CN114417573A - Structure health monitoring method based on random subspace modal parameter identification - Google Patents

Structure health monitoring method based on random subspace modal parameter identification Download PDF

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CN114417573A
CN114417573A CN202111636699.7A CN202111636699A CN114417573A CN 114417573 A CN114417573 A CN 114417573A CN 202111636699 A CN202111636699 A CN 202111636699A CN 114417573 A CN114417573 A CN 114417573A
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matrix
parameter identification
toeplitz
method based
monitoring method
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鲍华
胡健
沈磊
彭俊
熊学炜
刘桥
吕雷
滕飞
刘昶
陈前
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China Railway Siyuan Survey and Design Group Co Ltd
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Abstract

The invention relates to the technical field of equipment upgrading, in particular to a structure health monitoring method based on random subspace modal parameter identification, which comprises the following steps: s1, inputting a time domain response signal of the structure monitoring point, and constructing a Hankel matrix; s2, calculating a Toeplitz matrix, and extracting the Toeplitz matrix T1 with equal diagonal elements; s3, performing singular value decomposition on the T1 to obtain a U matrix, a sigma matrix and a V matrix; s4, estimating the order of the power system and correspondingly extracting U1、Σ1And V1A matrix; s5, calculating a considerable matrix thetaiThe controllable matrix xi, the observation matrix C and the system matrix A, and solving a characteristic value of the system matrix A; and S6, calculating the structural modal parameters to judge the structural health state. Without applying artificial excitation to the structure by using expensive excitation equipment, vehicles, pedestrians, wind and combinations thereof are directly adoptedThe lamp acts on the response generated by the structure to carry out parameter identification, thereby saving the cost of carrying, installing, debugging and the like of the excitation equipment, and saving the time and the cost of corresponding workers.

Description

Structure health monitoring method based on random subspace modal parameter identification
Technical Field
The invention relates to the technical field, in particular to a structure health monitoring method based on random subspace modal parameter identification.
Background
In recent years, health monitoring of civil structures is attracting more and more attention, and whether a structure is damaged or not can be conveniently displayed through the change condition of own modal parameters (frequency, damping ratio and vibration mode), so that identification of system modal parameters becomes the key point of structure health monitoring. For the traditional mode test method, an external excitation needs to be applied, and the method is difficult to realize generally because of high cost and influence on normal use of the structure.
Disclosure of Invention
The invention provides a structural health monitoring method based on random subspace modal parameter identification, which solves the technical problem that external excitation needs to be applied through a traditional modal test.
The invention provides a structure health monitoring method based on random subspace modal parameter identification for solving the technical problems, which comprises the following steps:
s1, inputting a time domain response signal of the structure monitoring point, and constructing a Hankel matrix;
s2, calculating a Toeplitz matrix, and extracting the Toeplitz matrix T1 with equal diagonal elements;
s3, carrying out singular value decomposition on the T1 to obtain a U matrix, a sigma matrix and a V matrix;
s4, estimating the order of the power system and correspondingly extracting U1、∑1And V1A matrix;
s5, calculating a considerable matrix thetaiThe controllable matrix xi, the observation matrix C and the system matrix A, and solving a characteristic value of the system matrix A;
and S6, calculating the structural modal parameters to judge the structural health state.
Preferably, the first group of division forms of the Hankel matrix are:
Figure DEST_PATH_IMAGE001
wherein, yk∈Rl×1The output data at a certain time is k is 0,1 … …, 2i + j-2, l is the output channel number, j is the column number of Hankel matrix, YpAnd YfDefined as the past matrix and the future matrix, respectively.
Preferably, the Toeplitz matrix corresponding to the first division form is:
Figure DEST_PATH_IMAGE002
wherein, T1|i∈Rli×liToeplitz matrices with equal diagonal elements.
Preferably, the first group of division forms of the Hankel matrix are:
Figure DEST_PATH_IMAGE003
wherein, yk∈Rl×1The output data at a certain time is k is 0,1 … …, 2i + j-2, l is the output channel number, j is the column number of Hankel matrix, YpAnd YfDefined as the past matrix and the future, respectivelyAnd (4) matrix.
Preferably, the Toeplitz matrix corresponding to the second division form is:
Figure DEST_PATH_IMAGE004
wherein, T1|i∈Rli×liToeplitz matrices with equal diagonal elements.
Preferably, the S3-S5 specifically include:
carrying out SVD on the Toeplitz matrix to obtain
Figure DEST_PATH_IMAGE005
Wherein U and V are orthogonal matrices, and
∑1＝diag(σk)，σk＞0，k＝1，2，…，n
and when
Figure BDA0003442537350000041
To obtain
Figure BDA0003442537350000042
Has the advantages that: the invention provides a structural health monitoring method based on random subspace modal parameter identification, which comprises the following steps: s1, inputting a time domain response signal of the structure monitoring point, and constructing a Hankel matrix; s2, calculating a Toeplitz matrix, and extracting the Toeplitz matrix T1 with equal diagonal elements; s3, carrying out singular value decomposition on the T1 to obtain a U matrix, a sigma matrix and a V matrix; s4, estimating the order of the power system and correspondingly extracting U1、∑1And V1A matrix; s5, calculating a considerable matrix thetaiThe controllable matrix xi, the observation matrix C and the system matrix A, and solving a characteristic value of the system matrix A; and S6, calculating the structural modal parameters to judge the structural health state.
Compared with the traditional input and output mode parameter identification method, the method has the following advantages that:
(1) the modal parameters of large structures which cannot be artificially excited are effectively identified, and compared with the traditional method which cannot identify the modal parameters of the structures, the method has practical engineering application value.
(2) The modal parameter identification can be carried out only by utilizing the response of the engineering structure under the environment excitation, the artificial excitation on the structure is not required to be exerted by utilizing expensive excitation equipment, and the parameter identification is carried out by directly adopting the response generated by the action of vehicles, pedestrians, wind and combination lamps thereof on the structure, so that the cost of carrying, installing, debugging and the like of the excitation equipment is saved, and the time and the cost of corresponding workers are also saved.
(3) The artificial excitation can only load a local structure, the structure of the structure is possibly damaged, the larger the excitation energy is, the higher the possibility of damage is, and the environmental excitation does not have the problem. In addition, the method can also be used for long-term detection and state evaluation of structures.
(4) The normal work of the structure is not affected. In the conventional method, in order to implement artificial excitation and reduce interference, the use of the structure is stopped during the test. The scheme only needs to measure the response of the structure, and the normal use of the structure is not influenced, so that the scheme has great economic value for the structure which is not allowed to interrupt normal work in economic fire safety.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood and to implement them in accordance with the contents of the description, the following detailed description is given with reference to the preferred embodiments of the present invention and the accompanying drawings. The detailed description of the present invention is given in detail by the following examples and the accompanying drawings.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention. In the drawings:
FIG. 1 is a flow chart of a structural health monitoring method based on random subspace modal parameter identification according to the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention. The invention is described in more detail in the following paragraphs by way of example with reference to the accompanying drawings. Advantages and features of the present invention will become apparent from the following description and from the claims. It is to be noted that the drawings are in a very simplified form and are not to precise scale, which is merely for the purpose of facilitating and distinctly claiming the embodiments of the present invention.
It will be understood that when an element is referred to as being "secured to" another element, it can be directly on the other element or intervening elements may also be present. When a component is referred to as being "connected" to another component, it can be directly connected to the other component or intervening components may also be present. When a component is referred to as being "disposed on" another component, it can be directly on the other component or intervening components may also be present. The terms "vertical," "horizontal," "left," "right," and the like as used herein are for illustrative purposes only.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
As shown in fig. 1, the present invention provides a structural health monitoring method based on stochastic subspace modal parameter identification, including: s1, inputting a time domain response signal of the structure monitoring point, and constructing a Hankel matrix; s2, calculating a Toeplitz matrix, and extracting the Toeplitz matrix T1 with equal diagonal elements; s3, performing singular value decomposition on the T1 to obtain a U matrix, a sigma matrix and a V matrix; s4, estimating the order of the power system and correspondingly extracting U1、Σ1And V1A matrix;s5, calculating a considerable matrix thetaiThe controllable matrix xi, the observation matrix C and the system matrix A, and solving a characteristic value of the system matrix A; and S6, calculating the structural modal parameters to judge the structural health state. The structure is not required to be artificially excited by expensive excitation equipment, and the response generated by the action of vehicles, pedestrians, wind and combined lamps thereof on the structure is directly adopted for parameter identification, so that the cost of carrying, installing, debugging and the like of the excitation equipment is saved, and the time and the cost of corresponding workers are also saved.
Specifically, a covariance-based random subspace method (SSI-COV) first constructs a Toeplitz matrix from output data, and then calculates a covariance sequence and constructs the Toeplitz matrix, where the calculation method is a known calculation process in the mathematical field and is not described herein again. And decomposing the catalpa bungei coefficient matrix through Singular Value Decomposition (SVD), and finally solving the modal parameters of the structure through the system matrix.
In order to solve a structural coefficient matrix from a monitoring structural response covariance matrix, firstly, a Hankel matrix is directly constructed by monitoring structural response data, and the first group of division forms of the Hankel matrix are as follows:
Figure DEST_PATH_IMAGE006
wherein, yk∈Rl×1The output data at a certain time is k is 0,1 … …, 2i + j-2, l is the output channel number, j is the column number of Hankel matrix, YpAnd YfDefined as the past matrix and the future matrix, respectively.
The Toeplitz matrix corresponding to the first division form is:
Figure DEST_PATH_IMAGE007
wherein, Tl|i∈Rli×liToeplitz matrices with equal diagonal elements. This form YpAnd YfI block lines are respectively arranged; y ispThe first i block rows of the Hankel matrix and the last i block rows of the Hankel matrix.
In a preferred embodiment, the second group of division forms of the Hankel matrix are:
Figure DEST_PATH_IMAGE008
wherein, yk∈Rl×1The output data at a certain time is k is 0,1 … …, 2i + j-2, l is the output channel number, j is the column number of Hankel matrix, YpAnd YfDefined as the past matrix and the future matrix, respectively.
The Toeplitz matrix corresponding to the second division form is:
Figure DEST_PATH_IMAGE009
wherein, Tl|i∈Rli×liToeplitz matrices with equal diagonal elements. This form YpThere are i +1 block rows; y isfThere are i-1 block rows, YpThe first i +1 block row of the Hankel matrix and the last i-1 block row of the Hankel matrix.
By calculation, it can be known that:
Figure DEST_PATH_IMAGE010
in the formula, thetaiTo observe the matrix, xiiTo control the matrix:
Figure DEST_PATH_IMAGE011
Ξi＝[Ai-1G，Ai-2G，…，G]
likewise, define T2|i+1Is composed of
Figure DEST_PATH_IMAGE012
From the formula (5.4-29), it can be obtained
Figure BDA0003442537350000094
To get from T1|iIn this procedure, theta is determinediXi and xiiTo T1|iPerforming SVD to obtain
Figure DEST_PATH_IMAGE013
Where U and V are orthogonal matrices, Σ1＝diag(σk)，σk＞0，k＝1，2，…，n
Order to
Figure BDA0003442537350000096
To obtain
Figure BDA0003442537350000097
Wherein the observation matrix C is a considerable matrix thetaiThe first 1 line of (1). At this point, the system state matrix a and the system output matrix, i.e., the observation matrix C, are all solved.
Has the advantages that: the invention provides a structural health monitoring method based on random subspace modal parameter identification, which comprises the following steps: s1, inputting a time domain response signal of the structure monitoring point, and constructing a Hankel matrix; s2, calculating a Toeplitz matrix, and extracting the Toeplitz matrix T1 with equal diagonal elements; s3, carrying out singular value decomposition on the T1 to obtain a U matrix, a sigma matrix and a V matrix; s4, estimating the order of the power system and correspondingly extracting U1、∑1And V1A matrix; s5, calculating a considerable matrix thetaiThe controllable matrix xi, the observation matrix C and the system matrix A, and solving a characteristic value of the system matrix A; and S6, calculating the structural modal parameters to judge the structural health state.
Compared with the traditional input and output mode parameter identification method, the method has the following advantages that:
(1) the modal parameters of large structures which cannot be artificially excited are effectively identified, and compared with the traditional method which cannot identify the modal parameters of the structures, the method has practical engineering application value.
(2) The modal parameter identification can be carried out only by utilizing the response of the engineering structure under the environment excitation, the artificial excitation on the structure is not required to be exerted by utilizing expensive excitation equipment, and the parameter identification is carried out by directly adopting the response generated by the action of vehicles, pedestrians, wind and combination lamps thereof on the structure, so that the cost of carrying, installing, debugging and the like of the excitation equipment is saved, and the time and the cost of corresponding workers are also saved.
(3) The artificial excitation can only load a local structure, the structure of the structure is possibly damaged, the larger the excitation energy is, the higher the possibility of damage is, and the environmental excitation does not have the problem. In addition, the method can also be used for long-term detection and state evaluation of structures.
(4) The normal work of the structure is not affected. In the conventional method, in order to implement artificial excitation and reduce interference, the use of the structure is stopped during the test. The scheme only needs to measure the response of the structure, and the normal use of the structure is not influenced, so that the scheme has great economic value for the structure which is not allowed to interrupt normal work in economic fire safety.
The foregoing is merely a preferred embodiment of the invention and is not intended to limit the invention in any manner; the present invention may be readily implemented by those of ordinary skill in the art as illustrated in the accompanying drawings and described above; however, those skilled in the art should appreciate that they can readily use the disclosed conception and specific embodiments as a basis for designing or modifying other structures for carrying out the same purposes of the present invention without departing from the scope of the invention as defined by the appended claims; meanwhile, any changes, modifications, and evolutions of the equivalent changes of the above embodiments according to the actual techniques of the present invention are still within the protection scope of the technical solution of the present invention.

Claims (6)

1. A structural health monitoring method based on random subspace modal parameter identification is characterized by comprising the following steps:
s1, inputting a time domain response signal of the structure monitoring point, and constructing a Hankel matrix;
s2, calculating a Toeplitz matrix, and extracting the Toeplitz matrix T1 with equal diagonal elements;
s3, performing singular value decomposition on the T1 to obtain a U matrix, a sigma matrix and a V matrix;
s4, estimating the order of the power system and correspondingly extracting U1、Σ1And V1A matrix;
s5, calculating a considerable matrix thetaiThe controllable matrix xi, the observation matrix C and the system matrix A, and solving a characteristic value of the system matrix A;
and S6, calculating the structural modal parameters to judge the structural health state.
2. The structural health monitoring method based on stochastic subspace modal parameter identification according to claim 1, wherein the first group of division forms of the Hankel matrix are as follows:
Figure RE-FDA0003574100000000011
wherein, yk∈Rl×1The output data at a certain time is k is 0,1 … …, 2i + j-2, l is the output channel number, j is the column number of Hankel matrix, YpAnd YfDefined as the past matrix and the future matrix, respectively.
3. The structural health monitoring method based on stochastic subspace modal parameter identification according to claim 2, wherein the Toeplitz matrix corresponding to the first partition form is:
Figure RE-FDA0003574100000000021
wherein, Tl|i∈Rli×liToeplitz matrices with equal diagonal elements.
4. The structural health monitoring method based on stochastic subspace modal parameter identification according to claim 1, wherein the second group of the Hankel matrix is divided into the following forms:
Figure RE-FDA0003574100000000022
wherein, yk∈Rl×1The output data at a certain time is k is 0,1 … …, 2i + j-2, l is the output channel number, j is the column number of Hankel matrix, YpAnd YfDefined as the past matrix and the future matrix, respectively.
5. The structural health monitoring method based on stochastic subspace modal parameter identification according to claim 4, wherein the Toeplitz matrix corresponding to the second division form is:
Figure RE-FDA0003574100000000031
wherein, T1|i∈Rli×liToeplitz matrices with equal diagonal elements.
6. The structural health monitoring method based on stochastic subspace modal parameter identification as claimed in claim 1, wherein the S3-S5 specifically comprises:
carrying out SVD on the Toeplitz matrix to obtain
Figure RE-FDA0003574100000000032
Wherein U and V are orthogonal matrices, and
∑1＝diag(σk)，σk＞0，k＝1，2，…，n
and when
Figure RE-FDA0003574100000000033
To obtain
Figure RE-FDA0003574100000000034
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115357853A (en) * 2022-08-22 2022-11-18 河海大学 Engineering structure modal parameter identification method based on fast random subspace
CN115436037A (en) * 2022-08-24 2022-12-06 国网新疆电力有限公司电力科学研究院 Transmission tower health state discrimination method and device based on SSI parameter identification

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115357853A (en) * 2022-08-22 2022-11-18 河海大学 Engineering structure modal parameter identification method based on fast random subspace
CN115357853B (en) * 2022-08-22 2023-08-04 河海大学 Engineering structure modal parameter identification method based on rapid random subspace
CN115436037A (en) * 2022-08-24 2022-12-06 国网新疆电力有限公司电力科学研究院 Transmission tower health state discrimination method and device based on SSI parameter identification

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