CN113392789B - Bridge full-bridge complete modal shape recognition method utilizing small amount of sensor information - Google Patents
Bridge full-bridge complete modal shape recognition method utilizing small amount of sensor information Download PDFInfo
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- CN113392789B CN113392789B CN202110702222.8A CN202110702222A CN113392789B CN 113392789 B CN113392789 B CN 113392789B CN 202110702222 A CN202110702222 A CN 202110702222A CN 113392789 B CN113392789 B CN 113392789B
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Abstract
The invention discloses a bridge full-bridge complete modal shape recognition method by using a small amount of sensor information, which comprises the following steps: a small number of displacement sensors are arranged at different positions on the beam bridge; measuring the vertical displacement response of the vehicle load when the vehicle load passes through a beam bridge to obtain a matrix A of displacement signals; performing cross-power spectrum calculation on the matrix A to obtain a cross-power spectrum matrix P; performing feature orthogonal decomposition on the cross-power spectrum matrix P to obtain a feature vector matrix U; multiplying the displacement signal matrix A by the eigenvector matrix U to obtain a component matrix C; and performing directional filtering processing on each column of the component matrix C by using a mobile filtering window function, wherein the first column and the second column of the filtered component matrix C are respectively the 1 st order full-bridge complete mode shapes and the 2 nd order full-bridge complete mode shapes of the bridge, and the like to obtain the first i order full-bridge complete mode shapes with the same number as the sensors. The method only needs a small amount of measured responses of the displacement sensors, and breaks through the bottleneck problem that the full-bridge complete mode shape cannot be obtained by the traditional method.
Description
Technical Field
The invention relates to the technical field of structural health monitoring, in particular to a bridge full-bridge complete modal shape recognition method by using a small amount of sensor information.
Background
The bridge becomes an important traffic tie for regional connection in the current society, and has important economic and social values, so that the regular and timely monitoring of the structural health of the bridge is an important guarantee for ensuring the stable traffic between regions. The bridge modal identification is an important content in structural health monitoring, and plays an important basic role in subsequent steps of structural health monitoring such as bridge structure working modal analysis, structural damage identification and the like. At present, the traditional modal identification method can only obtain sparse modal shape, the shape curve of the traditional modal identification method is a broken line obtained by directly connecting modal shape values at the position of a sensor, and a full-bridge complete modal shape of a bridge structure cannot be obtained, so that the traditional modal shape-based bridge damage identification and health monitoring method cannot be realized in engineering application. If a dense and complete modal shape curve needs to be obtained, the method can be realized only by arranging a large number of sensors on the bridge, which means that the method can be effectively implemented only by using large amount of monitoring data and high hardware cost, and the implementation of bridge structure health monitoring is restricted. In summary, it is urgently needed to provide a full-bridge complete mode shape recognition method for bridge structures by using a very small number of sensors, which is significant in reducing the structural mode recognition cost and popularizing and industrialization bridge health monitoring.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a bridge full-bridge complete modal shape identification method by using a small amount of sensor information, which does not need massive sensors and directly analyzes the current measured information.
The purpose of the invention can be achieved by adopting the following technical scheme:
a complete mode shape identification method of a bridge full-bridge by using a small amount of sensor information comprises the following steps:
s1, arranging i displacement sensors on the beam bridge, wherein i is more than or equal to 2 and less than or equal to 4, and the mounting direction is perpendicular to the bridge deck;
s2, measuring the vertical displacement response of the vehicle load when passing through the beam bridge at a constant speed to obtain a displacement signal matrix AN×iN is the length of the signal sampling point, AN×iA matrix of Nx i;
s3, aligning shift signal matrix AN×iPerforming cross-power spectrum calculation to obtain a displacement signal matrix AN×iCross power spectrum matrix Pi×iThe cross-power spectrum calculation expression is as follows:
Pi×i＝A′N×i·AN×i
wherein, A'N×iIs represented by AN×iThe transposed matrix of (2);
s4, cross-power spectrum matrix Pi×iPerforming characteristic orthogonal decomposition Eig (P)i×i) To obtain
Eig(Pi×i)＝[Ui×i,Λi×i]
Wherein U isi×iIs a matrix of eigenvectors of i × i, Λi×iIs corresponding to Ui×iMatrix of eigenvalues of Λi×iThe characteristic values are arranged from large to small on the diagonal line;
s5, displacement signal matrix AN×iAnd eigenvector matrix Ui×iMultiplying to obtain a component matrix CN×i，
CN×i＝AN×i·Ui×i；
S6, component matrix C is processed by moving filter window functionN×iEach column of the array matrix is filtered to obtain a filtered array matrix
Wherein the moving filter window function is
Wherein f issFor signal sampling frequency, fnThe n-th order natural frequency of the bridge can be obtained from a Fourier spectrogram of a measured signal, wherein l is the length of a moving filter window function window, and C (j, n) is an element of the n-th column and j-th row of a component matrix C;
s7 matrix
Obtaining the first i-order complete mode matrix of the bridge structure, wherein the matrix is
Column 1 is the 1 st order full-bridge complete mode shape of the bridge, matrix
The 2 nd column of (1) is the 2 nd order full-bridge complete mode shape of the bridge, and so on, thereby determining the first i-order mode of the bridge.
Further, the step S6 is to use a moving filter window function to pair the component matrix CN×iEach column of the component matrix is filtered to remove the dynamic signal and noise components of each order reflecting the dynamic property of the structure contained in each column of data of the component matrix.
Further, the method for calculating the window length l of the moving filter window function comprises
Compared with the prior art, the invention has the following advantages and effects:
1) the invention can identify the full-bridge complete vibration mode of the bridge structure only by a few sensors, and solves the problem that a large number of sensors are needed for structural mode identification. The traditional modal shape recognition method can only obtain sparse shape broken lines of the number of the sensors, and cannot obtain full-bridge complete modal shape, so that the mode shape obtained by the traditional modal shape recognition method cannot be applied to modal-based bridge structure damage detection due to the sparsity of the mode shape, and the engineering requirements cannot be met. The method can identify the full-bridge complete vibration mode by adopting a few measuring points, and has important significance for bridge structure health monitoring and damage detection.
2) The method provided by the invention has the advantages of simple operation, small calculated amount and obvious full-bridge modal shape recognition effect of the beam bridge structure.
Drawings
FIG. 1 is a flow chart of a bridge full-bridge perfect mode shape identification method using a small amount of sensor information disclosed in the embodiments of the present invention;
FIG. 2 is a schematic view of a bridge model in example 1 of the present invention;
FIG. 3 is a graph showing displacement signals measured by the sensors 1, 3, 5, 7 in example 1 of the present invention;
fig. 4 is a global mode diagram of a bridge structure identified by the sensors 1, 3, 5, and 7 in embodiment 1 of the present invention;
FIG. 5 is a graph showing displacement signals measured by the sensors 2, 4, 6 in example 1 of the present invention;
FIG. 6 is a global mode diagram of a bridge structure identified by the sensors 2, 4 and 6 in embodiment 1 of the present invention;
FIG. 7 is a drawing of a steel box girder in example 2 of the present invention;
FIG. 8 is a view of a carriage in embodiment 2 of the present invention;
FIG. 9 is a schematic view of a steel box girder model in example 2 of the present invention;
FIG. 10 is a graph showing displacement signals measured by the sensors 1, 2, 3 in example 2 of the present invention;
fig. 11 is a global mode diagram of a bridge structure identified by the sensors 1, 2, and 3 in embodiment 2 of the present invention;
FIG. 12 is a graph showing displacement signals measured by the sensors 1 and 2 in example 2 of the present invention;
fig. 13 is a global mode diagram of a bridge structure identified by the sensors 1 and 2 in embodiment 2 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. 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.
Example 1
As shown in fig. 1, fig. 1 is a flowchart of a full bridge full-bridge perfect mode shape recognition method using a small amount of sensor information disclosed in this embodiment. The schematic representation of the steel bridge model used in this example is shown in fig. 2. The length L of the model beam is 20m, and the sampling frequency fs200Hz, and the moving speed of the vehicle is 0.2 m/s. To illustrate the effectiveness of the method, displacement sensors are arranged on the bridge every 2.5m, and 7 displacement sensors are arranged at equal intervals in total, but the method is actually usedOf which a maximum of 4 sensor data is used, 7 sensors are divided into two groups of sensor combinations, respectively combination 1 comprising sensors 1, 3, 5, 7 and combination 2 comprising sensors 2, 4, 6. The specific implementation process is as follows:
s1, symmetrically arranging 7 displacement sensors on the beam bridge, wherein the installation direction is the direction vertical to the bridge deck, as shown in figure 2; firstly, measuring by using a sensor combination 1, wherein the number i of sensors is 4;
s2, obtaining a displacement signal matrix A by measuring the vertical displacement response of the vehicle load when passing through the beam bridge at a constant speedN×iAnd N is the length of the signal sample point, as shown in fig. 3. In this example, N is 20000.
S3, aligning shift signal matrix AN×iPerforming cross power spectrum calculation to obtain AN×iCross power spectrum matrix Pi×i，
Pi×i＝A′N×i·AN×i
Wherein, A'N×iIs represented by AN×iThe transposed matrix of (2).
S4, cross-power spectrum matrix Pi×iPerforming characteristic orthogonal decomposition Eig (P)i×i) To obtain
Eig(Pi×i)＝[Ui×i,Λi×i]
Wherein U isi×iIs a matrix of eigenvectors of i × i, Λi×iIs corresponding to Ui×iMatrix of eigenvalues of Λi×iThe characteristic values are arranged from large to small on the diagonal line;
s5, displacement signal matrix AN×iAnd eigenvector matrix UiMultiplying to obtain a component matrix CN×iThe calculation formula is as follows: cN×i＝AN×i·Ui×i；
S6, component matrix C is processed by moving filter window functionN×iEach column of the component matrix is filtered to remove the dynamic signal and noise components of each order reflecting the structure dynamic property contained in each column of data of the component matrix, and the moving filter window function is
Wherein f issFor signal sampling frequency, fnThe N-th order natural frequency of the bridge can be obtained from a Fourier spectrogram of a measured signal, C (j, N) is an element of the N-th column and j-th row of a component matrix C, k is a natural number from 1 to N, l is a window length of a moving filter window function, and the calculation method is that
S7 matrix
And obtaining the first i-order complete modal matrix of the bridge structure. Matrix
Column 1 is the 1 st full-bridge perfect mode shape of the bridge, column 2 is the 2 nd full-bridge perfect mode shape of the bridge, and so on, thereby determining the first 4 th full-bridge perfect mode shape of the bridge, as shown in fig. 4.
In order to verify whether the full-bridge complete mode shape can be successfully identified by different sensor combinations and fewer sensors, a displacement signal matrix is reconstructed by taking the displacement response measured by the combination 2 of the sensors 2, 4 and 6, the steps of S2-S7 are repeated as shown in FIG. 5, and the first 3-order full-bridge complete mode shape is obtained as shown in FIG. 6.
Example 2
In order to further illustrate the effectiveness of the bridge global mode identification method provided by the invention, an experimental steel box girder is used for verification. The steel box beam used in example 2 is shown in fig. 7 and the trolley is shown in fig. 8. The length l of the steel box girder is 20m, the width is 0.2m, the height is 0.1m, the thickness is 3mm, and the sampling frequency fsAt 500Hz, the vehicle was moving at a speed of 0.26 m/s. To illustrate the effectiveness of the method, three displacement sensors were placed on the bridge, but in actual use, the 3 sensors were divided into two groups of sensor combinationsCombination 1 including sensors 1, 2, 3 and combination 2 including sensors 1, 3, respectively. The specific implementation process is as follows:
s1, arranging 3 displacement sensors on the beam bridge, wherein the installation direction is the direction vertical to the bridge deck, as shown in figure 9; firstly, measuring by using a sensor combination 1, wherein the number i of sensors is 3;
s2, obtaining a displacement signal matrix A by measuring the vertical displacement response of the vehicle load when passing through the beam bridge at a constant speedN×iAnd N is the length of the signal sample point, as shown in fig. 10. In this embodiment, N is 11300.
S3, aligning shift signal matrix AN×iPerforming cross power spectrum calculation to obtain AN×iCross power spectrum matrix Pi×i，
Pi×i＝A′N×i·AN×i
Wherein, A'N×iIs represented by AN×iThe transposed matrix of (2).
S4, cross-power spectrum matrix Pi×iPerforming characteristic orthogonal decomposition Eig (P)i×i) To obtain
Eig(Pi×i)＝[Ui×i,Λi×i]
Wherein U isi×iIs a matrix of eigenvectors of i × i, Λi×iIs corresponding to Ui×iMatrix of eigenvalues of Λi×iThe characteristic values are arranged from large to small on the diagonal line;
s5, displacement signal matrix AN×iAnd eigenvector matrix Ui×iMultiplying to obtain a component matrix CN×i，
S6, component matrix C is processed by moving filter window functionN×iEach column of the component matrix is filtered to remove the dynamic signal and noise components of each order reflecting the structure dynamic property contained in each column of data of the component matrix, and the moving filter window function is
Wherein f issFor signal sampling frequency, fnThe N-th order natural frequency of the bridge can be obtained from a Fourier spectrogram of a measured signal, C (j, N) is an element of the N-th column and j-th row of a component matrix C, k is a natural number from 1 to N, l is a window length of a moving filter window function, and the calculation method is that
S7 matrix
And obtaining the first i-order complete modal matrix of the bridge structure. Matrix
The 1 st column of the complete mode shape of the full-bridge of the 1 st order of the bridge, the 2 nd column of the complete mode shape of the full-bridge of the 2 nd order of the bridge, analogize sequentially, thus confirm the first i-th order full-bridge mode shape of the bridge. As shown in fig. 11.
In order to verify whether the full-bridge complete mode shape can be successfully identified when different sensor combinations are adopted and the number limit value of the sensors is 2, a displacement signal matrix is reconstructed by taking the displacement response measured by the combination 2 of the sensors 1 and 3, the steps of S2-S7 are repeated as shown in FIG. 12, and the first i-order full-bridge complete mode shape of the bridge structure is obtained as shown in FIG. 13.
In summary, the method for identifying the complete full-bridge modal shape of the bridge structure by using a small amount of displacement sensor information provided by the invention can effectively identify the complete full-bridge modal shape of the bridge structure only by directly analyzing the current measured information and only by using a few sensors.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (3)
1. A complete mode shape identification method of a bridge full-bridge by using a small amount of sensor information is characterized by comprising the following steps:
s1, arranging i displacement sensors on the beam bridge, wherein i is more than or equal to 2 and less than or equal to 4, and the mounting direction is perpendicular to the bridge deck;
s2, measuring the vertical displacement response of the vehicle load when passing through the beam bridge at a constant speed to obtain a displacement signal matrix AN×iN is the length of the signal sampling point, AN×iA matrix of Nx i;
s3, aligning shift signal matrix AN×iPerforming cross-power spectrum calculation to obtain a displacement signal matrix AN×iCross power spectrum matrix Pi×iThe cross-power spectrum calculation expression is as follows:
Pi×i＝A′N×i·AN×i
wherein, A'N×iIs represented by AN×iThe transposed matrix of (2);
s4, cross-power spectrum matrix Pi×iPerforming characteristic orthogonal decomposition Eig (P)i×i) To obtain
Eig(Pi×i)＝[Ui×i，Λi×i]
Wherein U isi×iIs a matrix of eigenvectors of i × i, Λi×iIs corresponding to Ui×iMatrix of eigenvalues of Λi×iThe characteristic values are arranged from large to small on the diagonal line;
s5, displacement signal matrix AN×iAnd eigenvector matrix Ui×iMultiplying to obtain a component matrix CN×i，
CN×i＝AN×i·Ui×i；
S6, component matrix C is processed by moving filter window functionN×iEach column of the array matrix is filtered to obtain a filtered array matrix
Wherein the moving filter window function is
Wherein f issFor signal sampling frequency, fnThe n-th order natural frequency of the bridge can be obtained from a Fourier spectrogram of a measured signal, wherein l is the length of a moving filter window function window, and C (j, n) is an element of the n-th column and j-th row of a component matrix C;
s7 matrix
Obtaining the first i-order complete mode matrix of the bridge structure, wherein the matrix is
Column 1 is the 1 st order full-bridge complete mode shape of the bridge, matrix
The 2 nd column of (1) is the 2 nd order full-bridge complete mode shape of the bridge, and so on, thereby determining the first i-order mode of the bridge.
2. The method for identifying the full-bridge perfect mode shape of the bridge with a small amount of sensor information as claimed in claim 1, wherein the step S6 is performed by using a moving filter window function to the component matrix CN×iEach column of the component matrix is filtered to remove the dynamic signal and noise components of each order reflecting the dynamic property of the structure contained in each column of data of the component matrix.
3. The method for identifying the complete mode shape of the bridge full-bridge using a small amount of sensor information as claimed in claim 1, wherein the window length l of the moving filter window function is calculated by
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