Bridge frequency, damping ratio and vibration mode synchronous identification method based on mobile vehicle response

Abstract

The invention provides a bridge frequency, damping ratio and vibration mode synchronous identification method based on mobile vehicle response. According to the method, vertical acceleration sensors are installed on the mobile four-wheeler and axles, and the sensors are used for collecting vertical acceleration responses of a vehicle body and the axles. Due to the coupling effect of the axles, the acceleration response collected from the vehicle body and the axles contains the modal parameter components of the bridge. Based on the collected vertical response of the vehicle body and the axle, the method eliminates the frequency interference of the vehicle body by using a vehicle-bridge contact response algorithm, and achieves the efficient recognition of the modal parameters of the bridge. Separation of vertical and torsional vibration responses of the bridge and bridge frequency identification of corresponding components can be realized by utilizing the correlation of contact response space positions corresponding to left and right wheels of a moving vehicle passing through the bridge. A vertical and torsional damping and formation recognition formula of a bridge is established by utilizing contact response spatial position correlation of front and rear wheels of a four-wheeler passing through the bridge at the same instant and different positions and at the same position and different instant.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge health monitoring and detection, and in particular to a method for synchronously identifying bridge frequency, damping ratio and vibration mode based on mobile vehicle response. Background Art

[0002] Bridges, as engineering marvels that connect two places and cross obstacles, carry important transportation functions. In the long-term service process, bridges will inevitably be affected by factors such as environmental erosion and external loads, causing their structural performance to gradually decline. If this decline is not discovered and handled in time, it may cause serious safety problems.

[0003] Traditional bridge health monitoring methods rely on installing a large number of vibration sensors on bridges to collect real-time vibration response data of bridges. Although this method can provide detailed monitoring data, its high installation and maintenance costs make it mainly suitable for bridges with large spans, extra-large spans and special structures. For small and medium span bridges, the use of traditional methods for health monitoring will face huge economic pressure.

[0004] There are methods in the prior art that use moving vehicles passing over bridges to identify bridge frequencies. This type of method indirectly obtains bridge vibration information through the dynamic data of the vehicle, and can adapt to the diversity and wide distribution of bridges. This type of method has been applied in some occasions due to its mobility, economy and versatility. However, the health status of a bridge is a multidimensional concept, which involves multiple key dynamic characteristics of the bridge structure. The health status of a bridge is closely related to modal parameters including frequency, formation and damping. Existing monitoring technologies often identify the above three parameters separately. This single parameter monitoring method cannot fully reflect the dynamic characteristics of the bridge, and it is difficult to accurately diagnose the health status of the bridge and potential problems. In fact, these parameters do not exist in isolation, but are interrelated and jointly reflect the dynamic behavior of the bridge. Existing technologies often ignore the complexity of such modal parameter identification, resulting in the accuracy of the monitoring results being affected.

[0005] Therefore, it is of great significance to develop a method for synchronous identification of bridge frequency, damping ratio, and vibration mode based on moving vehicle response. Summary of the invention

[0006] The purpose of the present invention is to provide a method for synchronously identifying bridge frequency, damping ratio and vibration mode 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 the present invention is as follows: a method for synchronously identifying bridge frequency, damping ratio, and vibration mode based on the response of a moving vehicle, comprising the following steps:

[0008] 1) Drive the measuring vehicle across the bridge and 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-wheel vehicle. The vertical acceleration sensor is installed on the body and axle of the measuring vehicle. The measuring vehicle and the bridge form a coupling system. The vehicle-bridge coupling system includes vertical, lateral and torsional responses. When the measuring vehicle passes over the bridge, the bridge vibration is transmitted to the measuring vehicle through the wheels, causing the measuring vehicle to vibrate.

[0009] 2) The vehicle-bridge contact response algorithm is used to eliminate the interference of the vehicle body vertical frequency and the vehicle body lateral frequency.

[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 ridges of the corresponding modes of the bridge.

[0013] 4) Extract bridge damping and fit it. Use the attenuation characteristics of the front and rear wheels of the measuring vehicle at different instants at the same position to identify the discrete data of the damping ratio. Use the minimum absolute residual method with zero slope to fit the damping ratio identification results, and finally get the bridge damping ratio.

[0014] 5) Extract the bridge formation. The bridge formation is iteratively reconstructed by using the spatial correlation between the front and rear wheels at different positions at the same moment.

[0015] Furthermore, eight vertical acceleration sensors are respectively installed on the left front part of the vehicle body, the right front part of the vehicle body, the left rear part of the vehicle body, the right rear part 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] Furthermore, in step 3.1), the vertical and torsional responses of the vehicle-bridge contact point can be separated by using the spatial relationship of the contact point responses at the left and right wheels of the mobile vehicle, and then the Fourier transform is used to identify the frequency of the vertical response of the bridge and the frequency of the torsional response of the bridge. In step 3.2), the vertical and torsional responses of the vehicle-bridge contact point obtained in step 3.1) are processed by windowed Fourier transform to obtain the time-frequency images of the corresponding responses, and then the bridge modal ridges in the aforementioned time-frequency images corresponding to the frequencies obtained in step 3.1) are respectively extracted.

[0017] Furthermore, in step 4), the spatial correlation of the front and rear wheels of the four-wheel vehicle at different instants at the same position is used to extract the nth-order torsional response damping ratio ξ of the bridge using the damping ratio identification formula. bθ,n As shown in formula (1).

[0018]

[0019] In the formula, G(τG ,n θ ) is the time-frequency ridge of the corresponding frequency obtained by windowed Fourier transform. τ and n represent the modulation of the signal in time and frequency in the windowed Fourier transform. The subscripts F and R of G and τ represent the front wheel and the rear wheel respectively. n θ represents the selected time-frequency ridge position, is the torsional frequency of the nth-order bridge, t 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), the spatial correlation between the front and rear wheels of the four-wheel vehicle at different positions at the same instant is utilized, and the formation reconstruction iteration can be used to extract the nth order torsional formation of the bridge as shown in the following formula.

[0021]

[0022] In the formula, Represents the ratio of the time-frequency ridge amplitude at the front and rear wheels. Assume Φ 0,θ =1, and use formula (2b) to iteratively calculate the bridge formation.

[0023] The technical effect of the present invention is unquestionable: by utilizing the spatial position correlation of the contact responses corresponding to the left and right wheels of a mobile vehicle passing over a bridge, the separation of the vertical and torsional vibration responses of the bridge and the identification of the bridge frequencies of the corresponding components are achieved. By utilizing the spatial position correlation of the contact responses of the front and rear wheels of a four-wheeled vehicle passing over a bridge at the same position, different instants, and at the same instant, different positions, the vertical and torsional damping and formation identification formulas of the bridge are established, and the windowed Fourier transform technology is combined to identify the vertical and torsional damping and formation of the bridge. By utilizing the complete theory of the simultaneous identification of bridge frequency, damping and formation by a measuring vehicle, an effective formula and technical process for identifying the vertical and torsional damping ratio and formation of the bridge are established, which is of great significance for bridge health detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a method flow chart;

[0025] Figure 2 For theoretical mechanical models and measurement vehicle-bridge systems;

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

[0027] Figure 4 is the vehicle-bridge contact response diagram;

[0028] Figure 5 Separate frequency domain plots for vertical and torsional responses at the vehicle-bridge contact point;

[0029] Figure 6The time-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 the bridge used for identification of the bridge damping ratio;

[0031] Figure 8 Identification results of vertical and torsional damping ratios of bridges;

[0032] Fig. 9 The time-frequency ridges of the first two-order vertical and first-order torsional component responses of the bridge used for bridge formation identification;

[0033] Fig.10 The vertical and torsional formation identification results of the bridge. DETAILED DESCRIPTION

[0034] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0035] Embodiment 1:

[0036] Frequency is an inherent property of bridge structures during free vibration, which reflects the stiffness and mass distribution of the bridge. Changes in frequency can indicate whether the bridge structure has undergone physical or geometric changes, such as material aging, loose connections, or structural damage. However, frequency alone does not provide detailed information about the nature of these changes. Damping is a parameter that describes the energy dissipation characteristics of bridge vibration. The magnitude of damping is affected by many factors such as material properties, connection methods, and environmental conditions. Changes in damping may indicate material fatigue, loose connections, or changes in environmental conditions. Formation, also known as mode shape, describes the relative displacement of various parts of the bridge during vibration. Changes in formation can reveal local damage or stiffness changes in the bridge structure, because damage often changes the vibration mode of the structure. Formation analysis helps us identify the specific location and extent of damage. The three are actually interrelated. Frequency is the basis for the identification of bridge formation and damping, and the identified bridge formation will be distorted due to the influence of damping. Given the complexity of modal parameter identification, it is important to develop a method for simultaneously identifying the frequency, formation, and damping of a bridge based on the response of a moving vehicle for rapid detection of the health status of the bridge.

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

[0038] 1) Drive the measuring vehicle across the bridge and 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-wheel vehicle. The vertical acceleration sensor is installed on the body and axle of the measuring vehicle. Figure 3 The eight vertical acceleration sensors are respectively installed on the left front part of the vehicle body, the right front part of the vehicle body, the left rear part of the vehicle body, the right rear part 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 also Figure 2 , x, y and z are the three-dimensional coordinate axis system of the bridge model, the vehicle's speed is V, and the eccentric distance from the center of the vehicle to the center of the bridge is e. For the vehicle, it is a seven-degree-of-freedom system, including the vertical (z v ), pitch and swing (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 vehicle body is assumed to be a rigid body with a mass of m v , which is 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 the stiffness k s,ij and damping c s,ij is connected to the vehicle body, and the stiffness and damping between the wheel and the axle contact point are k w,ij and c w,ij The distance between the front wheels (Fl and Fr) and the rear wheels (Rl and Rr) of the vehicle is the vehicle length a. F +a R The distance between the left wheel (Fl and Rl) and the right wheel (Fr and Rr) of the vehicle is the vehicle width b l +b r For a bridge, E is the elastic modulus, G is the shear modulus, and the moment of inertia about the z and y axes is I z and I y J is the torsion constant, m is the mass per unit length of the bridge, c y ,c z , and c θ Respectively represent the vertical, lateral and torsional damping coefficients, u z and u y is the vertical and lateral displacement of the bridge, θ is the torsion angle, ζ is the distance between the shear center S and the bridge centroid C along the z axis, and I α (=m(ζ 2 +r p 2 )), rp is the polar radius of gyration. In the equations that follow, "a glance" means taking the derivative with respect to the coordinate axis x, and "a point" means taking the derivative with respect to time t.

[0040] The measuring vehicle and the bridge form a coupling system, in which the vehicle-bridge coupling system includes vertical, lateral and torsional responses. When the measuring vehicle passes over the bridge, the bridge vibration is transmitted to the measuring vehicle through the wheels, causing the measuring vehicle to vibrate. Therefore, by installing a response acquisition sensor on the measuring vehicle, the vibration response of the bridge can be identified.

[0041] When the measuring vehicle passes through the bridge, Figure 2 The bridge object appearance and bridge vibration response theoretical expressions are:

[0042]

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

[0044]

[0045] where δ represents the Dirkas function, H is the step function, and e ij is the eccentric distance from each wheel contact point to the bridge centerline. Load p ij , the front wheel enters at time t 1 , the rear wheel enters at time t 2 , and the vehicle travel time T on the bridge v yes:

[0046]

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

[0048] Here, g represents the acceleration due to gravity.

[0049] Based on the above control equations, the analytical expressions of 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] By moving the contact relationship between the vehicle and the bridge, the vehicle-bridge contact response theory can be expressed as:

[0056]

[0057] It can be found from formula (7) that the theoretical expression of the vehicle-bridge contact response actually includes the vertical and torsional modes of the bridge, which theoretically shows the feasibility of identifying the bridge frequency, damping, and formation from the moving vehicle-bridge contact response. In addition, formula (7) does not contain the vertical, sway, and pitch frequencies of the vehicle body, which proves the advantage of the vehicle-bridge contact response, that is, the vehicle-bridge contact response can filter out the vehicle frequency interference.

[0058] 2) Perform data processing to eliminate the interference of the vertical frequency and lateral frequency of the vehicle body. This embodiment uses the existing vehicle-bridge contact response algorithm or bridge deck response reconstruction method to eliminate the interference of the vehicle body frequency in the vehicle body, thereby increasing the visibility of bridge modal parameter identification. This step is only used as 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] It can be seen from the above mathematical processing that the vehicle-bridge contact response can be calculated by measuring the acceleration response of the vehicle system itself and its dynamic physical parameters, and has nothing to do with the physical properties of the bridge itself.

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

[0064]

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

[0066] 3.1) Separate the bridge response and identify the corresponding bridge frequency. Using the spatial relationship of the contact point response at the left and right wheels of the mobile vehicle, the vertical and torsional responses of the vehicle-bridge contact point can be separated, and then the Fourier transform can be used to identify the frequency of the vertical response of the bridge and the frequency of the torsional response of the bridge.

[0067] 3.2) Extract the time-frequency ridges of the bridge corresponding to the mode. Use the windowed Fourier transform to process the vertical and torsional responses of the vehicle-bridge contact point obtained in step 3.1) to obtain the time-frequency images of the corresponding responses, and then extract the bridge modal ridges in the aforementioned time-frequency images corresponding to the frequencies obtained in step 3.1).

[0068] 4) Extract bridge damping and fit. The present invention constructs a bridge damping ratio identification formula by using the spatial position relationship of the front and rear wheels of the measuring vehicle at the same position and at different instants, and realizes bridge damping ratio identification based on the vehicle-bridge contact response and combined with the windowed Fourier transform technology. When constructing the bridge damping ratio identification formula below, the torsional response component will be taken as an example.

[0069] In order to identify the bridge damping ratio, the vehicle-bridge contact response (Eq. 9) is separated by windowed Fourier transform processing to separate the bridge modal component of the specific response, that is,

[0070]

[0071] In the formula, It is a constant obtained by processing the signal with the windowed Fourier transform, which is related to the processed signal itself and the selected frequency, and the subscript p represents the front and rear wheels.

[0072]

[0073] Since the distance difference when the front and rear wheels successively pass the same position of the bridge is (a F +a R ), using this spatial position correlation, the damping can be extracted using the Fourier transform ridge at the front and rear wheel contact points:

[0074]

[0075]

[0076] It should be noted that the above formula is still applicable to the vertical damping ratio. 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. It is proposed to use the minimum absolute residual method with zero slope to fit the damping ratio identification result, and finally obtain the bridge damping ratio.

[0077] 5) Extracting bridge formation. The present invention constructs a bridge formation iteration formula by using the spatial position relationship of the front and rear wheels of the measuring vehicle at different positions at the same instant, and realizes bridge formation recognition based on the vehicle-bridge contact response and combined with the windowed Fourier transform technology. When constructing the bridge formation formula below, the torsional response component will be taken as an example.

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

[0079]

[0080] Then use the formation points of step q-1 to iteratively calculate the formation of step q

[0081]

[0082] In the calculation process, it is assumed that Φ 0,θ = 1. It should be noted that the above formula is still applicable to the vertical formation of the bridge, and the process is similar and will not be shown again.

[0083] Embodiment 2:

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

[0085] 1) Drive the measuring vehicle across the bridge and 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-wheel vehicle. The vertical acceleration sensor is installed on the body and axle of the measuring vehicle. The measuring vehicle and the bridge form a coupling system. The vehicle-bridge coupling system includes vertical, lateral and torsional responses. When the measuring vehicle passes over 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) The vehicle-bridge contact response algorithm is used to eliminate the interference of the vehicle body vertical frequency and the vehicle body lateral frequency.

[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 ridges of the corresponding modes of the bridge.

[0090] 4) Extract bridge damping and fit. Use the spatial correlation of the front and rear wheels of the measuring vehicle at different positions at the same instant to identify the discrete data of the damping ratio. Use the minimum absolute residual method with zero slope to fit the damping ratio identification result, and finally get the bridge damping ratio. Use the spatial correlation of the front and rear wheels of the four-wheel vehicle at different positions at the same instant to use the damping ratio identification formula to extract the nth order torsional response damping ratio ξ of the bridge. bθ,n :(Here only the identification of torsional damping ratio is shown. The vertical response damping ratio can be obtained similarly by replacing all torsional terms in the formula with vertical terms)

[0091]

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

[0093] The bridge damping ratio ξ calculated using formula (1) is bθ,n The result is discrete data and unstable. It is proposed to use the minimum absolute residual method with zero slope to fit the damping ratio identification result, and finally get the bridge damping ratio.

[0094] 5) Extract the bridge formation. The bridge formation is iteratively reconstructed using the spatial correlation of the front and rear wheels at the same position at different moments. The nth-order torsion formation of the bridge can be extracted using the formation reconstruction iteration formula using the spatial correlation of the front and rear wheels of the four-wheeled vehicle at the same position at different moments: (Here only the identification of the torsion formation is shown. The bridge formation with vertical response can be similarly obtained by replacing all the torsion terms in the formula with vertical terms)

[0095]

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

[0097] Embodiment 3:

[0098] The main contents of this embodiment are the same as those of Embodiment 2, wherein eight vertical acceleration sensors are respectively installed on the left front part of the vehicle body, the right front part of the vehicle body, the left rear part of the vehicle body, the right rear part 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.

[0099] Embodiment 4:

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

[0101] Embodiment 5:

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

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

[0104] Assume that the vertical and torsional damping ratios of the bridge are both 0.5%, the vehicle's travel speed V is 5m / s, and its travel eccentric distance e is 1.75m.

[0105] In order to verify that the method of the present invention can be used to identify the vertical and torsional frequencies, damping ratio and formation of the bridge from the vehicle-bridge contact response, numerical simulations were performed: Figure 4 4a is a time domain and frequency domain diagram of the vehicle-bridge contact point obtained by the sensor arrangement based on the method of the present invention, 4b is a time domain diagram of the vehicle-bridge contact point response, and 4b is a frequency domain diagram of the vehicle-bridge contact point response. Figure 5 5a is a vertical frequency domain diagram of the vehicle-bridge contact point response, and 5b is a torsional frequency domain diagram of the vehicle-bridge contact point response. Figure 6 These are time-frequency images of the vertical and torsional responses of the bridge obtained by windowed Fourier transform based on the method of the present invention, 6a is the vertical contact point response time-frequency diagram obtained from the front wheel, 6b is the vertical contact point response time-frequency diagram obtained from the rear wheel, 6c is the torsional contact point response time-frequency diagram obtained from the front wheel, and 6d is the torsional contact point response time-frequency diagram obtained from the rear wheel. Figure 7 The time-frequency ridge line of the first-order vertical and first-order torsional component responses of the bridge obtained based on the method of the present invention for identification of the bridge damping ratio is Figure 8 The identification results of the vertical and torsional damping ratios of the bridge obtained based on the method of the present invention are: Fig. 9 The time-frequency ridges of the first two-order vertical and first-order torsion component responses of the bridge for bridge formation identification obtained based on the method of the present invention are: Fig.10 It is the recognition result of the vertical and torsional formation of the bridge obtained based on the method of the present invention.

[0106] from Figure 5 , Figure 8 and Fig.10 It can be seen that the proposed technology can be successfully applied to the identification of bridge vertical and torsional frequencies, damping ratios and formations, and the identified bridge frequencies, damping ratios and formations have high recognition accuracy.

Claims

1. A method for synchronously identifying bridge frequency, damping ratio and vibration mode based on moving vehicle response, characterized in that: The following steps are involved: 1) Drive the measuring vehicle across the bridge and collect the vertical vibration response of the vehicle body and the vertical vibration response of the wheels during the driving process of the measuring vehicle; the measuring vehicle is a four-wheel vehicle; the vertical acceleration sensor is installed on the body and axle of the measuring vehicle; the measuring vehicle and the bridge form a coupling system; the vehicle-bridge coupling system includes vertical, lateral and torsional responses; when the measuring vehicle drives over 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 vertical frequency and lateral frequency of the vehicle body; 3) Separating and identifying bridge responses; Step 3) specifically includes the following sub-steps: 3.1) Separate the bridge response and identify the corresponding bridge frequency; 3.2) Extract the time-frequency ridges of the corresponding modes of the bridge; 4) Extract bridge damping and fit it; use the attenuation characteristics of the front and rear wheels of the measuring vehicle at different instants at the same position to identify the discrete data of the damping ratio; use the minimum absolute residual method with zero slope to fit the damping ratio identification result, and finally obtain the bridge damping ratio; 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.

2. The method for synchronously identifying bridge frequency, damping ratio and vibration mode based on the response of a moving vehicle according to claim 1, characterized in that: The eight vertical acceleration sensors are respectively installed on the left front portion of the vehicle body, the right front portion of the vehicle body, the left rear portion of the vehicle body, the right rear portion 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.

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

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

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

6. The method for synchronously identifying bridge frequency, damping ratio and vibration mode based on moving vehicle response according to claim 1 is characterized in that: In step 5), the spatial correlation between the front and rear wheels of the four-wheel vehicle at different positions at the same instant is used to extract the nth order torsional formation of the bridge using the formation reconstruction iteration as shown in the following formula; In the formula, represents the ratio of the time-frequency ridge amplitude at the front and rear wheels; assuming Φ 0,θ =1, and use formula (2b) to iteratively calculate the bridge formation.

Images