A bridge frequency, damping ratio and mode shape synchronous identification method based on mobile vehicle response

Abstract

The invention provides a bridge frequency, damping ratio and mode shape synchronous identification method based on mobile vehicle response. A vertical acceleration sensor is installed on a mobile four-wheel vehicle and an axle, which is used to collect the vertical acceleration response of the vehicle body and the axle. Due to the coupling effect of the axle, the acceleration response collected from the vehicle body and the axle contains the bridge modal parameter component. Based on the collected vertical response of the vehicle body and the axle, the method uses the vehicle-bridge contact response algorithm to eliminate the frequency interference of the vehicle body, and realizes the efficient identification of the bridge modal parameters. By using the spatial position correlation of the left and right wheels of the moving vehicle corresponding to the contact response when driving over the bridge, the vertical and torsional vibration responses of the bridge can be separated and the corresponding component bridge frequency can be identified. By using the spatial position correlation of the front and rear wheels of the four-wheel vehicle at the same time, different positions and the same position at different times, the vertical and torsional damping and mode shape identification formula of the bridge is established.

Description

Technical Field

[0001] This invention relates to the field of bridge health monitoring and detection technology, and in particular to a method for synchronous identification of bridge frequency, damping ratio, and vibration mode based on the response of a moving vehicle. Background Technology

[0002] Bridges, as engineering marvels connecting two places and spanning obstacles, bear vital transportation functions. During their long service life, bridges inevitably suffer from environmental erosion and external loads, leading to a gradual decline in their structural performance. If this decline is not detected and addressed in a timely manner, it can cause serious safety problems.

[0003] Traditional bridge health monitoring methods rely on installing numerous vibration sensors on the bridge to collect vibration response data in real time. While this method provides detailed monitoring data, its high installation and maintenance costs make it primarily suitable for bridges with long spans, extra-long spans, and special structures. For small- to medium-span bridges, using traditional methods for health monitoring would present a significant economic burden.

[0004] Existing technologies utilize moving vehicles crossing bridges to identify bridge frequencies. These methods indirectly obtain bridge vibration information through vehicle dynamic data, adapting to the diversity and wide distribution of bridges. Their mobility, economy, and versatility have led to their application in various situations. However, bridge health is a multi-dimensional concept involving multiple key dynamic characteristics of the bridge structure. Bridge health is closely related to modal parameters, including frequency, mode shape, and damping. Existing monitoring technologies often identify these three parameters separately. This single-parameter monitoring method cannot comprehensively reflect the dynamic characteristics of the bridge and is insufficient for accurately diagnosing its health and potential problems. In reality, these parameters are not isolated but interconnected, collectively reflecting the bridge's dynamic behavior. Existing technologies often overlook the complexity of modal parameter identification, affecting the accuracy of monitoring results.

[0005] Therefore, it is of great significance to develop a method for synchronously identifying bridge frequency, damping ratio, and mode shape based on the response of a moving vehicle. Summary of the Invention

[0006] The purpose of this invention is to provide a method for synchronously identifying bridge frequency, damping ratio, and mode shape based on the response of a moving vehicle, so as to solve the problems existing in the prior art.

[0007] The technical solution adopted to achieve the purpose of this invention is as follows: a method for synchronous identification of bridge frequency, damping ratio, and mode shape based on the response of a moving vehicle, comprising the following steps:

[0008] 1) The measuring vehicle is driven across a bridge to collect the vertical vibration response of the vehicle body and wheels during its movement. The measuring vehicle is a four-wheeled vehicle. Vertical acceleration sensors are installed on the vehicle body and axles. The measuring vehicle and the bridge form a coupled system. The vehicle-bridge coupling system includes vertical, lateral, and torsional responses. When the measuring vehicle travels across the bridge, the bridge vibration is transmitted to the measuring vehicle through the wheels, causing the measuring vehicle to vibrate.

[0009] 2) Use the vehicle-bridge contact response algorithm to eliminate interference from the vehicle's vertical and lateral frequencies.

[0010] 3) Bridge response separation and identification. Step 3) specifically includes the following sub-steps:

[0011] 3.1) Separate the bridge response and identify the corresponding bridge frequency.

[0012] 3.2) Extract the time-frequency ridge lines of the corresponding modes of the bridge.

[0013] 4) Extract and fit bridge damping. Utilize the attenuation characteristics of the front and rear wheels of the measuring vehicle at different instants at the same position to identify discrete damping ratio data. Fit the identified damping ratio results using the minimum absolute residual method with zero slope to finally obtain the bridge damping ratio.

[0014] 5) Extract the bridge formation. Utilize the spatial correlation between the front and rear wheels at different positions at the same instant to iteratively reconstruct the bridge formation.

[0015] Furthermore, eight vertical acceleration sensors are respectively installed on the front left side of the vehicle body, the front right side of the vehicle body, the rear left side of the vehicle body, the rear right side of the vehicle body, the left axle of the front axle, the right axle of the front axle, the left axle of the rear axle, and the right axle of the rear axle.

[0016] Further, in step 3.1), by utilizing the spatial relationship of the contact point responses at the left and right wheels of the moving vehicle, the vertical and torsional responses of the vehicle-bridge contact points can be separated. Then, Fourier transform is used to identify the frequencies of the bridge's vertical response and torsional response, respectively. In step 3.2), windowed Fourier transform is used to process the vertical and torsional responses of the vehicle-bridge contact points obtained in step 3.1) to obtain time-frequency images of the corresponding responses. Then, the bridge modal ridges corresponding to the frequencies obtained in step 3.1) are extracted from the aforementioned time-frequency images.

[0017] Furthermore, in step 4), by utilizing the spatial correlation between the front and rear wheels of the four-wheeled vehicle at different instants at the same position, the nth-order torsional response damping ratio ξ of the bridge can be extracted using the damping ratio identification formula. bθ,n As shown in equation (1).

[0018]

[0019] In the formula, G(τ)G ,n θ The given value is the time-frequency ridge obtained using the windowed Fourier transform. τ and n represent the modulation of the signal in time and frequency during the windowed Fourier transform, respectively. The subscripts F and R of G and τ represent the front and rear wheels, respectively. θ This represents the selected time-frequency ridge position. Let t be the torsional frequency of the nth-order bridge. R It is the length between the front and rear wheels of the vehicle divided by the vehicle's speed.

[0020] Furthermore, in step 5), by utilizing the spatial correlation between the front and rear wheels of the four-wheeled vehicle at different positions at the same instant, the nth order torsional array of the bridge can be extracted using the array reconstruction iterative method as shown in the following formula.

[0021]

[0022] In the formula, This represents the ratio of the amplitude of the time-frequency ridge lines at the front and rear wheels. Assume Φ 0,θ =1, and the bridge formation is calculated iteratively using equation (2b).

[0023] The technical effects of this invention are undeniable: by utilizing the spatial position correlation of the contact responses of the left and right wheels of a moving vehicle crossing a bridge, the separation of the vertical and torsional vibration responses of the bridge and the identification of the corresponding bridge frequencies are achieved. By utilizing the spatial position correlation of the contact responses of the front and rear wheels of a four-wheeled vehicle crossing a bridge at the same position but different instants, and at the same instant but different positions, formulas for identifying the vertical and torsional damping and pattern of the bridge are established. These are then combined with windowed Fourier transform technology to identify the vertical and torsional damping and pattern of the bridge. By utilizing the complete theory of simultaneously identifying bridge frequencies, damping, and pattern using a measuring vehicle, effective formulas and technical processes for identifying the vertical and torsional damping ratio and pattern of the bridge are established, which are of great significance for bridge health monitoring. Attached Figure Description

[0024] Figure 1 This is a flowchart of the method.

[0025] Figure 2 Theoretical mechanical model and measuring vehicle-bridge system;

[0026] Figure 3 Schematic diagram of vehicle sensor placement;

[0027] Figure 4 The vehicle-bridge contact response diagram is shown.

[0028] Figure 5 Separate frequency domain diagrams of the vertical and torsional responses at the axle contact point;

[0029] Figure 6Time-frequency images of the vertical and torsional responses of the bridge obtained by windowed Fourier transform;

[0030] Figure 7 The time-frequency ridges of the first-order vertical and first-order torsional component responses of a bridge used for bridge damping ratio identification;

[0031] Figure 8 The results are used to identify the vertical and torsional damping ratios of the bridge.

[0032] Figure 9 The time-frequency ridges of the first two vertical and first torsional components of the bridge response used for bridge array identification;

[0033] Figure 10 The results show the identification of the vertical and torsional formations of the bridge. Detailed Implementation

[0034] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0035] Example 1:

[0036] Frequency is an inherent property of a bridge structure during free vibration, reflecting its stiffness and mass distribution. Changes in frequency can indicate physical or geometric alterations in the bridge structure, such as material aging, loosening of connections, or structural damage. However, frequency itself does not provide detailed information about the nature of these changes. Damping is a parameter describing the energy dissipation characteristics of bridge vibration. The magnitude of damping is influenced by various factors, including material properties, connection methods, and environmental conditions. Changes in damping may indicate material fatigue, loosening of connections, or changes in environmental conditions. Mode shape describes the relative displacement of different parts of the bridge during vibration. Changes in mode shape can reveal localized damage or stiffness changes in the bridge structure, as damage often alters the structure's vibration modes. Mode shape analysis helps identify the specific location and extent of damage. These three parameters are interconnected; frequency forms the basis for identifying bridge mode shape and damping, while the identified bridge mode shape can be distorted by damping. Given the complexity of modal parameter identification, developing a method based on the response of a moving vehicle to simultaneously identify the frequency, mode shape, and damping of a bridge is of great significance for the rapid detection of bridge health status.

[0037] See Figure 1 This embodiment provides a method for synchronously identifying bridge frequency, damping ratio, and mode shape based on the response of a moving vehicle, including the following steps:

[0038] 1) The measuring vehicle is driven across a bridge to collect data on the vertical vibration response of the vehicle body and wheels during its movement. The measuring vehicle is a four-wheeled vehicle. Vertical acceleration sensors are installed on the vehicle body and axles. See [link / reference]. Figure 3 Eight vertical acceleration sensors are respectively installed on the front left side of the vehicle body, the front right side of the vehicle body, the rear left side of the vehicle body, the rear right side of the vehicle body, the left axle of the front axle, the right axle of the front axle, the left axle of the rear axle, and the right axle of the rear axle.

[0039] See Figure 2 Let x, y, and z be the three-dimensional coordinate system of the bridge model, V be the vehicle's speed, and e be the eccentricity distance from the vehicle's center to the bridge's center. For the vehicle, it is a seven-degree-of-freedom system, including vertical (z...) coordinates. v ), up and down and sway (θ) v ) and the vertical motion of the four wheels (z w,ij The subscripts i = F, R represent the front and rear wheels, and the subscripts j = l, r represent the left and right wheels. The car body is assumed to be a rigid body with a mass of m. v Its relative to the y-axis v and x v The moments of inertia are I vθ and Four wheels (each weighing m) w,ij Through stiffness k s,ij and damping c s,ij Connected to the vehicle body, the stiffness and damping between the wheel and the axle contact point are k and k, respectively. w,ij and c w,ij The distance between the front wheels (Fl and Fr) and the rear wheels (Rl and Rr) of a vehicle is the vehicle length a. F +a R The distance between the left wheels (Fl and Rl) and the right wheels (Fr and Rr) of the vehicle is the vehicle width b. l +b r For bridges, E is the elastic modulus, G is the shear modulus, and the moment of inertia relative to axes z and y is I. z and I y J is the torsional constant, m is the mass per unit length of the bridge, and c is the torsional constant. y ,c z , and c θ These represent the damping coefficients for vertical, lateral, and torsional forces, respectively. z and u y It represents the vertical and lateral displacements of the bridge, θ is the torsion angle, ζ is the distance along the z-axis between the shear center S and the centroid C of the bridge, and I... α (=m(ζ 2 +r p 2 )), rp It is the polar radius of gyration. In the following equations, "a glimpse" represents the derivative with respect to the x-axis, and "a point" represents the derivative with respect to time t.

[0040] The measuring vehicle and the bridge form a coupled system, which includes vertical, lateral, and torsional responses. When the measuring vehicle travels across the bridge, the bridge vibrations are transmitted to the measuring vehicle through its wheels, causing the measuring vehicle to vibrate. Therefore, by installing response acquisition sensors on the measuring vehicle, the vibration response of the bridge can be identified.

[0041] When the surveying vehicle crosses the bridge, with Figure 2 The apparent structure of a bridge and the theoretical expression of its vibration response are as follows:

[0042]

[0043] F and T on the right side of the equation are

[0044]

[0045] Where δ represents the Dixra function, H is the step function, and e ij It is the eccentric distance from each wheel contact point to the centerline of the bridge. Load p ij The front wheel entry time is t1, the rear wheel entry time is t2, and the vehicle travel time on the bridge is T. v yes:

[0046]

[0047] t F =0,t R =(a F +a R ) / V,T v =L / V, (6b)

[0048] Where g represents gravitational acceleration.

[0049] Based on the above governing equations, the analytical expressions for the vertical, lateral, and torsional displacement responses of the bridge can be derived as follows:

[0050]

[0051] The coefficients in the formula are:

[0052]

[0053]

[0054]

[0055] Based on the contact relationship between the moving vehicle and the bridge, the theoretical expression of the vehicle-bridge contact response can be obtained as follows:

[0056]

[0057] Equation (7) shows that the theoretical expression of vehicle-bridge contact response actually includes the vertical and torsional modes of the bridge, thus theoretically demonstrating the feasibility of identifying bridge frequencies, damping, and configurations from the moving vehicle-bridge contact response. In addition, Equation (7) does not include the vertical, sway, and pitch frequencies of the vehicle body, which proves the advantage of vehicle-bridge contact response, namely, that vehicle-bridge contact response can filter out vehicle frequency interference.

[0058] 2) Perform data processing to eliminate interference from the vehicle's vertical and lateral frequencies. This embodiment utilizes existing vehicle-bridge contact response algorithms or bridge deck response reconstruction methods to eliminate interference from vehicle frequencies within the vehicle body, thereby increasing the visibility of bridge modal parameters. This step is merely a prelude to the patented technology of this invention. In actual production, the vehicle-bridge contact response algorithm can be used in the data processing stage:

[0059]

[0060] in:

[0061]

[0062] As can be seen from the above mathematical processing, the vehicle-bridge contact response can be calculated by measuring the vehicle system's own acceleration response and its dynamic physical parameters, and is independent of the bridge's own physical properties.

[0063] 3) Bridge response separation and identification. Based on the assumption of bridge cross-sectional rigidity, the contact point response obtained in equation (8) can be separated into the bridge's vertical contact response and the bridge's torsional contact response.

[0064]

[0065] Note that Equation (10) does not require any bridge-related information, only the signals collected from the vehicle body. After separating the vertical and torsional responses at the vehicle-bridge contact point, the invention uses Fourier transform to process the signals and can easily identify the corresponding response frequency values ​​of the bridge. Step 3) specifically includes the following sub-steps:

[0066] 3.1) Separate the bridge response and identify the corresponding bridge frequencies. By utilizing the spatial relationship of the contact point responses at the left and right wheels of the moving vehicle, the vertical and torsional responses at the vehicle-bridge contact points can be separated. Then, Fourier transform is used to identify the frequencies of the bridge's vertical response and torsional response, respectively.

[0067] 3.2) Extract the time-frequency ridge lines of the corresponding bridge modes. The vertical and torsional responses of the vehicle-bridge contact points obtained in step 3.1) are processed using windowed Fourier transform to obtain the time-frequency images of the corresponding responses. Then, the bridge mode ridge lines corresponding to the frequencies obtained in step 3.1) are extracted from the aforementioned time-frequency images.

[0068] 4) Extract and fit bridge damping. By measuring the spatial positional relationship between the front and rear wheels of a vehicle at the same location at different instants, this invention constructs a bridge damping ratio identification formula. Based on the vehicle-bridge contact response and combined with windowed Fourier transform technology, the bridge damping ratio is identified. The torsional response component will be used as an example when constructing the bridge damping ratio identification formula below.

[0069] To identify the bridge damping ratio, a windowed Fourier transform was used to process the separated vehicle-bridge contact response (Equation 9) to separate the bridge modal components of a specific response, i.e.

[0070]

[0071] In the formula, It is a constant obtained from windowed Fourier transform signal processing, and it is related to the signal itself and the selected frequency. The subscript p indicates the front and rear wheels.

[0072]

[0073] Because the distance difference between the front and rear wheels when they successively pass the same position on the bridge is (a) F +a R Using this spatial correlation, the damping can be extracted from the Fourier transform ridges at the contact points of the front and rear wheels.

[0074]

[0075]

[0076] It should be noted that the above formula still applies to the vertical damping ratio, and the proof process is similar and will not be shown again. The damping ratio result calculated using the above formula is discrete data and is unstable. Therefore, a method using the minimum absolute residual with zero slope is proposed to fit the damping ratio identification result, ultimately obtaining the bridge damping ratio.

[0077] 5) Bridge Formation Extraction. By measuring the spatial relationship between the front and rear wheels of the vehicle at different positions at the same instant, this invention constructs an iterative formula for the bridge formation. Based on the vehicle-bridge contact response and combined with windowed Fourier transform technology, bridge formation identification is achieved. The torsional response component will be used as an example when constructing the bridge formation formula below.

[0078] Using the front and rear wheels at the same instant t q =τ qT G The relationship can be used to obtain the ratio of the array amplitude at the front and rear wheel positions.

[0079]

[0080] Then, the formation at step q is calculated iteratively using the formation points from step q-1.

[0081]

[0082] In the calculation process, assume Φ 0,θ =1. Note that the above formula still applies to the vertical array of bridges, and the process is similar, so it will not be shown again.

[0083] Example 2:

[0084] This embodiment provides a method for synchronously identifying bridge frequency, damping ratio, and mode shape based on the response of a moving vehicle, including the following steps:

[0085] 1) The measuring vehicle is driven across a bridge to collect the vertical vibration response of the vehicle body and wheels during its movement. The measuring vehicle is a four-wheeled vehicle. Vertical acceleration sensors are installed on the vehicle body and axles. The measuring vehicle and the bridge form a coupled system. The vehicle-bridge coupling system includes vertical, lateral, and torsional responses. When the measuring vehicle travels across the bridge, the vibration of the curved bridge is transmitted to the measuring vehicle through the wheels, causing the measuring vehicle to vibrate.

[0086] 2) Use the vehicle-bridge contact response algorithm to eliminate interference from the vehicle's vertical and lateral frequencies.

[0087] 3) Bridge response separation and identification. Step 3) specifically includes the following sub-steps:

[0088] 3.1) Separate the bridge response and identify the corresponding bridge frequency.

[0089] 3.2) Extract the time-frequency ridge lines of the corresponding modes of the bridge.

[0090] 4) Extract and fit bridge damping. Utilize the spatial correlation of the front and rear wheels of the measuring vehicle at different positions at the same instant to identify discrete data of the damping ratio. Fit the identified damping ratio using the minimum absolute residual method with zero slope to finally obtain the bridge damping ratio. Using the spatial correlation of the front and rear wheels of a four-wheeled vehicle at different positions at the same instant, the nth-order torsional response damping ratio ξ of the bridge can be extracted using the damping ratio identification formula. bθ,n (This section only demonstrates the identification of torsional damping ratio; the vertical response damping ratio can be obtained similarly by replacing all torsional terms with vertical terms in the formula.)

[0091]

[0092] In the formula, G(τ)G ,n θ The curve () represents the time-frequency ridge corresponding to the frequency obtained using the windowed Fourier transform (this section shows the extracted torsional damping ratio, therefore it is the time-frequency ridge corresponding to the nth torsional frequency). τ and n represent the modulation of the signal in time and frequency during the windowed Fourier transform, respectively. The subscripts F and R of G and τ here represent the front wheel (F) and rear wheel (R), respectively. θ This represents the selected time-frequency ridge position. Let t be the torsional frequency of the nth-order bridge. R The distance between the front and rear wheels of the vehicle is divided by the vehicle's speed, which is (a F +a R ) / V.

[0093] The bridge damping ratio ξ calculated using equation (1) bθ,n The results are discrete data and exhibit instability. A method using the minimum absolute residual with zero slope is proposed to fit the damping ratio identification results, ultimately yielding the bridge damping ratio.

[0094] 5) Extracting the bridge formation. Utilizing the spatial correlation between the front and rear wheels at the same position at different instants, the bridge formation is iteratively reconstructed. Using the spatial correlation between the front and rear wheels of a four-wheeled vehicle at the same position at different instants, the nth-order torsional formation of the bridge can be extracted using an iterative reconstruction formula: (This section only demonstrates the identification of the torsional formation; the bridge formation with a vertical response can be obtained similarly by replacing all torsional terms with vertical terms in the formula.)

[0095]

[0096] In the formula, This represents the ratio of the amplitude of the time-frequency ridge lines at the front and rear wheels. If we assume Φ... 0,θ =1, then the bridge formation can be calculated iteratively using equation (2b).

[0097] Example 3:

[0098] The main content of this embodiment is the same as that of embodiment 2, wherein the eight vertical acceleration sensors are respectively installed on the left front side of the vehicle body, the right front side of the vehicle body, the left rear side of the vehicle body, the right rear side of the vehicle body, the left front axle, the right front axle, the left rear axle, and the right rear axle.

[0099] Example 4:

[0100] The main content of this embodiment is the same as that of Embodiment 2 or 3. In step 3.1), the vertical and torsional responses of the vehicle-bridge contact points can be separated by utilizing the spatial relationship of the contact point responses at the left and right wheels of the moving vehicle. Then, Fourier transform is used to identify the frequencies of the bridge's vertical response and torsional response, respectively. In step 3.2), the vertical and torsional responses of the vehicle-bridge contact points obtained in step 3.1) are processed by windowed Fourier transform to obtain time-frequency images of the corresponding responses. Then, the bridge modal ridges corresponding to the frequencies obtained in step 3.1) are extracted from the aforementioned time-frequency images.

[0101] Example 5:

[0102] This embodiment further verifies the technical solutions of any one of Embodiments 1 to 4 using numerical values. In this embodiment, the bridge span L = 30m, and the bridge density ρ = 2,500kg / m³. 3 The cross-sectional area A = 5.3 m² 2 Elastic modulus E = 27.5 GPa, polar radius of gyration r p The value is 3.43m, the distance ζ between the shear center and the centroid is 0.66m, and the moment of inertia I z It is 57.8m 4 Moment of inertia I y It is 4.98m 4 The torsional constant J is 11.38m. 4 .

[0103] Vehicle body weight (m) v It is 1,085 kg, and the weight of the four wheels is m. w,ij It's 40kg, the vehicle is about x v Moment of inertia of the axis It is 1,100 kg·m 2 Regarding y v Moment of inertia I of the axis vθ It is 820 kg·m 2 The damping and stiffness of the suspension are c, respectively. s,ij =1×10 3 N·s / m, k s,ij =1×10 4 N / m, the damping and stiffness at the wheel are respectively c w,ij =2×10 3 N·s / m, k w,ij =1.5×10 5 N / m, vehicle wheel track dimension a F ,a R ,b l ,b r The measurements are 1.4m, 1.47m, 0.75m, and 0.75m respectively.

[0104] Assuming the bridge's vertical and torsional damping ratios are both 0.5%, the vehicle's speed V is 5 m / s, and its eccentricity e is 1.75 m.

[0105] To verify that the method of this invention can identify the vertical and torsional frequencies, damping ratio, and configuration of a bridge from the vehicle-bridge contact response, numerical simulations were performed: Figure 4 The images are time-domain and frequency-domain diagrams of the vehicle-bridge contact point obtained by sensor arrangement based on the method of the present invention. 4a is the time-domain diagram of the vehicle-bridge contact point response, and 4b is the frequency-domain diagram of the vehicle-bridge contact point response. Figure 5 The images show the separated frequency domain diagrams of the vertical and torsional responses of the vehicle-bridge contact point obtained based on the method of this invention. 5a is the vertical frequency domain diagram of the vehicle-bridge contact point response, and 5b is the torsional frequency domain diagram of the vehicle-bridge contact point response. Figure 6 The images are time-frequency images of the vertical and torsional responses of the bridge obtained by windowed Fourier transform based on the method of this invention. 6a is the time-frequency image of the vertical contact point response obtained from the front wheel, 6b is the time-frequency image of the vertical contact point response obtained from the rear wheel, 6c is the time-frequency image of the torsional contact point response obtained from the front wheel, and 6d is the time-frequency image of the torsional contact point response obtained from the rear wheel. Figure 7 The first-order vertical and first-order torsional component response time-frequency ridges of a bridge, obtained based on the method of this invention, are used for bridge damping ratio identification. Figure 8 The identification results of the bridge's vertical and torsional damping ratios are based on the method of this invention. Figure 9 The method of this invention provides time-frequency ridges for the first two vertical and first torsional components of a bridge for bridge formation identification. Figure 10 The results of the bridge vertical and torsional array identification are based on the method of this invention.

[0106] from Figure 5 , Figure 8 and Figure 10 It can be seen that the proposed technology can be successfully applied to the identification of bridge verticality, torsional frequency, damping ratio and array configuration, and the identified bridge frequency, damping ratio and array configuration have high identification accuracy.

Claims

1. A method for synchronously identifying bridge frequency, damping ratio, and mode shape based on the response of a moving vehicle, characterized in that, Includes the following steps: 1) The measuring vehicle is driven across the bridge to collect the vertical vibration response of the vehicle body and the vertical vibration response of the wheels during the driving process; the measuring vehicle is a four-wheeled vehicle; vertical acceleration sensors are installed on the vehicle body and axles; the measuring vehicle and the bridge form a coupled system; the vehicle-bridge coupling system includes vertical, lateral and torsional responses; when the measuring vehicle drives across the bridge, the bridge vibration is transmitted to the measuring vehicle through the wheels, causing the measuring vehicle to vibrate; 2) Perform data processing to eliminate interference from the vehicle's vertical and lateral frequencies; 3) Bridge response separation and identification; Step 3) specifically includes the following sub-steps: 3.1) Separate the bridge response and identify the corresponding bridge frequencies; 3.2) Extract the time-frequency ridge lines of the corresponding modes of the bridge; 4) Extract and fit the bridge damping; identify the discrete data of the damping ratio by using the attenuation characteristics of the front and rear wheels of the measuring vehicle at different instants at the same position; fit the damping ratio identification results using the minimum absolute residual method with zero slope, and finally obtain the bridge damping ratio. 5) Extract the bridge formation; use the spatial correlation between the front and rear wheels at different positions at the same instant to iteratively reconstruct the bridge formation.

2. The method for synchronous identification of bridge frequency, damping ratio, and mode shape based on moving vehicle response according to claim 1, characterized in that: Eight vertical acceleration sensors are installed on the front left, front right, rear left, rear right, front left axle, front right axle, rear left axle, and rear right axle of the vehicle body.

3. The method for synchronous identification of bridge frequency, damping ratio, and mode shape based on moving vehicle response according to claim 1, characterized in that: In step 2), the vehicle-bridge contact response algorithm or bridge deck response reconstruction method is selected to eliminate the interference of vehicle body frequency in the vehicle body, thereby increasing the visibility of bridge modal parameter identification.

4. The method for synchronous identification of bridge frequency, damping ratio, and mode shape based on moving vehicle response according to claim 1, characterized in that: In step 3.1), the vertical and torsional responses of the vehicle-bridge contact points can be separated by utilizing the spatial relationship of the contact point responses at the left and right wheels of the moving vehicle. Then, Fourier transform is used to identify the frequencies of the bridge's vertical response and torsional response, respectively. In step 3.2), the vertical and torsional responses of the vehicle-bridge contact points obtained in step 3.1) are processed by windowed Fourier transform to obtain time-frequency images of the corresponding responses. Then, the bridge modal ridges corresponding to the frequencies obtained in step 3.1) are extracted from the aforementioned time-frequency images.

5. The method for synchronous identification of bridge frequency, damping ratio, and mode shape based on moving vehicle response according to claim 1, characterized in that: In step 4), by utilizing the spatial correlation between the front and rear wheels of the four-wheeled vehicle at different instants at the same position, the nth-order torsional response damping ratio ξ of the bridge can be extracted using the damping ratio identification formula. bθ,n As shown in equation (1); In the formula, G(τ) G ,n θ G represents the time-frequency ridge obtained using the windowed Fourier transform; τ and n represent the modulation of the signal in time and frequency during the windowed Fourier transform, respectively; the subscripts F and R of G and τ represent the front and rear wheels, respectively; n θ This represents the selected time-frequency ridge position. Let t be the torsional frequency of the nth-order bridge. R It is the length between the front and rear wheels of the vehicle divided by the vehicle's speed.

6. The method for synchronous identification of bridge frequency, damping ratio, and mode shape based on moving vehicle response according to claim 1, characterized in that: In step 5), the spatial correlation between the front and rear wheels of the four-wheeled vehicle at different positions at the same instant is used to extract the nth order torsional array of the bridge using the array reconstruction iterative method, as shown in the following formula; In the formula, This represents the ratio of the time-frequency ridge amplitudes at the front and rear wheels; assuming Φ 0,θ =1, and the bridge formation is calculated iteratively using equation (2b).

Images