Bridge modal parameter identification method based on seismic interference method

Abstract

The invention belongs to the technical field of structural health monitoring, and particularly relates to a bridge modal parameter identification method based on an earthquake interference method. The method comprises the following steps: arranging a sensor according to a monitoring point position of a detected bridge, and collecting a displacement response of the sensor in a working state; constructing an impulse response function for displacement response based on a seismic interference method; using a least square method to identify initial modal parameters of the pulse response function, the obtained initial modal parameters including frequency and vibration mode; calculating a stiffness matrix and a mass matrix of the bridge based on the initial modal parameters; the coupled item in the stiffness matrix and the mass matrix is set to be infinite, and the decoupled modal parameters are extracted, so that the defect that a traditional seismic interference method is only suitable for a high-rise structure, that is, only the interaction of a single-side soil structure can be decoupled is overcome.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural health monitoring, and in particular relates to a bridge modal parameter identification method based on seismic interferometry. Background Art

[0002] With the increasing demand for identifying structural dynamic characteristics in strong vibration scenarios such as earthquakes and rail transit, the interaction between the time-varying characteristics of the excitation source and the soil-structure coupling effect (SSI) in engineering practice has become a key technical challenge. Traditional vibration modal identification methods have inherent limitations in separating the spatial distribution characteristics of the excitation source from the dynamic response of the soil-structure system, resulting in the obtained modal parameters deviating from the actual structural characteristics. In this context, seismic interferometry, as an emerging wave mode identification technology, achieves the theoretical elimination of the spatial heterogeneity of external excitation and the effective decoupling of the SSI effect by constructing a mathematical reconstruction mechanism for the structural impulse response function. The structural intrinsic dynamic parameters obtained in this way show significant technical advantages in terms of modal identification accuracy, finite element model modification reliability, and damage diagnosis sensitivity.

[0003] Current seismic interferometry methods are primarily used for high-rise structures because they are only able to decouple one-sided soil-structure interactions. Bridges, however, are in contact with the ground at least at two ends. Therefore, current seismic interferometry methods cannot meet the requirements for bridge modal identification applications.

[0004] Combining the actual needs of the project, such as whether it is possible to break through the limitation of the one-sided seismic interferometry method under different excitation conditions and propose a corresponding improved seismic interferometry method, is the key to accurate modal identification of bridges. Summary of the Invention

[0005] The purpose of the present invention is to provide a bridge modal parameter identification method based on seismic interferometry, which aims to directly decouple the input excitation, avoid the coupling effect of the Gaussian white noise assumption on the identification results, and eliminate the interaction between soil and structure, avoiding the inclusion of the dynamic characteristics of the soil in the identification results.

[0006] The purpose of the present invention can be achieved through the following technical solutions: A bridge modal parameter identification method based on seismic interferometry, the method comprising: Arrange sensors according to the monitoring points of the bridge to be tested and collect its displacement response in working state; Construct impulse response function based on displacement response based on seismic interferometry; Using the least square method to identify initial modal parameters of the impulse response function, wherein the initial modal parameters include frequency and vibration shape; Calculate the stiffness matrix and mass matrix of the bridge based on the initial modal parameters; Set one of the coupled terms in the stiffness matrix and the mass matrix to infinity and extract the decoupled modal parameters.

[0007] Furthermore, constructing the impulse response function based on the displacement response based on the seismic interferometry method specifically includes the following process: ; in, is the impulse response function, represents the displacement of the structural motion trajectory field, Indicates at the reference point The displacement, is the inverse Fourier transform, * represents the complex conjugate, and the regularization parameter is introduced It is intended to stabilize computations by preventing division by zero instabilities.

[0008] Furthermore, the identification of the initial modal parameters of the impulse response function using the least squares method specifically includes the following process: Constructing the residual function The residual function is defined as the error between the observed data and the model prediction value: r(t)=y(t)-f(p,t) Where: y(t) is the observed signal vector; f(p,t) is the model prediction signal, P is the modal parameter, and the modal parameter is The frequency and damping ratio of the order, r(t) is the residual vector; The objective function is to minimize the residual sum of squares: ; in, is the modulus value of r(t), M is the number of sampling points; Solve the minimization problem using an optimization algorithm: .

[0009] Furthermore, the calculation of the stiffness matrix and mass matrix of the bridge based on the initial modal parameters specifically includes the following process: According to the obtained initial modal parameters, use the associated formula: , where K is the stiffness matrix, M is the mass matrix, is the frequency in the initial modal parameters, is the vibration mode in the initial modal parameters.

[0010] Furthermore, the bridge under test is a three-span continuous beam bridge.

[0011] Furthermore, extracting the decoupled modal parameters specifically includes the following process: Identify the source of coupling problems: Spatial coupling: The vibration correlation between adjacent measuring points leads to non-orthogonal vibration modes; Parameter coupling: off-diagonal terms of the stiffness matrix and mass matrix; Decoupling method: Diagonalization: For the coupling matrix [A]=[K]-ω2[M], through similarity transformation Diagonalization, where is a reversible matrix; Infinite stiffness assumption: For the fully constrained direction, set the corresponding stiffness term kij→∞, forcing decoupling; Parameter extraction after decoupling: Independent modal analysis: After diagonalization, each mode corresponds to an independent equation: ; where λr is a diagonal matrix The rth element of ; Parameter correction: Update the finite element model with the decoupled modal parameters to verify consistency.

[0012] Furthermore, vertical displacement sensors are arranged at the mid-span, 1 / 4 span and supports of each span of the bridge under test.

[0013] Compared with the existing solutions, the present invention achieves the following beneficial effects: The present invention arranges sensors according to monitoring points of the measured bridge to collect its displacement response in a working state; constructs an impulse response function for the displacement response based on the seismic interferometry method; uses the least squares method to identify the initial modal parameters of the impulse response function, wherein the obtained initial modal parameters include frequency and vibration mode; calculates the stiffness matrix and mass matrix of the bridge based on the initial modal parameters; sets one of the coupling items in the stiffness matrix and the mass matrix to infinity, and extracts the decoupled modal parameters, thereby overcoming the defect that the traditional seismic interferometry method is only applicable to high-rise structures, that is, it can only decouple the soil-structure interaction on one side.

[0014] Compared with existing operational mode identification methods, the present invention does not require the Gaussian white noise assumption, but directly decouples the input excitation, avoiding the coupling influence of the Gaussian white noise assumption on the identification results, while eliminating the interaction between soil and structure, and avoiding the dynamic characteristics of the soil being included in the identification results. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments described in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0016] Figure 1 1 is a flow chart of a bridge modal parameter identification method based on seismic interferometry according to an embodiment of the present invention; Figure 2 This is a monitoring point distribution diagram of a measured bridge according to an embodiment of the present invention; Figure 3 1 is a comparison diagram of the first three vibration modes of a partially decoupled bridge according to an embodiment of the present invention and the theoretical vibration modes; Figure 4 This is a comparison diagram of the first three vibration modes of the fully decoupled bridge according to an embodiment of the present invention and the theoretical vibration modes. DETAILED DESCRIPTION

[0017] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0018] In addition, the described features, structures or characteristics can be combined in any suitable manner in one or more example embodiments. In the following description, many specific details are provided to provide a full understanding of the example embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure can be practiced while omitting one or more of the specific details, or other methods, components, steps, etc. can be adopted. In other cases, well-known structures, methods, implementations or operations are not shown or described in detail to avoid obscuring various aspects of the present disclosure.

[0019] The following uses the vibration measurement of a fixed-end beam structure as an example to illustrate the implementation steps of the bridge modal parameter identification method based on seismic interferometry proposed in this invention. First, the measurement conditions are introduced. Figure 2 is a monitoring point distribution diagram of a measured bridge in an embodiment of the present invention; Figure 2 As shown in the figure, it is assumed that the measurement object is a three-span bridge and the excitation method is multi-point random vibration signal excitation, where m1 to m10 are monitoring points.

[0020] Figure 1 FIG. 1 is a flow chart of a bridge modal parameter identification method based on seismic interferometry according to an embodiment of the present invention. Figure 1 As shown, the method includes the following steps: Arrange sensors according to the monitoring points of the bridge to be tested and collect its displacement response in working state; Specifically, an array of accelerometers was deployed at key monitoring points on the three-span bridge to synchronously collect acceleration time history data under multi-point random vibration excitation. Accelerometers were placed at decoupled boundary conditions (such as abutments) for fixed boundary conditions at both ends, creating a sensor network consisting of multiple measurement points to ensure the precise temporal and spatial synchronization of vibration signals. Environmental vibration data was continuously collected and preprocessed to obtain a valid vibration signal dataset.

[0021] Construct impulse response function based on displacement response based on seismic interferometry; Specifically, ; in, is the impulse response function, represents the displacement of the structural motion trajectory field, Indicates at the reference point The displacement, is the inverse Fourier transform, * represents the complex conjugate, and the regularization parameter is introduced It is intended to stabilize computations by preventing division by zero instabilities.

[0022] The least squares method is used to identify the initial modal parameters of the impulse response function, where the initial modal parameters include frequency and vibration shape: Constructing the residual function The residual function is defined as the error between the observed data and the model prediction value: r(t)=y(t)-f(p,t) Where: y(t) is the observed signal vector; f(p,t) is the model prediction signal, P is the modal parameter, and the modal parameter is The frequency and damping ratio of the order, r(t) is the residual vector; The objective function is to minimize the residual sum of squares: ; in, is the modulus value of r(t), M is the number of sampling points; Solve the minimization problem using an optimization algorithm: .

[0023] Calculate the stiffness matrix and mass matrix of the bridge based on the initial modal parameters: Specifically, according to the obtained initial modal parameters, the correlation formula is used: , where K is the stiffness matrix, M is the mass matrix, is the frequency in the initial modal parameters, is the vibration mode in the initial modal parameters.

[0024] Set one of the coupled terms in the stiffness matrix and the mass matrix to infinity and extract the decoupled modal parameters.

[0025] Extracting the decoupled modal parameters specifically includes the following steps: Identify the source of coupling problems: Spatial coupling: The vibration correlation between adjacent measuring points leads to non-orthogonal vibration modes; Parameter coupling: off-diagonal terms of the stiffness matrix and mass matrix; Decoupling method: Diagonalization: For the coupling matrix [A]=[K]-ω2[M], through similarity transformation Diagonalization, where is a reversible matrix; Infinite stiffness assumption: For the fully constrained direction, set the corresponding stiffness term kij→∞, forcing decoupling; Parameter extraction after decoupling: Independent modal analysis: After diagonalization, each mode corresponds to an independent equation: ; where λr is a diagonal matrix The rth element of .

[0026] Parameter correction: Update the finite element model with the decoupled modal parameters to verify consistency.

[0027] It is worth noting that vertical displacement sensors are arranged at the mid-span, 1 / 4 span and supports of each span of the bridge under test.

[0028] In some embodiments, Figure 3 : is a comparison diagram of the first three vibration modes of the partially decoupled bridge in the embodiment of the present invention and the theoretical vibration modes, as shown in FIG. Figure 3 As shown, the comparison between the first-order vibration mode and the theoretical vibration mode can be obtained: the frequency in the theoretical value is 0.316, the damping ratio is 0.012, the recognition result is 0.295, the damping ratio is 0.000; the comparison between the second-order vibration mode and the theoretical vibration mode shows that: the theoretical value of the frequency is 0.456, the damping ratio is 0.016, and the recognition result is is 0.396, the damping ratio is 0.000; the comparison between the third-order vibration mode and the theoretical vibration mode shows that: the theoretical value of the frequency is 0.593, the damping ratio is 0.020, and the recognition result is is 0.597, the damping ratio is 0.000; the green line is the theoretical vibration shape, and the red line is the identified vibration shape. It can be seen that the recognition effect is not good.

[0029] In some embodiments, Figure 4 : is a comparison diagram of the first three vibration modes of the fully decoupled bridge in the embodiment of the present invention and the theoretical vibration modes, as shown in FIG. Figure 4 As shown, the green line is the theoretical vibration shape, and the red line is the identified vibration shape. The identified result can completely coincide with the theoretical value.

[0030] The above embodiments can be implemented in whole or in part via software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions or computer programs. When loaded or executed on a computer, the processes or functions described in the embodiments of this application are fully or partially generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, tapes), optical media (e.g., DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0031] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0032] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0033] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is only for some logical functions. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0034] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0035] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A bridge modal parameter identification method based on seismic interferometry, characterized in that the method include: Arrange sensors according to the monitoring points of the bridge to be tested and collect its displacement response in working state; Construct impulse response function based on displacement response based on seismic interferometry; Using the least square method to identify initial modal parameters of the impulse response function, wherein the initial modal parameters include frequency and vibration shape; Calculate the stiffness matrix and mass matrix of the bridge based on the initial modal parameters; Set one of the coupled terms in the stiffness matrix and the mass matrix to infinity and extract the decoupled modal parameters.

2. The bridge modal parameter identification method based on seismic interferometry according to claim 1 is characterized in that: The impulse response function is constructed based on the displacement response of the seismic interferometry method. The following processes are included: ； in, is the impulse response function, represents the displacement of the structural motion trajectory field, Indicates at the reference point The displacement, is the inverse Fourier transform, * represents the complex conjugate, and the regularization parameter is introduced It is intended to stabilize computations by preventing division by zero instabilities.

3. The bridge modal parameter identification method based on seismic interferometry according to claim 1 is characterized in that: The identification of the initial modal parameters of the impulse response function using the least squares method specifically includes the following steps: Constructing the residual function The residual function is defined as the error between the observed data and the model prediction value: r(t)=y(t)-f(p,t) Where: y(t) is the observed signal vector; f(p,t) is the model prediction signal, P is the modal parameter, and the modal parameter is The frequency and damping ratio of the order, r(t) is the residual vector; The objective function is to minimize the residual sum of squares: ； in, is the modulus value of r(t), M is the number of sampling points; Solve the minimization problem using an optimization algorithm: 。 4. The bridge modal parameter identification method based on seismic interferometry according to claim 1, characterized in that: The calculation of the stiffness matrix and mass matrix of the bridge based on the initial modal parameters specifically includes the following process: According to the obtained initial modal parameters, use the associated formula: , where K is the stiffness matrix, M is the mass matrix, is the frequency in the initial modal parameters, is the vibration mode in the initial modal parameters.

5. The bridge modal parameter identification method based on seismic interferometry according to claim 1 is characterized in that: The bridge under test is a three-span continuous beam bridge.

6. The bridge modal parameter identification method based on seismic interferometry according to claim 1, characterized in that: Extracting the decoupled modal parameters specifically includes the following steps: Identify the source of coupling problems: Spatial coupling: The vibration correlation between adjacent measuring points leads to non-orthogonal vibration modes; Parameter coupling: off-diagonal terms of the stiffness matrix and mass matrix; Decoupling method: Diagonalization: For the coupling matrix [A]=[K]-ω2[M], through similarity transformation Diagonalization, where is a reversible matrix; Infinite stiffness assumption: For the fully constrained direction, set the corresponding stiffness term kij→∞, forcing decoupling; Parameter extraction after decoupling: Independent modal analysis: After diagonalization, each mode corresponds to an independent equation: ; where λr is a diagonal matrix The rth element of ; Parameter correction: Update the finite element model with the decoupled modal parameters to verify consistency.

7. The bridge modal parameter identification method based on seismic interferometry according to claim 1 is characterized in that: Vertical displacement sensors are arranged at the mid-span, 1 / 4 span and supports of each span of the bridge being tested.

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