A bridge modal identification method based on blind source separation of moving vehicle acceleration response

Abstract

The present invention discloses a bridge modal identification method based on blind source separation of mobile vehicle acceleration response, and belongs to the technical field of state detection and evaluation of transportation infrastructure. It includes: obtaining the vertical acceleration response of the vehicle-bridge contact point based on the vehicle-bridge coupling theory and the measured vehicle acceleration response; analyzing the relationship between the bridge deck unevenness effect contained in the vehicle-bridge contact point response and the bridge response signal; using the blind source separation method to process the contact point acceleration signal according to the relationship between the bridge deck unevenness signal and the bridge response signal; analyzing the signal after blind source separation, and obtaining the response signal required for modal identification according to the characteristics of the bridge vibration signal; and identifying the modal frequency and vibration mode of the bridge based on the required signal for modal identification obtained above. The present invention effectively filters out the influence of bridge deck unevenness on bridge modal identification, and the signal acquisition is convenient. In addition, the signal separation process does not require relevant information of the source signal, and the frequencies and vibration modes of the bridge are identified with high accuracy.

Description

Technical Field

[0001] The invention relates to a bridge modal recognition method based on blind source separation of mobile vehicle acceleration response, and belongs to the technical field of state detection and evaluation of traffic infrastructure. Background Art

[0002] The construction of transportation infrastructure promotes the national economic and social development. With the increasing number of highway bridges in my country, the condition of bridge structures and the safety of operation have received widespread attention. As the operation time increases, bridges are constantly subjected to vehicle loads, wind loads, temperature loads, etc., and the structural performance gradually degrades to a certain extent, and is damaged compared to the initial design. The modal parameters of bridges can be used to judge the condition of bridge structures in bridge monitoring and detection.

[0003] At present, bridge inspection technologies can be mainly divided into manual visual inspection, non-destructive testing technology, load testing and health monitoring systems. These methods are affected by personal subjective factors, require traffic closure during the test, and consume a lot of manpower and material resources. The health monitoring system can realize real-time monitoring of the bridge status, but it requires a large number of sensors and has the characteristics of one bridge and one system. It is very expensive and difficult to promote to small and medium-sized bridges.

[0004] The indirect measurement method based on vehicle response can avoid the drawbacks of the above methods. The sensor is installed on the vehicle, which saves the number of sensors required compared to installing a large number of sensors on the bridge. When the vehicle passes over the bridge, the vehicle and the bridge form a coupled vibration system that affects each other. Therefore, the vehicle response measured by the sensor contains the vibration information of the bridge structure. Therefore, when the bridge is damaged, the vehicle response will also be affected. The bridge vibration signal can be separated from the vehicle response, and the modal information of the bridge can be identified based on it to determine the change in the structural state of the bridge. The presence of bridge deck unevenness will affect the identification of bridge modal parameters. Therefore, filtering out the influence of bridge deck unevenness in bridge vibration information is extremely critical for bridge modal identification. Existing methods for filtering out the influence of bridge deck unevenness can identify bridge frequencies, but the high-order recognition accuracy is poor. Summary of the invention

[0005] Based on the above problems, the present invention provides an accurate and efficient bridge modal identification method based on mobile vehicle response and blind source separation for filtering out the influence of bridge deck unevenness in the process of indirect detection of bridge dynamic characteristics by mobile vehicles, so as to solve the problems existing in the prior art.

[0006] A bridge modal recognition method based on blind source separation of moving vehicle acceleration response, the bridge modal recognition method based on blind source separation of moving vehicle acceleration response comprises the following steps:

[0007] Step 1: Based on the vehicle-bridge coupling theory, the vertical acceleration response of the vehicle-bridge contact point is obtained through the measured dynamic response of the vehicle body;

[0008] Step 2: Analyze the relationship between the bridge deck roughness effect and the bridge response signal in the vehicle-bridge contact point response;

[0009] Step 3: According to the relationship between the bridge deck roughness signal and the bridge response signal, the contact point acceleration signal is processed using the blind source separation method;

[0010] Step 4: Analyze the signal after blind source separation, and select the response signal required for bridge modal identification according to the characteristics of the bridge vibration signal;

[0011] Step 5: Identify the modal frequency and vibration shape of the bridge by performing frequency domain transformation and Hilbert transform on the signals required for modal identification.

[0012] Furthermore, in step 1, specifically, it is assumed that the vehicle mass is much smaller than the bridge mass, the influence of damping is not considered, the vehicle travels at a constant speed on the simply supported beam, and the vehicle model mass is m v , the spring stiffness is k v , speed is v; bridge length is L, material elastic modulus is E, section moment of inertia is I, unit length mass The vertical acceleration response of the axle contact point is calculated using the following formula:

[0013]

[0014] Among them, Δ st,n is the nth modal static displacement of the bridge caused by the vehicle, which is:

[0015]

[0016] S n is the dimensionless vehicle speed parameter, which is:

[0017]

[0018] In actual measurement, the response at the contact point between the vehicle tire and the bridge cannot be directly measured, but the vehicle acceleration can be used to estimate it.

[0019]

[0020] In the formula, the second derivative of vehicle body velocity with respect to time is calculated using the central difference method:

[0021]

[0022] Furthermore, in step 2, specifically, a simplified model of two vehicles crossing a bridge is established, the distance between the two vehicles is ΔL, and the parameters are selected the same as above, and the subscripts 1 and 2 are used to distinguish the two vehicles. The motion equations of the bridge and the two vehicles are:

[0023]

[0024]

[0025]

[0026] In the above formula, δ is the Dirac function, is the second derivative of the bridge displacement with respect to time, u″″(x,t) represents the fourth derivative of the bridge displacement with respect to the vehicle position x, and q v (t) represents the displacement of the vehicle relative to the equilibrium position, f c (t) is the vehicle-bridge interaction force. When the unevenness of the bridge deck is considered to be r(x), the modal synthesis method is used to solve it. Based on the assumption, the effect of vehicle inertia is ignored, and the following is obtained:

[0027]

[0028] It is concluded that under the assumed conditions, the bridge deck unevenness signal is uncorrelated with the bridge vibration signal, and the displacement responses of the contact points between the tires of the two vehicles and the bridge at time t are:

[0029] u c,1 =u(vt,t)+r(vt) (10)

[0030] u c,2 =u(vt+ΔL,t)+r(vt+ΔL) (11)

[0031] That is, the displacement of the vehicle-bridge contact point is the linear superposition of the bridge displacement and the bridge deck unevenness, that is, the acceleration response of the vehicle-bridge contact point is the linear superposition of the bridge vibration and the bridge deck unevenness effect, and the vehicle-bridge contact point responses of the two vehicles at the same position are equally affected by the bridge deck unevenness.

[0032] Further, in step 3, the following steps are specifically included:

[0033] Step 31: Take two or more groups of axle contact point acceleration response signals as observation signals, represented by x(t), which is composed of source signals s(t) through linear aliasing, that is, x(t) = As(t), where,

[0034] x(t)=[x1(t),x2(t),…,x m (t)] T ,s(t)=[s1(t),s2(t),…,s n (t)]T , A is the mixing matrix of the m×n order system;

[0035] Step 32: Using the second-order blind source separation algorithm, first pre-whiten the observed signal x(t), and estimate the zero time delay correlation matrix from the observed signal, i.e., R xx (0) = E[x(t)x T (t)]; for R xx (0) Perform singular value decomposition, that is, R xx (0) = UΛU T , then the pre-whitening matrix W is an n×m-dimensional whitening matrix, and the signal after pre-whitening becomes z(t)=Wx(t);

[0036] Step 33: Define the delay correlation matrix R s (τ) = E[s(t)s T (t+τ)],R z (τ)=E[z(t)z T (t+τ)]. Let τ be a set of different values ​​τ1,τ2,…τ p , and obtain a set of R z (τ i ), i = 1 ~ p. From z(t) = Qs(t), we get R Z (τ i )=QR S (τ i )Q T ,i=1~p. S (τ i )=Q T R Z (τ i )Q,i=1~p;

[0037] Step 34: R Z (τ i ) to obtain Q by joint diagonalization approximation, thus obtaining A = W -1 Q, unmixing matrix B = Q T W, estimated source signal y(t)=Bx(t);

[0038] Step 35: When two groups of vehicle-bridge contact point response signals are taken as observation signals, one of the two groups of original signals estimated by the SOBI algorithm is a bridge vibration response signal that does not include bridge unevenness.

[0039] Furthermore, in step 4, the following steps are specifically included:

[0040] Step 41, two groups of vehicle-bridge contact point responses are separated by SOBI to obtain two source signals, one of which is source signal 1, which is randomly distributed in the time domain, and the signal changes without any regularity, and is manifested as no obvious regular peak in the frequency domain; the other group of source signals is source signal 2, which is manifested as signals fluctuating around 0 value in the time domain, and the fluctuation amplitude changes gently, and the amplitude envelope is a uniform arc, which is manifested as a group of obvious peak signals appearing at intervals in the frequency domain diagram, wherein the frequency corresponding to each peak is the vibration frequency of each order of the bridge;

[0041] Step 42: Select source signal 2 as the estimated bridge vibration signal to perform bridge modal identification.

[0042] Furthermore, in step 5, the following steps are specifically included:

[0043] Step 51, selecting the horizontal coordinate corresponding to the peak position from the separated bridge vibration signal frequency domain diagram as the frequency of each order of the bridge;

[0044] Step 52: Using a bandpass filter to separate the bridge vibration signal obtained by separation, a partial signal corresponding to each order frequency component is obtained;

[0045] Step 53, obtain a signal corresponding to each frequency order by Hilbert transform, and obtain its envelope diagram to obtain the instantaneous amplitude;

[0046] Step 54, performing positive and negative sign judgment and regularization to obtain the vibration mode corresponding to the bridge frequency of this order;

[0047] Step 55, evaluate the identified vibration mode using vibration mode correlation coefficient MAC:

[0048]

[0049] where {φ i} and {φ j} are the identified vibration mode vector and the theoretical vibration mode vector respectively. When the two are closer, the MAC value is close to 1.

[0050] Beneficial effects of the present invention: The present invention is based on the fact that the vehicle response under the vehicle-bridge coupling theory includes the bridge vibration response. The bridge modal parameters are identified by collecting the vertical acceleration response signal of the vehicle-bridge contact point when the vehicle passes the bridge at a uniform speed. Installing the sensor on the vehicle overcomes the difficulty of installing a large number of sensors on the bridge to measure the full bridge response, saving the manpower and material resources required for installing the sensor, and improving the economy and convenience. At the same time, the blind source separation algorithm is used to filter out the influence of the unevenness of the bridge surface on the identification of the bridge modal parameters. The required observation signal can have temporal and spatial independence. The observation signal required by the blind source separation method has temporal and spatial independence, which makes the collection of actual signals more free and convenient for signal acquisition. In addition, the signal separation process does not require the knowledge of the relevant information of the source signal, which improves the practicality of the method. The various frequencies and vibration modes of the bridge are identified by this algorithm with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A simplified model diagram of a vehicle-bridge coupling system based on which the vehicle response is derived in the present invention;

[0052] Figure 2 It is a time history comparison diagram of estimating the acceleration response of the axle contact point using the central difference method in the present invention;

[0053] Figure 3 A simplified model of two vehicles crossing a bridge considering the unevenness of the bridge deck in the present invention;

[0054] Figure 4 is a blind source separation system model of the present invention;

[0055] Figure 5 The finite element model of the bridge of the present invention;

[0056] Figure 6 The present invention obtains the source signal frequency domain diagram through SOBI calculation and estimation;

[0057] Figure 7 This is a frequency domain comparison diagram of the SOBI estimated source signal and the actual bridge vibration signal of the present invention;

[0058] Figure 8 is the vibration mode identification result diagram of the present invention, wherein: Figure 8 (a) is the first-order vibration mode; Figure 8 (b) is the second-order vibration mode Figure 8 (c) is the third-order vibration mode; Figure 8 (d) is the fourth-order vibration mode; Figure 8 (e) is the fifth-order vibration mode;

[0059] Fig. 9 The present invention is a simplified flow chart of a bridge modal recognition method based on blind source separation of mobile vehicle acceleration response. DETAILED DESCRIPTION

[0060] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] Embodiment 1:

[0062] The present invention proposes a bridge modal recognition method based on blind source separation of moving vehicle acceleration response, and the bridge modal recognition method based on blind source separation of moving vehicle acceleration response comprises the following steps:

[0063] Step 1: Based on the vehicle-bridge coupling theory, the vertical acceleration response of the vehicle-bridge contact point is obtained through the measured dynamic response of the vehicle body;

[0064] Step 2: Analyze the relationship between the bridge deck roughness effect and the bridge response signal in the vehicle-bridge contact point response;

[0065] Step 3: According to the relationship between the bridge deck roughness signal and the bridge response signal, the contact point acceleration signal is processed using the blind source separation method;

[0066] Step 4: Analyze the signal after blind source separation, and select the response signal required for bridge modal identification according to the characteristics of the bridge vibration signal;

[0067] Step 5: Identify the modal frequency and vibration shape of the bridge by performing frequency domain transformation and Hilbert transform on the signals required for modal identification.

[0068] Furthermore, in step 1, specifically, it is assumed that the vehicle mass is much smaller than the bridge mass, the influence of damping is not considered, the vehicle travels at a constant speed on the simply supported beam, and the vehicle model mass is m v , the spring stiffness is k v , speed is v; bridge length is L, material elastic modulus is E, section inertia moment is I, unit length mass is m, the vertical acceleration response of the vehicle-bridge contact point is calculated using the following formula:

[0069]

[0070] Among them, Δ st,n is the nth modal static displacement of the bridge caused by the vehicle, which is:

[0071]

[0072] S n is the dimensionless vehicle speed parameter, which is:

[0073]

[0074] In actual measurement, the response at the contact point between the vehicle tire and the bridge cannot be directly measured, but the vehicle acceleration can be used to estimate it.

[0075]

[0076] In the formula, the second derivative of vehicle body velocity with respect to time is calculated using the central difference method:

[0077]

[0078] Furthermore, in step 2, specifically, a simplified model of two vehicles crossing a bridge is established, the distance between the two vehicles is ΔL, and the parameters are selected the same as above, and the subscripts 1 and 2 are used to distinguish the two vehicles. The motion equations of the bridge and the two vehicles are:

[0079]

[0080]

[0081]

[0082] In the above formula, δ is the Dirac function, is the second derivative of the bridge displacement with respect to time, u″″(x,t) represents the fourth derivative of the bridge displacement with respect to the vehicle position x, and q v (t) represents the displacement of the vehicle relative to the equilibrium position, f c (t) is the vehicle-bridge interaction force. When the unevenness of the bridge deck is considered to be r(x), the modal synthesis method is used to solve it. Based on the assumption, the effect of vehicle inertia is ignored, and the following is obtained:

[0083]

[0084] It is concluded that under the assumed conditions, the bridge deck unevenness signal is uncorrelated with the bridge vibration signal, and the displacement responses of the contact points between the tires of the two vehicles and the bridge at time t are:

[0085] u c,1 =u(vt,t)+r(vt) (10)

[0086] u c,2 =u(vt+ΔL,t)+r(vt+ΔL) (11)

[0087] That is, the displacement of the vehicle-bridge contact point is the linear superposition of the bridge displacement and the bridge deck unevenness, that is, the acceleration response of the vehicle-bridge contact point is the linear superposition of the bridge vibration and the bridge deck unevenness effect, and the vehicle-bridge contact point responses of the two vehicles at the same position are equally affected by the bridge deck unevenness.

[0088] Further, in step 3, the following steps are specifically included:

[0089] Step 31: Take two or more groups of axle contact point acceleration response signals as observation signals, represented by x(t), which is composed of source signals s(t) through linear aliasing, that is, x(t) = As(t), where,

[0090] x(t)=[x1(t),x2(t),…,x m (t)] T ,s(t)=[s1(t),s2(t),…,s n (t)] T , A is the mixing matrix of the m×n order system;

[0091] Step 32: Using the second-order blind source separation algorithm, first pre-whiten the observed signal x(t), and estimate the zero time delay correlation matrix from the observed signal, i.e., R xx (0) = E[x(t)x T (t)]; for R xx (0) Perform singular value decomposition, that is, R xx (0) = UΛU T , then the pre-whitening matrix W is an n×m-dimensional whitening matrix, and the signal after pre-whitening becomes z(t)=Wx(t);

[0092] Step 33: Define the delay correlation matrix R s (τ) = E[s(t)s T (t+τ)],R z (τ)=E[z(t)z T (t+τ)]. Let τ be a set of different values ​​τ1,τ2,…τ p , and obtain a set of R z (τ i ), i = 1 ~ p. From z(t) = Qs(t), we get R Z (τ i )=QR S (τ i )Q T ,i=1~p. S (τ i )=Q T R Z (τ i )Q,i=1~p;

[0093] Step 34: R Z (τ i ) to obtain Q by joint diagonalization approximation, thus obtaining A = W -1 Q, unmixing matrix B = Q TW, estimated source signal y(t)=Bx(t);

[0094] Step 35: When two groups of vehicle-bridge contact point response signals are taken as observation signals, one of the two groups of original signals estimated by the SOBI algorithm is a bridge vibration response signal that does not include bridge unevenness.

[0095] Furthermore, in step 4, the following steps are specifically included:

[0096] Step 41, two groups of vehicle-bridge contact point responses are separated by SOBI to obtain two source signals, one of which is source signal 1, which is randomly distributed in the time domain, and the signal changes without any regularity, and is manifested as no obvious regular peak in the frequency domain; the other group of source signals is source signal 2, which is manifested as signals fluctuating around 0 value in the time domain, and the fluctuation amplitude changes gently, and the amplitude envelope is a uniform arc, which is manifested as a group of obvious peak signals appearing at intervals in the frequency domain diagram, wherein the frequency corresponding to each peak is the vibration frequency of each order of the bridge;

[0097] Step 42: Select source signal 2 as the estimated bridge vibration signal to perform bridge modal identification.

[0098] Furthermore, in step 5, the following steps are specifically included:

[0099] Step 51, selecting the horizontal coordinate corresponding to the peak position from the separated bridge vibration signal frequency domain diagram as the frequency of each order of the bridge;

[0100] Step 52: Using a bandpass filter to separate the bridge vibration signal obtained by separation, a partial signal corresponding to each order frequency component is obtained;

[0101] Step 53, obtain a signal corresponding to each frequency order by Hilbert transform, and obtain its envelope diagram to obtain the instantaneous amplitude;

[0102] Step 54, performing positive and negative sign judgment and regularization to obtain the vibration mode corresponding to the bridge frequency of this order;

[0103] Step 55, evaluate the identified vibration mode using vibration mode correlation coefficient MAC:

[0104]

[0105] where {φ i} and {φ j} are the identified vibration mode vector and the theoretical vibration mode vector respectively. When the two are closer, the MAC value is close to 1.

[0106] Embodiment 2:

[0107] (I) Programming and calculation process

[0108] The bridge modal recognition calculation method based on blind source separation processing of moving vehicle acceleration response proposed in this invention is recommended to be implemented by programming. The calculation is based on the vehicle-bridge relationship such as Figure 3 The calculation process is implemented in three steps:

[0109] Step 1, calculation parameter input. First, input the structural parameters of the bridge to be evaluated, including the span of the bridge, the width of the bridge deck, the length of vehicles traveling before and after the bridge, etc.; secondly, input the parameters of the traveling vehicle, including the mass of the vehicle, the driving speed, the driving distance of the vehicle, etc.; finally, input the time step of the calculation and set the roughness level.

[0110] Step 2, model solution. Based on the calculation principle of vehicle-bridge coupling, the program will solve the vertical acceleration response at the vehicle-bridge contact point. The calculation results are calculated using the written SOBI calculation program to obtain the vibration response of the bridge after filtering out the influence of unevenness. The response data is Hilbert transformed to obtain its envelope diagram and the positive and negative signs are judged and regularized to calculate the vibration mode corresponding to the bridge frequency;

[0111] Step 3: Output the results. The program will output the obtained bridge vibration frequency domain diagram and the identified vibration modes of each order, and calculate the MAC value.

[0112] (II) Program example

[0113] Select the bridge span L = 25m, unit mass length m = 2000kg / m, elastic modulus E = 27.5GPa, section inertia moment I = 0.15m2, the whole bridge is divided into 250 units, and the finite element model is established, such as Figure 5 The calculated frequencies of the first few bridge orders are 3.6037Hz, 14.3338Hz, 31.9541Hz, 56.0920Hz, and 86.2669Hz.

[0114] Two vehicles with the same parameters are used to obtain the vehicle-bridge contact point response data. Vehicle mass m v =1000kg, stiffness k v =200kN / m, without considering damping, the vehicle frequency is calculated to be 2.25Hz. Two vehicles pass the bridge at a constant speed with a distance of 1m, the speed is 2m / s, and the time step is 0.001s.

[0115] The above parameters are input into the calculation program, and the estimated bridge vibration frequency domain diagram after filtering out the influence of bridge deck unevenness, as well as the comparison diagram between the SOBI estimated signal and the actual bridge vibration signal, are solved and output. The vibration mode diagrams of each order of the bridge are calculated based on the SOBI estimated signal. The program calculation results and finite element verification results are shown in Figure 6-Figure 8 The identification of each frequency and vibration mode is shown in

[0116] As shown in Table 1.

[0117]

[0118] Table 1

[0119] The first five frequencies of the bridge can be identified. The source signal 2 is compared with the bridge vibration signal corresponding to the bridge contact position during the driving process of vehicle 2 in the frequency domain. It can be seen that the distribution of the two in the frequency domain is basically the same, that is, the source signal 2 obtained after SOBI processing has basically filtered out the adverse effects of unevenness, and the bridge frequency can be directly identified.

[0120] It can be seen from Table 1 that the bridge modal identification calculation method based on blind source separation processing of mobile vehicle acceleration response proposed in the present invention can accurately identify the various frequencies and vibration modes of the bridge, with small error and strong applicability.

Claims

1. A bridge modal recognition method based on blind source separation of moving vehicle acceleration response, characterized in that: The bridge modal identification method based on blind source separation of moving vehicle acceleration response comprises the following steps: Step 1: Based on the vehicle-bridge coupling theory, the vertical acceleration response of the vehicle-bridge contact point is obtained through the measured dynamic response of the vehicle body; Step 2: Analyze the relationship between the bridge deck roughness effect and the bridge response signal in the vehicle-bridge contact point response; Step 3: According to the relationship between the bridge deck roughness signal and the bridge response signal, the contact point acceleration signal is processed using the blind source separation method; Step 4: Analyze the signal after blind source separation, and select the response signal required for bridge modal identification according to the characteristics of the bridge vibration signal; Step 5: Identify the modal frequency and vibration shape of the bridge by performing frequency domain transformation and Hilbert transformation on the signals required for modal identification; In step 2, specifically, a simplified model of two vehicles crossing a bridge is established, the distance between the two vehicles is ΔL, and the parameters are selected the same as above. The subscripts 1 and 2 are used to distinguish the two vehicles. The motion equations of the bridge and the two vehicles are: In the above formula, δ is the Dirac function, is the second derivative of the bridge displacement with respect to time, u″″(x,t) represents the fourth derivative of the bridge displacement with respect to the vehicle position x, and q v (t) represents the displacement of the vehicle relative to the equilibrium position, f c (t) is the vehicle-bridge interaction force. When the bridge deck roughness is considered to be r(x), the modal synthesis method is used to solve it. According to the assumption, the effect of vehicle inertia force is ignored and the vehicle model mass is m v , the spring stiffness is k v , speed is v; bridge length is L, material elastic modulus is E, section moment of inertia is I, unit length mass get: Among them, n is the nth mode of the bridge. It is concluded that under the assumed conditions, the bridge deck unevenness signal and the bridge vibration signal are uncorrelated. At time t, the displacement responses of the contact points between the tires of the two vehicles and the bridge are: u c,1 =u(vt,t)+r(vt) (10) u c,2 =u(vt+ΔL,t)+r(vt+ΔL) (11) That is, the displacement of the vehicle-bridge contact point is the linear superposition of the bridge displacement and the bridge deck unevenness, that is, the acceleration response of the vehicle-bridge contact point is the linear superposition of the bridge vibration and the bridge deck unevenness effect, and the vehicle-bridge contact point responses of the two vehicles at the same position are equally affected by the bridge deck unevenness.

2. The bridge modal identification method based on blind source separation of moving vehicle acceleration response according to claim 1 is characterized in that: In step 1, specifically, assuming that the vehicle mass is less than the bridge mass, ignoring the influence of damping, the vehicle travels at a constant speed on a simply supported beam, the vertical acceleration response of the vehicle-bridge contact point is calculated using the following formula: Among them, Δ st,n is the nth modal static displacement of the bridge caused by the vehicle, which is: S n is the dimensionless vehicle speed parameter, which is: In actual measurement, the response at the contact point between the vehicle tire and the bridge cannot be directly measured, but the vehicle acceleration can be used to estimate it. In the formula, the second derivative of the vehicle acceleration with respect to time is calculated using the central difference method:

3. The bridge modal identification method based on blind source separation of moving vehicle acceleration response according to claim 1 is characterized in that: In step 3, the following steps are specifically included: Step 31: Take two or more groups of axle contact point acceleration response signals as observation signals, represented by x(t), which is composed of source signals s(t) through linear aliasing, that is, x(t) = As(t), where, A is the m×n order system mixing matrix; Step 32: Using the second-order blind source separation algorithm, first pre-whiten the observed signal x(t), and estimate the zero time delay correlation matrix from the observed signal, i.e., R xx (0) = E[x(t)x T (t)]; for R xx (0) Perform singular value decomposition, that is, R xx (0) = UΛU T , then the pre-whitening matrix W is an n×m dimensional whitening matrix, and the signal after pre-whitening becomes Step 33: Define the delay correlation matrix R s (τ) = E[s(t)s T (t+τ)], Take τ as a set of different values Get a set of R z (τ i ), i = 1 ~ p, by Get R Z (τ i )=QR S (τ i )Q T ,i=1~p,R S (τ i )=Q T R Z (τ i )Q,i=1~p; Step 34: R Z (τ i ) to obtain Q by joint diagonalization approximation, thus obtaining A = W -1 Q, unmixing matrix B = Q T W, estimated source signal y(t)=Bx(t); Step 35: When two groups of vehicle-bridge contact point response signals are taken as observation signals, one of the two groups of original signals estimated by the SOBI algorithm is a bridge vibration response signal that does not include bridge unevenness.

4. The bridge modal identification method based on blind source separation of moving vehicle acceleration response according to claim 1 is characterized in that: In step 4, the following steps are specifically included: Step 41, two groups of vehicle-bridge contact point responses are separated by SOBI to obtain two source signals, one of which is source signal 1, which is randomly distributed in the time domain, and the signal changes without any regularity, and is manifested as no obvious regular peak in the frequency domain; the other group of source signals is source signal 2, which is manifested as signals fluctuating around 0 value in the time domain, and the fluctuation amplitude changes gently, and the amplitude envelope is a uniform arc, which is manifested as a group of obvious peak signals appearing at intervals in the frequency domain diagram, wherein the frequency corresponding to each peak is the vibration frequency of each order of the bridge; Step 42: Select source signal 2 as the estimated bridge vibration signal to perform bridge modal identification.

5. The bridge modal identification method based on blind source separation of moving vehicle acceleration response according to claim 1 is characterized in that: In step 5, the following steps are specifically included: Step 51, selecting the horizontal coordinate corresponding to the peak position from the separated bridge vibration signal frequency domain diagram as the frequency of each order of the bridge; Step 52: Separate the separated bridge vibration signal using a bandpass filter to obtain signals corresponding to frequency components of each order; Step 53, obtain a signal corresponding to each frequency order by Hilbert transform, and obtain its envelope diagram to obtain the instantaneous amplitude; Step 54, performing positive and negative sign judgment and regularization to obtain the vibration mode corresponding to the bridge frequency; Step 55, evaluate the identified vibration mode using vibration mode correlation coefficient MAC: where {φ i } and {φ j } are the identified vibration mode vector and the theoretical vibration mode vector respectively. The closer the two are, the closer the MAC value is to 1.

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