Bridge damage identification method considering social vehicles
By constructing a vehicle-bridge coupled vibration dynamics model and using Hilbert transform technology, the problem of the unutilized role of social vehicles in existing technologies has been solved, enabling efficient and accurate identification of bridge damage under complex traffic conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHONGQING UNIV
- Filing Date
- 2026-06-10
- Publication Date
- 2026-07-31
AI Technical Summary
Existing vehicle scanning methods fail to effectively utilize the role of social vehicles in bridge damage identification, cannot improve damage identification sensitivity under complex traffic conditions, and are difficult to perform accurate detection without interrupting traffic.
A coupled vibration dynamics model of the test vehicle, other vehicles, and the bridge was constructed. The analytical solutions of the response during the two vehicles' joint driving and individual driving phases were derived using the modal superposition method and the central difference method. The bridge damage identification index was calculated by Hilbert transform, and the peak characteristics of the instantaneous amplitude square curve were analyzed to determine the damage location.
It significantly improves the sensitivity and detection efficiency of bridge damage identification, enabling efficient and low-cost bridge damage detection without disrupting traffic.
Smart Images
Figure CN122490854A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of bridge damage identification, and in particular to a bridge damage identification method that takes into account social vehicles. Background Technology
[0002] With the increasing traffic load, bridges are prone to cumulative damage during long-term service, making safety inspection and health monitoring a critical engineering requirement. Traditional bridge damage detection methods suffer from drawbacks such as low detection efficiency, high cost, susceptibility to human interference, and the need to interrupt traffic, making it difficult to meet the engineering inspection needs of rapid, online, and non-road-closure testing.
[0003] Vehicle scanning, based on the theory of vehicle-bridge coupled vibration, collects bridge vibration signals via a test vehicle equipped with sensors. This allows for the indirect identification of bridge frequencies, mode shapes, and damage states. It offers advantages such as non-contact operation, no traffic disruption, and low cost, making it a research hotspot in bridge non-destructive testing. However, current vehicle scanning methods often employ a single test vehicle or two vehicles (one stationary and one moving) to identify bridge conditions. They lack a theoretical model of vehicle-bridge coupled vibration under the combined influence of both test and other vehicles, failing to accurately analyze the response patterns of the bridge, test vehicle, and contact points when other vehicles are involved. Furthermore, they do not utilize the positive effects of other vehicles and cannot improve damage identification sensitivity under complex traffic conditions, thus limiting the engineering application of vehicle scanning in real-world, non-disruptive traffic scenarios. Summary of the Invention
[0004] The purpose of this invention is to provide a bridge damage identification method that takes into account social vehicles, thereby improving the identification sensitivity by utilizing social vehicles.
[0005] To achieve the above objectives, the present invention provides a bridge damage identification method considering social vehicles, comprising the following steps: S1. Establish a coupled vibration dynamics model of test vehicle-social vehicle-bridge. Both test vehicle and social vehicle are simplified to single-degree-of-freedom spring-mass models, and the bridge is simplified to a simply supported beam. S2. Based on the modal superposition method, derive the analytical solutions for the vertical response of the test vehicle and the vehicle-bridge contact point in two stages: two vehicles traveling together and the test vehicle traveling alone after the other vehicle has exited the bridge. S3. The acceleration response at the vehicle-bridge contact point is obtained by inverting the acceleration signal of the test vehicle using the central difference method. S4. Obtain the driving frequency component from the acceleration analysis of the contact point between the test vehicle and the bridge during the two-vehicle joint driving phase. S5. Perform Hilbert transform on the driving frequency component to calculate the instantaneous amplitude square of the driving frequency component, and use the instantaneous amplitude square as the bridge damage identification index. S6. Analyze the peak characteristics of the instantaneous amplitude square curve and determine the location of bridge damage based on the peak position.
[0006] Preferably, in the mechanical model of step S1, the following reasonable assumptions are made: the simply supported beam is a homogeneous Euler-Bernoulli beam with a uniform cross section; the bridge is completely stationary before the vehicle enters, and the social vehicle and the test vehicle enter the bridge at the same time; the mass of the social vehicle and the test vehicle is much smaller than the mass of the bridge; the speed of the social vehicle is greater than the speed of the test vehicle.
[0007] Preferably, step S2 specifically includes the following steps: S21. Construct the bridge vibration equation and the test vehicle vibration equation during the two-vehicle joint driving phase. S22. Based on the modal superposition method, solve the analytical solutions for the vertical displacement of the bridge, the vertical displacement and acceleration of the test vehicle-bridge contact point, and the vertical displacement and acceleration of the test vehicle during the joint driving phase of the two vehicles. S23. Determine the time of exiting the bridge based on the speed of social vehicles, and construct the bridge vibration equation for the test vehicle's solo driving phase after the social vehicles have left. S24. Using the final response value during the co-driving phase of the two vehicles as the initial condition, the analytical solutions for the vertical displacement of the bridge, the vertical displacement and acceleration of the test vehicle-bridge contact point, and the vertical displacement of the test vehicle during the solo driving phase after the social vehicles have left are obtained based on the modal superposition method.
[0008] Preferably, in step S21, the bridge vibration equation and the test vehicle vibration equation are respectively: ; ; in, Let the centroidal axis of the simply supported beam be... The vertical axis The horizontal axis , These represent the vertical displacements of the bridge and the test vehicle during the phase when both vehicles are traveling together. For the Dirac function, Mass per unit length of the bridge For the elastic modulus of the bridge, For bridge cross sections Moment of inertia of the axis, and These are the contact points between the test vehicle, other vehicles, and the bridge. To test the frequency of the vehicle, , and These are the test vehicle's stiffness and mass, respectively. The formula for calculating the contact force between vehicles is as follows: ; The contact force between the social vehicle and the test vehicle is calculated using the following formula: ; in, and These refer to the stiffness and mass of social vehicles, respectively. For the vertical displacement of social vehicles. This is the vertical acceleration.
[0009] Preferably, step S22 specifically includes the following steps: S221. Obtain the vertical displacement response of the bridge based on the modal superposition method: ; in, For the bridge's first First modal coordinates, For simply supported beams; S222. Substituting the vertical displacement response of the bridge into the bridge vibration equation, we obtain the bridge dynamic equation: ; in, and These represent the driving frequencies of the test vehicle and other vehicles, respectively. ; S223. By using zero initial conditions, the generalized coordinates of the bridge are obtained by solving the bridge's dynamic equations: ; in, and These represent the static modal deflections of the test vehicle and other vehicles at mid-span of the bridge, respectively. and These represent dimensionless parameters related to the speed of the test vehicle and other vehicles, respectively. S224. Substitute the generalized coordinates of the bridge into the bridge vertical displacement response expression from step S22 to obtain the bridge vertical displacement response: ; make Thus, the analytical expression for the vertical displacement response at the contact point between the test vehicle and the bridge can be obtained; S225. Taking the second-order time derivative of the vertical displacement response at the contact point between the test vehicle and the bridge, we obtain the analytical expression for the acceleration at the contact point between the test vehicle and the bridge: ; S226. Substituting the solution of the vertical displacement at the contact point between the test vehicle and the bridge into the vertical vibration equation of the test vehicle, the analytical expression of the vertical displacement of the test vehicle during the joint travel phase is obtained: ; in, , , , , ; S227. Taking the second-order time derivative of the vertical displacement expression of the test vehicle, we obtain the expression for the vertical acceleration of the test vehicle during the joint driving phase of the two vehicles: .
[0010] Preferably, in step S23, the vertical vibration equation of the bridge during the test vehicle's solitary driving phase after the other vehicles have left is: .
[0011] Preferably, in step S24, the vertical vibration response of the bridge during the test vehicle's solitary driving phase after the other vehicles have left is as follows: ; in, , , ; The analytical expression for the vertical vibration response at the contact point is: ; The analytical expression for the acceleration response at the contact point is: ; The analytical expression for the vertical displacement of the test vehicle is: ; in, , , , , , , ; .
[0012] Preferably, in step S3, the formula for obtaining the vehicle-bridge contact point acceleration response from the test vehicle acceleration signal is as follows: ; in, Indicates the first One sampling point; Indicates the sampling interval.
[0013] Preferably, in step S4, the driving frequency component is obtained from the acceleration analysis formula of the test vehicle at the contact point with the bridge during the joint driving phase: .
[0014] Preferably, in step S5, the driving frequency component is subjected to Hilbert transform processing to obtain the processed signal: ; Based on the original driving frequency components and the processed signal obtained through Hilbert transform, the squared terms are summed to construct the instantaneous amplitude square: .
[0015] Therefore, the present invention employs the above-described bridge damage identification method that takes into account social vehicles, which has the following advantages: (1) In this invention, a complete theoretical system of coupled vibration of two vehicles and bridges is constructed, the analytical solution of the two-stage response is accurately derived and the acceleration at the contact point is inverted, and the interference of vehicle natural frequency and road surface roughness is reduced from the source. It has excellent robustness in identifying single damage and multiple damage at close range.
[0016] (2) In this invention, social vehicles play an excitation role, which can significantly amplify the amplitude of the instantaneous amplitude squared damage index and greatly improve the sensitivity of bridge damage identification.
[0017] (3) In this invention, there is no need to interrupt traffic or deploy fixed sensors on the bridge. The detection can be completed by simply using a mobile test vehicle. The detection efficiency is high and the cost is low, which greatly improves the engineering applicability and implementation capability of the vehicle scanning method in actual bridge operation and maintenance.
[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0019] Figure 1 This is a flowchart illustrating a bridge damage identification method considering social vehicles according to the present invention. Figure 2 This is a schematic diagram of the vehicle-bridge coupling mechanics model provided in an embodiment of the present invention; Figure 3 The diagram shows the vibration response results of the test vehicle provided in this embodiment of the invention. Figure 3 (a) is a diagram showing the displacement results of the test vehicle. Figure 3 (b) is a spectrum diagram of the test vehicle; Figure 4This is a diagram showing the vibration response results at the contact point between the test vehicle and the bridge, provided in an embodiment of the present invention. Figure 4 (a) is a diagram showing the displacement results at the contact point between the test vehicle and the bridge. Figure 4 (b) is a spectrum diagram of the contact point between the test vehicle and the bridge; Figure 5 The image shows the result of identifying the squared instantaneous amplitude at mid-span of a bridge, as provided in an embodiment of the present invention. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Specific model specifications need to be selected and determined according to the actual specifications of the device, etc. The specific selection calculation method adopts existing technology in the art, and therefore will not be described in detail.
[0021] Example like Figures 1-2 As shown, the present invention provides a bridge damage identification method considering social vehicles, comprising the following steps: S1. Establish a coupled vibration dynamics model of the test vehicle, social vehicles, and bridge. Both the test vehicle and social vehicles are simplified as single-degree-of-freedom spring-mass models, and the bridge is simplified as a simply supported beam. The following reasonable assumptions are made for this mechanical model: the simply supported beam is a homogeneous Euler-Bernoulli beam with a uniform cross-section; the bridge is completely stationary before the vehicle enters; the social vehicle and the test vehicle enter the bridge simultaneously; the mass of the social vehicle and the test vehicle is much smaller than the mass of the bridge; the speed of the social vehicle is greater than the speed of the test vehicle.
[0022] S2. Based on the modal superposition method, derive the analytical solutions for the vertical response of the test vehicle and the vehicle-bridge contact point in two stages: two vehicles traveling together and the test vehicle traveling alone after the other vehicle has exited the bridge. S21. Construct the bridge vibration equation and the test vehicle vibration equation during the joint driving phase of the two vehicles. The bridge vibration equation and the test vehicle vibration equation are as follows: ; ; in, Let the centroidal axis of the simply supported beam be... The vertical axis The horizontal axis , These represent the vertical displacements of the bridge and the test vehicle during the phase when both vehicles are traveling together. For the Dirac function, Mass per unit length of the bridge For the elastic modulus of the bridge, For bridge cross sections Moment of inertia of the axis, and These are the contact points between the test vehicle, other vehicles, and the bridge. To test the frequency of the vehicle, , and These are the test vehicle's stiffness and mass, respectively. The formula for calculating the contact force between vehicles is as follows: ; The contact force between the social vehicle and the test vehicle is calculated using the following formula: ; in, and These refer to the stiffness and mass of social vehicles, respectively. For the vertical displacement of social vehicles. This is the vertical acceleration.
[0023] S22. Based on the modal superposition method, solve the analytical solutions for the vertical displacement of the bridge, the vertical displacement and acceleration of the test vehicle-bridge contact point, and the vertical displacement and acceleration of the test vehicle during the joint driving phase of the two vehicles. S221. Obtain the vertical displacement response of the bridge based on the modal superposition method: ; in, For the bridge's first First modal coordinates, For simply supported beams; S222. Substituting the vertical displacement response of the bridge into the bridge vibration equation, we obtain the bridge dynamic equation: ; in, and These represent the driving frequencies of the test vehicle and other vehicles, respectively. ; S223. By using zero initial conditions, the generalized coordinates of the bridge are obtained by solving the bridge's dynamic equations: ; in, and These represent the static modal deflections of the test vehicle and other vehicles at mid-span of the bridge, respectively. and These represent dimensionless parameters related to the speed of the test vehicle and other vehicles, respectively. S224. Substitute the generalized coordinates of the bridge into the bridge vertical displacement response expression from step S22 to obtain the bridge vertical displacement response: ; make Thus, the analytical expression for the vertical displacement response at the contact point between the test vehicle and the bridge can be obtained; S225. Taking the second-order time derivative of the vertical displacement response at the contact point between the test vehicle and the bridge, we obtain the analytical expression for the acceleration at the contact point between the test vehicle and the bridge: ; S226. Substituting the solution of the vertical displacement at the contact point between the test vehicle and the bridge into the vertical vibration equation of the test vehicle, the analytical expression of the vertical displacement of the test vehicle during the joint travel phase is obtained: ; in, , , , , ; S227. Taking the second-order time derivative of the vertical displacement expression of the test vehicle, we obtain the expression for the vertical acceleration of the test vehicle during the joint driving phase of the two vehicles: .
[0024] S23. Determine the time of exiting the bridge based on the speed of other vehicles, and construct the bridge vibration equation for the test vehicle's solo driving phase after the other vehicles have left. The bridge vertical vibration equation for the test vehicle's solo driving phase after the other vehicles have left is as follows: .
[0025] S24. Using the final response value of the two-vehicle joint driving phase as the initial condition, the vertical displacement of the bridge, the vertical displacement and acceleration of the test vehicle-bridge contact point, and the analytical solution of the vertical displacement of the test vehicle during the test vehicle's solo driving phase after the social vehicles have left are solved based on the modal superposition method. Using the same method as in the two-vehicle joint driving phase, the vertical vibration response of the bridge during the test vehicle's solo driving phase after the social vehicles have left is obtained as follows: ; in, , , ; The analytical expression for the vertical vibration response at the contact point is: ; The analytical expression for the acceleration response at the contact point is: ; The analytical expression for the vertical displacement of the test vehicle is: ; in, , , , , , , ; .
[0026] S3. The acceleration response at the vehicle-bridge contact point is obtained by inverting the acceleration signal of the test vehicle using the central difference method: ; in, Indicates the first One sampling point; Indicates the sampling interval.
[0027] S4. Obtain the driving frequency component from the acceleration analysis of the contact point between the test vehicle and the bridge during the joint driving phase: .
[0028] S5. Perform Hilbert transform on the driving frequency component to calculate the instantaneous amplitude square of the driving frequency component, and use the instantaneous amplitude square as the bridge damage identification index. The driving frequency component is subjected to Hilbert transform to obtain the processed signal: ; Based on the original driving frequency components and the processed signal obtained through Hilbert transform, the squared terms are summed to construct the instantaneous amplitude square: .
[0029] S6. Analyze the peak characteristics of the instantaneous amplitude square curve and determine the location of bridge damage based on the peak position.
[0030] In this embodiment, the iteration time step in the finite element model is selected as 0.001s. The social vehicle and the test vehicle travel on the bridge at uniform speeds of 6m / s and 5m / s, respectively. The theoretical calculations utilize the first five modes of the bridge. Figures 3-4 As shown, Figure 3 (a) is a diagram showing the displacement results of the test vehicle. Figure 3 (b) is a spectrum diagram of the test vehicle. Figure 4 (a) is a diagram showing the displacement results at the contact point between the test vehicle and the bridge. Figure 4 (b) is a spectrum of the test vehicle-bridge contact point. It can be seen that the analytical solution and the numerical solution are in good agreement, which verifies the accuracy of the theoretical solution.
[0031] In addition, it is assumed that there is crack damage at the mid-span of the bridge ( ), the result is as follows Figure 5 As shown in the figure. The results indicate that even with the involvement of other vehicles, the instantaneous squared amplitude still exhibits a significant peak at the damage location, thus enabling clear localization of the damage.
[0032] Therefore, this invention adopts a bridge damage identification method that takes into account social vehicles, which fully considers the coupling effect of social vehicles in actual traffic, does not require traffic closure, effectively amplifies the amplitude of the instantaneous amplitude squared damage index, and significantly improves the sensitivity of bridge damage identification.
[0033] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A bridge damage identification method considering social vehicles, characterized in that: Includes the following steps: S1. Establish a coupled vibration dynamics model of test vehicle-social vehicle-bridge. Both test vehicle and social vehicle are simplified to single-degree-of-freedom spring-mass models, and the bridge is simplified to a simply supported beam. S2. Based on the modal superposition method, derive the analytical solutions for the vertical response of the test vehicle and the vehicle-bridge contact point in two stages: two vehicles traveling together and the test vehicle traveling alone after the other vehicle has exited the bridge. S3. The acceleration response at the vehicle-bridge contact point is obtained by inverting the acceleration signal of the test vehicle using the central difference method. S4. Obtain the driving frequency component from the acceleration analysis of the contact point between the test vehicle and the bridge during the two-vehicle joint driving phase. S5. Perform Hilbert transform on the driving frequency component to calculate the instantaneous amplitude square of the driving frequency component, and use the instantaneous amplitude square as the bridge damage identification index. S6. Analyze the peak characteristics of the instantaneous amplitude square curve and determine the location of bridge damage based on the peak position. 2.The bridge damage identification method considering social vehicles according to claim 1, wherein: In the mechanical model of step S1, the following reasonable assumptions are made: the simply supported beam is a homogeneous Euler-Bernoulli beam with a uniform cross section; the bridge is completely stationary before the vehicle enters, and the social vehicle and the test vehicle enter the bridge at the same time; the mass of the social vehicle and the test vehicle is much smaller than the mass of the bridge; the speed of the social vehicle is greater than the speed of the test vehicle.
3. The bridge damage identification method considering social vehicles according to claim 2, characterized in that: Step S2 specifically includes the following steps: S21. Construct the bridge vibration equation and the test vehicle vibration equation during the two-vehicle joint driving phase. S22. Based on the modal superposition method, solve the analytical solutions for the vertical displacement of the bridge, the vertical displacement and acceleration of the test vehicle-bridge contact point, and the vertical displacement and acceleration of the test vehicle during the joint driving phase of the two vehicles. S23. Determine the time of exiting the bridge based on the speed of social vehicles, and construct the bridge vibration equation for the test vehicle's solo driving phase after the social vehicles have left. S24. Using the final response value during the co-driving phase of the two vehicles as the initial condition, the analytical solutions for the vertical displacement of the bridge, the vertical displacement and acceleration of the test vehicle-bridge contact point, and the vertical displacement of the test vehicle during the solo driving phase after the social vehicles have left are obtained based on the modal superposition method.
4. The bridge damage identification method considering social vehicles according to claim 3, characterized in that: In step S21, the bridge vibration equation and the test vehicle vibration equation are as follows: ； ； in, Let the centroidal axis of the simply supported beam be... The vertical axis The horizontal axis , These represent the vertical displacements of the bridge and the test vehicle during the phase when both vehicles are traveling together. For the Dirac function, Mass per unit length of the bridge For the elastic modulus of the bridge, For bridge cross sections Moment of inertia of the axis, and These are the contact points between the test vehicle, other vehicles, and the bridge. To test the frequency of the vehicle, , and These are the test vehicle's stiffness and mass, respectively. The formula for calculating the contact force between vehicles is as follows: ； The contact force between the social vehicle and the test vehicle is calculated using the following formula: ； in, and These refer to the stiffness and mass of social vehicles, respectively. For the vertical displacement of social vehicles. This is the vertical acceleration.
5. The bridge damage identification method considering social vehicles according to claim 4, characterized in that: Step S22 specifically includes the following steps: S221. Obtain the vertical displacement response of the bridge based on the modal superposition method: ； in, For the bridge's first First modal coordinates, For simply supported beams; S222. Substituting the vertical displacement response of the bridge into the bridge vibration equation, we obtain the bridge dynamic equation: ； in, and These represent the driving frequencies of the test vehicle and other vehicles, respectively. ; S223. By using zero initial conditions, the generalized coordinates of the bridge are obtained by solving the bridge's dynamic equations: ； in, and These represent the static modal deflections of the test vehicle and other vehicles at mid-span of the bridge, respectively. and These represent dimensionless parameters related to the speed of the test vehicle and other vehicles, respectively. S224. Substitute the generalized coordinates of the bridge into the expression for the vertical displacement response of the bridge obtained in step S22 to obtain the vertical displacement response of the bridge: ； make Thus, the analytical expression for the vertical displacement response at the contact point between the test vehicle and the bridge can be obtained; S225. Taking the second-order time derivative of the vertical displacement response at the contact point between the test vehicle and the bridge, we obtain the analytical expression for the acceleration at the contact point between the test vehicle and the bridge: ； S226. Substituting the solution of the vertical displacement at the contact point between the test vehicle and the bridge into the vertical vibration equation of the test vehicle, the analytical expression of the vertical displacement of the test vehicle during the joint travel phase is obtained: ； in, , ， ， ， ； S227. Taking the second-order time derivative of the vertical displacement expression of the test vehicle, we obtain the expression for the vertical acceleration of the test vehicle during the joint driving phase of the two vehicles: 。 6. The bridge damage identification method considering social vehicles according to claim 5, characterized in that: In step S23, the equation for the vertical vibration of the bridge during the test vehicle's solitary driving phase after the other vehicles have left is: 。 7. The bridge damage identification method considering social vehicles according to claim 6, characterized in that: In step S24, the vertical vibration response of the bridge during the test vehicle's solitary driving phase after the other vehicles have left is as follows: ； in, , , ; The analytical expression for the vertical vibration response at the contact point is: ； The analytical expression for the acceleration response at the contact point is: ； The analytical expression for the vertical displacement of the test vehicle is: ； in, , , ， ， ， ， ； 。 8. The bridge damage identification method considering social vehicles according to claim 7, characterized in that: In step S3, the formula for inverting the vehicle-bridge contact point acceleration response from the test vehicle acceleration signal is as follows: ； in, Indicates the first One sampling point; Indicates the sampling interval.
9. A bridge damage identification method considering social vehicles according to claim 8, characterized in that: In step S4, the driving frequency component is obtained from the acceleration analysis of the test vehicle's contact point with the bridge during the joint driving phase: 。 10. A bridge damage identification method considering social vehicles according to claim 9, characterized in that: In step S5, the driving frequency component is subjected to Hilbert transform to obtain the processed signal: ； Based on the original driving frequency components and the processed signal obtained through Hilbert transform, the squared terms are summed to construct the instantaneous amplitude square: 。