CN111781001A - Identification method of bridge damping ratio based on vehicle-bridge coupling - Google Patents

Abstract

The invention belongs to the technical field of building structure damage identification, and particularly relates to a bridge damping ratio identification method based on axle coupling, which comprises the following steps: the method comprises the following steps that firstly, acceleration response signals of each point of a bridge are collected by a moving test vehicle according to a certain sampling frequency; step two, filtering the acceleration response signal of the step one through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge; step three, assuming a damping ratio and the original frequency omega of the bridge₁Knowing, an exponential function can then be obtained

Then, the filtered acceleration response of the second step is divided by the exponential function, and the filtered acceleration response of the undamped bridge can be obtained; step four, passing shortAnd (3) acquiring the mode of the signal processed in the step three by using a time-frequency domain decomposition method, and judging whether the assumed damping ratio is the real damping ratio by judging whether the maximum value of the mode is in the middle point of the mode. Compared with the prior art, the method has the advantages that the identification result of the bridge damping ratio is better, and the operation is convenient.

Description

Identification method of bridge damping ratio based on vehicle-bridge coupling

technical field

The invention belongs to the technical field of building structure damage identification, in particular to a bridge damping ratio identification method based on vehicle-bridge coupling.

Background technique

As an important part of national traffic engineering, bridges play a vital role in the social and economic development of our country. If the bridge fails unexpectedly for some reason, it may cause property damage and even heavy casualties. Therefore, it is particularly important to understand the damage characteristics of bridges from the perspective of structural safety. The current bridge health monitoring method is to directly arrange sensors on the bridge to be tested to obtain bridge parameters, which is called direct measurement method, but this method has sensors It is prone to aging and damage during continuous measurement, and at the same time, it is time-consuming and labor-intensive, hindering traffic, and costing a lot of disadvantages.

Based on the shortcomings of direct testing, Yang Yongbin et al. proposed a mobile intelligent bridge detection method in 2004, that is, the test vehicle runs on the bridge, based on the signal processing collected by the sensors on the test vehicle, the indirect measurement idea of identifying bridge parameters and identifying damage came out as the times require . After that, scholars from all over the world have applied this method to the identification of parameters such as bridge frequency, mode, and damping, and finally identified bridge damage. Yang et al. extracted the most basic parameter of the bridge—frequency based on the research basis of vehicle-bridge coupling. The team introduced empirical mode decomposition (EDM) to generate intrinsic mode functions (IMFs), and finally performed fast Fourier transform (FFT) on it to successfully identify frequencies, and then improved the frequency identification effect by introducing singular spectrum analysis bandpass filtering, etc. At the same time, based on the adverse effect of roughness on the recognition effect and the characteristics of the mobile smart vehicle measurement method, Yang et al. proposed to use two test vehicles to pass the same road twice, and then perform signal subtraction to reduce the impact of road roughness. In addition, The research team proposed to use the vehicle-bridge contact point signal to extract the bridge frequency, and the results show that the contact point response can better extract the bridge frequency. Since then, researchers have begun to try to identify another parameter of the bridge - the mode. In 2014, Professor Yang's team successfully extracted the bridge mode by constructing the instantaneous amplitude through the Hilbert transform (HT) of the vehicle body response. The concept of decomposition constructs the bridge modes from local to whole segment and step by step. Li and Au et al. improved the mode identification method proposed by Yang et al. By applying excitation on the vehicle body to increase the bridge response and improve anti-noise so as to improve the mode recognition effect. Bridge damping - another important parameter in bridge health monitoring, many studies have pointed out that damping may be more sensitive to bridge damage. Obrien and coworkers proposed a method to detect changes in bridge damping using a vehicle-trailer vehicle system. This method requires a large number of repeated simulations and lacks a clear theoretical basis. Gonzalez et al. proposed a six-step algorithm for identifying bridge damping from the body response of a two-degree-of-freedom detection vehicle, and used an iterative method to identify bridge damping more accurately. Zhang Bin et al. obtained the contact point signal through the signals measured by the acceleration sensor and the displacement sensor installed on the two-axis mobile test vehicle, which were used to identify the bridge damping ratio, but lacked experimental verification.

The above content describes the identification process of bridge parameters, but the identification method of damping ratio is not yet mature.

SUMMARY OF THE INVENTION

In view of the above deficiencies in the prior art, the present invention provides a bridge damping ratio identification method based on vehicle-bridge coupling, which has better identification results and is easy to operate.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions:

The identification method of bridge damping ratio based on vehicle-bridge coupling includes the following steps:

Step 1. Use the mobile test vehicle to collect the acceleration response signal of each point of the bridge at a certain sampling frequency;

Step 2: Filter the acceleration response signal of Step 1 through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge;

的数值，然后将步骤二滤波后的加速度响应除以该指数函数，即可获得无阻尼桥梁滤波后的加速度响应；Step 3. Assuming a damping ratio and the original bridge frequency ω ₁ is known, the exponential function can be obtained

, and then divide the filtered acceleration response in step 2 by the exponential function to obtain the filtered acceleration response of the undamped bridge;

Step 4. Obtain the modal of the signal processed in step 3 through the short-time frequency domain decomposition method, and judge whether the assumed damping ratio is the real damping ratio by identifying whether the maximum value of the modal is at the modal midpoint. If the maximum value is at the midpoint of the mode, the assumed damping ratio can be used as the real damping ratio of the bridge, otherwise a damping ratio is assumed again until the maximum value of the mode is at the midpoint of the mode, and the bridge damping ratio is finally identified.

Further, the upper limit of the band-pass filter in step 2 is

Further, the lower limit of the bandpass filter in step 2 is

Further, the sampling frequency of the test vehicle in step 1 is 100 Hz.

Further, the test vehicle in step 1 is a single-degree-of-freedom vehicle.

Further, the mass of the test vehicle in step 1 is 1000kg.

Further, the speed of the test vehicle in step 1 is always 1 m/s.

Compared with the prior art, the invention has better identification results of the bridge damping ratio and is easy to operate.

Description of drawings

Fig. 1 is the flow chart of the bridge damping ratio identification method based on vehicle-bridge coupling of the present invention;

2 is a simplified model diagram of a double-axle system based on a vehicle-axle coupling-based bridge damping ratio identification method of the present invention;

3 is a schematic diagram of the number of elements and nodes in the bridge model of the bridge damping ratio identification method based on vehicle-bridge coupling according to the present invention;

FIG. 4 is a time-domain signal diagram of a test vehicle sensor collection based on a vehicle-bridge coupling-based bridge damping ratio identification method of the present invention;

Fig. 5 is the time domain signal diagram after filtering the collected signal of the bridge damping ratio identification method based on vehicle-bridge coupling of the present invention;

6 is a filtered time-domain signal diagram of the bridge damping ratio identification method based on vehicle-bridge coupling of the present invention divided by the attenuation signal;

Fig. 7 is the fitting modal diagram of the bridge damping ratio identification method based on vehicle-bridge coupling of the present invention;

8 is a fitting modal diagram after symmetrical processing of the bridge damping ratio identification method based on vehicle-bridge coupling according to the present invention;

Fig. 9 is the identification result diagram of different assumed damping ratios under the A-level roughness of the bridge damping ratio identification method based on vehicle-bridge coupling of the present invention;

10 is a diagram showing the identification results of different assumed damping ratios under the B-level roughness of the bridge damping ratio identification method based on vehicle-bridge coupling of the present invention;

11 is a diagram showing the identification result of the damping ratio of the bridge damping ratio identification method based on vehicle-bridge coupling under 50db;

12 is a diagram showing the identification result of the damping ratio of the bridge damping ratio identification method based on vehicle-bridge coupling under 40db;

FIG. 13 is a diagram showing the identification result of the damping ratio of the bridge damping ratio identification method based on vehicle-bridge coupling under 30db.

Detailed ways

In order to enable those skilled in the art to better understand the present invention, the technical solutions of the present invention are further described below with reference to the accompanying drawings and embodiments.

As shown in FIG. 1 , the method for identifying bridge damping ratio based on vehicle-bridge coupling of the present invention includes the following steps:

Step 1. Use the mobile test vehicle to collect the acceleration response signal of each point of the bridge at a certain sampling frequency;

Step 2: Filter the acceleration response signal of Step 1 through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge;

的数值，然后将步骤二滤波后的加速度响应除以该指数函数，即可获得无阻尼桥梁滤波后的加速度响应；Step 3. Assuming a damping ratio and the original bridge frequency ω ₁ is known, the exponential function can be obtained

, and then divide the filtered acceleration response in step 2 by the exponential function to obtain the filtered acceleration response of the undamped bridge;

Step 4. Obtain the modal of the signal processed in step 3 through the short-time frequency domain decomposition method, and judge whether the assumed damping ratio is the real damping ratio by identifying whether the maximum value of the modal is at the modal midpoint. If the maximum value is at the midpoint of the mode, the assumed damping ratio can be used as the real damping ratio of the bridge, otherwise a damping ratio is assumed again until the maximum value of the mode is at the midpoint of the mode, and the bridge damping ratio is finally identified.

As a preferred solution, the upper limit of the band-pass filter in step 2 is

As a preferred solution, the lower limit of the band-pass filter in step 2 is

As a preferred solution, the sampling frequency of the test vehicle in step 1 is 100 Hz.

As a preferred solution, the test vehicle in step 1 is a single-degree-of-freedom vehicle.

As a preferred solution, the mass of the test vehicle in step 1 is 1000kg.

As a preferred solution, the speed of the test vehicle in step 1 is always 1m/s.

In Figure 2, the test vehicle and the tractor with a distance of ΔL travel on the bridge at a constant speed v. The test vehicle and the tractor are simplified to the moving spring masses m _v,2 and m _v,1 supported on them, the buffers with damping coefficients cv2, cv1 and springs with stiffness kv2, kv1. The bridge is a simple support of length L, mass per unit length m* and bending stiffness EI (nth order damping ratio), where bending stiffness EI includes the effect of non-structural members such as bridge railings and bridge decks in real bridges The sidewalk and mass per unit length m* can be obtained from actual bridge design data or estimated from the cross-sectional area step. The bridge is assumed to be stationary until the test vehicle arrives.

The equation of motion of the vehicle-axle coupling system can be written as:

where u(x,t) represents the vertical displacement of the bridge structure from the left support point x, u _v1 (t), u _v2 (t) are the test vehicle and the tractor from their static equilibrium position and time t _a = t + ΔL/v=t+t _s The static displacement measured at the beginning, it should be noted that the time t refers to the time after the vehicle enters the bridge. The dotted character represents the derivative with respect to time t and coordinate x. The interaction forces f _c1 (t) and f _c2 (t) of the contact point between the test vehicle and the tractor and the platform can be written as:

g is the acceleration of gravity

The bridge displacement can be expressed as:

Assuming that the vehicle mass mv1, mv2 is much smaller than the mass of the bridge deck, m _v1 << m ^* L and m _v2 << m ^* L, this assumption is easy to realize for a practical bridge. By substituting equation (6) into equation (3), multiplying by sin(nπx/L), and integrating from 0 to L, the nth modal equilibrium equation of the structure can then be calculated from the quadrature condition of the sine function written as:

ω _n is the nth angular frequency of the bridge deck

For zero initial conditions, the generalized coordinates qn( _t ) of the bridge can be obtained from equation (7) as:

Substituting formula (9) into formula (6), the bridge displacement is obtained as:

Substituting equation (10) into equation (1) also yields the displacement u _v1 (t) of the test vehicle.

和

的带通滤波器。产生的信号是来自桥梁结构第n个振动模式的瞬态响应，该瞬态响应与方程式(10)的最后一项直接相关。In fact, the response components related to the nth modal frequency of the bridge can be separated from the response of the test vehicle. In this study, the upper and lower limits were used as

and

bandpass filter. The resulting signal is the transient response from the nth vibration mode of the bridge structure, which is directly related to the last term of equation (10).

Substituting the last term of equation (10) into equation (1), the vehicle displacement related to the shape of the nth mode of the bridge deck (11) can be obtained as:

In the above formula, the damping ratio of the test vehicle is ξ _v1 =c _v1 /(2m _v1 ω _v1 ), in addition

In the modified direct stiffness method, only a single vibration mode of the bridge deck needs to be used for damage identification. Since accurate high frequency vibration modes cannot be guaranteed in the field, unless otherwise stated, frequencies and modes in the following discussion refer to the first vibration mode of the bridge deck. The response component R1 of the test vehicle related to the first vibration mode of the bridge deck can also be written as:

The coefficients A1 to A2 can be determined by comparing the terms in equations (9) and (10),

The corresponding acceleration response components of the first vibration mode of the bridge deck can also be obtained by:

Observation formula (16): when ξ ₁ =0,

This formula is the acceleration response component of the first vibration mode of the undamped bridge deck. Then the relationship between them is

That is, the ratio of the acceleration response obtained by the damped bridge to the acceleration response of the undamped bridge is an exponential function. Using this relationship, a method for identifying the damping ratio can be proposed.

In order to verify the correctness of the above theory, the feasibility of the method is verified under the condition of no roughness on a bicycle. Numerical simulation is carried out using finite element to verify the reliability of the method. In this numerical simulation, the bridge length is 30 meters, the mass per unit length m ^* =19116kg, the cross-sectional area A= ^7.965m2 , the cross-sectional inertia moment Ix=2.959m4, the bridge elastic modulus E=2.9×1010N/m2, and the mass of the test vehicle 1000kg, the vehicle speed is constant 1m/s, the sampling frequency is 100Hz, and the real damping ratio of the bridge is assumed to be 0.01.

When using the short-time frequency domain decomposition method to extract the modes, the bridge is divided into 10 units, which are E1~E10, as shown in Figure 3, and the remaining numbers are the unit node numbers (j=1,2,...,11) , it should be noted that the nodes of the mode obtained by the present invention are 2 to 10, and nodes 1 and 11 are exactly the positions of the bridge entry and exit. The invention does not consider the nodal modal values of edge elements.

为常数，利用上述滤波后信号除以该衰减系数得到图6信号图，同时采用短时频域分解法获取图7模态信号，观察图6信号可知，与无桥梁阻尼相比，前半段基本吻合，越往后，信号结果越差，这也导致图7信号在尾端出现失真现象，这是因为桥梁阻尼至桥梁后半段衰减作用更强，桥频信号可能衰减殆尽，所以相除后还原效果不好，此时采用部分信号对称的做法获得图8的模态，发明人通过大量数值模拟得出图8结果，当假定阻尼比为0.01时(此时正好为真实阻尼比)，模态最大值居中，当假定的阻尼比为0.0092时(此时小于真实阻尼比)，该模态最大值偏左，即出现左偏，当假定的阻尼比为0.0107时(此时大于真实阻尼比)，该模态最大值偏右，即出现右偏，而当假定阻尼比处于0.0092-0.0107之间时，此时左偏右偏现象不明显，均可作为真实阻尼比，此时该方法的最大误差为

处于误差范围内。可以得知在单车无外界信号干扰下的识别结果很好。但实际情况下外界各类影响还是存在的。Figure 4 is the acceleration time-domain signal diagram obtained by the test vehicle driving on the bridge at the sampling frequency of 100Hz (the signal contains the vehicle frequency and bridge frequency information at this time), and then filtered by the band-pass filter to obtain the acceleration of the first-order frequency of the bridge Signal. As shown in Figure 5, a damping ratio is assumed at this time, and the actual damping ratio is assumed to be 0.01, then the attenuation coefficient

is a constant, the signal diagram in Figure 6 is obtained by dividing the above filtered signal by the attenuation coefficient, and the short-time frequency domain decomposition method is used to obtain the modal signal in Figure 7. Observing the signal in Figure 6, it can be seen that compared with no bridge damping, the first half is basically match, the further back, the worse the signal result, which also leads to the distortion of the signal in Figure 7 at the tail end, this is because the bridge damping to the second half of the bridge has a stronger attenuation effect, and the bridge frequency signal may be attenuated completely, so divide The post-reduction effect is not good. At this time, the mode of Fig. 8 is obtained by the method of partial signal symmetry. The inventor obtained the result of Fig. 8 through a large number of numerical simulations. When the damping ratio is assumed to be 0.01 (this is exactly the real damping ratio), The modal maximum value is centered. When the assumed damping ratio is 0.0092 (at this time, it is smaller than the real damping ratio), the modal maximum value is left, that is, left deviation occurs. When the assumed damping ratio is 0.0107 (at this time, it is greater than the real damping ratio), the modal maximum value is to the right, that is, right deviation occurs, and when the assumed damping ratio is between 0.0092-0.0107, the phenomenon of left deviation to right deviation is not obvious at this time, which can be used as the real damping ratio. At this time, the method The maximum error is

within the margin of error. It can be seen that the recognition result of the bicycle without external signal interference is very good. But in reality, various external influences still exist.

The above is the conclusion drawn by the inventor based on the fact that the real damping ratio is 0.01. In order to obtain the applicable range of the damping ratio that can be identified by this method, the inventor has obtained through a large number of numerical simulations that when the real damping ratio is less than or equal to 0.02, This method can effectively identify the damping ratio, but the reason why the real damping ratio is greater than 0.02 cannot be identified is as described above. When the real damping ratio is larger, the bridge signal attenuates faster, that is, the mode identification effect at the back end of the signal is worse. . In conclusion, this method is suitable for the identification of small damping less than or equal to 0.02.

About the effect of roughness

The actual bridge pavement has unevenness, so the roughness of the present invention is simulated by the functional density function suggested by the ISO 8608 (1995) standard [36]. Its functional density function G _d (n) is as follows:

In the formula, n is the spatial frequency per unit length, w is a constant 2, n ₀ is 0.1 cycle/m, and G _d (n ₀ ) is the displacement function density function value, which is determined by the road surface roughness grade. The square root of the geometric mean value of the function value provided by the ISO 8608 (1995) standard, that is, the functional density function G _d (n ₀ ) of the road surface roughness displacement at all levels is as follows:

Class A: G _d (n ₀ )=4×10 ⁻⁶ m ³ ; Class B: G _d (n ₀ )=8×10 ⁻⁶ m ³ ; Class C: G _d (n ₀ )=16×10 ^{− 6} m ³

The displacement amplitude value d of the pavement roughness at all levels of roughness can be expressed as:

where Δn is the sampling interval of the spatial frequency

Then, the cosine functions of different spatial frequencies are superimposed to simulate the road surface roughness r(x), which can be expressed as:

where ns _,i is the spatial frequency of roughness, d _i and θ _i are the amplitude and random phase angle of roughness, respectively.

In order to study the identification of bridge damping ratio under the influence of roughness, this numerical simulation adopts the method proposed by Yang Yongbin et al. to use two test vehicles to pass through the same road twice, and then perform signal subtraction to reduce the influence of road roughness. method. Among them, the mass of the large test car is 2000kg and the stiffness is 20000N/m, and the mass of the small test car is 1000kg and the stiffness is 10000N/m. The determination of the damping identification accuracy under the roughness of grade A, grade B and grade C is studied respectively. And assume that the real damping ratio of the bridge is 0.01. Then assume a series of damping ratios and use the above method to identify the real damping ratio. The recognition result is shown in Figure 9-10.

符合误差范围。It can be seen from Figure 9 and Figure 10 that under the roughness of grades A and B, when the damping ratio is assumed to be exactly the real damping ratio, or near the real damping ratio, the modal maximum value is at the modal midpoint, and when It is assumed that when the damping ratio deviates from the real damping relatively large, there will be different degrees of left deviation or right deviation, that is, the maximum value is not at the midpoint of the mode. As shown in Figure 9, under the B-level roughness, when the damping ratio is assumed to be 0.0095-0.0103, the modal maximum value is at the modal midpoint, and when the damping ratio is assumed to be less than 0.0095, there will be left When the damping ratio is assumed to be greater than 0.0103, there will be a right-bias phenomenon. This phenomenon can also help us how to assume the damping ratio, so as to identify the real damping ratio more efficiently, and the maximum error at this time is

within the margin of error.

The identification result of the damping ratio is not ideal under the C-level roughness. This is because the roughness is too large at this time, and the effect of reducing the roughness by signal subtraction is not ideal, so the roughness elimination is not ideal. In addition, the roughness is too large. The acquisition of the terminal signal is not ideal (this is also the reason for the partial symmetry processing in the method introduction), so that the ideal modal signal cannot be obtained, and the damping ratio is therefore not ideal for identification.

About the effect of noise

In practical applications, the signal collected by the acceleration sensor will inevitably be interfered by noise. In order to explore the effectiveness of the damping ratio identification method under noise interference, the present invention adds Gaussian white noise to the acceleration signal obtained in the numerical simulation. To study the noise resistance of the method, and use the signal-to-noise ratio as an indicator, the signal-to-noise ratio is defined as follows:

In the formula: N is the number of data points, _yi is the acceleration response of the test vehicle with noise at the i-th moment, σ _i is the noise value at the i-th moment, and SNR is the signal-to-noise ratio, in dB. The smaller the impact of noise, the lower the degree of signal interference, the smaller the value, the greater the impact of noise, the greater the degree of signal interference.

The present invention assumes that the real damping ratio is 0.01, and then assumes the damping ratio of 0.01 plus the interference of noise, so as to analyze the error of the identification result. The simulation was set up to study the effect of noise at a roughness class A, and numerically simulate the noise at each level, taking its value to obtain modal mode shape identification.

符合误差范围。而随着信噪比越小，噪音干扰越大，该方法同样能够很好地识别阻尼比，而且识别精度更加准确。但是信噪比小于或等于20db时，此时噪音的干扰已经较大，此时识别的结果较差，这也就说明该方法识别阻尼比有一定的抗噪性。This simulation plots the modal results of damping ratio identification under three different noise levels. It can be seen from Figure 11, Figure 12 and Figure 13 that: when the signal-to-noise ratio is 50db, when the assumed damping ratio is 0.091-0.0108, then The modal maximum value is all at the modal midpoint, and when the assumed damping ratio is less than or equal to 0.0091, the modal maximum value is not at the modal midpoint, that is, a left-bias phenomenon occurs. When the assumed damping ratio is greater than When 0.0108, there will be a right-bias phenomenon, and the maximum error at this time is

within the margin of error. With the smaller the signal-to-noise ratio, the greater the noise interference, the method can also identify the damping ratio well, and the identification accuracy is more accurate. However, when the signal-to-noise ratio is less than or equal to 20db, the interference of noise is already large at this time, and the recognition result is poor at this time, which means that the method has a certain anti-noise performance for the recognition damping ratio.

Based on the above numerical simulation results, under the influence of roughness and noise, under the roughness of grades A and B, when the signal-to-noise ratio is greater than or equal to 30db, the identification result of the damping ratio is better, so this method can identify the damping ratio.

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 the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be Modifications or equivalent substitutions without departing from the spirit and scope of the technical solutions of the present invention should be included in the scope of the claims of the present invention.

Claims (7)

1. The bridge damping ratio identification method based on vehicle-bridge coupling is characterized in that, comprises the following steps: Step 1. Use the mobile test vehicle to collect the acceleration response signal of each point of the bridge at a certain sampling frequency; Step 2: Filter the acceleration response signal of Step 1 through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge; Step 3. Assuming a damping ratio and the original bridge frequency ω ₁ is known, the exponential function can be obtained

, and then divide the filtered acceleration response in step 2 by the exponential function to obtain the filtered acceleration response of the undamped bridge; Step 4. Obtain the modal of the signal processed in step 3 through the short-time frequency domain decomposition method, and judge whether the assumed damping ratio is the real damping ratio by identifying whether the maximum value of the modal is at the modal midpoint. If the maximum value is at the midpoint of the mode, the assumed damping ratio can be used as the real damping ratio of the bridge, otherwise a damping ratio is assumed again until the maximum value of the mode is at the midpoint of the mode, and the bridge damping ratio is finally identified. 2. the bridge damping ratio identification method based on vehicle-bridge coupling according to claim 1, is characterized in that: in step 2, the upper limit value of band-pass filter is

3. the bridge damping ratio identification method based on vehicle-bridge coupling according to claim 2, is characterized in that: in step 2, the lower limit of bandpass filter is

4 . The bridge damping ratio identification method based on vehicle-bridge coupling according to claim 3 , wherein the sampling frequency of the test vehicle in step 1 is 100 Hz. 5 . 5 . The bridge damping ratio identification method based on vehicle-bridge coupling according to claim 4 , wherein the test vehicle in step 1 is a single-degree-of-freedom vehicle. 6 . 6 . The bridge damping ratio identification method based on vehicle-axle coupling according to claim 5 , wherein the mass of the test vehicle in step 1 is 1000kg. 7 . 7 . The bridge damping ratio identification method based on vehicle-axle coupling according to claim 6 , wherein the vehicle speed of the test vehicle in step 1 is always 1 m/s. 8 .

Images