CN112506058A - Working modal parameter identification method and system of linear time-varying structure - Google Patents
Working modal parameter identification method and system of linear time-varying structure Download PDFInfo
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Abstract
The invention relates to a working mode parameter identification method and a system of a linear time-varying structure, wherein the method comprises the following steps: acquiring a data matrix of a vibration response signal of a linear time-varying structure within set time; dividing the data matrix into a plurality of sub-matrixes with set time length; establishing Laplace feature mapping of the submatrix; solving the Laplace feature mapping to obtain a modal response matrix of the submatrix; obtaining the mode vibration mode of the submatrix according to the mode response matrix; solving frequency domain data of the modal response matrix; and taking the maximum value in the frequency domain data as the modal frequency of the sub-matrix. The invention calculates the modal parameter of each sub-matrix independently, can reduce the calculation time and space complexity of the modal parameter, and improves the identification efficiency of the modal parameter.
Description
Technical Field
The invention relates to the technical field of modal parameter identification, in particular to a method and a system for identifying working modal parameters of a linear time-varying structure.
Background
The mode is the vibration characteristic of the structure, parameters (such as mode natural frequency, vibration mode, damping ratio and the like) of each order of mode are identified through an experimental mode analysis method, the dynamic characteristic of the structure can be known, and further damage identification of the structure, fault detection of equipment and the like can be carried out. However, for many large complex structures, the only excitation available is ambient excitation in the operating state, which results in an inability to measure excitation input. Unlike conventional Experimental Modal Analysis (EMA), Operational Modal Analysis (OMA) may identify modal parameters from only the measured vibration response signal. In recent years, OMA is a hot spot in the field of mechanical vibration research and has been widely used.
In reality, most engineering structures have time-varying characteristics, and the physical characteristics (mass, rigidity, damping, and the like) of the structures change with time, so the modal parameters of the structures also change with time. For example, train bridges, launching satellites, rotating machinery, etc. all exhibit time-varying characteristics of the structure. The vibration response signal of the structure cannot be obtained all at once, but is obtained by slowly sampling along with time variation, so that a method for identifying the working modal parameters of the time-varying structure needs to be provided according to the time-varying characteristic of the structure.
The sliding window method based on the 'time freezing' theory is a method capable of identifying the working modal parameters of a time-varying system, and the sliding window method is already applied to some algorithms. The official Wien et al propose that the sliding window principal component analysis is carried out on the working modal parameter identification of the time-varying structure, and the method has higher time and space complexity and is not easy to be embedded into portable equipment.
Disclosure of Invention
The invention aims to provide a method and a system for identifying working modal parameters of a linear time-varying structure, which improve the identification efficiency of the modal parameters.
In order to achieve the purpose, the invention provides the following scheme:
a working mode parameter identification method of a linear time-varying structure comprises the following steps:
acquiring a data matrix of a vibration response signal of a linear time-varying structure within set time;
dividing the data matrix into a plurality of sub-matrixes with set time length;
establishing Laplace feature mapping of the submatrix;
solving the Laplace feature mapping to obtain a modal response matrix of the submatrix;
obtaining the mode vibration mode of the submatrix according to the mode response matrix;
solving frequency domain data of the modal response matrix;
and taking the maximum value in the frequency domain data as the modal frequency of the sub-matrix.
Optionally, the vibration response signal is obtained by a vibration response sensor.
Optionally, the modal response matrix is obtained by performing least square generalized inverse solution on the modal response matrix.
Optionally, the least squares generalized inverse solution formula is
Wherein the content of the first and second substances,
represents the mode shape of the ith sub-matrix,
it represents the i-th sub-matrix,
and a mode response matrix representing the ith sub-matrix, wherein L represents the set time length.
Optionally, the frequency domain data of the modal response matrix is solved by a single degree of freedom system or fourier transform.
The invention also discloses a working mode parameter identification system of the linear time-varying structure, which comprises the following steps:
the data matrix acquisition module is used for acquiring a data matrix of a vibration response signal of the linear time-varying structure within set time;
the sub-matrix acquisition module is used for dividing the data matrix into a plurality of sub-matrices with set time length;
the Laplace eigenmap establishing module is used for establishing Laplace eigenmap of the sub-matrix;
the modal response matrix solving module is used for solving the Laplace feature mapping to obtain a modal response matrix of the submatrix;
the modal shape determining module is used for obtaining the modal shape of the submatrix according to the modal response matrix;
the frequency domain data solving module is used for solving the frequency domain data of the modal response matrix;
and the modal frequency determining module is used for taking the maximum value in the frequency domain data as the modal frequency of the submatrix.
Optionally, the vibration response signal is obtained by a vibration response sensor.
Optionally, the modal response matrix is obtained by performing least square generalized inverse solution on the modal response matrix.
Optionally, the least squares generalized inverse solution formula is
Wherein the content of the first and second substances,
represents the mode shape of the ith sub-matrix,
it represents the i-th sub-matrix,
and a mode response matrix representing the ith sub-matrix, wherein L represents the set time length.
Optionally, the frequency domain data of the modal response matrix is solved by a single degree of freedom system or fourier transform.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a method and a system for identifying working modal parameters of a linear time-varying structure, which are used for acquiring a data matrix of a vibration response signal of the linear time-varying structure within set time; dividing the data matrix into a plurality of sub-matrixes with set time length; the modal parameters of each submatrix are independently calculated, so that the calculation time and space complexity of the modal parameters can be reduced, and the identification efficiency of the modal parameters is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a schematic flow chart of a method for identifying working mode parameters of a linear time-varying structure according to an embodiment of the present invention;
FIG. 2 is a finite element model with three degrees of freedom with slow mass and time varying according to an embodiment of the present invention;
FIG. 3 is a MATLAB/Simulink linear time-varying three-degree-of-freedom simulation model according to an embodiment of the present invention;
FIG. 4 shows a Gaussian white noise and displacement response signal according to an embodiment of the present invention;
FIG. 5 is a graph illustrating identification of first and third order natural frequencies over a 0-20 time period based on sliding window LE time varying structural operating mode parameters according to an embodiment of the present invention;
fig. 6 is a graph illustrating changes in the confidence coefficient MAC values during a time period from 0 to 20 based on the identification of the working mode parameters of the sliding window LE-based time-varying structure in the embodiment of the present invention;
FIG. 7 is a graph illustrating the identification of the first and third order natural frequencies during the time period 0-1950s based on the working mode parameters of the sliding window LE time varying structure according to an embodiment of the present invention;
FIG. 8 is a graph illustrating the variation of the confidence coefficient MAC value during the time period from 0s to 1950s based on the identification of the working mode parameters of the LE time varying structure of the sliding window according to the embodiment of the present invention;
fig. 9 is a schematic structural diagram of a system for identifying working mode parameters of a linear time-varying structure according to an embodiment of the present invention;
FIG. 10 shows the partitioning result of the data matrix X (t) in the partition decomposition.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for identifying working modal parameters of a linear time-varying structure, which improve the identification efficiency of the modal parameters.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a schematic flow diagram of a method for identifying working mode parameters of a linear time-varying structure according to the present invention, and the method for identifying working mode parameters of a linear time-varying structure according to the present invention is a method for identifying working mode parameters of a time-varying structure based on a sliding window LE, as shown in fig. 1, the method for identifying working mode parameters of a linear time-varying structure includes the following steps:
step 101: a data matrix of vibration response signals of a linear time-varying structure within a set time is obtained.
Wherein, step 101 specifically includes: obtaining a stationary signal data matrix of a plurality of vibration response sensors of a linear time-varying structure under environmental excitation over a period of time
Step 102: and dividing the data matrix into a plurality of sub-matrixes with set time length.
Wherein, step 102 specifically comprises:
data matrix
And (5) performing division decomposition. The sliding window length L is initially set,
for a vibration response signal with a first window length L,
for the vibration response signal of ith window length L, i.e.
For setting the sub-matrix with the time length L, the division result is as follows:
the division results are shown in fig. 10.
Where n represents the number of sensors, and T represents the sampling time, i.e., the set time is T. At each window
Within, the system is considered to be time invariant.
Step 103: and establishing Laplace feature mapping of the submatrices.
Step 104: and solving the Laplace eigen mapping to obtain a modal response matrix of the submatrix.
Wherein, the step 103-104 specifically comprises:
in the ith (i ═ 1,2, …, T +1-L) window after decomposition
Establishing a Laplace feature mapping (LE), and solving a model of the window working modal parameter, specifically for each point in the ith (i ═ 1,2, …, T +1-L) window
Find the k nearest neighbors to it
Weight w of each neighborlj(j ∈ k) size can be scaled by a Gaussian kernel function
Calculating (w)ljRepresenting sample points
And
weights on the graph, σ is a width parameter of the function), thereby constructing an adjacency matrix W ═ Wlj]To reconstruct the data set
Local structural features of (1). Let the diagonal matrix D be
The mapping degree matrix is
L (L ═ D-W) is the laplacian matrix of the graph. Laplace eigenmap pass pair formulation
Decomposing the eigenvalue, and dividing d (d < n) minimum non-zero eigenvalues lambda1,λ2,…λi…,λdCorresponding feature vector
And is output as a result of the dimension reduction,
representation featureThe value λ corresponds to the feature vector. Feature vector
LE algorithm to obtain low dimensional embeddings
Modal response matrix corresponding to ith moment
Namely, it is
Step 105: and obtaining the mode vibration mode of the submatrix according to the mode response matrix.
Wherein, step 105 specifically comprises: data matrix of vibration response signals in modal coordinates
Can be decomposed into x (T) ═ Φ q (T), and thus, the ith (i ═ 1,2, …, T +1-L) windows
In, satisfy the formula
It is known that
Modal response matrix
The modal shape is solved by using least square method generalized inverse solution, and the formula of least square method generalized inverse solution is
Step 106: and solving the frequency domain data of the modal response matrix.
Wherein, step 106 specifically includes: by passingThe frequency domain data of the modal response matrix is obtained by a single degree of freedom (SDOF) technology or Fourier transform (FFT). For example: shape response matrix
Substituting into Fourier transform (FFT) formula
And obtaining frequency domain data.
Step 107: and taking the maximum value in the frequency domain data as the modal frequency of the sub-matrix.
Wherein after step 107, the i (i-1, 2, …, T +1-L) th window is identified
After the working mode parameters in the window are included, the working mode parameters include the mode shape and the mode frequency, the window is slid to the right to (i +1) (i ═ 1,2, …, T-L) windows (i +1) (i ═ 1,2, …, T-L) sub-matrices), and the working mode parameters in the window (time period) are calculated according to steps 103 to 107. And continuously sliding in the way until the (T +1-L) th window is identified, and arranging the working modal parameters obtained in each time period in a time sequence, so as to track the time-varying characteristic of the structure and form the modal parameters of the time-varying structure.
The following describes the method for identifying the working mode parameters of the linear time-varying structure disclosed in the present invention in detail with reference to specific vibration response signals.
1) The working modal parameters of the time-varying structure vary with time, and according to the structure dynamics theory, the problem of working modal identification of the time-varying structure can be described as that the duration is T epsilon [ T ∈ [ ]BEGIN,TEND]For an n-degree-of-freedom linear time-varying vibration structure system, the motion equation of the system in a physical coordinate system is as follows:
wherein the content of the first and second substances,
and
respectively represent T ∈ [ T ] over timeBEGIN,TEND]A varying mass matrix, a damping matrix, and a stiffness matrix. At the same time, they change over time under the influence of the structure.
An excitation vector representing the external load,
and
respectively representing an acceleration response signal matrix, a velocity response signal matrix and a displacement response signal matrix.
2) According to the theory of 'time freezing', the discrete multi-degree-of-freedom system with the time-varying structure is in a certain extremely small time period tau epsilon [ tbegin,tend]Its mass, damping and stiffness can be considered to be time invariant, and therefore, at the complete T e TBEGIN,TEND]The kinetic equation of the time-varying structure in the physical coordinate system during the time period can be expressed as:
where S '(t) denotes a time-invariant structure at the time when t ═ τ, and S' denotes a set of time-variant structures composed of K linear time-invariant structures.
3) For a small damping time-varying structure, the response data can be divided into a finite number of parts, in the τ th part, a certain window length is selected, and the modal coordinate response of the linear system is:
wherein the content of the first and second substances,
represents the mode shape of the τ -th window,
a modal response matrix representing the τ -th window.
4) Modal frequency ω of each order of the time varying structureiWhen the two modes are not equal, the normalized orthogonality is satisfied between the mode shapes of the orders, and the mode responses of the orders are not related to each other, as follows:
5) suppose that for a very short period of time τ e [ t ]begin,tend]The system is considered to be time invariant, i.e., time t e tBEGIN,tEND]Is divided into finite segments tau e [ t [ [ T ]begin,tend]At each time period tau e [ t ∈ [ ]begin,tend]And finally, arranging each time period according to the time sequence to form the modal parameters of the time-varying structure.
The window length of the response data is L, n represents the number of sensors, and T represents the sampling time.
6) For n degrees of freedomAnd the damping is small, the time-varying vibration response data of the structure can be obtained by selecting the length L of a certain window to be tbegin-tendDivided into a finite number of parts in the ith window (τ e [ t ]begin,tend]) The modal coordinate response of a linear system is:
wherein the content of the first and second substances,
the mode shape vector of the n-order mode of the structure in the ith window
The formed mode shape matrix is composed of a plurality of modes,
is a response of the n-order mode of the structure
And forming a modal response matrix. The natural frequency ω of each order mode in the ith window of the structureiWhen the two modes are not equal, the mode shapes of all orders meet the normalized orthogonality, and the mode responses of all orders are not related to each other, as follows:
wherein m islIs the order l modal quality.
7) The ith (i ═ 1,2 … T) is knownEND+1-L) time instant data window
And establishing a model for solving the working modal parameters of the window by the LE in the data window. Specifically, for the ith (i ═ 1,2 … T)END+1-L) points in each window
Find the k nearest neighbors to it
Weight w of each neighborlj(j ∈ k) size can be scaled by a Gaussian kernel function
Calculating (w)ljRepresenting sample points
And
weights on the graph, σ is a width parameter of the function), thereby constructing an adjacency matrix W ═ Wlj]To reconstruct the data set
Local structural features of (1). Let diagonal matrix D be
Is obtained by the graph degree matrix
L (L ═ D-W) is the laplacian matrix of the graph. Laplace eigenmap is by pair
Decomposing the eigenvalue, and dividing d (d < n) minimum non-zero eigenvalues lambda1,λ2,…λi…,λdCorresponding feature vector
After reducing dimensionAnd (4) outputting the result. Feature vector
Low dimensional embedding for LE algorithm
Then
Modal response corresponding to time i
8) Ith (i ═ 1,2 … T)END+1-L) windows
In, satisfy the formula
It is known that
Modal response matrix
Therefore, the least square method is used for solving the mode shape matrix in a generalized inverse way, and the formula is
Finally, by means of single degree of freedom (SDOF) or Fourier transform (FFT), e.g. fitting a modal response matrix
Substituting into Fourier transform (FFT) formula
And obtaining frequency domain data, wherein the frequency maximum value in the frequency domain data corresponds to the modal natural frequency of the order.
9) In identifying the ith (i ═ 1,2, …, T +1-L) window
After the working mode parameters in (i), the window is slid to the right to (i +1) (i ═ 1,2 … TEND-L) windows, continuing to identify the (i +1) th window (i ═ 1,2 … T) according to the method described aboveEND-L) operating mode parameters of the windows. Until the identification is completed (T)ENDAnd +1-L) windows, connecting the modal parameters of the windows (time) in a time sequence, thereby tracking the time-varying characteristic of the structure and obtaining the modal parameters of the linear time-varying structure.
10) The accuracy of vibration mode identification is quantitatively evaluated by adopting a modal confidence parameter MAC, which specifically comprises the following steps:
wherein phi isiIs the identified i-th mode shape,
representing the true ith mode shape,
and
respectively represents phiiAnd
the transpose of (a) is performed,
represents the inner product of two vectors and represents the inner product of the two vectors,
is indicative of phiiAnd
to the extent of the similarity in the direction of the line,
if it has a value ofThe closer to 1, the higher the modal shape recognition accuracy.
And comparing the measured working modal parameters with the working modal parameters under the normal operation condition of the equipment to be tested to determine whether the equipment has a fault or not and the position of the fault.
In this embodiment, a method for identifying working mode parameters of a linear time-varying structure simulates a time-varying structure by using a mass slow time-varying three-degree-of-freedom structure, and for the mass slow time-varying three-degree-of-freedom structure, under the condition that shear deformation is not considered, a finite element modeling model is used as shown in fig. 2.
The sampling frequency is 40Hz, the sampling interval is 0.025s, the sampling time is t 2000s, the initial conditions of the three-order modal displacement of the system are all zero, and the rigidity is set to be k1(t)＝k2(t)＝k3(t) 1000N/m, t is more than or equal to 0 and less than or equal to 2000 s; damping is set as c1(t)＝c2(t)＝c3(t) 0.01N.s/m, t is more than or equal to 0 and less than or equal to 2000 s; mass is set as m2(t)＝m3(t) 1kg, t 0 ≦ t ≦ 2000 s. The above-mentioned parameter being time-invariant, m1(t) is slowly time-varying.
the kinetic equation of the time-varying mass at time t is expressed as:
m1(t) received stimulus F1And (t) is Gaussian white noise, and slow time-varying data after 50s is taken for research. Fig. 3 depicts the modeling of a three-degree-of-freedom spring vibrator system in MATLAB/Simulink. A non-stationary displacement response signal X (t) is obtained by solving in a Simulink module by using a Runge-Kutta algorithm, and white noise and the displacement response signal are shown in FIG. 4.
When white noise excitation is applied to the three-degree-of-freedom structure to obtain response data, a time-varying structure working modal parameter identification method based on a sliding window LE is used for identification, and the identified modal parameters are compared with modal parameters obtained through calculation by a finite element method and real modal parameters.
FIG. 5 is a graph of identifying first and third order modal frequencies over a time period of 0-20 based on sliding window LE time varying structure operating modal parameters; FIG. 6 is a graph of confidence coefficient MAC value change over a 0-20s time period based on sliding window LE time varying structure operating mode parameter identification; FIG. 7 is a graph of identifying first and third order natural frequencies for a time period of 0-1950s based on sliding window LE time varying structure operating mode parameters; fig. 8 is a graph of confidence coefficient MAC value change over a time period of 0-1950s based on sliding window LE time varying structure operating mode parameter identification. The natural frequencies in the figure refer to modal frequencies.
The method for identifying the working modal parameters of the linear structure of the sliding window LE can be used for carrying out real-time online parameter identification on a structure with time-varying characteristics, identifying the working modal parameters (modal shape and modal frequency) of a system, effectively monitoring the dynamic change characteristics of the system in real time, and can be used for equipment fault diagnosis, health monitoring and system structure analysis and optimization. The method is a working modal parameter identification method (the characteristics of the system can be identified only by actually measured response signals), and is proved from mathematical theory analysis and experiments, so that the method is endowed with physical explanation, and has greater advantages compared with the traditional experimental modal parameter identification technology which needs to measure excitation and response signals simultaneously. The method has the main idea that a short-time invariant theory and a sliding window LE algorithm are combined, the statistical characteristics of the Laplace characteristic mapping algorithm in each window are utilized, working modal parameters (including the natural frequency and the modal shape of each order of mode) at each moment are estimated, and then the working modal parameters obtained at each moment are connected, so that the working modal parameter identification of the time-varying linear structure is realized. Compared with the traditional PCA-based linear time-varying structure working mode parameter identification method, the method has lower time and space complexity and is beneficial to being embedded into portable hardware equipment.
The method mainly comprises the steps of setting the window length of a sliding window, establishing an LE (equivalent routine) solution structure working modal parameter model in each window, and finally fitting modal parameters at all moments, so that the time-varying characteristic of the structure is tracked, and the modal parameters of the linear time-varying structure are obtained. Compared with a sliding window PCA algorithm, all the principal components are obtained by calculation every time when the sliding window PCA algorithm is used for solving, the time and memory expenditure can be reduced by the sliding window LE, and the time and space complexity is low, so that the portable equipment is easier to embed, and the online real-time monitoring of the equipment condition is realized. The linear structure working modal parameter identification method based on the sliding window LE is a working modal parameter identification method, can achieve the purpose of identifying time-varying transient working modal parameters (instantaneous working modal shape and instantaneous working modal natural frequency) of a linear time-varying structure on line in real time only by acquiring a non-stationary vibration response signal of the structure, and has great advantages compared with the traditional test modal parameter identification technology which needs to measure excitation and response signals simultaneously.
The invention combines a sliding window method with a Laplace characteristic mapping algorithm (LE) and is applied to the identification of working modal parameters of a linear time-varying structure. Compared with a working modal parameter identification method of the sliding window PCA, the time and space complexity consumed by the sliding window LE in the process of solving the working modal parameters in each window is low. Therefore, the linear structure working modal parameter identification method based on the sliding window LE can achieve the identification precision, reduce the time and space complexity of the algorithm and better achieve the real-time effective detection of the structural working modal parameters. This facilitates the use of the method for hardware embedding, device fault diagnosis, health monitoring, and system architecture analysis and optimization.
Fig. 9 is a schematic structural diagram of a working mode parameter identification system of a linear time-varying structure according to the present invention, and as shown in fig. 9, the working mode parameter identification system of the linear time-varying structure includes:
a data matrix obtaining module 201, configured to obtain a data matrix of a vibration response signal of a linear time-varying structure within a set time;
a sub-matrix obtaining module 202, configured to divide the data matrix into a plurality of sub-matrices with set time lengths;
a laplacian eigenmap establishing module 203, configured to establish a laplacian eigenmap of the sub-matrix;
a modal response matrix solving module 204, configured to solve the laplacian eigenmap to obtain a modal response matrix of the submatrix;
a modal shape determining module 205, configured to obtain a modal shape of the submatrix according to the modal response matrix;
a frequency domain data solving module 206, configured to solve frequency domain data of the modal response matrix;
a modal frequency determining module 207, configured to use a maximum value in the frequency domain data as a modal frequency of the sub-matrix.
The data matrix obtaining module 201 specifically includes obtaining the vibration response signal through a vibration response sensor.
The modal response matrix solving module 204 specifically includes performing least square generalized inverse solution on the modal response matrix to obtain the modal response matrix.
The least square generalized inverse solution formula is
Wherein the content of the first and second substances,
represents the mode shape of the ith sub-matrix,
it represents the i-th sub-matrix,
and a mode response matrix representing the ith sub-matrix, wherein L represents the set time length.
The frequency domain data solving module 206 specifically includes solving the frequency domain data of the modal response matrix through a single degree of freedom system or fourier transform.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A method for identifying working mode parameters of a linear time-varying structure is characterized by comprising the following steps:
acquiring a data matrix of a vibration response signal of a linear time-varying structure within set time;
dividing the data matrix into a plurality of sub-matrixes with set time length;
establishing Laplace feature mapping of the submatrix;
solving the Laplace feature mapping to obtain a modal response matrix of the submatrix;
obtaining the mode vibration mode of the submatrix according to the mode response matrix;
solving frequency domain data of the modal response matrix;
and taking the maximum value in the frequency domain data as the modal frequency of the sub-matrix.
2. The method of claim 1, wherein the vibrational response signal is obtained by a vibrational response sensor.
3. The method for identifying working modal parameters of a linear time-varying structure according to claim 1, wherein the modal response matrix is obtained by performing least squares generalized inverse solution on the modal response matrix.
4. The method for identifying working modal parameters of a linear time-varying structure according to claim 3, wherein the least squares generalized inverse solution formula is
Wherein the content of the first and second substances,
represents the mode shape of the ith sub-matrix,
it represents the i-th sub-matrix,
and a mode response matrix representing the ith sub-matrix, wherein L represents the set time length.
5. The method according to claim 1, wherein the frequency domain data of the modal response matrix is solved by a single degree of freedom system or fourier transform.
6. A system for identifying parameters of an operating mode of a linear time-varying structure, the system comprising:
the data matrix acquisition module is used for acquiring a data matrix of a vibration response signal of the linear time-varying structure within set time;
the sub-matrix acquisition module is used for dividing the data matrix into a plurality of sub-matrices with set time length;
the Laplace eigenmap establishing module is used for establishing Laplace eigenmap of the sub-matrix;
the modal response matrix solving module is used for solving the Laplace feature mapping to obtain a modal response matrix of the submatrix;
the modal shape determining module is used for obtaining the modal shape of the submatrix according to the modal response matrix;
the frequency domain data solving module is used for solving the frequency domain data of the modal response matrix;
and the modal frequency determining module is used for taking the maximum value in the frequency domain data as the modal frequency of the submatrix.
7. The system of claim 6, wherein the vibrational response signal is obtained by a vibrational response sensor.
8. The system according to claim 6, wherein the modal response matrix is obtained by performing least squares generalized inverse solution on the modal response matrix.
9. The system for identifying working modal parameters of a linear time-varying structure according to claim 8, wherein the least squares generalized inverse solution is formulated as
Wherein the content of the first and second substances,
represents the mode shape of the ith sub-matrix,
it represents the i-th sub-matrix,
and a mode response matrix representing the ith sub-matrix, wherein L represents the set time length.
10. The system for identifying the operational modal parameters of a linearly time-varying structure according to claim 6, wherein the frequency domain data of the modal response matrix is solved by a single degree of freedom system or fourier transform.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
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