阅读说明：本技术 一种结构-tld系统的子系统动力特性检测方法 (Subsystem power characteristic detection method of structure-TLD system ) 是由 周子杰 谢壮宁 张蓝方 张乐乐 石碧青 江毅 于 2021-07-28 设计创作，主要内容包括：本发明公开了一种结构-TLD系统的子系统动力特性检测方法,方法包括以下步骤：S1、测量高层建筑和TLD耦合振动响应,实时记录耦合振动信号；S2、由耦合信号构造Hankel矩阵从而计算Toeplitz矩阵；S3、由Toeplitz矩阵识别耦合系统的模态参数并由稳定性准则判断识别结果的准确性；S4、判断识别结果是否连续5阶保持一致性；S5、通过重构耦合系统的连续状态矩阵检测结构和TLD对应的模态参数；S6、通过结构和TLD的动力特性参数对系统减振性能进行评价。本发明方法避免了对功率谱进行预先假设的问题,而且不需要测量安装TLD之前的结构振动响应,只需要重构耦合系统的状态空间模型即可对系统动力特性参数进行检测。(The invention discloses a method for detecting the subsystem power characteristics of a structure-TLD system, which comprises the following steps: s1, measuring the coupling vibration response of the high-rise building and the TLD, and recording the coupling vibration signal in real time; s2, constructing a Hankel matrix by the coupling signals so as to calculate a Toeplitz matrix; s3, identifying the modal parameters of the coupling system by the Toeplitz matrix and judging the accuracy of the identification result by the stability criterion; s4, judging whether the identification result is continuous and 5-order and keeps consistent; s5, detecting the modal parameters corresponding to the structure and the TLD through a continuous state matrix of the reconstruction coupling system; and S6, evaluating the system vibration damping performance through the structure and the dynamic characteristic parameters of the TLD. The method avoids the problem of pre-supposing the power spectrum, does not need to measure the structural vibration response before TLD installation, and can detect the dynamic characteristic parameters of the system only by reconstructing the state space model of the coupling system.)

1. A subsystem power characteristic detection method of a structure-TLD system is characterized by comprising the following steps:

s1, measuring the coupling vibration response of the high-rise building and the TLD, and recording the coupling vibration signal in real time;

s2, constructing a Hankel matrix by the coupling signals so as to calculate a Toeplitz matrix;

s3, identifying the modal parameters of the coupling system by the Toeplitz matrix and judging the accuracy of the identification result by the stability criterion;

s4, judging whether the identification result is continuous and 5-order and keeps consistent;

s5, detecting the modal parameters corresponding to the structure and the TLD through a continuous state matrix of the reconstruction coupling system;

and S6, evaluating the system vibration damping performance through the structure and the dynamic characteristic parameters of the TLD.

2. The method for detecting the subsystem power characteristic of the structure-TLD system as claimed in claim 1, wherein the step S1 is specifically as follows:

installing an accelerometer in a high-rise building to detect a floor wind vibration acceleration signal, installing a wave height meter in the TLD to detect a liquid level vibration signal, and collecting a coupling vibration signal;

the coupling data includes the structural acceleration response of the floor on which the TLD is located and the TLD level wave height response.

3. The method for detecting the subsystem power characteristic of the structure-TLD system as claimed in claim 1, wherein the step S2 comprises the following steps:

s21, preprocessing the coupling signal to enable the coupling signal to meet the modeling requirement of a state space model;

s22, constructing a Hankel matrix by specifying the number of the sub-blocks;

s23, equally dividing the Hankel matrix into two parts, wherein each part has the same sub-block number;

and S24, calculating the Toeplitz matrix according to the definition of the covariance.

4. The method for detecting the subsystem power characteristic of the structure-TLD system as claimed in claim 3, wherein the step S2 is specifically as follows:

carrying out mean value removing processing on the building acceleration signal and the TLD wave height signal, converting the wave height signal into equivalent displacement of an equivalent TMD model according to the property of the TLD, and solving a second derivative of the displacement to obtain equivalent acceleration;

the number of the sub-blocks of the Hankel matrix needs to be set to be an even number, the number of the false sub-blocks is 2i, the Hankel matrix is constructed by coupling signals, and the specific formula is as follows:

wherein, y_iRepresenting a sequence formed by coupling signals at the ith moment, j represents the signal calculation time length, and assuming that the number of output channels of the coupling signals is l, the Hankel matrix belongs to the R^2il×jR represents the size of the matrix, and superscripts 2il and j represent the number of rows and columns;

the Hankel matrix in the formula (1) is equally divided into two parts, each part has i sub-block numbers, and the specific formula is as follows:

wherein the subscripts p and f represent past and future, Y, respectively_p∈R^il×j，Y_f∈R^il×j；

For the coupled vibration process under random excitation, the covariance matrix of the coupled signals is defined as:

wherein r is_ab(i) For the cross-correlation function of the measured data of the a-th and b-th output channels, the superscript T in formula (3) represents the matrix transposition, and E is the mathematical expectation symbol;

assuming that the coupled signal has ergodicity, combining the state space principle and the covariance matrix to define lambda_iThe calculation formula of (2) is as follows:

a, C, G is a state space matrix of the coupling system;

constructing a Toeplitz matrix by using the covariance matrix of the coupled signals, wherein the concrete formula is as follows:

wherein, O_iBeing observable matrices, gamma_iIs a controllable matrix.

5. The method for detecting the subsystem power characteristic of the structure-TLD system as claimed in claim 1, wherein the step S3 comprises the following steps:

s31, carrying out singular value decomposition on the Toeplitz matrix to obtain an observable matrix and a controllable matrix;

s32, calculating a state matrix and an output matrix of the coupling system;

s33, calculating modal parameters and modal shape of the coupling system;

and S34, screening the identification result by the stability criterion.

6. The method for detecting the subsystem power characteristic of the structure-TLD system as claimed in claim 5, wherein the step S3 is specifically as follows:

singular value decomposition is carried out on the Toeplitz matrix, the rank of the matrix is reflected on the number of singular values which are not zero, and the specific formula is as follows:

wherein, U₁、V₁Is an orthogonal matrix, S₁A diagonal matrix composed of singular values;

considering system matrixes under different orders, supposing that the calculation order is n, comparing a formula (5) with a formula (6), and observing the U for the matrixes₁And S₁The first n columns are expressed, and the specific formula is as follows:

calculating a state matrix and an output matrix of the coupling system, wherein the specific formula is as follows:

wherein, superscript + represents the pseudo-inverse;

and (3) carrying out eigenvalue decomposition on the discrete state matrix, wherein the specific formula is as follows:

A＝ΨZΨ^-1 (9)

wherein the content of the first and second substances, for the eigenvalues of the discrete time system, ψ ∈ R^n×nIs a feature vector matrix;

because the actually acquired coupling signals are all on discrete time points, the parameter identification cannot be directly carried out, and calculation is needed in a continuous state, the characteristic value of a discrete time system is converted into continuous time, and the specific formula is as follows:

wherein the content of the first and second substances,is a characteristic value of a continuous-time system, Δ t is a time interval, a_m、b_mRespectively representing a real part and an imaginary part;

calculating modal parameters of the coupling system, including frequency and damping ratio, and the specific formula is as follows:

and obtaining the system modal shape from the output matrix and the characteristic vector, wherein the specific formula is as follows:

Φ＝CΨ (12)

setting stability criteria about frequency, damping ratio and modal shape for recognition results of different orders, wherein the specific formula is as follows:

and (4) screening results of each order through three conditions of a formula (13) to obtain modal parameters meeting the stability.

7. The method for detecting the subsystem power characteristic of the structure-TLD system as claimed in claim 1, wherein the step S4 is specifically as follows:

obtaining a stable graph according to the recognition results of different orders, stopping calculation if the modal parameters of the 5 continuous orders are kept unchanged, taking the last result as the modal parameters of the coupling system, and entering step S5; if the requirement that the 5 continuous orders are not changed is not met all the time, the method returns to the step S2, the number of the Hankel matrix sub-blocks is re-designated to be larger, and then the steps S2 to S3 are repeated.

8. The method for detecting the subsystem power characteristic of the structure-TLD system as claimed in claim 1, wherein the step S5 comprises the following steps:

s51, constructing a diagonal matrix and a mode matrix;

s52, reconstructing a continuous state matrix of the structure controlled mode and the TLD coupling system;

s53, detecting respective dynamic characteristic parameters of the structure and the TLD.

9. The method for detecting the subsystem power characteristic of the fabric-TLD system as claimed in claim 8, wherein the step S5 is specifically as follows:

establishing a state space model of a multi-free structure and a TLD coupling system, establishing an equivalent TMD model according to the property of the TLD, and assuming that the TLD is installed on the nth degree of freedom of the structure and only the nth mode shape participates in vibration, the motion equation under the modal coordinate is as follows:

wherein m is_r、c_rAnd k_rRespectively, structure r-order modal mass, modal damping and modal stiffness, m_e、c_eAnd k_eEquivalent mass, equivalent damping and equivalent stiffness, x, of the TLD, respectively_nAnd x_eRespectively, the displacement of the nth degree of freedom of the structure and the equivalent displacement of the TLD, phi_rIn order to be of the r-th order mode,displacement of nth degree of freedom in the r-th order vibration mode, G is an excitation force action position matrix, and F is an excitation force vector;

the continuous state space equation of the coupled system according to the state space theory is expressed as:

wherein the content of the first and second substances,A_cis a state matrix, B_cAs an input matrix, A_cThe concrete expression is as follows:

where μ denotes the effective mass ratio, λ denotes the structural effective mass gain factor, ω_rAnd ζ_rThe frequency and the damping ratio of the structure' r order circle, omega_tAnd ζ_tRespectively TLD circle frequencyAnd a damping ratio;

obtaining the modal parameters of the structure-TLD coupled system from the step S4, and reconstructing the continuous state matrix A 'of the structure controlled modal and the TLD coupled system'_c：

Wherein, gamma is_eBeing a mode-imparting matrix, Γ_e＝[φ₁,φ₂]，Λ_eIn the form of a diagonal matrix,diag denotes a matrix of elements in diagonal, the system identifies the continuous state matrix A 'being evaluated'_cContinuous state matrix A evaluated by theoretical analysis_cShould be approximately equal, therefore comparing equations (16) and (17) yields the dynamic characteristics of the structure and TLD, including the effective mass ratio and the respective frequencies and damping ratios of the subsystems, with the specific equation:

wherein, a_MNRepresents A'_cThe matrix has the elements of the M row and the N column.

10. The method for detecting the subsystem power characteristic of the fabric-TLD system as claimed in claim 9, wherein the step S6 is specifically as follows:

comparing the structural frequency obtained in the step S5 with the TLD frequency, if the difference is larger, indicating that the TLD is not tuned sufficiently, and changing the TLD frequency by lifting the water level;

simultaneously comparing the identification value and the design value of the TLD damping ratio, and evaluating an additional damping value added to the structure by the TLD; and dynamically evaluating the control effect of the coupling system by carrying out online batch processing on the data and tracking the change conditions of the structure and the TLD modal parameters.

Technical Field

The invention belongs to the technical field of structural vibration control, and particularly relates to a method for detecting the subsystem dynamic characteristics of a structure-TLD system.

Background

With the development of cities and the technological progress, the number and height of super high-rise buildings are rapidly increased, and the wind vibration comfort degree is brought into the standard and becomes one of the main control indexes of the super high-rise building design. Tuned Liquid Dampers (TLDs) have been the subject of attention and interest from wind engineers and structural engineers as passive dampers that have a high cost-performance ratio, are easy to retrofit and maintain, and particularly can also be used as fire tanks.

The main factors influencing the vibration damping effect of the super high-rise building in actual engineering include the effective mass ratio, the frequency and the damping ratio of the structure and the TLD. During coupled vibration of the super high-rise building and the TLD, the natural frequency and the modal damping ratio of the structure change along with the change of the vibration response amplitude, which brings great challenges to the tuning control of the TLD. Therefore, the structure and the dynamic characteristic parameters of the TLD in the coupling vibration process must be accurately identified, and the optimal frequency and damping parameter setting can be carried out, so that the ideal control effect is achieved. The existing structure-TLD coupling system performance detection method mainly comprises the following steps: 1. and (3) directly identifying parameters by adopting modal analysis tools such as a random subtraction method, a linear fitting method and the like, obtaining the integral frequency and damping ratio of the coupling system, and subtracting the damping ratio when the structure is not controlled under the same wind speed and wind direction from the integral damping ratio to obtain the effective damping ratio of the TLD, thereby evaluating the vibration attenuation effect of the system. 2. And (3) acquiring the vibration mode of the coupling signal by adopting decoupling tools such as a blind source separation method, a wavelet transformation method and the like, then performing parameter identification on the modal response signal to obtain the modal parameters of the system, and then performing inverse pushing to obtain the respective dynamic characteristics of the structure and the TLD.

In the method, the method 1 directly identifies that only the integral frequency and damping ratio can be obtained, if the effective damping ratio of the TLD is to be obtained, the structural vibration response before the TLD is installed must be measured, but the conditions of the same wind speed and the same wind direction are difficult to meet due to the uncertainty and the non-repeatability of wind load and the time-varying characteristic of the modal parameter of the controlled structure; the decoupling effect of the method 2 is ideal when the damping ratio is small, but the decoupling cannot be fully realized when the damping ratio is large, the power spectrum at the moment does not meet the linear fitting assumption, and accurate power characteristic parameters cannot be obtained by adopting a conventional identification method.

Disclosure of Invention

The invention mainly aims to overcome the defects of the prior art and provide a subsystem dynamic characteristic detection method of a structure-TLD system, which avoids the problem of pre-supposing a power spectrum, does not need to measure the structural vibration response before TLD installation, and can detect the dynamic characteristic parameters of the system only by reconstructing a state space model of a coupling system.

In order to achieve the purpose, the invention adopts the following technical scheme:

a subsystem power characteristic detection method of a structure-TLD system comprises the following steps:

s1, measuring the coupling vibration response of the high-rise building and the TLD, and recording the coupling vibration signal in real time;

s2, constructing a Hankel matrix by the coupling signals so as to calculate a Toeplitz matrix;

s3, identifying the modal parameters of the coupling system by the Toeplitz matrix and judging the accuracy of the identification result by the stability criterion;

s4, judging whether the identification result is continuous and 5-order and keeps consistent;

s5, detecting the modal parameters corresponding to the structure and the TLD through a continuous state matrix of the reconstruction coupling system;

and S6, evaluating the system vibration damping performance through the structure and the dynamic characteristic parameters of the TLD.

Further, step S1 is specifically:

installing an accelerometer in a high-rise building to detect a floor wind vibration acceleration signal, installing a wave height meter in the TLD to detect a liquid level vibration signal, and collecting a coupling vibration signal;

the coupling data includes the structural acceleration response of the floor on which the TLD is located and the TLD level wave height response.

Further, step S2 specifically includes the following steps:

s21, preprocessing the coupling signal to enable the coupling signal to meet the modeling requirement of a state space model;

s22, constructing a Hankel matrix by specifying the number of the sub-blocks;

s23, equally dividing the Hankel matrix into two parts, wherein each part has the same sub-block number;

and S24, calculating the Toeplitz matrix according to the definition of the covariance.

Further, step S2 is specifically:

carrying out mean value removing processing on the building acceleration signal and the TLD wave height signal, converting the wave height signal into equivalent displacement of an equivalent TMD model according to the property of the TLD, and solving a second derivative of the displacement to obtain equivalent acceleration;

the number of the sub-blocks of the Hankel matrix needs to be set to be an even number, the number of the false sub-blocks is 2i, the Hankel matrix is constructed by coupling signals, and the specific formula is as follows:

wherein, y_iRepresenting a sequence formed by coupling signals at the ith moment, j represents the signal calculation time length, and assuming that the number of output channels of the coupling signals is l, the Hankel matrix belongs to the R^2il×jR represents the size of the matrix, and superscripts 2il and j represent the number of rows and columns;

the Hankel matrix in the formula (1) is equally divided into two parts, each part has i sub-block numbers, and the specific formula is as follows:

wherein the subscripts p and f represent past and future, Y, respectively_p∈R^il×j，Y_f∈R^il×j；

For the coupled vibration process under random excitation, the covariance matrix of the coupled signals is defined as:

wherein r is_ab(i) For the cross-correlation function of the measured data of the a-th and b-th output channels, the superscript T in formula (3) represents the matrix transposition, and E is the mathematical expectation symbol;

assuming that the coupled signal has ergodicity, combining the state space principle and the covariance matrix to define lambda_iThe calculation formula of (2) is as follows:

a, C, G is a state space matrix of the coupling system;

constructing a Toeplitz matrix by using the covariance matrix of the coupled signals, wherein the concrete formula is as follows:

wherein, O_iBeing observable matrices, gamma_iIs a controllable matrix.

Further, step S3 specifically includes the following steps:

s31, carrying out singular value decomposition on the Toeplitz matrix to obtain an observable matrix and a controllable matrix;

s32, calculating a state matrix and an output matrix of the coupling system;

s33, calculating modal parameters and modal shape of the coupling system;

and S34, screening the identification result by the stability criterion.

Further, step S3 is specifically:

singular value decomposition is carried out on the Toeplitz matrix, the rank of the matrix is reflected on the number of singular values which are not zero, and the specific formula is as follows:

wherein, U₁、V₁Is an orthogonal matrix, S₁A diagonal matrix composed of singular values;

considering system matrixes under different orders, supposing that the calculation order is n, comparing a formula (5) with a formula (6), and observing the U for the matrixes₁And S₁The first n columns are expressed, and the specific formula is as follows:

calculating a state matrix and an output matrix of the coupling system, wherein the specific formula is as follows:

wherein, superscript + represents the pseudo-inverse;

and (3) carrying out eigenvalue decomposition on the discrete state matrix, wherein the specific formula is as follows:

A＝ΨZΨ^-1 (9)

wherein the content of the first and second substances, for the eigenvalues of the discrete time system, ψ ∈ R^n×nIs a feature vector matrix;

because the actually acquired coupling signals are all on discrete time points, the parameter identification cannot be directly carried out, and calculation is needed in a continuous state, the characteristic value of a discrete time system is converted into continuous time, and the specific formula is as follows:

wherein the content of the first and second substances,is a characteristic value of a continuous-time system, Δ t is a time interval, a_m、b_mRespectively representing a real part and an imaginary part;

calculating modal parameters of the coupling system, including frequency and damping ratio, and the specific formula is as follows:

and obtaining the system modal shape from the output matrix and the characteristic vector, wherein the specific formula is as follows:

Φ＝CΨ (12)

setting stability criteria about frequency, damping ratio and modal shape for recognition results of different orders, wherein the specific formula is as follows:

and (4) screening results of each order through three conditions of a formula (13) to obtain modal parameters meeting the stability.

Further, step S4 is specifically:

obtaining a stable graph according to the recognition results of different orders, stopping calculation if the modal parameters of the 5 continuous orders are kept unchanged, taking the last result as the modal parameters of the coupling system, and entering step S5; if the requirement that the 5 continuous orders are not changed is not met all the time, the method returns to the step S2, the number of the Hankel matrix sub-blocks is re-designated to be larger, and then the steps S2 to S3 are repeated.

Further, step S5 specifically includes the following steps:

s51, constructing a diagonal matrix and a mode matrix;

s52, reconstructing a continuous state matrix of the structure controlled mode and the TLD coupling system;

s53, detecting respective dynamic characteristic parameters of the structure and the TLD.

Further, step S5 is specifically:

establishing a state space model of a multi-free structure and a TLD coupling system, establishing an equivalent TMD model according to the property of the TLD, and assuming that the TLD is installed on the nth degree of freedom of the structure and only the nth mode shape participates in vibration, the motion equation under the modal coordinate is as follows:

wherein m is_r、c_rAnd k_rRespectively, structure r-order modal mass, modal damping and modal stiffness, m_e、c_eAnd k_eEquivalent mass, equivalent damping and equivalent stiffness, x, of the TLD, respectively_nAnd x_eRespectively, the displacement of the nth degree of freedom of the structure and the equivalent displacement of the TLD, phi_rIn order to be of the r-th order mode,displacement of nth degree of freedom in the r-th order vibration mode, G is an excitation force action position matrix, and F is an excitation force vector;

the continuous state space equation of the coupled system according to the state space theory is expressed as:

wherein the content of the first and second substances,A_cis a state matrix, B_cAs an input matrix, A_cThe concrete expression is as follows:

where μ denotes the effective mass ratio, λ denotes the structural effective mass gain factor, ω_rAnd ζ_rThe frequency and the damping ratio of the structure' r order circle, omega_tAnd ζ_tThe round frequency and damping ratio of the TLD, respectively;

obtaining the modal parameters of the structure-TLD coupled system from the step S4, and reconstructing the continuous state matrix A 'of the structure controlled modal and the TLD coupled system'_c：

Wherein, gamma is_eBeing a mode-imparting matrix, Γ_e＝[φ₁,φ₂]，Λ_eIn the form of a diagonal matrix,diag denotes a matrix of elements in diagonal, the system identifies the continuous state matrix A 'being evaluated'_cContinuous state matrix A evaluated by theoretical analysis_cShould be approximately equal, therefore comparing equations (16) and (17) yields the dynamic characteristics of the structure and TLD, including the effective mass ratio and the respective frequencies and damping ratios of the subsystems, with the specific equation:

wherein, a_MNRepresents A'_cThe matrix has the elements of the M row and the N column.

Further, step S6 is specifically:

comparing the structural frequency obtained in the step S5 with the TLD frequency, if the difference is larger, indicating that the TLD is not tuned sufficiently, and changing the TLD frequency by lifting the water level;

simultaneously comparing the identification value and the design value of the TLD damping ratio, and evaluating an additional damping value added to the structure by the TLD; and dynamically evaluating the control effect of the coupling system by carrying out online batch processing on the data and tracking the change conditions of the structure and the TLD modal parameters.

Compared with the prior art, the invention has the following advantages and beneficial effects:

1. the method does not need to measure the structural vibration response before TLD installation, and can directly detect the dynamic characteristic parameters of the system through the coupling vibration signal.

2. According to the method, the mass ratio, the frequency and the damping ratio corresponding to the structure and the TLD are obtained by reconstructing a state space model of a coupling system without performing decoupling processing on the coupling signal in advance and making a pre-assumption on the form of a power spectrum.

3. According to the invention, the accuracy of the identification result can be judged by calculating the frequency deviation, the damping ratio deviation and the vibration mode correlation and drawing a corresponding modal parameter stability graph.

Drawings

FIG. 1 is a flow chart of a method of the present invention;

FIG. 2 is a flow chart of the present invention for computing a Toeplitz matrix from coupling data;

FIG. 3 is a flow chart of the present invention for identifying modal parameters of a coupled system;

FIG. 4 is a flow chart of the present invention for detecting respective dynamic characteristic parameters of the fabric and TLD;

FIG. 5 is a schematic view of a grated TLD in an embodiment of the present invention;

FIG. 6 is a schematic diagram of an equivalent TMD model according to an embodiment of the present invention;

FIG. 7a is a graph of the response time course of the structure acceleration for structure-TLD coupled vibration of an embodiment of the present invention;

FIG. 7b is a time-course response of the TLD liquid surface wave height for structure-TLD coupled vibration of an embodiment of the present invention;

fig. 8 is a parameter identification stability diagram of a coupling system according to an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.

Examples

As shown in fig. 1, a method for detecting subsystem dynamics of a fabric-TLD system includes the following steps:

s1, measuring coupling vibration responses of the super high-rise building and the TLD, and recording coupling vibration signals in real time, wherein the coupling vibration signals comprise structural acceleration responses of a floor where the TLD is located and TLD liquid level wave height responses; in this embodiment, the following are specifically mentioned:

an accelerometer is installed in the super high-rise building to monitor a floor wind vibration acceleration signal, a wave height meter is installed in the TLD to monitor a liquid level vibration signal, and then collected coupling data are transmitted back to the central server through the internet.

S2, constructing a Hankel matrix by the coupling signals so as to calculate a Toeplitz matrix; as shown in fig. 2, in this embodiment, the method specifically includes the following steps:

s21, preprocessing the coupling signal to enable the coupling signal to meet the modeling requirement of the state space model, specifically:

carrying out mean value removing processing on the building acceleration signal and the TLD wave height signal, converting the wave height signal into equivalent displacement of an equivalent TMD model according to the property of the TLD, and solving a second derivative of the displacement to obtain equivalent acceleration;

s22, constructing a Hankel matrix by specifying the number of the sub-blocks, specifically:

for the convenience of construction, the number of the Hankel matrix subblocks needs to be set to be an even number, the accuracy generally improves as the number of the subblocks increases, but the calculation period also greatly increases, so that the number of the subblocks with the proper size needs to be set in order to take speed and accuracy into consideration. The number of the false stator blocks is 2i, a Hankel matrix is constructed by coupling signals, and the specific formula is as follows:

wherein, y_iRepresenting a sequence formed by coupling signals at the ith moment, j represents signal calculation time, j is as large as possible in order to meet statistical estimation, and assuming that the number of output channels of the coupling signals is l in the invention, a Hankel matrix belongs to R^2il×jR represents the size of the matrix, and superscripts 2il and j represent the number of rows and columns;

s23, equally dividing the Hankel matrix into two parts, wherein each part has the same sub-block number, and the specific steps are as follows:

the Hankel matrix in the formula (1) is equally divided into two parts, each part has i sub-block numbers, and the specific formula is as follows:

wherein the subscripts p and f represent the past and future, respectively, and thus Y_p∈R^il×j，Y_f∈R^il×j；

S24, calculating a Toeplitz matrix according to the definition of the covariance, specifically:

for the coupled vibration process under random excitation, the covariance matrix of the coupled signals is defined as:

wherein r is_ab(i) For the cross-correlation function of the measured data of the a-th and b-th output channels, the superscript "T" represents the matrix transposition, and E is the mathematical expectation symbol;

given that the coupled signal has ergodicity, the combination of the state space principle and the covariance matrix defines the obtained Lambda_iThe calculation formula of (A) is as follows:

a, C, G is the state space matrix of the coupled system. Constructing a Toeplitz matrix by using the covariance matrix of the coupled signals, wherein the concrete formula is as follows:

wherein, O_iBeing observable matrices, gamma_iIs a controllable matrix.

S3, identifying the modal parameters of the coupling system by the Toeplitz matrix and judging the accuracy of the identification result by the stability criterion; as shown in fig. 3, in this embodiment, the method specifically includes the following steps:

s31, performing singular value decomposition on the Toeplitz matrix to obtain an observable matrix and a controllable matrix, specifically:

singular value decomposition is carried out on the Toeplitz matrix, the rank of the matrix is reflected on the number of singular values which are not zero, and the specific formula is as follows:

wherein, U₁、V₁Is an orthogonal matrix, S₁A diagonal matrix composed of singular values;

considering system matrixes under different orders, supposing that the calculation order is n, comparing formula (5) with formula (6), the observable matrix can use U₁And S₁The first n columns are expressed, and the specific formula is as follows:

s32, calculating a state matrix and an output matrix of the coupling system, wherein the specific formula is as follows:

A＝O_i(1:l,:)⁺O_i(l+1:2l,:)

C＝O_i(1:l,:) (8)

wherein, superscript + represents the pseudo-inverse;

s33, identifying modal parameters and modal shapes of the coupling system;

s34, screening the identification result by a stability criterion, specifically:

in the actual monitoring process, the coupling vibration signal is discrete data, so that the characteristic value decomposition is carried out on a discrete state matrix, and the specific formula is as follows:

A＝ΨZΨ^-1 (9)

wherein the content of the first and second substances, is a characteristic value of a discrete time system; psi ∈ R^n×nIs a feature vector matrix;

because the actually acquired coupling signals are all on discrete time points, the parameter identification cannot be directly carried out, and calculation is needed in a continuous state, the characteristic value of a discrete time system is converted into continuous time, and the specific formula is as follows:

wherein the content of the first and second substances,is a characteristic value of a continuous-time system, Δ t is a time interval, a_m、b_mRespectively representing a real part and an imaginary part; therefore, the modal parameters of the coupling system are evaluated, including frequency and damping ratio, and the specific formula is as follows:

the system mode shape is obtained by the output matrix and the characteristic vector, and the specific formula is as follows:

Φ＝CΨ (12)

setting stability criteria about frequency, damping ratio and modal shape for recognition results of different orders, wherein the specific formula is as follows:

and screening results of each order according to the three conditions to obtain modal parameters meeting the stability.

S4, judging whether the identification result is continuous and 5-order and keeps consistent; in this embodiment, the following are specifically mentioned:

obtaining a stable graph according to the recognition results of different orders, stopping calculation if the modal parameters of the 5 continuous orders are kept unchanged, taking the last result as the modal parameters of the coupling system, and entering step S5; if the requirement that the 5 continuous orders are not changed is not met all the time, the method returns to the step S2, the number of the Hankel matrix sub-blocks is re-designated to be larger, and then the steps S2 to S3 are repeated.

S5, detecting the modal parameters corresponding to the structure and the TLD through a continuous state matrix of the reconstruction coupling system; as shown in fig. 4, in this embodiment, the method specifically includes the following steps:

s51, constructing a diagonal matrix and a mode shape matrix;

s52, reconstructing a continuous state matrix of the structure controlled mode and the TLD coupling system;

s53, detecting respective dynamic characteristic parameters of the structure and the TLD; the method specifically comprises the following steps:

establishing a state space model of a multi-free structure and a TLD coupling system, establishing an equivalent TMD model according to the property of the TLD, and assuming that the TLD is installed on the nth degree of freedom of the structure and only the nth mode shape participates in vibration, the motion equation under the modal coordinate is as follows:

wherein m is_r、c_rAnd k_rRespectively, structure r-order modal mass, modal damping and modal stiffness, m_e、c_eAnd k_eEquivalent mass, equivalent damping and equivalent stiffness, x, of the TLD, respectively_nAnd x_eRespectively, the displacement of the nth degree of freedom of the structure and the equivalent displacement of the TLD, phi_rIn order to be of the r-th order mode,displacement of nth degree of freedom in the r-th order vibration mode, G is an excitation force action position matrix, and F is an excitation force vector; FIG. 6 is a schematic diagram of an equivalent TMD model.

The continuous state-space equation of the coupled system according to state-space theory can be expressed as:

wherein the content of the first and second substances,A_cis a state matrix, B_cIs an input matrix in which A_cCan be expressed as:

where μ denotes the effective mass ratio, λ denotes the structural effective mass gain factor, ω_rAnd ζ_rThe frequency and the damping ratio of the structure' r order circle, omega_tAnd ζ_tThe round frequency and damping ratio of the TLD, respectively;

obtaining the modal parameters of the structure-TLD coupled system from the step S4, and reconstructing the continuous state matrix A 'of the structure controlled modal and the TLD coupled system'_c：

Wherein, gamma is_eBeing a mode-imparting matrix, Γ_e＝[φ₁,φ₂]，Λ_eIn the form of a diagonal matrix,diag denotes the diagonal element composition matrix, the system identifies the continuous state matrix A 'being evaluated'_cContinuous state matrix with theoretical analytical evaluationA_cShould be approximately equal, so comparing equation (16) with equation (17), the effective mass ratio, frequency and damping ratio of the structure and TLD can be obtained, with the following equations:

wherein, a_MNRepresents A'_cThe matrix has the elements of the M row and the N column.

S6, evaluating the system vibration damping performance through the structure and the dynamic characteristic parameters of the TLD; in this embodiment, the following are specifically mentioned:

comparing the structural frequency obtained in the step S5 with the TLD frequency, wherein if the difference is large, the TLD is not tuned sufficiently, and the TLD frequency needs to be changed in a mode of lifting the water level and the like; simultaneously comparing the identification value and the design value of the TLD damping ratio, and evaluating an additional damping value which can be added to the structure by the TLD; and dynamically evaluating the control effect of the coupling system by carrying out online batch processing on the data and tracking the change conditions of the structure and the TLD modal parameters.

In the present example, the TLD size L × b × H (length × width × height) is 21m × 6.4m × 7m, and the still water depth H is 4.4 m. Inside the TLD, grid elements with a consistency ratio of 0.42 and a thickness of 2cm were installed at 8.4m and 12.6m, respectively, to increase the damping ratio of the TLD. The TLD peripheral walls and the grid members are all considered rigid bodies, irrespective of deformation. Fig. 5 is a schematic view of the grille TLD in this embodiment. Assuming that the frequency of the single-freedom-degree structure is 0.146Hz, the damping is 0.02, the TLD first-order modal frequency and the damping ratio are 0.146Hz and 0.036 from theoretical values, and the mass ratio of the structure to the TLD is 0.01. The structure-TLD coupled system may be equivalent to a structure-TMD coupled system, assuming only TLD first order modal vibrations are considered. As shown in fig. 7a and 7b, the coupled system is monitored in real time, acceleration response and TLD liquid level wave height response after the structure is controlled can be obtained, the maximum acceleration of the structure is 0.119m/s2, the maximum TLD wave height is 4.93m, and the height of the water tank is not exceeded.

The number of the Hankel matrix sub-blocks is finally determined to be 600 by trial calculation, the modal parameters of the coupled system within 50 th order are identified and drawn into a stable graph, and the result is shown in figure 8. From fig. 8, it can be known that the coincidence degree of the result and the structural response power spectrum is high, the frequency stability axis exactly corresponds to the peak value of the power spectrum, and the 50-order result meets the condition of continuous 5-order conformity stability, so the modal characteristic value and the corresponding mode shape of the result are taken as the modal parameters of the coupling system, and the diagonal matrix Λ is constructed_eAnd a mode matrix gamma_e。

According to the formula (17) and the formula (18), by_eAnd Γ_eAnd reconstructing a continuous state matrix of the coupling system, namely calculating to obtain a mass ratio, a frequency and a damping ratio of the structure and the TLD, wherein the mass ratio, the frequency and the damping ratio are shown in a table 1 below and are a modal parameter identification result table corresponding to the structure and the TLD. In order to further illustrate the advantages of the invention, the calculation result of the MBSDA method for decoupling based on blind source separation is also provided.

TABLE 1

As can be seen from Table 1, the method and the MBSDA method can identify the frequency more accurately, and the calculation result is close to the theoretical frequency. But for the mass ratio and the structure and TLD damping ratio, the calculation result of the method is closer to the theoretical value, and the accuracy is higher than that of the MBSDA method. Therefore, the method is more suitable for detecting and evaluating the structure and TLD dynamic characteristic parameters, and provides reference for further optimizing TLD tuning control and performance evaluation measures.

According to the method, firstly, the coupling vibration response of the super high-rise building and the TLD is measured, then parameter identification is carried out on the coupling system according to a state space theory, then a state space equation of the coupling system is reconstructed according to an identification result, and further the mass ratio, the frequency and the damping ratio of the structure and the TLD are obtained through calculation. Compared with the prior art, the method and the device avoid the problem of pre-supposing the power spectrum, do not need to measure the structural vibration response before TLD installation, and can detect the dynamic characteristic parameters of the system only by reconstructing the state space model of the coupling system. The method has the characteristics of high precision, good stability and wide applicability, is clear and concise in implementation form, is suitable for engineering application, and can provide accurate data support for TLD tuning control and performance evaluation.

It should also be noted that in this specification, terms such as "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.