated loads in the main girder span under medium-load and eccentric-load conditions are determined using the bridge finite element model. Based on the measured displacement compliance matrix of the main girder and the equivalent concentrated load vector in the main girder span, the modal deflection at mid-span of the simply supported beam bridge is calculated using the following formula:

[0026] D = F d f L (12)

[0027] Where D = {d1, d2, ..., d} j}(j=1,2,3,...) is a column vector composed of the measured modal deflections d at each measuring point at mid-span of the bridge under equivalent load, f L It is a column vector composed of the equivalent concentrated loads at the mid-span of the bridge under medium-load or eccentric-load conditions;

[0028] The deflection verification coefficient η is calculated from the measured modal deflection at the mid-span measuring point of the bridge and the theoretical design deflection. If the deflection verification coefficient η < 1, the design requirements are met; if η ≥ 1, it indicates that the bridge needs to be reinforced.

[0029] Preferably, in step S3

[0030] Measured local vibration modes φ of each order of the simply supported beam bridge identified Ei Satisfying the orthogonality condition, the stiffness matrix K of the bridge structure can be diagonalized to obtain k... i The stiffness matrix has diagonal elements:

[0031] φ Ei T Kφ Ei =diag(k) i (5)

[0032] Normalized local vibration modes of a simply supported beam bridge Substitute φ Ei T Kφ Ei =diag(k) i From this, we obtain:

[0033]

[0034] exist In the case of a square matrix with full rank, it is possible to... Multiply both sides by left Right multiplication The stiffness matrix of the structure is obtained as follows:

[0035]

[0036] The displacement compliance matrix F of the structure d It is the inverse of the stiffness matrix K:

[0037]

[0038]

[0039] The structure's natural frequency w Ei With modal mass Modal stiffness The relationship between them is:

[0040]

[0041] With normalized local vibration modes corresponding so Bring it in In the process, the final measured displacement compliance matrix F of the simply supported beam bridge was obtained. d for:

[0042]

[0043] Preferably, in step S1, a three-dimensional finite element model is established for the superstructure of the simply supported beam bridge.

[0044] Preferably, in step S2, an acceleration sensor is placed at the bottom of the mid-span of the bridge using a bridge inspection vehicle or aerial work platform to collect the acceleration time history response data of the vibration at the mid-span measuring point of the main beam under environmental excitation; when testing the key local vibration modes of a simply supported beam bridge, only a small number of measuring points need to be set up at the mid-span cross section of the main beam; only the first three vibration modes at the mid-span measuring point need to be identified; the measured first three local vibration modes have the characteristics of "one flat, two oblique, and three curved"; the modal parameter identification method can adopt the random subspace method (SSI), or any of the following modal identification methods: characteristic system realization method, complex modal indicator function method, multi-reference point least squares complex frequency domain method, and frequency domain decomposition method.

[0045] Preferably, in step S3, the dimension of the flexibility matrix is ​​the number of measuring points at the mid-span section of the main beam.

[0046] Preferably, in step S4, the equivalent concentrated load at the measuring point of the main beam mid-span section under the static load test conditions and the eccentric load conditions is determined.

[0047] Beneficial effects

[0048] This invention utilizes a small number of acceleration sensors deployed at the mid-span section of a simply supported beam bridge to test the first three frequencies and local mode shapes of the bridge under environmentally excited conditions without interrupting traffic. The measured first three local mode shapes exhibit a pattern of "one horizontal, two inclined, and three curved." Combined with a finite element model, the displacement compliance matrix of the main beam structure is calculated and identified. The actual modal deflection at the mid-span measuring point under the equivalent load of a static load test is predicted. The modal deflection values ​​at the mid-span measuring point are compared with the theoretical design deflection values ​​to calculate the deflection verification coefficient of the main beam, determining whether the actual load-bearing state of the bridge structure meets the design requirements. This method is convenient and quick to implement. Vibration sensors are installed at the mid-span section of an operational simply supported beam bridge, allowing for the collection of vibration information without interrupting traffic. It enables convenient and quick identification and prediction of the modal deflection of a simply supported beam bridge with a minimal number of sensors, thereby rapidly assessing the load-bearing stiffness state of a bridge in service. It combines the advantages of traditional static load testing and environmentally excited modal testing. It not only incorporates current bridge specifications, providing clear and reliable test and evaluation results, but also offers theoretical innovations and has significant advantages. It improves the speed of bridge load-bearing status detection and evaluation while saving manpower and reducing testing costs. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating the method of the present invention.

[0050] Figure 2 This is a cross-sectional view of a simply supported T-beam bridge.

[0051] Figure 3 This is a diagram showing the layout of all measuring points for a simply supported T-beam bridge.

[0052] Figure 4The measured first-order overall vibration mode diagram of a simply supported T-beam bridge.

[0053] Figure 5 The measured second-order overall vibration mode diagram of a simply supported T-beam bridge.

[0054] Figure 6 This is the measured third-order overall vibration mode diagram of a simply supported T-beam bridge.

[0055] Figure 7 This is a typical cross-sectional view of a simply supported small box girder bridge.

[0056] Figure 8 This is a schematic diagram of the bridge's acceleration sensor arrangement in a specific implementation.

[0057] Figure 9 This is the measured first-order local vibration mode diagram of the test bridge during modal testing.

[0058] Figure 10 This is the measured second-order local vibration mode diagram of the test bridge during modal testing.

[0059] Figure 11 This is the measured third-order local vibration mode diagram of the test bridge during modal testing.

[0060] Figure 12 A three-dimensional diagram of the flexibility matrix calculated for the test bridge.

[0061] Figure 13 This is a diagram showing the position of the vehicle under medium load conditions.

[0062] Figure 14 This diagram shows the position of the vehicle under off-center loading conditions. Detailed Implementation

[0063] The following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application.

[0064] The method of this invention combines the local modal testing technology of bridges under environmental excitation with the displacement flexibility matrix identification technology to identify and predict the actual modal deflection of the control section at the mid-span of the main beam under the equivalent load of the static load test, and quickly assess the bearing stiffness state of the simply supported beam bridge.

[0065] The invention will now be described in detail using an actual simply supported beam bridge as an example.

[0066] S1. Select the bridge span to be tested as the evaluation object, establish a three-dimensional finite element model of the simply supported beam bridge. Beam elements are used for the main beam, solid crossbeams, virtual crossbeams, and crash barriers. Shell elements are used for the bridge deck concrete leveling layer. The asphalt layer is simplified as a concentrated mass and incorporated into the main body of the bridge. Spring elements are used to simulate the vertical support of the beam end supports. Based on the three-dimensional finite element model of the main beam of the simply supported beam bridge, the theoretical modal parameters of the structure are analyzed and calculated. The theoretical vibration modes of local measuring points at the mid-span section are extracted from the theoretical vibration modes of the simply supported beam bridge finite element model. The correlation coefficient between the theoretical vibration modes of the local measuring points and the theoretical vibration modes of the finite element model is calculated. The first r-order minimum effective vibration mode order with a correlation coefficient greater than 0.98 is selected, usually r is 3. It should be noted that only a small number of measuring points need to be set up at the mid-span cross-section of the main beam for the key local vibration modes of the simply supported beam bridge.

[0067] S2. A small number of acceleration sensors are deployed transversely at the mid-span section of a simply supported beam bridge. Without interrupting traffic on the bridge deck, the acceleration time-history response data of the vibration at the mid-span measuring points of the main beam under environmental excitation are collected. Modal parameter identification methods are used to identify the first three measured frequencies and measured local vibration modes of the simply supported beam bridge. The measured local vibration modes of a bridge differ from the overall vibration modes. The overall vibration modes are measured at numerous measuring points covering the entire bridge deck, representing a comprehensive representation of the structural dynamic characteristics. Local vibration modes, on the other hand, are measured at a small number of mid-span measuring points. They represent a local measurement point diagram of a certain order of the overall vibration mode diagram of the bridge structure. Local vibration modes can be several orders of the entire vibration mode diagram of the bridge structure. While local vibration modes of a simply supported beam bridge may not fully represent all the dynamic characteristics of the bridge structure, they sufficiently represent the vertical vibration characteristics of the mid-span section. In this invention, the mid-span deflection of the simply supported beam bridge predicted by local vibration mode identification is essentially equal to the mid-span deflection predicted by the overall vibration mode identification of the entire bridge.

[0068] S3. Based on the measured frequency ω of the bridge Ei Compared with the measured local vibration mode φ Ei =[φ E1 ,φ E2 ,...,φ En ], select the theoretical modal shape φ of the simply supported beam bridge finite element model that matches it. Ai =[φ A1 ,φ A2 ,...,φ An ], in φ Ai Extract the vibration mode data corresponding to the measuring points to form the theoretical modal local vibration mode φ * Ai =[φ * A1 ,φ * A2 ,...,φ * An ];

[0069] φ, a local vibration mode measured from a simply supported beam bridge Ei =[φ E1 ,φ E2 ,...,φ En ] and finite element theory modal local vibration modes φ * Ai =[φ * A1 ,φ * A2 ,...,φ * An Calculate m respectively Ei and m Ai ,in:

[0070]

[0071]

[0072] In the formula M * The mass matrix of a simply supported beam bridge;

[0073] Calculate the measured local vibration modes φ of each order of a simply supported beam bridge. Ei The corresponding normalization factor a i The measured local vibration modes were normalized, and the normalized local vibration modes of the bridge structure were calculated.

[0074]

[0075]

[0076] Measured local vibration modes φ of each order of the simply supported beam bridge identified Ei Satisfying the orthogonality condition, the stiffness matrix K of the bridge structure can be diagonalized to obtain k... i The stiffness matrix has diagonal elements:

[0077] φ Ei T Kφ Ei =diag(k) i )

[0078] Normalized local vibration modes of a simply supported beam bridge Substitute φ Ei T Kφ Ei =diag(k) i From this, we obtain:

[0079]

[0080] exist In the case of a square matrix with full rank, it is possible to... Multiply both sides by left Right multiplication The stiffness matrix of the structure is obtained as follows:

[0081]

[0082] The displacement compliance matrix F of the structure d It is the inverse of the stiffness matrix K:

[0083]

[0084]

[0085] The structure's natural frequency w Ei With modal mass Modal stiffness The relationship between them is:

[0086]

[0087] With normalized local vibration modes corresponding so Bring it in In the process, the final measured displacement compliance matrix F of the simply supported beam bridge was obtained. d for:

[0088]

[0089] S4. Using the bridge finite element model, the equivalent concentrated loads in the main girder span under the static load and eccentric load conditions are calculated and determined. Combining the measured displacement compliance matrix of the main girder with the equivalent concentrated load vector in the main girder span, the modal deflection at the mid-span measuring point of the simply supported beam bridge is calculated using the following formula:

[0090] D = F d f L

[0091] Where D = {d1, d2, ..., d} j}(j=1,2,3,...) is a column vector composed of the measured modal deflections d at each measuring point at mid-span of the bridge under equivalent load, f L It is a column vector composed of the equivalent concentrated loads at the mid-span of the bridge under medium-load or eccentric-load conditions;

[0092] The deflection verification coefficient η is calculated from the measured modal deflection at the mid-span measuring point of the bridge and the theoretical design deflection. If the deflection verification coefficient η < 1, the design requirements are met; if η ≥ 1, it indicates that the bridge needs to be reinforced.

[0093] The main innovation of this invention lies in the fact that the vertical deflection of the main beam mid-span section, which meets engineering accuracy requirements, can be tested and identified using only a few measuring points on the local vibration mode of the main beam mid-span section of a simply supported beam bridge. Highway and urban road simply supported beam bridges are typically wide, and the main beam in the transverse direction consists of many prefabricated hollow slabs, T-beams, or small box girders, making the entire main beam bridge deck a large rectangular plane with both considerable length and width. To test the overall modal vibration mode of the main beam structure, conventional bridge modal testing requires the deployment of more than 50 sensors on the bridge deck. To illustrate the complex and time-consuming testing process of obtaining the overall vibration mode of the entire bridge in conventional modal testing of simply supported beam bridges, the following example uses a common prefabricated simply supported T-beam highway bridge:

[0094] A highway simply supported beam bridge is a 25m span simply supported T-beam bridge. The bridge deck is divided into two sections, each consisting of seven precast prestressed concrete T-beams in the transverse direction. The supports are ordinary plate rubber bearings. The substructure consists of column piers, gravity U-shaped abutments, and bored pile foundations. The cross-section of the simply supported T-beam bridge is shown in the attached figure. Figure 2 As shown.

[0095] To test the overall vibration modes of this simply supported beam bridge, an environmental random excitation testing method was adopted. High-sensitivity accelerometers were placed at eight-eighths of the span of each main girder. A reference point was fixed, and other measuring points were moved. Modal synthesis technology was used to test the overall vibration modes of the bridge. To fully obtain the vibration response of the bridge structure, the sampling time for each batch was 30 minutes, and vibration data was collected in a total of 8 batches. The layout of the measuring points for the entire bridge is shown in the attached figure. Figure 3 As shown, a total of 63 vibration measurement points were set up on the bridge deck. It would take more than 5 hours to complete all the tests. In particular, the sensor wires were prone to getting tangled and messy during the movement of the measurement points, which wasted a lot of time during the test.

[0096] After collecting vibration acceleration data from all measuring points on the bridge, the modal parameters of the simply supported T-beam bridge were identified using time-domain or frequency-domain modal identification methods. The first three measured vibration modes of the bridge are shown in the attached figure. Figure 4 - Appendix Figure 6 As shown. Based on the first three overall vibration modes of the bridge identified, the overall displacement compliance matrix of the simply supported beam bridge is calculated. This compliance matrix is ​​a high-dimensional matrix of order 63*63.

[0097] Therefore, due to the large span of simply supported beam bridges, the main beam deck is similar to a large square plate. The testing process for the overall vibration mode of the entire bridge is complex, tedious, time-consuming, and labor-intensive. The large number of measuring points increases the probability of errors and mistakes during the testing process. The large number of measuring points may directly lead to a large identification error in the actual testing process. Moreover, if the data quality of individual measuring points is poor, it will seriously affect the identification accuracy of the overall vibration mode of the bridge.

[0098] If the local mode shape testing method of this invention is used, only one sensor needs to be installed on each of the seven T-beams at the mid-span section of the simply supported beam bridge, resulting in a total of seven measuring points at the mid-span section. This number of measuring points is only 1 / 9 of the number of measuring points required for conventional overall mode shape testing. Local mode shapes of the simply supported beam bridge can be tested and identified without interrupting traffic on the bridge deck. This allows for the calculation of the 7*7 displacement compliance matrix at the mid-span measuring points, and then accurate prediction of the modal deflection at the mid-span measuring points under vertical loads. Compared to the overall mode shape testing of the entire bridge, local mode shape testing is faster, more convenient, saves time and effort, and has a lower error rate.

[0099] Modal parameter identification methods can employ the highly accurate Random Subspace Identification (SSI) method. Based on a discrete-time state-space model, the SSI directly processes the time series of test data. Common algorithms can be divided into two categories: covariance-driven SSI and data-driven SSI. The basic principle is based on the minimum realization theory of linear systems, utilizing the special relationship between the Hankel matrix and the system's observability and controllability matrices to obtain the system matrix and output matrix, thereby identifying the system's modal parameters in the state space. The covariance-driven SSI method uses the covariance of the measured response signals to form a Hankel matrix. Then, singular value decomposition of the Hankel matrix is ​​used to eliminate noise and determine the order, thus identifying the structure's modal parameters.

[0100] In this example, the test bridge has a deck width of 12.9m, with a transverse layout of 0.5m (crash barrier) + 11.9m (carriageway) + 0.5m (crash barrier). The deck slope is -18°. The superstructure is a 6×30m precast prestressed concrete simply supported small box girder, with four main beams arranged transversely. The bridge deck is paved with asphalt concrete, and uses plate rubber bearings and irregularly shaped steel single-slit expansion joints. The bridge cross-section is shown in the attached figure. Figure 7 As shown, traditional static load tests and environmentally excited local modal tests were conducted on the simply supported beam bridge. The deflection verification coefficients obtained from the local modal tests and those obtained from the traditional static load tests were compared and analyzed. The load-bearing stiffness state of the bridge was evaluated using the main beam deflection verification coefficient, demonstrating the accuracy and feasibility of the rapid load-bearing stiffness evaluation method for simply supported beam bridges based on local vibration modes. The bridge testing and evaluation steps are as follows:

[0101] (1) Collect relevant data on the simply supported beam bridge to be tested, and establish a three-dimensional finite element model of the simply supported beam bridge based on the relevant data. The main beam, solid crossbeam, virtual crossbeam and crash barrier are all simulated by beam elements. The bridge deck concrete leveling layer is simulated by shell elements. The asphalt layer is simplified as a concentrated mass and incorporated into the main body of the bridge. The vertical support of the beam end support is simulated by spring elements. Based on the three-dimensional finite element model of the bridge, analyze the theoretical modal parameters of the structure, calculate the correlation coefficient between the theoretical local measurement point vibration mode and the vibration mode of the theoretical finite element model, and select the first three vibration modes as effective vibration modes.

[0102] (2) Without interrupting bridge traffic, eight acceleration sensors are arranged transversely at the mid-span section of the bridge using a bridge inspection vehicle or aerial work platform. The arrangement of the acceleration sensors is shown in the attached figure. Figure 8 As shown. Acceleration time history response data of the main girder vibration at the mid-span measuring point under environmental excitation were collected. The first three frequencies of the simply supported beam bridge were identified using the random subspace method (SSI), which are 4.453 Hz, 6.857 Hz, and 13.778 Hz. The first three local vibration modes of the bridge were also identified. The measured local vibration modes of this simply supported small box girder bridge are shown in the attached figure. Figure 9 Appendix Figure 10 Appendix Figure 11 As shown (attached) Figure 9 For the measured first-order local vibration mode, see attached. Figure 10 For the measured second-order local vibration mode, see attached. Figure 11 (For the actual measurement of the third local vibration mode), it can be seen from the figure that the shapes of the first three local vibration modes in the transverse direction of the bridge conform to the characteristics of "one horizontal, two oblique, and three curved".

[0103] (3) Based on the measured frequency ω of the bridge Ei Compared with the measured first three local vibration modes φ Ei =[φ E1 ,φ E2 ,...,φ En ], select the theoretical modal shape φ of the simply supported beam bridge finite element model that matches it. Ai =[φ A1 ,φ A2 ,...,φ An ], in φ Ai Extract the mode shape data corresponding to the test degrees of freedom to form the theoretical modal local mode shape φ. * Ai =[φ * A1 ,φ * A2 ,...,φ * An ].

[0104] φ, a local vibration mode measured from a simply supported beam bridge Ei =[φ E1 ,φE2 ,...,φ En ] and finite element theory modal local vibration modes φ * Ai =[φ * A1 ,φ * A2 ,...,φ * An Substitute the parameters into equations (1) and (2) respectively to calculate the parameter m. Ei and m Ai , will m Ei and m Ai Substitute equation (3) to calculate the measured local vibration modes φ of each order of the simply supported beam bridge. Ei The corresponding normalization factor a i The normalization factors for the third-order local modes are 2.4872 × 10⁻⁶. -4 2.6004×10 -4 2.5394×10 -4 Its magnitude is related to the amplitude of the measured local vibration mode and the strength of environmental excitation.

[0105] The measured local vibration modes were normalized using equation (4), and the normalized local vibration modes of the bridge structure were calculated. Normalized local vibration modes of a simply supported beam bridge Substituting the measured frequency into equation (11), the final measured displacement compliance matrix F of the simply supported beam bridge is obtained. d To visually represent the matrix, it is plotted as shown in the attached diagram. Figure 12 The three-dimensional diagram of the compliance matrix is ​​shown.

[0106] (4) According to the "Specifications for Load Testing of Highway Bridges", the equivalent concentrated load of the main beam mid-span section under the static load test and the eccentric load condition is calculated using the bridge finite element model, and the load requirement of the test bridge loading efficiency between 0.95 and 1.05 is met. The modal deflection of the simply supported beam bridge at the mid-span measuring point under each load condition is calculated using formula (12) based on the measured displacement compliance matrix of the main beam and the equivalent concentrated load vector of the main beam mid-span section. The measured modal deflection values ​​are shown in Table 1.

[0107] The deflection verification coefficient η was calculated from the measured modal deflection at the mid-span measuring point of the bridge, and the calculation results are shown in Table 2. The deflection verification coefficient η < 1 for this simply supported beam bridge indicates that the actual bearing stiffness of the bridge structure has a certain safety reserve, meeting the design requirements and safe operation requirements.

[0108] To demonstrate the reliability and accuracy of the invention, a conventional static load test was conducted on the simply supported small box girder bridge. The deflection verification coefficient obtained from the conventional static load test was compared and analyzed with the deflection verification coefficient obtained from the local vibration mode test. The test comparison is as follows:

[0109] (1) A traditional static load test scheme for this simply supported beam bridge was developed. Displacement gauges were installed at the mid-span of the main beam. Loading vehicles were selected based on loading efficiency. The planar layout of the loading vehicles under medium and eccentric load conditions is shown in the attached figure. Figure 13-14 As shown in Table 3, the test bridge was loaded with vehicle loads and positions under medium-load and eccentric-load conditions. The measured static deflection of the displacement gauge at the mid-span was recorded under each condition.

[0110] (2) Using the measured static deflection value at the mid-span of the bridge, the deflection verification coefficient η of the traditional static load test is calculated. The calculation results are shown in Table 4.

[0111] The deflection verification coefficients obtained from traditional static load tests and local modal tests were compared, and the relative errors are shown in Table 5. Table 5 shows that, regardless of whether the load is medium or eccentric, the deflection verification coefficients obtained from the local modal tests of this invention are in excellent agreement with those obtained from traditional static load tests, with relative errors of less than 5%, which meets the accuracy requirements for actual bridge engineering testing.

[0112] Therefore, the above-described invention process and the results of the invention content demonstrate that the invention method utilizes a small number of sensors to conduct local modal tests on simply supported beam bridges. This allows for accurate measurement of the modal deflection at the mid-span section of the main beam without interrupting bridge traffic, replacing the measured static deflection of traditional static load tests. This enables the calculation of the deflection verification coefficient of the main beam, and quickly and effectively assesses the load-bearing stiffness state of simply supported beam bridges.

[0113] Table 1 Measured Modal Deflection Values ​​of Simply Supported Beam Bridges

[0114]

[0115] Table 2 Modal Deflection Verification Coefficients for Simply Supported Beam Bridges

[0116]

[0117] Table 3 Measured static deflection values ​​of simply supported beam bridges under conventional static load tests

[0118]

[0119] Table 4. Verification coefficients for deflection in traditional static load tests of simply supported beam bridges.

[0120]

[0121] Table 5. Relative Errors of Deflection Verification Coefficients for Simply Supported Beam Bridges

[0122]

[0123]

[0124] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for rapid test and evaluation of the bearing stiffness of a simply supported beam bridge based on local mode shapes, characterized in that, Comprise the following steps: S1. Select the bridge span to be tested as the detection evaluation object, establish a simply supported beam bridge three-dimensional finite element model, the main beam, the real beam, the virtual beam, the crash barrier are all beam elements, the bridge deck concrete leveling layer is shell element, the asphalt layer is simplified as concentrated mass and is into the bridge main body, the vertical support action of the beam end support is simulated by spring element, based on the three-dimensional finite element model of the main beam of the simply supported beam bridge, the theoretical modal parameters of the structure are analyzed and calculated; the theoretical mode of the local measuring point of the mid-span cross section is extracted from the theoretical mode of the finite element model of the simply supported beam bridge, the correlation coefficient of the local measuring point theoretical mode and the finite element model theoretical mode is calculated, the first r-order effective minimum mode shape whose mode shape correlation coefficient is greater than 0.98 is selected, r is 3 orders; S2. A small number of acceleration sensors are arranged in the transverse direction of the mid-span cross section of the simply supported beam bridge, the acceleration time history response data of the mid-span cross section measuring point vibration of the main beam under environmental excitation is collected under the condition of not interrupting the bridge traffic, and the first three orders of measured frequency and measured local mode of the simply supported beam bridge are obtained by using the modal parameter identification method, and the first three orders of local mode shape of the mid-span cross section measuring point has the characteristics of "one flat two inclined three curved"; S3. According to the measured frequency ω Ei With the measured local mode φ Ei = [φ E1 , φ E2 ,..., φ En ], select the theoretical modal shape φ Ai = [φ A1 , φ A2 ,..., φ An ] of the finite element model of the simply supported beam bridge matched therewith, extract the mode shape data corresponding to the measuring point in φ Ai To form the theoretical modal local mode φ * Ai = [φ * A1 , φ * A2 ,..., φ * An ]; By simply supported beam bridge measured local mode φ Ei = [φ E1 ,φ E2 ,...,φ En ] and finite element theory modal local mode φ * Ai = [φ * A1 ,φ * A2 ,...,φ * An ] respectively m Ei And m Ai , wherein: m Ai = φ * Ai T M * φ * Ai i = 1, 2, 3,..., n m Ei = φ * Ei T M * φ * Ei i = 1, 2, 3,..., n In the formula, M * is the mass matrix of the simply supported beam bridge; The measured local mode φ of each order of the simply supported beam bridge is calculated Ei The corresponding normalization factor a i The measured local mode is normalized, and the normalized local mode of the bridge structure is calculated Then the measured displacement flexibility matrix F of the simply supported beam bridge is calculated d : S4. The main beam mid-span equivalent concentrated load of the load case and the eccentric load case in the static load test is calculated and determined by using the bridge finite element model, the measured displacement flexibility matrix of the main beam and the main beam mid-span equivalent concentrated load vector are combined, and the modal deflection of the simply supported beam bridge mid-span measuring point is calculated by using the following formula: D = F d f L where D = {d1, d2,..., d j} is a column vector of measured modal deflections dj at each measuring point in the midspan of the bridge under the equivalent load, f L is a column vector of equivalent concentrated loads in the midspan of the bridge under the uniform load or eccentric load. The deflection checking coefficient η is calculated from the measured modal deflection of the bridge mid-span measuring point and the theoretical design deflection, if the deflection checking coefficient η is less than 1, it meets the design requirements; if η is greater than or equal to 1, it indicates that the bridge needs to be reinforced.

2. The method according to claim 1, wherein, In step S3 The identified local vibration mode φ of each order of the simply supported beam bridge Ei Satisfying the orthogonality condition, the stiffness matrix K of the bridge structure can be diagonalized to obtain the stiffness matrix with k i as the diagonal elements: φ Ei T Kφ Ei = diag(k i ) Normalized local mode of simply supported beam bridge φ Ei T Kφ Ei = diag(k i ) in which we get: In In the case of square matrix and full rank, the Both sides are left multiplied by Right multiplication The stiffness matrix of the structure is obtained as the displacement flexibility matrix F of the structure d is the inverse of the stiffness matrix K: The structural natural frequency w Ei The relationship between the modal mass The modal stiffness is: With normalized local mode shape Corresponding So Substituting it into The final measured displacement flexibility matrix F of simply supported beam bridge is obtained d :

3. The method according to claim 1, wherein In step S1, a three-dimensional finite element model of the main beam structure of the simply supported beam bridge is established.

4. The method according to claim 1, wherein, In step S2, the bridge inspection vehicle or the aerial work vehicle is used to arrange acceleration sensors on the bottom of the bridge mid-span, and the acceleration time history response data of the main beam mid-span measuring point vibration under environmental excitation is collected; only a small number of measuring points need to be arranged on the main beam mid-span cross section during the test of the key local mode of the simply supported beam bridge, the first three orders of mode of the bridge mid-span measuring point are identified; the first three orders of local mode shape have the characteristics of "one flat two inclined three curved"; the modal parameter identification method adopts the random subspace method, and any one of the modal identification methods in the characteristic system implementation method, the complex modal indicator function method, the multi-reference point least square complex frequency domain method and the frequency domain decomposition method can also be used.

5. The method according to claim 1, wherein In step S3, the dimension of the flexibility matrix is the number of measuring points of the main beam mid-span cross section.

6. The method of claim 1, wherein the method is characterized by: In step S4, the equivalent concentrated load of the main beam mid-span cross section measuring point in the load case and the eccentric load case in the static load test is determined.

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