CN113686528B - Subsystem power characteristic detection method of structure-TLD system - Google Patents

Subsystem power characteristic detection method of structure-TLD system Download PDF

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CN113686528B
CN113686528B CN202110855817.7A CN202110855817A CN113686528B CN 113686528 B CN113686528 B CN 113686528B CN 202110855817 A CN202110855817 A CN 202110855817A CN 113686528 B CN113686528 B CN 113686528B
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周子杰
谢壮宁
张蓝方
张乐乐
石碧青
江毅
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South China University of Technology SCUT
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Abstract

The invention discloses a subsystem power characteristic detection method of a structure-TLD system, which comprises the following steps: s1, measuring coupling vibration response of a high-rise building and a TLD (traffic light detection) and recording a 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 a structure and modal parameters corresponding to the TLD through a continuous state matrix of a 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.

Description

Subsystem power characteristic detection method of structure-TLD system
Technical Field
The invention belongs to the technical field of structural vibration control, and particularly relates to a subsystem dynamic characteristic detection method 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 practical 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 decoupling tools such as a blind source separation method, a wavelet transform 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 direction are difficult to meet due to the uncertainty and the non-repeatability of wind load and the time-varying characteristic of a controlled structure modal parameter; 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 method avoids the problem of pre-assumption of a power spectrum, does not need to measure 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 coupling vibration response of a high-rise building and a TLD (total temperature detector), and recording a coupling vibration signal in real time;
s2, constructing a Hankel matrix by the coupling signals so as to calculate a Toeplitz matrix;
s3, identifying 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 keeps consistency in 5 continuous orders or not;
s5, detecting a structure and modal parameters corresponding to the TLD through a continuous state matrix of a 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 specifically includes:
installing an accelerometer in a high-rise building to detect a floor wind vibration acceleration signal, installing a wave height meter in a 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 a Toeplitz matrix according to the definition of the covariance.
Further, step S2 specifically includes:
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:
Figure BDA0003184143800000031
wherein, y i Representing 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×j R 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:
Figure BDA0003184143800000032
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 signal is defined as:
Figure BDA0003184143800000041
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 coupling signal has ergodicity, and combining the state space principle and covariance matrix to define lambda i The calculation formula of (c) is:
Figure BDA0003184143800000042
wherein, A, C and G are state space matrixes of the coupling system;
constructing a Toeplitz matrix by using the covariance matrix of the coupled signals, wherein the concrete formula is as follows:
Figure BDA0003184143800000043
wherein, O i Being observable matrices, gamma i Is a controllable matrix.
Further, step S3 specifically includes the following steps:
s31, performing 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 vibration modes of the coupling system;
and S34, screening the identification result according to the stability criterion.
Further, step S3 specifically includes:
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:
Figure BDA0003184143800000044
wherein, U 1 、V 1 Is an orthogonal matrix, S 1 A 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 matrixes 1 And S 1 The first n columns are expressed, and the specific formula is as follows:
Figure BDA0003184143800000051
calculating a state matrix and an output matrix of the coupling system, wherein the specific formula is as follows:
Figure BDA0003184143800000052
wherein, superscript + represents the pseudo-inverse;
and carrying out eigenvalue decomposition on the discrete state matrix, wherein the specific formula is as follows:
A＝ΨZΨ -1 (9)
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003184143800000053
Figure BDA0003184143800000054
for the eigenvalues of the discrete time system, ψ ∈ R n×n Is 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:
Figure BDA0003184143800000055
wherein the content of the first and second substances,
Figure BDA0003184143800000056
is a characteristic value of a continuous-time system, Δ t is a time interval, a m 、b m Respectively 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:
Figure BDA0003184143800000057
and obtaining the system modal shape from the output matrix and the characteristic vector, wherein the specific formula is as follows:
Φ＝CΨ (12)
for the recognition results of different orders, stability criteria about frequency, damping ratio and modal shape are set, and the specific formula is as follows:
Figure BDA0003184143800000061
and (4) screening results of each order through three conditions of a formula (13) to obtain modal parameters meeting the stability.
Further, step S4 specifically includes:
obtaining a stable graph according to the recognition results of different orders, stopping calculation if the modal parameters of 5 continuous orders are kept unchanged, taking the last result as the modal parameters of the coupling system, and entering step S5; and if the requirement that the 5 continuous orders are not changed is not met all the time, returning to the step S2, reassigning a larger Hankel matrix sub-block number, and repeating the step S2 to the step S3.
Further, step S5 specifically includes the following steps:
s51, constructing a diagonal matrix and a vibration mode matrix;
s52, reconstructing a continuous state matrix of the structure controlled mode and the TLD coupling system;
and S53, detecting respective dynamic characteristic parameters of the structure and the TLD.
Further, step S5 specifically includes:
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:
Figure BDA0003184143800000062
wherein m is r 、c r And k r Respectively, the structure r-order modal mass, modal damping and modal stiffness, m e 、c e And k e Equivalent mass, equivalent damping and equivalent stiffness, x, of the TLD, respectively n And x e Respectively, the displacement of the nth degree of freedom of the structure and the equivalent displacement of the TLD, phi r In order to be of the r-th order mode,
Figure BDA0003184143800000063
the displacement of the nth degree of freedom in the r-order vibration mode, G is an action position matrix of the exciting force, and F is an exciting force vector;
the continuous state space equation of the coupled system according to the state space theory is expressed as:
Figure BDA0003184143800000071
wherein the content of the first and second substances,
Figure BDA0003184143800000072
A c is a state matrix, B c As an input matrix, A c The concrete expression is as follows:
Figure BDA0003184143800000073
where μ denotes the effective mass ratio, λ denotes the structure effective mass gain coefficient, ω r And ζ r Respectively, the structure r order circle frequency and the damping ratio, omega t And ζ t The circular frequency and damping ratio of the TLD, respectively;
obtaining the modal parameters of the structure-TLD coupling system from the step S4, and reconstructing the continuous state matrix A 'of the structure controlled modal and the TLD coupling system' c ：
Figure BDA0003184143800000074
Wherein, gamma is e Being a mode-imparting matrix, Γ e ＝[φ 1 ,φ 2 ]，Λ e In the form of a diagonal matrix,
Figure BDA0003184143800000075
diag denotes a matrix of elements in diagonal, the system identifies the continuous state matrix A 'being evaluated' c Continuous state matrix A evaluated by theoretical analysis c Should be approximately equal, so comparing equations (16) and (17) yields the structure and power of the TLDThe characteristic parameters comprise effective mass ratio and respective frequency and damping ratio of the subsystems, and the specific formula is as follows:
Figure BDA0003184143800000076
wherein, a MN Is represented by A' c The matrix has the elements of the M row and the N column.
Further, step S6 specifically includes:
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 for 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 condition 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 embodiments of the present invention are 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 a super high-rise building and a TLD (thermal liquid level detector), 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 a state space model, and specifically comprises the following steps:
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:
Figure BDA0003184143800000101
wherein, y i Representing 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×j R 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:
Figure BDA0003184143800000102
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:
Figure BDA0003184143800000103
wherein r is ab (i) For the cross-correlation function of the measured data of the a-th and b-th output channel, the superscript "T" denotes the matrix transposition,e is a 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 i The calculation formula of (A) is as follows:
Figure BDA0003184143800000111
wherein, A, C and G are state space matrixes of the coupling system. Constructing a Toeplitz matrix by using the covariance matrix of the coupled signals, wherein the concrete formula is as follows:
Figure BDA0003184143800000112
wherein, O i Being observable matrices, gamma i Is 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, carrying out 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:
Figure BDA0003184143800000113
wherein, U 1 、V 1 Is an orthogonal matrix, S 1 A diagonal matrix composed of singular values;
considering the system matrix under different orders, if the calculation order is n, comparing formula (5) and formula (6), the available U of the matrix can be observed 1 And S 1 The first n columns are expressed, and the specific formula is as follows:
Figure BDA0003184143800000114
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 vibration modes of the coupling system;
s34, screening identification results according to a stability criterion, which specifically comprises the following steps:
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 first and the second end of the pipe are connected with each other,
Figure BDA0003184143800000121
Figure BDA0003184143800000122
a characteristic value of a discrete time system; psi ∈ R n×n Is 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:
Figure BDA0003184143800000123
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003184143800000124
is a characteristic value of a continuous-time system, Δ t is a time interval, a m 、b m Respectively 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:
Figure BDA0003184143800000125
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:
Figure BDA0003184143800000126
Figure BDA0003184143800000127
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 5 continuous orders are kept unchanged, taking the last result as the modal parameters of the coupling system, and entering step S5; and if the requirement that the 5 continuous orders are not changed is not met all the time, returning to the step S2, reassigning a larger Hankel matrix sub-block number, and repeating the step S2 to the step S3.
S5, detecting a structure and modal parameters corresponding to the TLD through a continuous state matrix of a 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 vibration 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; 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:
Figure BDA0003184143800000131
Figure BDA0003184143800000132
wherein m is r 、c r And k r Respectively, structure r-order modal mass, modal damping and modal stiffness, m e 、c e And k e Equivalent mass, equivalent damping and equivalent stiffness, x, of the TLD, respectively n And x e Respectively, the displacement of the nth degree of freedom of the structure and the equivalent displacement of the TLD, phi r Is of the r-th order vibration mode,
Figure BDA0003184143800000133
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 for a coupled system according to state space theory can be expressed as:
Figure BDA0003184143800000134
wherein the content of the first and second substances,
Figure BDA0003184143800000135
A c is a state matrix, B c Is an input matrix in which A c Can be expressed as:
Figure BDA0003184143800000141
where μ denotes the effective mass ratio, λ denotes the structural effective mass gain factor, ω r And ζ r The frequency and the damping ratio of the structure' r order circle, omega t And ζ t The circular frequency and damping ratio of the TLD, respectively;
obtaining the modal parameters of the structure-TLD coupling system from the step S4, and reconstructing the continuous state matrix A 'of the structure controlled modal and the TLD coupling system' c ：
Figure BDA0003184143800000142
Wherein, gamma is e Being a mode-imparting matrix, Γ e ＝[φ 1 ,φ 2 ]，Λ e Is a diagonal matrix of the two angles,
Figure BDA0003184143800000143
diag denotes the diagonal element composition matrix, the system identifies the continuous state matrix A 'being evaluated' c Continuous state matrix A evaluated by theoretical analysis c Should 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:
Figure BDA0003184143800000144
Figure BDA0003184143800000145
wherein, a MN Represents A' c The 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 specific:
comparing the structural frequency obtained in the step S5 with the TLD frequency, and if the difference is large, indicating that the TLD is not sufficiently tuned, changing the TLD frequency 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 this embodiment, the TLD size L × b × H (length × width × height) is 21m × 6.4m × 7m, and the still water depth H =4.4m. 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 surrounding walls and grid members are 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 and 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 peak is 0.119m/s2, the maximum TLD wave height is 4.93m, and the maximum TLD wave height does not exceed the height of the water tank.
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 e And F matrix e 。
According to the formula (17) and the formula (18), the expression is expressed by Λ e And Γ e And 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 shown.
Figure BDA0003184143800000151
TABLE 1
As can be seen from Table 1, the method and the MBSDA method can identify the frequency more accurately, and the calculation results are 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 the present 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 phrases "comprising a," "8230," "8230," or "comprising" does not exclude the presence of additional like 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.

Claims (5)

1. A subsystem power characteristic detection method of a structure-TLD system is characterized by comprising the following steps:
s1, measuring coupling vibration response of a high-rise building and a TLD (total temperature detector), and recording a coupling vibration signal in real time;
s2, constructing a Hankel matrix by the coupling vibration signals so as to calculate a Toeplitz matrix;
s3, identifying modal parameters of the coupling system by the Toeplitz matrix and judging the accuracy of the identification result by the stability criterion; the method specifically comprises the following steps:
s31, performing 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 vibration modes of the coupling system;
s34, screening the identification result according to the stability criterion;
the method specifically comprises the following steps:
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:
Figure FDA0003695500030000011
wherein, U 1 、V 1 Is an orthogonal matrix, S 1 A diagonal matrix composed of singular values;
considering the system matrix at different orders, assuming the calculation order is n, comparing the Toeplitz matrix calculated in step S2 with equation (6),u for observable matrix 1 And S 1 The first n columns are expressed, and the specific formula is as follows:
Figure FDA0003695500030000012
calculating a state matrix and an output matrix of the coupling system, wherein the specific formula is as follows:
Figure FDA0003695500030000013
wherein, superscript + represents the pseudo-inverse; l is the number of output channels of the coupled vibration signal;
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,
Figure FDA0003695500030000014
for the eigenvalues of the discrete time system, ψ ∈ R n×n Is a feature vector matrix;
because the actually acquired coupling vibration signals are all at discrete time points, the parameters cannot be directly identified, 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:
Figure FDA0003695500030000021
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003695500030000022
is a characteristic value of a continuous-time system, Δ t is a time interval, a m 、b m Respectively 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:
Figure FDA0003695500030000023
and solving the system modal shape according to the output matrix and the characteristic vector matrix, 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:
Figure FDA0003695500030000024
screening results of each order through three conditions of a formula (13) to obtain modal parameters meeting the stability;
s4, judging whether the identification result is continuous and 5-order and keeps consistent; the method specifically comprises the following steps:
obtaining a stable graph according to the recognition results of different orders, stopping calculation if the modal parameters of 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 continuous 5-order matrix is not changed is not met all the time, returning to the step S2, appointing a larger number of Hankel matrix sub-blocks again, and then repeating the steps S2 to S3;
s5, detecting a structure and modal parameters corresponding to the TLD through a continuous state matrix of a reconstruction coupling system; the method specifically 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;
the step S5 specifically comprises the following steps:
establishing a state space model of a multi-degree-of-freedom 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 vibration mode participates in vibration, the motion equation under the modal coordinate is as follows:
Figure FDA0003695500030000031
wherein m is r 、c r And k r Respectively, structure r-order modal mass, modal damping and modal stiffness, m e 、c e And k e Equivalent mass, equivalent damping and equivalent stiffness, x, of the TLD, respectively n And x e Respectively, the displacement of the nth degree of freedom of the structure and the equivalent displacement of the TLD, phi r In order to be of the r-th order mode,
Figure FDA0003695500030000032
the displacement of the nth degree of freedom in the r-order vibration mode, G is an action position matrix of the exciting force, and F is an exciting force vector;
the continuous state space equation of the coupled system according to the state space theory is expressed as:
Figure FDA0003695500030000033
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003695500030000034
A c is a state matrix, B c As an input matrix, A c The concrete expression is as follows:
Figure FDA0003695500030000035
where μ denotes the effective mass ratio, λ denotes the structural effective mass gain factor, ω r And ζ r Respectively, the structure r order circle frequency and the damping ratio, omega t And ζ t The round frequency and damping ratio of the TLD, respectively;
obtaining the modal parameters of the structure-TLD coupling system by the step S4, reconstructing the controlled mode of the structure and the TLD couplingContinuous state matrix A 'of the system' c ：
Figure FDA0003695500030000036
Wherein, gamma is e Being a mode-imparting matrix, Γ e ＝[φ 1 ,φ 2 ]，Λ e Is a diagonal matrix of the two angles,
Figure FDA0003695500030000037
diag denotes a matrix of elements in diagonal, the system identifies the continuous state matrix A 'being evaluated' c Continuous state matrix A evaluated by theoretical analysis c Should 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:
Figure FDA0003695500030000041
wherein, a MN Is represented by A' c The M row and the N column of the matrix;
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 characteristics of the structure-TLD system according to claim 1, wherein the 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.
3. The method for detecting the subsystem dynamics of a fabric-TLD system as claimed in claim 1, wherein the step S2 comprises the steps of:
s21, preprocessing the coupled vibration signal to enable the coupled vibration signal to meet the modeling requirement of a state space model;
s22, constructing a Hankel matrix by specifying the number of subblocks;
s23, equally dividing the Hankel matrix into two parts, wherein each part has the same sub-block number;
and S24, calculating a Toeplitz matrix according to the definition of the covariance.
4. The method for detecting the subsystem power characteristics of the structure-TLD system according to claim 3, wherein the 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 equivalent 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 vibration signals, and the specific formula is as follows:
Figure FDA0003695500030000051
wherein, y i Representing a sequence formed by coupling vibration signals at the ith moment, j represents the signal calculation time length, and assuming that the number of output channels of the coupling vibration signals is l, the Hankel matrix belongs to the R 2il×j R 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:
Figure FDA0003695500030000052
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 vibration signal is defined as:
Figure FDA0003695500030000053
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 vibration signal has ergodicity, and combining the state space principle and the covariance matrix to define lambda i The calculation formula of (2) is as follows:
Figure FDA0003695500030000054
wherein, A, C and G are state space matrixes of the coupling system;
constructing a Toeplitz matrix by using the covariance matrix of the coupled vibration signals, wherein the concrete formula is as follows:
Figure FDA0003695500030000061
wherein, O i Being observable matrices, F i Is a controllable matrix.
5. The method for detecting the subsystem power characteristic of the fabric-TLD system as claimed in claim 1, 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.
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