A bridge modal vibration shape identification method considering the influence of bridge damping

Abstract

The present invention proposes a bridge modal vibration mode driving identification method considering the influence of bridge damping. First, a vehicle-bridge interaction model involving two measuring vehicles is established, one of which is a stationary measuring vehicle and the other is a moving measuring vehicle traveling at a constant speed; sensors for collecting vertical vibration data are installed on the two vehicle bodies respectively, and the vertical response of the vehicle body is calculated accordingly, and the vehicle-bridge contact response is indirectly calculated from the vehicle body response; then a vehicle-bridge contact response inverse algorithm is established, which can extract the bridge frequency from the contact response regardless of the structural form of the bridge; combined with Hilbert transform, the bridge modal vibration mode amplitude is extracted from the vehicle-bridge contact response, the bridge damping effect in the bridge vibration mode amplitude is eliminated, and the bridge modal vibration mode is accurately extracted. In actual bridge monitoring, this method can more accurately and efficiently evaluate the health status of the bridge.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge health monitoring and detection, and specifically relates to a bridge modal vibration driving identification technology based on two measuring vehicle-bridge models to eliminate the influence of bridge damping. Background Art

[0002] Bridges are an indispensable medium for connecting water and land transportation. As a hub of water and land transportation, bridges play an important role in promoting regional economic development and cultural exchanges. After being built and put into use, bridges face natural disasters such as rain erosion and earthquakes, as well as natural aging and human damage caused by overload use. Therefore, engineers and scholars pay special attention to the health of bridge structures. In order to facilitate engineers to continue to pay attention to the condition of bridge structures, structural health detection methods based on bridge vibration are widely used in bridge structural health monitoring. How to scientifically maintain nearly one million bridges in my country and ensure the safety of bridge operations has become a major challenge that my country needs to face.

[0003] In recent years, a method of extracting the dynamic response of bridges using a mobile measurement vehicle equipped with sensors has been proposed. Because the bridge response is extracted from the vehicle dynamic response, it is called an indirect method. It is also called the vehicle scanning method (VSM) to better explain its essence of extracting bridge characteristics using a mobile vehicle. Since the mobile vehicle and the bridge are a coupled system, when the mobile vehicle passes through the bridge, the bridge will generate vibrations and transmit them to the mobile vehicle. The sensors in the mobile vehicle can collect the bridge response caused by the vehicle passing. This method has the characteristics of mobility, economy, and universality, and has been widely studied by scholars from various countries.

[0004] Damping is one of the inherent properties of a structure, and the presence of damping will reduce the vibration effect generated by the structure. After being excited by a vehicle, the bridge will produce a vibration response, but the bridge damping will attenuate the bridge vibration. After the bridge vibration is attenuated, the basic excitation received by the mobile measurement vehicle is reduced, and the vibration response received by the mobile measurement vehicle's onboard receiver is correspondingly reduced. However, bridges have characteristics such as large structures, and their damping values ​​are difficult to obtain through experiments. Therefore, the specific attenuation of the data received by the receiver cannot be calculated, resulting in large data errors and low accuracy of the results.

[0005] As an important characteristic parameter, modal vibration shape is one of the important indicators for evaluating the health status of bridges. The data structure collected by the mobile measurement vehicle is a diagonal matrix in time and space, that is, one moment corresponds to the vibration data of a bridge position. When the mobile measurement vehicle passes through the bridge, due to the existence of bridge damping, the vibration data is attenuated, but its attenuation value cannot be calculated, resulting in the deviation of the bridge modal vibration shape identified from the mobile measurement vehicle. How to effectively reduce the influence of bridge damping and improve the robustness of bridge modal vibration shape identification is of great significance for bridge health detection. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a bridge modal vibration driving identification method which eliminates bridge damping interference in view of the deficiencies in the above-mentioned prior art.

[0007] The method strategy of the present invention:

[0008] (1) Considering the influence of bridge damping, the present invention creatively establishes a vehicle-bridge interaction model involving two measuring vehicles, one of which is a stationary measuring vehicle and the other is a moving measuring vehicle traveling at a constant speed. Sensors for collecting vertical vibration data are installed on the two vehicle bodies respectively, and the vertical response of the vehicle body is calculated accordingly. Based on the principle of structural dynamics and vehicle-bridge coupling, the vehicle-bridge contact response is indirectly calculated from the vehicle body response.

[0009] (2) Based on the motion equations of the two moving and stationary measuring vehicles, an inverse algorithm for vehicle-bridge contact response is established to extract the bridge frequency from the contact response, which is not limited to the structural form of the bridge and enhances the recognition effect of the bridge dynamic response. Based on the contact response of the two moving and stationary measuring vehicles, the present invention creatively combines the Hilbert transform to extract the bridge modal vibration amplitude from the bridge response, eliminate the influence of the bridge damping in the bridge vibration amplitude, and realize the accurate extraction of the bridge modal vibration.

[0010] The process of the present invention:

[0011] A vehicle-bridge interaction model involving two measuring vehicles is established to obtain two sets of bridge vibration response data. The data structure of the bridge amplitude collected by the moving measuring vehicle is a diagonal matrix in time and space, while the amplitude measured by the stationary measuring vehicle has the same attenuation trend, but its data is only related to time; the bridge amplitude measured by both is used to perform the data processing method proposed in the present invention, which can eliminate the bridge damping calculation item, and further construct the bridge modal vibration shape after correction. This method can eliminate the influence of bridge damping and extract more accurate bridge vibration mode. Using the contact response motion equations of the moving and stationary vehicles, combined with the Hilbert transform, the bridge modal vibration amplitude solution equations are determined respectively (Formula (20)(21)):

[0012]

[0013] Where:

[0014]

[0015]

[0016] The mathematical processing method proposed in the present invention is used to process the vibration amplitude of the bridge extracted from the contact response of the moving and stationary measuring vehicles:

[0017]

[0018] The calculated amplitude changes, but the vibration mode shape does not change, where Δ st,ns , Δ st,nm , are all constant coefficients. After normalization, we can further obtain the nth-order modal vibration shape of the bridge:

[0019]

[0020] in is the vertical contact acceleration response of the moving and stationary measuring vehicles under the nth-order mode of the bridge; is the Hilbert transform function. A m (t), A s (t) are the bridge vibration amplitudes extracted from the contact responses of the moving and stationary measurement vehicles, respectively. By using the relationship between the bridge amplitudes measured by the two measurement vehicles, the amplitude measured by the moving measurement vehicle is divided by the amplitude measured by the stationary measurement vehicle, and the correction is made to further realize the efficient construction of the bridge modal vibration shape.

[0021] Principle of the invention:

[0022] Compared with the moving measurement vehicle, the response value measured by the stationary measurement vehicle has the same attenuation trend caused by damping, but is not affected by spatial changes. That is, the data structure collected by the stationary measurement vehicle is a matrix that changes only with time, and the attenuation effect caused by bridge damping in its data is consistent with that measured by the moving measurement vehicle. Based on this principle, the bridge vibration amplitude measured by the moving and stationary measurement vehicles is eliminated by the bridge damping term in the theoretical solution of the bridge modal vibration amplitude using the data processing method proposed in the present invention, thereby eliminating the signal attenuation effect caused by bridge damping, obtaining a theoretical solution without bridge damping parameters, and realizing efficient construction of bridge modal vibration, so as to be better used for bridge structure health monitoring.

[0023] Technical solution:

[0024] A bridge modal vibration driving identification method considering the influence of bridge damping comprises the following steps:

[0025] 1. Data collection stage:

[0026] S1 Arrangement of two moving and stationary measuring vehicles-bridge system: Two single-axis measuring vehicles equipped with acceleration sensors are arranged on the bridge respectively. Based on the vehicle-bridge interaction, the measuring vehicle excites the bridge, and the bridge generates a vertical vibration response and transmits it to the measuring vehicle, causing the measuring vehicle to generate a vertical response; one of the measuring vehicles is stationary, and the receiver on it is used to collect the vertical acceleration response of the stationary measuring vehicle A measuring vehicle starts to move from rest, and its receiver is used to collect the vertical acceleration response of the moving measuring vehicle.

[0027] S2 establishes the corresponding differential equation of motion;

[0028] 2. Contact response calculation stage:

[0029] S3 uses the inversion of the motion equation of the single-axis measurement vehicle to obtain the vertical acceleration contact response of the vehicle bridge;

[0030] S4 uses the moving and stationary measurement vehicles and the bridge motion equations to derive the vertical displacement responses of the two vehicle bridges, and then derives the vertical acceleration contact response;

[0031] 3. Mode vibration type identification stage:

[0032] S5 uses Hilbert transform to process the vertical acceleration contact response and obtains the bridge amplitude;

[0033] Based on the characteristics that the bridge amplitude extracted by the stationary measurement vehicle has the same attenuation trend caused by damping but is not affected by spatial changes, S6 processes the bridge vibration amplitude, eliminates the signal attenuation caused by bridge damping, and realizes the efficient construction of bridge modal vibration.

[0034] Beneficial effects of the method of the present invention:

[0035] The present invention combines Hilbert transform and utilizes two test vehicle-bridge models, in which the vibration amplitudes extracted by the stationary measurement vehicle have the same attenuation trend but are only affected by a single variable of time. Based on this characteristic, a mathematical method is used to eliminate the bridge damping calculation term from the bridge vibration amplitude obtained by the moving measurement vehicle, thereby eliminating the influence of bridge damping and accurately constructing the bridge modal vibration shape. This is the core of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the process of the present invention;

[0037] Figure 2 The two measuring vehicles test system arrangement scheme for the method of the present invention;

[0038] Figure 3 It is a mechanical model of a single-axle vehicle system used for numerical verification of the present invention;

[0039] Figure 4 The vertical acceleration contact response time domain diagram and the corresponding frequency domain diagram obtained by the motion measurement vehicle in step S3 and S4 in embodiment 1 of the present invention;

[0040] Figure 5 The vertical acceleration contact response time domain diagram and the corresponding frequency domain diagram obtained by the stationary measurement vehicle in step S3 and S4 in embodiment 1 of the present invention;

[0041] Figure 6 is the modal vibration shape identification result of a single-span bridge obtained based on the uncorrected method in Example 1 of the present invention;

[0042] Figure 7 This is the modal vibration type identification result of a single-span bridge obtained based on the method of the present invention in Example 1 of the present invention. DETAILED DESCRIPTION

[0043] To achieve the above purpose, the method and technical solution adopted by the present invention are as follows: Figure 1 As shown, it includes the following steps:

[0044] 1. Data collection stage:

[0045] S1 Arrangement of two moving and stationary measuring vehicles-bridge system: Two single-axis measuring vehicles equipped with acceleration sensors are arranged on the bridge respectively. Based on the vehicle-bridge interaction, the measuring vehicle excites the bridge, and the bridge generates a vertical vibration response and transmits it to the measuring vehicle, causing the measuring vehicle to generate a vertical response. One of the measuring vehicles is stationary, and the receiver on it is used to collect the vertical acceleration response of the stationary measuring vehicle. A measuring vehicle starts to move from rest, and its receiver is used to collect the vertical acceleration response of the moving measuring vehicle. See attached Figure 2 ;

[0046] S2 establishes the corresponding motion differential equation.

[0047] According to the two-measurement vehicle-bridge coupling system, the motion equations of the vertical vibration response of the moving and stationary measurement vehicles (Formulas (1) and (2)) and the motion equation of the vertical vibration response of the bridge (Formula (3)) are established and expressed as follows:

[0048]

[0049] Where M m 、M s are the moving and stationary measurement vehicle masses, k m , k s are the stiffness coefficients of the moving and stationary measuring vehicles, c m 、c s are the damping coefficients of the moving and stationary measurement vehicles respectively. m ,ω s are the circular frequencies of the moving and stationary measurement vehicles respectively. m ,y s are the vertical displacements of the dynamic and static measuring vehicles, u and u cm and u cs are the vertical displacement of the bridge and the vertical displacement of the dynamic and static measuring vehicles and the bridge contact point (CP), where u cm =u| x＝vt 、ucs =u| x＝L ; In the formula and represents the first partial derivative of the corresponding displacement with respect to time, u″″ represents the fourth partial derivative of the bridge displacement with respect to displacement; δ is the Dirac function. The bridge under consideration is a homogeneous Bernoulli-Euler beam with an effective span of L, bending stiffness of EI, damping coefficient of C, and mass per unit length of M.

[0050] Second contact response calculation stage:

[0051] S3 uses the inversion of the motion equation of the single-axis measurement vehicle to obtain the vertical acceleration contact response of the bridge.

[0052] The motion equation of the moving single-axis measuring vehicle is shown in formula (1). The second derivative of formula (1) with respect to time t is taken to convert the vertical vibration signal into a quantity related to the acceleration response, and the acceleration contact response is obtained by solving:

[0053]

[0054] Where:

[0055]

[0056] Formula (4) is applicable to continuous function data, while the data collected by the receiver is discrete data. For discrete data, formula (4) can be changed to formula (6):

[0057]

[0058] Similarly, the above-mentioned inverse calculation method can be used to convert the motion equation of the stationary measurement vehicle (Formula (2)) into the vertical acceleration contact response equation under the corresponding discrete data of the stationary measurement vehicle:

[0059]

[0060] Where:

[0061]

[0062] in is the vertical contact acceleration response of the moving and stationary measurement vehicle, (| i ) is represented as the i-th data, the total number of i is t / Δt, Δt is the analysis step length, t is the total time the motion measurement vehicle moves on the bridge, is the vertical acceleration response data of the i-th moving and stationary measurement vehicle. The damping ratios of the moving and stationary measurement vehicles are f m 、f s is the moving and stationary measurement vehicle movement frequency, Fm | i 、F s | i is the i-th contact force between the moving and stationary measuring vehicles and the bridge. The vertical acceleration contact response of the two measuring vehicles obtained by inversion here only involves the motion equation of the vehicle body, that is, the inversion of the vertical acceleration contact response only relies on the acceleration response of the single-axis measuring vehicle and the physical parameters of the vehicle body, and has nothing to do with the physical parameters of the bridge. Therefore, it is not limited to the structural form of the bridge and can enhance the identification effect of the dynamic response of the bridge.

[0063] Substitute the vertical vibration response data of the two measuring vehicles collected in step S1 into formulas (6) and (7). The vertical acceleration contact response of the two measuring vehicles can be obtained by calculation. After processing the contact response data by Fourier transform, the bridge frequency can be extracted, realizing more convenient monitoring of bridge structure health assessment.

[0064] S4 uses the moving and stationary measurement vehicles and the bridge motion equations to derive the vertical displacement responses of the two vehicle bridges, and then derives the vertical acceleration contact response.

[0065] After the integral processing and trigonometric function change calculation of formula (3), the vertical displacement response of the two measuring vehicles is solved and summarized as:

[0066]

[0067] Where:

[0068]

[0069] A b,n =-A d,n , (12f)

[0070]

[0071] Then, by taking the time second derivative of formula (10) (11), we can obtain the vertical acceleration contact response of the dynamic and static measuring vehicles, and then get formula (13) (14):

[0072]

[0073] Where:

[0074]

[0075] The vertical acceleration contact responses of the two measuring vehicles derived using the vehicle-bridge coupling system can be used to verify the correctness of the vertical acceleration contact responses of the measuring vehicles using the inversion method proposed in S3.

[0076] Three-mode vibration shape identification stage:

[0077] S5 uses Hilbert transform to process the vertical acceleration contact response and obtains the bridge amplitude.

[0078] In order to identify the vibration mode of the bridge, the calculated vertical acceleration contact response equations of the moving and stationary measuring vehicles (Formulas (13) and (14)) are simplified by trigonometric functions, and their theoretical form is:

[0079]

[0080] Perform Hilbert transform on formula (16) and (17) respectively, and we get

[0081]

[0082] The instantaneous amplitude of the dynamic response of the bridge under the nth mode is obtained as follows:

[0083]

[0084] Where:

[0085]

[0086]

[0087] S6 is based on the fact that the bridge amplitude extracted by the stationary measuring vehicle has the same attenuation trend caused by damping but is not affected by spatial changes, that is, the data structure collected by the stationary measuring vehicle is a matrix that only changes with time, and the attenuation effect caused by bridge damping in its data is consistent with that measured by the moving measuring vehicle. Based on this principle, the bridge vibration amplitudes measured by the moving and stationary measuring vehicles are processed using the data processing method proposed in the present invention, and the bridge damping term in the theoretical solution of the bridge modal vibration amplitude is eliminated, thereby eliminating the signal attenuation effect caused by bridge damping, obtaining a theoretical solution without bridge damping parameters, and realizing efficient construction of bridge modal vibration. Since the position of the stationary measuring vehicle remains unchanged, its amplitude calculation value is not affected by space and has the same attenuation trend as the amplitude calculation value of the moving measuring vehicle. By dividing formula (20) by formula (21), the calculation term containing bridge damping can be eliminated, and the following is obtained:

[0088]

[0089] The calculated amplitude changes, but the vibration mode shape does not change, where Δ st,ns , Δ st,nm , are all constant coefficients. After normalization, we can further obtain the nth-order modal vibration shape of the bridge:

[0090]

[0091] 4. Application:

[0092] In actual bridge monitoring applications, this method can be used to process the extracted bridge modal amplitudes to eliminate the influence of bridge damping and extract more accurate bridge modal vibration shapes, thereby accurately and efficiently evaluating the health status of the bridge.

[0093] The technical solution of the present invention is further described in detail below through embodiments. Figure 1 It is a schematic diagram of the process of the present invention; Figure 3 A mechanical model of a single-axle vehicle system used for numerical verification in the embodiments;

[0094] The validity and correctness of the method are verified by finite element analysis of examples

[0095] Example 1 Numerical Verification

[0096] Example parameters:

[0097] The bridge span is L = 30m, the unit length mass of the bridge is M = 2400kg / m, and the bridge damping is ξ b =1%, elastic modulus E = 27.5 GPa, section moment of inertia I = 0.2 m 4 The mass of the moving and stationary single-axis measurement vehicles are M m =1000kg, M s =800kg, elastic stiffness is k m =1500kN / m, k s =800kN / m, the vehicle body damping is ξ m =5%,ξ s =5%, the stationary test vehicle is placed 12m away from the beginning of the upper bridge, and the moving test vehicle runs at a speed of v=5m / s.

[0098] In order to verify the effect of the inversion method proposed in step S3 of the present invention on solving the vertical contact acceleration response, a finite element numerical simulation was performed. Figure 4 The vertical acceleration contact response time domain diagram and corresponding frequency domain diagram obtained by the motion measurement vehicle in steps S3 and S4 are used to calculate the vertical acceleration contact response time domain diagram and the corresponding frequency domain diagram. Figure 5 The vertical acceleration contact response time domain diagram and the corresponding frequency domain diagram solved in steps S3 and S4 are used for the stationary measurement vehicle.

[0099] from Figure 4 , Figure 5It can be seen that the vertical acceleration contact response of the measuring vehicle obtained by the inversion method is almost consistent with the vertical contact response of the theoretical measuring vehicle, and the vehicle body frequency is filtered out, which improves the visibility of the bridge frequency, which is beneficial for the identification of the dynamic response of the bridge. In step S3, the entire contact response identification process only uses the response of the single-axle vehicle body itself. Therefore, the inversion acceleration contact response calculation method proposed in the present invention is not limited to the structural form of the bridge, and can improve the visibility of the bridge frequency.

[0100] In order to verify the effect of the method in step S6 of the present invention on the identification of bridge modal vibration shapes, a numerical simulation was performed. Figure 7 The modal vibration type identification result of a single-span bridge obtained based on the method of the present invention.

[0101] from Figure 7 It can be seen that the proposed method can accurately identify the modal vibration mode of the bridge, and the identification result is consistent with the theoretical value of the modal vibration mode of the bridge, which verifies the correctness of the method in step S6. The modal assurance criterion (MAC) is often used as an indicator to evaluate the accuracy of modal identification. The closer the MAC is to 1, the more accurate the identification result is. Compared with the MAC value of 0.9710 ( Figure 6 ), the MAC value of the single-span bridge modal vibration shape obtained by the method of the present invention is 0.9980, and its modal confidence criterion value is higher, that is, the influence of bridge damping is eliminated, and the bridge modal vibration shape is extracted more efficiently and accurately, verifying the effectiveness of the proposed method.

Claims

1. A bridge modal vibration driving identification method considering the influence of bridge damping, characterized in that: Firstly, a vehicle-bridge interaction model involving two measuring vehicles is established, one of which is a stationary measuring vehicle and the other is a moving measuring vehicle traveling at a constant speed. Sensors for collecting vertical vibration data are installed on the two vehicles respectively, and the vertical response of the vehicle body is calculated accordingly, and the vehicle-bridge contact response is indirectly calculated from the vehicle body response. Then, based on the motion equations of the two moving and stationary measurement vehicles, an inverse algorithm for vehicle-bridge contact response is established, which can extract the bridge frequency from the contact response regardless of the structural form of the bridge. Combined with Hilbert transform, the bridge modal vibration amplitude is extracted from the bridge response, the influence of bridge damping in the bridge vibration amplitude is eliminated, and the bridge modal vibration amplitude is accurately extracted; The specific steps include:

1. Data collection stage: S1 Arrangement of two moving and stationary measuring vehicles-bridge system: Two single-axis measuring vehicles equipped with acceleration sensors are arranged on the bridge respectively. Based on the vehicle-bridge interaction, the measuring vehicle excites the bridge, and the bridge generates a vertical vibration response and transmits it to the measuring vehicle, causing the measuring vehicle to generate a vertical response; one of the measuring vehicles is stationary, and the receiver on it is used to collect the vertical acceleration response of the stationary measuring vehicle A measuring vehicle starts to move from rest, and its receiver is used to collect the vertical acceleration response of the moving measuring vehicle. S2 establishes the corresponding differential equation of motion; 2. Contact response calculation stage: S3 uses the inversion of the motion equation of the single-axis measurement vehicle to obtain the vertical acceleration contact response of the vehicle bridge; S4 uses the moving and stationary measurement vehicles and the bridge motion equations to derive the vertical displacement responses of the two vehicle bridges, and then derives the vertical acceleration contact response; 3. Mode shape identification stage: S5 uses Hilbert transform to process the vertical acceleration contact response and obtains the bridge amplitude; Based on the characteristics that the bridge amplitude extracted by the stationary measurement vehicle has the same attenuation trend caused by damping but is not affected by spatial changes, S6 processes the bridge vibration amplitude, eliminates the signal attenuation caused by bridge damping, and realizes the efficient construction of bridge modal vibration; The step S2: According to the two-measurement vehicle-bridge coupling system, the motion equations of the vertical vibration response of the moving and stationary measurement vehicles are established as shown in formulas (1) and (2), and the motion equation of the vertical vibration response of the bridge is established as shown in formula (3), which is expressed as follows: Where M m 、M s are the mass of the moving and stationary measurement vehicles, k m , k s are the stiffness coefficients of the moving and stationary measuring vehicles, c m 、c s are the damping coefficients of the moving and stationary measurement vehicles respectively; y m ,y s are the vertical displacements of the dynamic and static measuring vehicles, u and u cm and u cs They are the vertical displacement of the bridge and the vertical displacement of the contact points between the dynamic and static measuring vehicles and the bridge, where u cm =u| x＝vt 、u cs =u| x＝L ; In the formula and represents the first partial derivative of the corresponding displacement with respect to time, u″″ represents the fourth partial derivative of the bridge displacement with respect to the displacement; δ is the Dirac function; the bridge considered is a homogeneous Bernoulli-Euler beam with an effective span of L, bending stiffness of EI, damping coefficient of C, and mass per unit length of M; The step S3: The motion equation of the moving single-axis measuring vehicle is shown in formula (1). The second derivative of formula (1) with respect to time t is taken to convert the vertical vibration signal into a quantity related to the acceleration response, and the acceleration contact response is obtained by solving: Where: Formula (4) is applicable to continuous function data, while the data collected by the receiver is discrete data. For discrete data, formula (4) is changed to formula (6): Similarly, the above-mentioned inverse calculation method can be used to convert the motion equation of the stationary measurement vehicle, that is, formula (2), into the vertical acceleration contact response equation under the corresponding discrete data of the stationary measurement vehicle: Where: in is the vertical contact acceleration response of the moving and stationary measurement vehicle, (| i ) is represented as the i-th data, the total number of i is t / Δt, Δt is the analysis step length, t is the total time the motion measurement vehicle moves on the bridge, is the vertical acceleration response data of the i-th moving and stationary measurement vehicle; the damping ratios of the moving and stationary measurement vehicles are f m 、f s is the moving and stationary measurement vehicle movement frequency, F m | i 、F s | i is the i-th contact force between the moving and stationary measuring vehicle and the bridge; where ω m ,ω s are the circular frequencies of the moving and stationary measurement vehicles, respectively; The step S4 is specifically: After the integration and trigonometric function change calculation of formula (3), the vertical displacement response of the two measuring vehicles is solved and summarized as: Where: Then, the time second derivative of formula (10) (11) is calculated to obtain the vertical acceleration contact response of the dynamic and static measuring vehicles, and the formula (13) (14) is obtained: Where: ； In the above, n is the order of the mode.

2. The method according to claim 1, characterized in that The step S5 is specifically: In order to identify the vibration mode of the bridge, the calculated vertical acceleration contact response equations of the moving and stationary measuring vehicles, namely formulas (13) and (14), are simplified by trigonometric functions, and their theoretical form is: Perform Hilbert transform on formula (16) and (17) respectively, and we get The instantaneous amplitude of the dynamic response of the bridge under the nth mode is obtained as follows: Where:

3. The method according to claim 2, characterized in that The step S6 is specifically: Since the stationary measuring vehicle is in a constant position, its amplitude calculation value is not affected by space and has the same attenuation trend as the amplitude calculation value of the moving measuring vehicle. By dividing formula (20) by formula (21), the calculation term containing bridge damping can be eliminated, and the following is obtained: The calculated amplitude changes, but the vibration mode shape does not change, where Δ sts,n , Δ stm,n , are all constant coefficients. After normalization, we can further obtain the nth-order modal vibration shape of the bridge:

4. The application of the bridge modal vibration type driving identification method considering the influence of bridge damping as described in any one of claims 1 to 3 in actual bridge monitoring is characterized in that: By processing the extracted bridge modal vibration amplitudes, the influence of bridge damping is eliminated, and the bridge modal vibration shapes are extracted from them, thereby evaluating the health status of the bridge.

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