CN115015390A - MWTLMDS-based curtain wall working modal parameter identification method and system - Google Patents
MWTLMDS-based curtain wall working modal parameter identification method and system Download PDFInfo
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Abstract
The invention relates to a curtain wall working modal parameter identification method and system based on MWTLMDS, comprising the following steps: acquiring a vibration displacement response signal of the curtain wall within a preset time, and intercepting the vibration displacement response signal by using a sliding window to obtain intercepted data in the sliding window; representing the intercepted data in the sliding window by using a modal coordinate to obtain a modal vibration mode of the curtain wall; applying a multidimensional scale analysis method and transfer learning to the intercepted vibration displacement data in the sliding window to obtain a distance matrix; introducing a centralized matrix into a distance matrix of the sliding window to obtain a deformation matrix, decomposing characteristic values and characteristic vectors, and applying a single-degree-of-freedom technology or Fourier transform to obtain modal natural frequency of the curtain wall; and traversing all the sliding windows and finishing the identification. The method provided by the invention has the advantages that the sliding window is applied to intercept data, and meanwhile, the intercepted data is processed by using a multidimensional scale analysis method and transfer learning, so that the modal parameters of the curtain wall can be more accurately identified.
Description
Technical Field
The invention relates to the field of modal parameter identification, in particular to a curtain wall structure working modal parameter identification method and system based on a sliding window transfer learning multidimensional scaling analysis (MWTLMDS).
Background
The working modal parameter identification is to identify the modal parameters by measuring the structural displacement response signals under the random excitation of the environment, has important significance in large-scale application engineering, and can carry out real-time structural monitoring and damage detection.
At present, a Principal Component Analysis (PCA) and an equidistant mapping algorithm (ISOMAP) are proposed by wancheng et al aiming at a time invariant structure, but the PCA algorithm has the problems of mode loss, false modes and the like. And then, a Sanger neural network is used for parallel PCA working mode parameter identification, so that the problems of singularity, sensitivity to measurement noise, low efficiency and the like of the traditional PCA are solved. Hao Caifeng and the like use a mode identification method combining an LLE algorithm and an HHT, and effective mode parameters are extracted by using damping of an HHT identification structure after dimension reduction through the LLE algorithm. Zhang Tianshu et al propose three-dimensional continuum structure working modal parameter identification by principal component extraction using a matrix direct assembly method. For the vibration response characteristic of a linear slow time-varying structure, modal information cannot be completely extracted at one time, and continuous sampling and analysis are required on a time sequence. Therefore, a sliding Window (MW) method is proposed, which considers data in a short time interval as "constant in time" based on the "time freezing" theory. At present, the sliding window has some practical applications in the aspect of working modal parameter identification, and the officer et al combines the sliding window with a principal component analysis method to provide an MWRPCA algorithm so as to effectively identify modal parameters of a linear time-varying structure; the yellow haiyang et al propose an EASI algorithm based on sliding variable step length; the charvian et al combines the sliding window technique with a domain preserving projection algorithm (NPE), and performs parameter identification of a time-varying structure by using the characteristic that the NPE algorithm can maintain the characteristics of an original data set. However, in the existing research, the LLE algorithm has the defects of mode loss and poor anti-noise capability; the ISOMAP algorithm is very sensitive to noise due to the consideration of global characteristics, has a large error on the identification of a working mode, and has high time complexity; the MWRPCA algorithm is difficult to identify high-order modes, and the problem of mode repeated identification can occur. Therefore, the existing working mode parameter identification methods of linear slow time-varying structures have the problem of inaccurate identification, and therefore, the invention provides a method and a system for identifying the working mode parameters of the linear slow time-varying structures (curtain wall structures) by using the MWTLMDS algorithm.
Disclosure of Invention
The invention aims to provide a curtain wall working modal parameter identification method and system based on MWTLMDS, and aims to solve the problem that modal identification is inaccurate due to modal loss, modal repetition and overhigh time complexity in the prior art.
In order to achieve the purpose, the invention provides the following scheme:
a curtain wall working modal parameter identification method based on MWTLMDS comprises the following steps:
acquiring vibration displacement response signals of n displacement vibration sensors on the curtain wall within preset time; the preset time comprises T sampling time points;
determining the length L and the moving step length of the sliding window;
intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window; 1,2, T-L + 1;
representing the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate to obtain a modal shape of the curtain wall of the w-th sliding window;
applying a multidimensional scale analysis method and transfer learning according to the intercepted vibration displacement data in the w-th sliding window to obtain a distance matrix in the w-th sliding window;
introducing a centralized matrix into the distance matrix of the w-th sliding window to obtain a deformation matrix;
decomposing the eigenvalue and the eigenvector of the deformation matrix to obtain a decomposed matrix;
applying a single degree of freedom technology or Fourier transform to the decomposed matrix to obtain the modal natural frequency of the curtain wall of the w-th sliding window;
and (2) setting w as w +1, and returning to the step of intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window until working modal parameters of all the sliding windows are obtained.
A curtain wall working modal parameter identification system based on MWTLMDS, the system comprises:
the data acquisition module is used for acquiring vibration displacement response signals of the n displacement vibration sensors on the curtain wall within preset time; the preset time comprises T sampling time points;
the sliding window setting module is used for determining the length L and the moving step length of the sliding window;
the sliding window intercepting module is used for intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window;
the modal shape obtaining module is used for representing the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate to obtain the modal shape of the curtain wall of the w-th sliding window;
the distance matrix acquisition module is used for applying a multidimensional scale analysis method and transfer learning according to the intercepted vibration displacement data in the w-th sliding window to obtain a distance matrix in the w-th sliding window;
the inherent frequency acquisition module is used for introducing a centralized matrix into the distance matrix of the w-th sliding window to obtain a deformation matrix; decomposing the eigenvalue and the eigenvector of the deformation matrix to obtain a decomposed matrix; and applying a single degree of freedom technology or Fourier transform to the decomposed matrix to obtain the modal natural frequency of the curtain wall of the w-th sliding window, and returning to the sliding window intercepting module when w is w + 1.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a curtain wall working modal parameter identification method and system based on MWTLMDS, wherein the method comprises the following steps: acquiring vibration displacement response signals of n displacement vibration sensors on the curtain wall within preset time; the preset time comprises T sampling time points; determining the length L and the moving step length of the sliding window; intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window; 1,2, T-L + 1; representing the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate to obtain a modal shape of the curtain wall of the w-th sliding window; applying a multidimensional scale analysis method and transfer learning according to the intercepted vibration displacement data in the w-th sliding window to obtain a distance matrix in the w-th sliding window; introducing a centralized matrix into the distance matrix of the w-th sliding window to obtain a deformation matrix; decomposing the eigenvalue and the eigenvector of the deformation matrix to obtain a decomposed matrix; applying a single degree of freedom technology or Fourier transform to the decomposed matrix to obtain the modal natural frequency of the curtain wall of the w-th sliding window; and (2) setting w as w +1, and returning to the step of intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window until working modal parameters of all the sliding windows are obtained. When working modal parameters are identified, the obtained vibration displacement response signals are intercepted by utilizing the sliding window, the vibration displacement response signals are continuously sampled and analyzed by continuously moving the sliding window, the problem that modal information cannot be completely extracted at one time and modal loss is caused is avoided, a multi-dimensional scale analysis method can identify high-order modes and avoid repeated modal identification, and a migration learning algorithm is combined when the multi-dimensional scale analysis method is applied, so that the time complexity of calculation can be reduced, and therefore, the modal identification method can realize high-precision identification.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed 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 creative efforts.
Fig. 1 is a flowchart of a method for identifying parameters of a curtain wall working mode based on MWTLMDS according to embodiment 1 of the present invention;
fig. 2 is a modal coordinate response identified by the MWTLMDS-based curtain wall structure working modal parameter identification method according to embodiment 1 of the present invention, and a frequency identification result obtained by performing FFT on the modal coordinate response;
fig. 3 is a modal shape of a curtain wall structure operating modal parameter identification method based on MWTLMDS according to embodiment 1 of the present invention, which is respectively 100s, 650s, 1650s and 1900 s;
fig. 4 is a graph of a change of a confidence coefficient MAC value of a curtain wall structure working mode parameter identification method based on MWTLMDS in a time period from 0 to 1950 according to embodiment 1 of the present invention;
fig. 5 is a result graph of comparison between each stage of natural frequency identified by the MWTLMDS based curtain wall structure working mode parameter identification method according to embodiment 1 of the present invention and a theoretical value;
fig. 6 is a block diagram of a MWTLMDS-based curtain wall working mode parameter identification system provided in embodiment 2 of the present invention.
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 multidimensional scaling analysis method projects points in high-dimensional coordinates into a low-dimensional space, and the similarity between the points is kept as unchanged as possible, so that data after dimensionality reduction is obtained. The PCA algorithm only reserves main components, so that the noise resistance is better, but a part of effective information is ignored; the ISOMAP algorithm is sensitive to noise due to the consideration of global characteristics, and has a large error on the identification of the working mode. The MDS algorithm well balances the influence of noise on modal identification, and the identification precision is greatly improved before comparison, so that the influence on environmental noise in the engineering field is smaller. Meanwhile, the identification effect of the MDS algorithm in the linear time-varying structure can be well exerted by using a sliding window technology and a transfer learning technology.
The invention aims to provide a curtain wall working modal parameter identification method and system based on MWTLMDS, and aims to solve the problem that modal identification is inaccurate due to modal loss, modal repetition and overhigh time complexity in the prior art.
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.
Example 1
As shown in fig. 1, the present embodiment provides a method for identifying a working modal parameter of a curtain wall based on MWTLMDS, where the method includes:
s1: obtaining vibration displacement response signals of n displacement vibration sensors on the curtain wall within preset time
The preset time comprises T sampling time points.
And arranging a plurality of vibration sensor devices on key points of the measuring structure, and identifying working mode parameters through vibration response signals obtained by the measurement of the sensors. And when the curtain wall is excited randomly in the environment, acquiring a vibration displacement response signal.
S2: determining the length L and the moving step length of the sliding window; the moving step length can be set to 1 or any value, and is determined according to requirements. To facilitate understanding of the scheme of the present embodiment, the scheme of the present embodiment is explained with the moving step as 1.
S3: according to the length of the sliding windowIntercepting the vibration displacement response signal by L and moving step length to obtain intercepted vibration displacement data in the w-th sliding window
Wherein T represents time, X (T) is a time domain displacement response signal, n represents the number of detection points of a displacement vibration sensor arranged on the curtain wall structure, T represents the number of sampling points of a time domain,
a matrix with dimension n × T in a real number range; i denotes the ith sensor, i ═ 1,2, …, n. k denotes the kth sample sequence point, k is 1,2, …, T, L is the length of the sliding window,
representing the response signal collected by the nth displacement vibration sensor during time t.
The sliding window cuts a window of length L in X (t) each time, wherein
For the position of the first window, the step length is increased to 1 at the start of each sliding window, and when the (k +1) th sampling sequence point is reached, the window slides to
Finally in the T-L +1 th window, i.e.
And then the process is finished. The data in each window is viewed as L n-dimensional column vector datasets
i represents the number of the displacement vibration sensor;
and
respectively representing vibration displacement response signals of the n displacement vibration sensor at the kth sampling time point and the l sampling time point in the w sliding window; k 1,2,. and L; 1,2,. and L;
s4: representing the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate to obtain a modal shape of the curtain wall of the w-th sliding window; as shown in fig. 2 and 3.
Wherein, S4 specifically includes:
intercepting vibration displacement data in the w-th sliding window
Expressed as in modal coordinates
Wherein
A statistical average modal shape matrix of the curtain wall structure in a time period from a sampling time point k to k + L-1 is obtained; d is the order of mode shape;
the method is a modal coordinate response matrix of the curtain wall structure in a time period from a sampling time point k to k + L-1.
Wherein each order of modal response
Independently of one another, the modal order j is 1,2, …, d.
After the modal shape of the curtain wall is obtained in step S4, the identified modal shape may be verified accurately, and the specific verification method is as follows:
evaluating the accuracy of the modal shape recognition by adopting modal confidence parameters; as shown in fig. 4. Wherein the expression of the modal confidence parameter is as follows:
wherein the content of the first and second substances,
is the w-th mode shape identified;
representing the true w-th mode shape;
and
respectively represent
And
transposing;
represents the inner product of two vectors;
to represent
And
the degree of similarity of (c); j is 1,2, …, d.
S5: and applying a multidimensional scale analysis method and transfer learning according to the intercepted vibration displacement data in the w-th sliding window to obtain a distance matrix in the w-th sliding window.
Step S5 specifically includes:
calculating the vibration displacement response signal of the n displacement vibration sensors in the kth sampling sequence time point according to the intercepted vibration displacement data in the first sliding window
And the vibration displacement response signal of the n displacement vibration sensor at the ith sampling time point
Obtaining a distance matrix in the first sliding window;
taking a migration matrix except the first m row and the first m column in the distance matrix in the w-th sliding window as the first L-m row and the first L-m column in the distance matrix in the w + 1-th sliding window, and calculating values from the L-m +1 row to the L-th row and from the L-m +1 column to the L-th column in the distance matrix in the w + 1-th sliding window according to the intercepted vibration displacement data in the w + 1-th sliding window to obtain a distance matrix in the w + 1-th sliding window; 1,2, T-L + 1; the intercepted vibration displacement data in each sliding window are L n-dimensional column vector data sets
i represents the number of the displacement vibration sensor;
and
respectively representing vibration displacement response signals of the n displacement vibration sensor at the kth sampling time point and the l sampling time point in the w sliding window; k 1,2,. and L; 1,2,. and L; m is the step size of the move.
The expression of the distance matrix between two sampling time points is:
wherein
To represent
Transposing;
to represent
The transposing of (1).
The distances among all the sampling time points are solved to form a distance matrix of the w-th window
To be provided with
And
for example, after the sliding window is slid from 1 st to 2 nd, the distance matrix
For sampled data
The distance to other data is deleted,
the distance data of the L +1 th sampling sequence point is updated. So that the values in the lower right (L-1) × (L-1) square matrices do not occurChanges are made. Therefore, migration learning is added, and the distance matrix invariant part in the previous window is migrated to the next window, so that the time complexity is reduced.
Except for the first starting matrix, the distance matrix of L multiplied by L needs to be calculated, other windows only need to calculate the distance of a new data point on the basis of the last window, and the time complexity of the whole algorithm in the aspect of calculating the distance matrix is represented by O ((T-L +1) multiplied by L 2 ) To O (T × L).
When the distance matrix is calculated by using the multidimensional scale analysis method, all numerical values of the distance matrix do not need to be calculated every time, and only a migration learning algorithm needs to be applied to directly migrate the distance matrix invariant part in the previous sliding window to the corresponding part of the distance matrix of the next sliding window, so that the time for calculating the distance matrix can be greatly shortened, and the time complexity is greatly reduced.
S6: introducing a centralized matrix into the distance matrix of the w-th sliding window to obtain a deformation matrix; decomposing the eigenvalue and the eigenvector of the deformation matrix to obtain a decomposed matrix; and applying a single degree of freedom technology or Fourier transform to the decomposed matrix to obtain the modal natural frequency of the curtain wall of the w-th sliding window, enabling w to be w +1, and returning to the step S3 until w is T-L + 1. Step S6 specifically includes:
1) defining an n-dimensional vector:
2) Defining a centralized matrix
Wherein
Is an L × L identity matrix. Definition matrix
Combining the distance matrix in step 3)
Can be derived
3) Will be provided with
Carrying out characteristic value eigenvector decomposition to obtain
Wherein
Is an orthogonal matrix, and the matrix is,
to represent
The transpose of (a) is performed,
representing the L-1 th feature vector.
Is represented by
Is a diagonal matrix of diagonal elements,
representing the d diagonal element in the w window.
The result after dimension reduction (decomposed matrix) is obtained as
In the formula
D maximum eigenvalues in front of the current window
Matrix of corresponding eigenvectors
Is composed of
The transposing of (1). Dimension reduction is carried out on the dimension d corresponding to the d characteristic values before the extraction, and d is used for representing the dimension after the dimension reduction.
After all the steps are executed, the working modal parameters of the curtain wall in each sliding window are obtained, and then the identified working modal parameters can be compared with the working modal parameters when the curtain wall is not in fault, so that whether the curtain wall structure is in fault or not and the position of the fault can be accurately determined, as shown in fig. 5.
In this embodiment, a multi-dimensional Scaling (MDS) algorithm in manifold learning is combined with migration learning to introduce a dynamic structure to identify working modal parameters of a linear time-varying structure such as a curtain wall, and a vibration test method is used to obtain dynamic characteristic parameters of curtain wall glass to identify looseness of a glass curtain wall support structure and aging and damage degrees of structural adhesive thereof. And identifying the change rule of dynamic parameters (natural frequency and modal shape) of the curtain wall structural system after loosening, aging and damage.
In the curtain wall structure vibration response with measurement noise, the identification precision and the noise resistance in a high-order mode are obviously higher than those of an MWRPCA algorithm, and the robustness is better. Meanwhile, compared with the MWMDS algorithm, the MWTLMDS algorithm has the advantages that the time complexity is greatly reduced, and the method is more suitable for online working mode parameter identification.
The migration learning multidimensional scaling analysis method based on the sliding window can identify the working modal parameters of the curtain wall with higher precision, does not need special manual excitation, does not need a large number of experiments, and reduces the consumption of manpower and material resources. The MWTLMDS can be used for identifying high-order modes and is insensitive to noise interference. The operation is simple, and the requirement on equipment configuration is low.
Example 2
As shown in fig. 6, the present embodiment provides a curtain wall working mode parameter identification system based on MWTLMDS, where the system includes:
the data acquisition module M1 is used for acquiring vibration displacement response signals of the n displacement vibration sensors on the curtain wall within preset time; the preset time comprises T sampling time points;
a sliding window setting module M2, configured to determine a length L and a moving step of the sliding window;
a sliding window intercepting module M3, configured to intercept the vibration displacement response signal according to the length L and the moving step length of the sliding window, to obtain intercepted vibration displacement data in the w-th sliding window;
a modal shape obtaining module M4, configured to represent the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate, to obtain a modal shape of the curtain wall of the w-th sliding window;
a distance matrix obtaining module M5, configured to apply a multidimensional scale analysis method and transfer learning according to the intercepted vibration displacement data in the w-th sliding window to obtain a distance matrix in the w-th sliding window;
a natural frequency obtaining module M6, configured to introduce a centering matrix to the distance matrix of the w-th sliding window to obtain a deformation matrix; decomposing the eigenvalue and the eigenvector of the deformation matrix to obtain a decomposed matrix; and applying a single degree of freedom technology or Fourier transform to the decomposed matrix to obtain the modal natural frequency of the curtain wall of the w-th sliding window, and returning to the sliding window intercepting module M3 when w is w + 1.
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 (9)
1. A curtain wall working modal parameter identification method based on MWTLMDS is characterized by comprising the following steps:
acquiring vibration displacement response signals of n displacement vibration sensors on the curtain wall within preset time; the preset time comprises T sampling time points;
determining the length L and the moving step length of the sliding window;
intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window; 1,2, T-L + 1;
representing the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate to obtain a modal shape of the curtain wall of the w-th sliding window;
applying a multidimensional scale analysis method and transfer learning according to the intercepted vibration displacement data in the w-th sliding window to obtain a distance matrix in the w-th sliding window;
introducing a centralized matrix into the distance matrix of the w-th sliding window to obtain a deformation matrix;
decomposing the eigenvalue and the eigenvector of the deformation matrix to obtain a decomposed matrix;
applying a single degree of freedom technology or Fourier transform to the decomposed matrix to obtain the modal natural frequency of the curtain wall of the w-th sliding window;
and (2) setting w as w +1, and returning to the step of intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window until working modal parameters of all the sliding windows are obtained.
2. The method according to claim 1, wherein the step of representing the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate to obtain a modal shape of the curtain wall specifically comprises:
intercepting vibration displacement data within the sliding window of the w-th sliding window
Expressed in modal coordinates as
Wherein
The statistical average modal shape matrix of the curtain wall structure in the time period from the sampling time point k to k + L < -1 >; d is the order of the mode shape;
is the modal coordinate response matrix of the curtain wall structure during the period from the sampling time point k to k + L-1.
3. The method according to claim 1, wherein the obtaining of the distance matrix in the w-th sliding window by applying multidimensional scaling analysis and transfer learning according to the intercepted vibration displacement data in the w-th sliding window specifically comprises:
calculating the vibration displacement response signal of the n displacement vibration sensors in the kth sampling sequence time point according to the intercepted vibration displacement data in the first sliding window
And the vibration displacement response signal of the n displacement vibration sensor at the ith sampling time point
The distance between the first and second sliding windows is obtained；
Taking a migration matrix except the first m row and the first m column in the distance matrix in the w-th sliding window as the first L-m row and the first L-m column in the distance matrix in the w + 1-th sliding window, and calculating values from the L-m +1 row to the L-th row and from the L-m +1 column to the L-th column in the distance matrix in the w + 1-th sliding window according to the intercepted vibration displacement data in the w + 1-th sliding window to obtain a distance matrix in the w + 1-th sliding window; the intercepted vibration displacement data in each sliding window are L n-dimensional column vector data sets
i represents the number of the displacement vibration sensor;
and
respectively representing vibration displacement response signals of the n displacement vibration sensor at the kth sampling time point and the l sampling time point in the w sliding window; k 1,2,. and L; 1,2,. and L; m is the step size of the move.
4. The method of claim 3, wherein the distance matrix is expressed by:
wherein
To represent
Transposing;
to represent
The transposing of (1).
5. The method according to claim 1, wherein the introducing a centering matrix into the distance matrix of the w-th sliding window to obtain a deformation matrix specifically comprises:
representing the distance matrix as
Wherein the content of the first and second substances,
to represent
Transposing;
to represent
Transposing;
introducing a centralised matrix
And defining a matrix
According to the centralized matrix and the matrix
And the distance matrix
Deriving a matrix
The matrix
Is the deformation matrix; wherein, the first and the second end of the pipe are connected with each other,
is an L × L identity matrix.
6. The method according to claim 5, wherein the decomposing the eigenvalues and eigenvectors of the deformation matrix to obtain a decomposed matrix specifically comprises:
for matrix
Decomposing the eigenvalue and the eigenvector to obtain
Wherein
Is an orthogonal matrix, and the matrix is,
to represent
The transpose of (a) is performed,
represents the L-1 th feature vector;
is represented by
Is a diagonal matrix of diagonal elements,
represents the d characteristic value in the w sliding window;
according to a matrix
Obtaining decomposed matrix
In the formula
For the first d largest eigenvalues in the w-th sliding window
A matrix composed of corresponding feature vectors;
is composed of
The transposing of (1).
7. The method according to claim 6, wherein the step of representing the intercepted vibration displacement data in the w-th sliding window by using modal coordinates further comprises the following steps after obtaining the modal shape of the curtain wall of the w-th sliding window:
evaluating the accuracy of the modal shape recognition by adopting modal confidence parameters; wherein the expression of the modal confidence parameter is as follows:
wherein the content of the first and second substances,
is the w-th mode shape identified;
representing the true w-th mode shape;
and
respectively represent
And
transposing;
represents the inner product of two vectors;
represent
And
the degree of similarity of (c); j is 1,2, …, d.
8. The method of claim 1, wherein after applying a single degree of freedom technique or fourier transform to the decomposed matrix of all the sliding windows to obtain modal natural frequencies of the curtain wall of all the sliding windows, further comprising:
comparing the modal shape and the natural frequency of the curtain wall with modal parameters of the curtain wall in a fault-free state, determining whether the curtain wall fails or not at present, and determining the position of the fault when the curtain wall fails.
9. A system based on the method of any one of claims 1 to 8, comprising:
the data acquisition module is used for acquiring vibration displacement response signals of the n displacement vibration sensors on the curtain wall within preset time; the preset time comprises T sampling time points;
the sliding window setting module is used for determining the length L and the moving step length of the sliding window;
the sliding window intercepting module is used for intercepting the vibration displacement response signal according to the length L and the moving step length of the sliding window to obtain intercepted vibration displacement data in the w-th sliding window;
the modal shape obtaining module is used for representing the intercepted vibration displacement data in the w-th sliding window by using a modal coordinate to obtain the modal shape of the curtain wall of the w-th sliding window;
the distance matrix acquisition module is used for applying a multidimensional scale analysis method and transfer learning according to the intercepted vibration displacement data in the w-th sliding window to obtain a distance matrix in the w-th sliding window;
the inherent frequency acquisition module is used for introducing a centralized matrix into the distance matrix of the w-th sliding window to obtain a deformation matrix; decomposing the eigenvalue and the eigenvector of the deformation matrix to obtain a decomposed matrix; and applying a single degree of freedom technology or Fourier transform to the decomposed matrix to obtain the modal natural frequency of the curtain wall of the w-th sliding window, and returning to the sliding window intercepting module when w is w + 1.
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