CN116012760A - Structural vibration mode visualization method based on Euler-Lagrange mixed frame - Google Patents

Structural vibration mode visualization method based on Euler-Lagrange mixed frame Download PDF

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CN116012760A
CN116012760A CN202310032737.0A CN202310032737A CN116012760A CN 116012760 A CN116012760 A CN 116012760A CN 202310032737 A CN202310032737 A CN 202310032737A CN 116012760 A CN116012760 A CN 116012760A
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beam structure
image plane
motion
representing
image
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杨冬
张飞
陈伟
严波
薛为浩
张大山
张安东
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MaAnshan Power Supply Co of State Grid Anhui Electric Power Co Ltd
Institute of Advanced Technology University of Science and Technology of China
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MaAnshan Power Supply Co of State Grid Anhui Electric Power Co Ltd
Institute of Advanced Technology University of Science and Technology of China
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Abstract

The invention discloses a structural vibration mode visualization method based on an Euler-Lagrange mixed frame, which comprises the following steps: 1, acquiring motion video data of a structure to be measured, and extracting vibration signals of discrete areas of the structure by using an image matching algorithm with sub-pixel precision; 2, decoupling the vibration signal by using a blind source separation algorithm to obtain each-order modal response signals of the structure; 3, calculating the spatial weight of each order mode of the structure according to the acquired response signals of each order mode; 4, calculating the image gray scale related to the structural singlemode according to the modal response signals of each order and the spatial weight; 5, extracting an interframe dense motion field related to the single mode of the structure by utilizing an optimized Demons algorithm; and 6, realizing the visualization of the structural mode shape by using a motion compensation algorithm according to the acquired motion field. The method can better realize global space motion decoupling and improve the precision of the motion field, thereby reducing the complexity of the algorithm and improving the quality of the vibration mode of the visual structure.

Description

Structural vibration mode visualization method based on Euler-Lagrange mixed frame
Technical Field
The invention belongs to the technical field of structural vibration analysis, and particularly relates to a structural vibration mode visualization method based on an Euler-Lagrange mixed frame.
Background
Vibrations of the structure during movement often imply intrinsic parameters of the structure itself or reflect the state of movement of the structure. The visual detection technology is used as an important component of a non-contact measurement method and is well applied to various engineering fields. The visual measurement method has the advantages that: the remote measurement can be realized, no load effect is generated, the measurement under the full-field multi-scale can be realized, the automation degree of execution software is high, and the like. However, for small amplitude changes in video, the conventional vision measurement method is difficult to capture the signals, and for such application scenes, the motion amplification algorithm is very suitable for analyzing small motions and structural deformation conditions in video, and analysis of object motions generated by small excitation in the environment becomes possible.
As a technique to visualize subtle changes in video, motion amplification algorithms enhance spatial vibration in video by manipulating in-plane pixels (lagrangian viewing angles) or time-sequential pixel gray scale changes (euler viewing angles). The lagrangian-view-angle-based motion processing method achieves motion amplification by moving pixels on an image plane, so that no artifacts occur, but has the disadvantage of being insensitive to fine motions and limited by noise immunity, so that lagrangian-view-angle-based motion amplification is rarely used for structural modal testing. Unlike the linear method of increasing noise power, the motion processing method based on the euler angle is not easy to receive the interference of image noise, but has lower calculation efficiency, and the reconstructed video can generate artifacts when a larger amplification factor is taken.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a structural vibration mode visualization method based on an Euler-Lagrange mixed frame, so that global space motion decoupling can be better realized, the precision of a motion field can be improved, the complexity of an algorithm can be reduced, and the quality of a visual structural vibration mode can be improved.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the invention discloses a structural vibration mode visualization method based on an Euler-Lagrange mixed frame, which is characterized by comprising the following steps of:
step 1, acquiring a motion video data set D of a beam structure by using a camera, and adding the previous t in the motion video data set D 1 The beam structure in the moment image plane is divided into m discrete areas { r } j (t)|j＝1,2,…,m；t＝0,1,2,…,t 1 -where r j (t) represents the j-th discrete area divided by the beam structure in the image plane at the t moment, and m represents the number of discrete areas;
image matching algorithm utilizing sub-pixel precision for all divided m blocks of discrete regions { r } j (t)|j＝1,2,…,m；t＝0,1,2,…,t 1 Processing to obtain vibration signals { delta (r) j ,t)|j＝1,2,…,m；t＝0,1,2,…,t 1 And, wherein, delta (r) j T) represents the j-th discrete region r j (t) sub-pixel displacement at time t;
step 2, coupling vibration signal { delta (r) by using Lagrangian view-based motion processing method shown in formula (1) j ,t)|j＝1,2,…,m；t＝0,1,2,…,t 1 Characterizing, thereby solving the vibration signal after characterization by using a blind source separation algorithm to obtain a mixed matrix A and a decoupled front t 1 Front k-order modal response signal { delta ] of moment beam structure i (t)|i＝1,2,…,k；t＝0,1,2,…,t 1 }；
Figure BDA0004047895850000021
In the formula (1), k represents the number of activated modes; delta i (t) an ith order modal response signal representative of the beam structure at time t;
step 3, constructing a relation between space motion and structural pixel gray change by using a motion processing method based on Euler angles and shown in a formula (2) according to a mode superposition principle, and solving the formula (2) to obtain a space weight of the beam structure in an image plane
Figure BDA0004047895850000022
In the formula (2), ω i (x n ) Representing the nth pixel x in the image plane n Spatial weight coefficients associated with the ith order mode of the beam structure; f (x) n ) Representing the nth pixel x in the image plane n An initial displacement equation at the location of (2);
Figure BDA0004047895850000023
representing the nth pixel x in the image plane n Spatial weighting of the ith order modal response of the beam structure; n represents the total number of pixels in the image plane; b (x) n T) represents the nth pixel x at the time t in the image plane n The position of the nth pixel x from the initial time n Gray scale differences between positions of (a);
step 4, the nth pixel x in the image plane at the time t is obtained according to the formula (3) n Image gray scale related to the ith order mode of the beam structure
Figure BDA0004047895850000031
Thereby obtaining the front t 1 Image gray scale of all N pixel positions in the temporal image plane related to the first k-th order mode of the beam structure>
Figure BDA0004047895850000032
Figure BDA0004047895850000033
In the formula (3), I (x) n 0) represents the nth pixel x in the image plane at the initial time n Image gray scale on location;
step 5, optimizing a Demons algorithm by means of convolution smoothing and mask construction, and utilizing the optimized Demons algorithm to perform image gray { I (x) on all N pixel positions in an image plane at the initial moment n 0) |n=1, 2, …, N } and t before 1 Image gray scale associated with the first k-th order mode of beam structure at time
Figure BDA0004047895850000034
Processing to obtain inter-frame dense motion field +.>
Figure BDA0004047895850000035
Representing inter-dense motion fields associated only with the ith order mode of the beam structure;
step 6, according to the inter-frame dense motion field
Figure BDA0004047895850000036
Image gray scale { I (x) n 0) |n=1, 2, …, N } to obtain the previous t 1 Image gray scale of all N pixel positions in moment image plane related to front k-order mode of beam structure
Figure BDA0004047895850000037
Wherein (1)>
Figure BDA0004047895850000038
Representing the nth pixel x in the image plane at time t n Is associated with the i-th order mode of the beam structure.
The structural vibration mode visualization method based on the Euler-Lagrange mixed frame is characterized in that the step 5 comprises the following steps:
step 5.1, defining the current iteration number as g, and initializing g=1; define the maximum iteration number as g max The method comprises the steps of carrying out a first treatment on the surface of the Defining an inter-dense motion field associated with an ith order mode of the beam structure at a g-th iteration as
Figure BDA0004047895850000039
And initialize +.>
Figure BDA00040478958500000310
A zero vector field of the same dimension as the image plane;
step 5.2 solving the update motion field at the g-th iteration by the minimum value of equation (4)
Figure BDA00040478958500000311
Figure BDA0004047895850000041
In the formula (4), the amino acid sequence of the compound,
Figure BDA0004047895850000042
representing a cost function for the ith order modality at the g-th iteration; sigma (sigma) p Representing image noise; sigma (sigma) x Representing a spatial uncertainty parameter; />
Figure BDA00040478958500000414
Representing a mapping operation; I.I representing norms;
step 5.3 updating the motion field for the g-th iteration according to equation (5)
Figure BDA0004047895850000043
Performing Gaussian convolution operation to obtain the regularized updated motion field ++g under the g-th iteration>
Figure BDA0004047895850000044
Figure BDA0004047895850000045
In the formula (5), the amino acid sequence of the compound,
Figure BDA0004047895850000046
representing a gaussian convolution operation; g represents a Gaussian kernel;
step 5.4 obtaining an inter-frame motion field related to the ith order mode of the beam structure after removing background motion interference according to equation (6)
Figure BDA0004047895850000047
Figure BDA0004047895850000048
In the formula (6), M represents an image mask constructed according to a beam structure; d represents a convolution kernel; * Representing a multiplication operation;
step 5.5 judging that g is more than g max If so, executing the step 5.6; otherwise, will
Figure BDA0004047895850000049
Assign to->
Figure BDA00040478958500000410
After g+1 is assigned to g, returning to the step 5.2 for sequential execution;
step 5.6 pairing according to formula (7)
Figure BDA00040478958500000411
Performing Gaussian convolution operation to output optimal motion field +.>
Figure BDA00040478958500000412
As an inter dense motion field related only to the i-th order mode of the beam structure:
Figure BDA00040478958500000413
the invention provides an electronic device comprising a memory and a processor, wherein the memory is used for storing a program for supporting the processor to execute the structure vibration mode visualization method, and the processor is configured to execute the program stored in the memory.
The invention relates to a computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being run by a processor, performs the steps of the method for visualizing the structure mode shape.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention utilizes the structural modal response as the medium for describing interaction of Euler and Lagrange motions, and better realizes the decoupling of global space motions.
2. The method utilizes the optimized Demons algorithm to obtain the inter-frame dense motion field related to the single mode of the structure, improves the precision of the motion field, reduces the complexity of the algorithm and improves the quality of the vibration mode of the visual structure.
Drawings
FIG. 1 is a flow chart of a structural vibration mode visualization method based on an Euler-Lagrange hybrid framework of the present invention;
FIG. 2 is a diagram of a structure of a beam under test with targets disposed in discrete areas in accordance with the present invention;
FIG. 3 is a graph of coupled vibration signals extracted from discrete areas of a beam structure in accordance with the present invention;
FIG. 4 is a graph of a modal response signal and a spectrum thereof related to a single mode after decoupling according to the present invention;
FIG. 5 is a mask diagram of the present invention;
fig. 6 is a diagram of the vibration mode of the visual structure of the present invention.
Detailed Description
In this embodiment, a structure vibration mode visualization method based on euler-lagrangian hybrid frame, as shown in fig. 1, includes the following steps:
step 1, acquiring a motion video data set D of a beam structure by using a camera, and based on the assumption of local rigidity of the structure, obtaining the previous t in the motion video data set D 1 The beam structure in the moment image plane is divided into m discrete areas { r } j (t)j＝1,2,…,m；t＝0,1,2,…,t 1 As shown in fig. 2, targets are arranged at discrete areas on the beam structure under test for extracting vibration signals, where r j (t) represents the j-th discrete area divided by the beam structure in the image plane at the t moment, and m represents the number of discrete areas;
image matching algorithm utilizing sub-pixel precision for all divided m blocks of discrete regions { r } j (t)j＝1,2,…,m；t＝0,1,2,…,t 1 Processing to obtain vibration signals { delta (r) j ,t)j＝1,2,…,m；t＝0,1,2,…,t 1 As shown in fig. 3, the vibration signals extracted from the first three discrete areas on the beam structure are shown in fig. 3 as part (a) in fig. 3, part (b) in fig. 3, and part (c) in fig. 3, respectively, where it can be observed that the vibration signals are coupled, where δ (r) j T) represents the j-th discrete region r j (t) sub-pixel displacement at time t;
step 2, in practical application, the vibration of the beam structure can be expressed as a linear combination of modal responses of each order according to formula (1):
Figure BDA0004047895850000051
in the formula (1), i represents a mode order; k represents the number of active modalities; w (w) i (x n ) Representing the nth pixel x in the image plane n Spatial weight coefficients associated with the ith order mode of the beam structure; delta i (t) an ith order modal response signal representative of the beam structure at time t; sigma represents the summation symbol.
In the Lagrangian view, a pixel can be seen as a particle, tracking the motion of the beam structure by capturing the trajectories of these particles. In practical application, the tracks of all particles are tracked on the image, and a great amount of calculation resources and time are consumed for decoupling the tracks, so that the modal response signals of each stage of the beam structure can be calculated through the vibration signals in the discrete area of the beam structure.
Coupled vibration signal { delta (r) is processed by using Lagrangian view-based motion processing method shown in formula (2) j ,t)|j＝1,2,…,m；t＝0,1,2,…,t 1 Characterizing, thereby solving the vibration signal after characterization by using a blind source separation algorithm to obtain a mixed matrix A and a decoupled front t 1 Front k-order modal response signal { delta ] of moment beam structure i (t)|i＝1,2,…,k；t＝0,1,2,…,t 1 As shown in fig. 4, the first column of fig. 4 is a modal response signal, and the second column of fig. 4 is a spectrogram corresponding to the first column. The part (a) in fig. 4, the part (b) in fig. 4 and the part (c) in fig. 4 are respectively the modal response signals of the front third order of the beam structure and the spectrograms thereof, and it can be observed that the modal response signals are uncoupled at this time;
Figure BDA0004047895850000061
step 3, based on the motion processing method of the euler angles, the temporal pixel gray level change can represent the spatial motion of the structure in the image plane, and therefore can be represented according to the formula (3):
I(x n ,t)＝f(x n +δ(x n ,t)) (3)
in the formula (3), I (x) n T) represents the nth pixel x in the image plane at the time t n Image gray scale at the location of (2); delta (x) n T) represents the nth pixel x of the beam structure in the image plane at the time t n Is a displacement in position; f (x) n +δ(x n T) represents the nth pixel x of the beam structure in the image plane at the time instant t n Is provided.
Equation (3) can also be approximated by a first-order taylor expansion, as shown in equation (4):
Figure BDA0004047895850000062
in the formula (4), the amino acid sequence of the compound,
Figure BDA0004047895850000063
the remainder representing a first order taylor expansion; f (x) n ) Representing the nth pixel x in the image plane n Is provided.
Therefore, the relation between the spatial motion and the gray level change of the structural pixels can be expressed according to the formula (5), and the formula (5) is solved to obtain the spatial weight of the beam structure in the image plane
Figure BDA0004047895850000071
Figure BDA0004047895850000072
/>
In the formula (5), the amino acid sequence of the compound,
Figure BDA0004047895850000073
representing the nth pixel x in the image plane n Spatial weighting of the ith order modal response of the beam structure; n represents the total number of pixels in the image plane;{B(x n ,t)|n＝1,2,…,N；t＝0,1,2,…,t 1 the first t in the image plane 1 Time nth pixel x n The position of the nth pixel x from the initial time n All gray scale differences between the positions of (a);
B(x n t) represents the nth pixel x at the time t in the image plane n The position of the nth pixel x from the initial time n Gray scale differences between positions of (a);
step 4, obtaining the nth pixel x in the image plane at the nth moment according to the formula (6) n Image gray scale related to the ith order mode of the beam structure
Figure BDA0004047895850000074
Thereby obtaining the front t 1 Image gray scale of all N pixel positions in the temporal image plane related to the first k-th order mode of the beam structure>
Figure BDA0004047895850000075
Figure BDA0004047895850000076
In the formula (6), I (x) n 0) represents the nth pixel x in the image plane at the initial time n Image gray scale on location;
and 5, optimizing a Demons algorithm by means of convolution smoothing and mask construction, wherein the convolution smoothing is used for filtering high-frequency noise in the image, and the mask construction is used for eliminating interference of background motion in the image. Image gray { I (x) of all N pixel positions in the image plane at the initial moment by using optimized Demons algorithm n 0) |n=1, 2, …, N } and t before 1 Image gray scale associated with the first k-th order mode of beam structure at time
Figure BDA0004047895850000077
Processing to obtain inter-frame dense motion field +.>
Figure BDA0004047895850000078
Representing inter-dense motion fields associated only with the ith order mode of the beam structure;
step 5.1, defining the current iteration number as g, and initializing g=1; define the maximum iteration number as g max The method comprises the steps of carrying out a first treatment on the surface of the Defining an inter-dense motion field associated with an ith order mode of the beam structure at a g-th iteration as
Figure BDA0004047895850000081
And initialize +.>
Figure BDA0004047895850000082
A zero vector field of the same dimension as the image plane;
step 5.2 solving the update motion field at the g-th iteration by the minimum value of equation (7)
Figure BDA0004047895850000083
Figure BDA0004047895850000084
In the formula (7), the amino acid sequence of the compound,
Figure BDA0004047895850000085
representing a cost function for the ith order modality at the g-th iteration; sigma (sigma) p Representing image noise; sigma (sigma) x Representing a spatial uncertainty parameter; />
Figure BDA00040478958500000818
Representing a mapping operation; I.I representing norms;
step 5.3 updating the motion field for the g-th iteration according to equation (8)
Figure BDA0004047895850000086
Performing Gaussian convolution operation to obtain the regularized updated motion field ++g under the g-th iteration>
Figure BDA0004047895850000087
Figure BDA0004047895850000088
In the formula (5), the amino acid sequence of the compound,
Figure BDA0004047895850000089
representing a gaussian convolution operation; g represents a Gaussian kernel;
step 5.4 obtaining an inter-frame motion field related to the ith order mode of the beam structure after removing background motion interference at the g-th iteration according to equation (9)
Figure BDA00040478958500000810
Figure BDA00040478958500000811
/>
In the formula (9), M represents an image mask, and as shown in fig. 5, the mask is constructed according to the outline of the beam structure; d represents a convolution kernel; * Representing a multiplication operation;
step 5.5 judging that g is more than g max If so, executing the step 5.6; otherwise, will
Figure BDA00040478958500000812
Assign to->
Figure BDA00040478958500000813
After g+1 is assigned to g, returning to the step 5.2 for sequential execution;
step 5.6 pairing according to formula (7)
Figure BDA00040478958500000814
Performing Gaussian convolution operation to output optimal motion field +.>
Figure BDA00040478958500000815
As inter-dense motion fields related only to the ith order mode of the beam structure
Figure BDA00040478958500000816
Step 6, according to the inter-frame dense motion field
Figure BDA00040478958500000817
Selecting proper amplification coefficient alpha, and utilizing motion compensation algorithm to make image gray scale { I (x) n 0) |n=1, 2, …, N } to obtain the previous t 1 Image gray scale of all N pixel positions in moment image plane related to front k-order mode of beam structure
Figure BDA0004047895850000091
As shown in fig. 6, the part (a) in fig. 6, the part (b) in fig. 6 and the part (c) in fig. 6 are respectively a comparison diagram of an image of the initial moment of the beam structure and the vibration pattern of the previous three-order visual structure, and it can be observed that the visual structure vibration pattern obtained by the method of the invention has no artifact and high image quality, wherein>
Figure BDA0004047895850000092
Representing the nth pixel x in the image plane at time t n Is associated with the i-th order mode of the beam structure.
In this embodiment, an electronic device includes a memory for storing a program for supporting the processor to execute the above-described structure mode shape visualizing method, and a processor configured to execute the program stored in the memory.
In this embodiment, a computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the structure-mode visualization method described above.

Claims (4)

1. The structural vibration mode visualization method based on the Euler-Lagrange mixed frame is characterized by comprising the following steps of:
step 1, acquiring a motion video data set D of a beam structure by using a camera, and adding the previous t in the motion video data set D 1 The beam structure in the moment image plane is divided into m discrete areas { r } j (t)|j＝1,2,…,m；t＝0,1,2,…,t 1 -where r j (t) represents the j-th discrete area divided by the beam structure in the image plane at the t moment, and m represents the number of discrete areas;
image matching algorithm utilizing sub-pixel precision for all divided m blocks of discrete regions { r } j (t)|j＝1,2,…,m；t＝0,1,2,…,t 1 Processing to obtain vibration signals { delta (r) j ,t)|j＝1,2,…,m；t＝0,1,2,…,t 1 And, wherein, delta (r) j T) represents the j-th discrete region r j (t) sub-pixel displacement at time t;
step 2, coupling vibration signal { delta (r) by using Lagrangian view-based motion processing method shown in formula (1) j ,t)|j＝1,2,…,m；t＝0,1,2,…,t 1 Characterizing, thereby solving the vibration signal after characterization by using a blind source separation algorithm to obtain a mixed matrix A and a decoupled front t 1 Front k-order modal response signal { delta ] of moment beam structure i (t)|i＝1,2,…,k；t＝0,1,2,…,t 1 }；
Figure FDA0004047895840000011
In the formula (1), k represents the number of activated modes; delta i (t) an ith order modal response signal representative of the beam structure at time t;
step 3, constructing a relation between space motion and structural pixel gray change by using a motion processing method based on Euler angles and shown in a formula (2) according to a mode superposition principle, and solving the formula (2) to obtain a space weight of the beam structure in an image plane
Figure FDA0004047895840000012
Figure FDA0004047895840000021
In the formula (2), ω i (x n ) Representing the nth pixel x in the image plane n Spatial weight coefficients associated with the ith order mode of the beam structure; f (x) n ) Representing the nth pixel x in the image plane n An initial displacement equation at the location of (2);
Figure FDA0004047895840000022
representing the nth pixel x in the image plane n Spatial weighting of the ith order modal response of the beam structure; n represents the total number of pixels in the image plane; b (x) n T) represents the nth pixel x at the time t in the image plane n The position of the nth pixel x from the initial time n Gray scale differences between positions of (a);
step 4, the nth pixel x in the image plane at the time t is obtained according to the formula (3) n Image gray scale related to the ith order mode of the beam structure
Figure FDA0004047895840000023
Thereby obtaining the front t 1 Image gray scale of all N pixel positions in the temporal image plane related to the first k-th order mode of the beam structure>
Figure FDA0004047895840000024
Figure FDA0004047895840000025
In the formula (3), I (x) n 0) represents the nth pixel x in the image plane at the initial time n Image gray scale on location;
step 5, optimizing the Demons algorithm by means of convolution smoothing and mask construction, and utilizing the optimized Demons algorithmThe method is applied to the image gray scale { I (x) n 0) |n=1, 2, …, N } and t before 1 Image gray scale associated with the first k-th order mode of beam structure at time
Figure FDA0004047895840000026
Processing to obtain inter-frame dense motion field +.>
Figure FDA0004047895840000027
Figure FDA0004047895840000028
Representing inter-dense motion fields associated only with the ith order mode of the beam structure;
step 6, according to the inter-frame dense motion field
Figure FDA0004047895840000029
Image gray scale { I (x) n 0) |n=1, 2, …, N } to obtain the previous t 1 Image gray scale +.f. of all N pixel positions in the moment image plane related to the front k-order mode of the beam structure>
Figure FDA0004047895840000031
Wherein (1)>
Figure FDA0004047895840000032
Representing the nth pixel x in the image plane at time t n Is associated with the i-th order mode of the beam structure.
2. The method for visualizing a structural vibration mode based on an euler-lagrangian hybrid framework according to claim 1, wherein said step 5 comprises:
step 5.1, defining the current iteration number as g, and initializing g=1; define the maximum iteration number as g max The method comprises the steps of carrying out a first treatment on the surface of the Definition of the definitionThe inter-dense motion field related to the ith order mode of the beam structure at the g-th iteration is
Figure FDA0004047895840000033
And initialize +.>
Figure FDA0004047895840000034
A zero vector field of the same dimension as the image plane;
step 5.2 solving the update motion field at the g-th iteration by the minimum value of equation (4)
Figure FDA0004047895840000035
Figure FDA0004047895840000036
In the formula (4), the amino acid sequence of the compound,
Figure FDA0004047895840000037
representing a cost function for the ith order modality at the g-th iteration; sigma (sigma) p Representing image noise; sigma (sigma) x Representing a spatial uncertainty parameter; />
Figure FDA00040478958400000318
Representing a mapping operation; I.I representing norms;
step 5.3 updating the motion field for the g-th iteration according to equation (5)
Figure FDA0004047895840000038
Performing Gaussian convolution operation to obtain the regularized updated motion field ++g under the g-th iteration>
Figure FDA0004047895840000039
Figure FDA00040478958400000310
In the formula (5), the amino acid sequence of the compound,
Figure FDA00040478958400000311
representing a gaussian convolution operation; g represents a Gaussian kernel;
step 5.4 obtaining an inter-frame motion field related to the ith order mode of the beam structure after removing background motion interference according to equation (6)
Figure FDA00040478958400000312
Figure FDA00040478958400000313
In the formula (6), M represents an image mask constructed according to a beam structure; d represents a convolution kernel; * Representing a multiplication operation;
step 5.5 judging that g is more than g max If so, executing the step 5.6; otherwise, will
Figure FDA00040478958400000314
Assign to->
Figure FDA00040478958400000315
After g+1 is assigned to g, returning to the step 5.2 for sequential execution;
step 5.6 pairing according to formula (7)
Figure FDA00040478958400000316
Performing Gaussian convolution operation to output optimal motion field +.>
Figure FDA00040478958400000317
As an inter dense motion field related only to the i-th order mode of the beam structure:
Figure FDA0004047895840000041
3. an electronic device comprising a memory and a processor, wherein the memory is configured to store a program for supporting the processor to execute the structure mode shape visualization method according to claim 1 or 2, the processor being configured to execute the program stored in the memory.
4. A computer readable storage medium having a computer program stored thereon, characterized in that the computer program when run by a processor performs the steps of the structure mode shape visualization method of claim 1 or 2.
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