A structural mode shape visualization method based on euler-lagrange hybrid framework

Abstract

This invention discloses a method for visualizing structural mode shapes based on an Euler-Lagrange hybrid frame, comprising: 1. acquiring motion video data of the structure to be measured, and extracting vibration signals of discrete regions of the structure using a sub-pixel precision image matching algorithm; 2. decoupling the vibration signals using a blind source separation algorithm to obtain modal response signals of each order of the structure; 3. calculating the spatial weights of each mode of the structure based on the acquired modal response signals; 4. calculating the image grayscale values ​​associated with a single mode of the structure based on the modal response signals and spatial weights; 5. extracting the dense motion field between frames associated with a single mode of the structure using an optimized Demons algorithm; 6. visualizing the structural mode shapes using a motion compensation algorithm based on the acquired motion field. This invention can better achieve global spatial motion decoupling and improve the accuracy of the motion field, thereby reducing the complexity of the algorithm and improving the quality of visualized structural mode shapes.

Description

Technical Field

[0001] This invention belongs to the field of structural vibration analysis technology, specifically a method for visualizing structural vibration modes based on a hybrid Euler-Lagrange frame. Background Technology

[0002] Vibrations of a structure during motion often contain intrinsic parameters of the structure itself or reflect its motion state. Visual inspection technology, as an important component of non-contact measurement methods, has been widely applied in various engineering fields. The advantages of visual measurement methods include: the ability to perform measurements over long distances, no load effects, the ability to perform measurements across multiple scales in the entire field, and a high degree of software automation. However, traditional visual measurement methods struggle to capture minute amplitude changes in videos. For these applications, motion magnification algorithms are well-suited for analyzing minute movements and structural deformations within videos, making it possible to analyze the motion of objects generated by subtle stimuli in the environment.

[0003] As a technique for visualizing subtle changes in videos, motion magnification algorithms enhance spatial vibrations by manipulating in-plane pixels (Lagrange perspective) or temporal pixel grayscale changes (Eulerian perspective). Lagrange-based motion processing methods achieve motion magnification by moving pixels across the image plane, thus avoiding artifacts. However, they are insensitive to subtle movements and limited by noise resistance, limiting their use in structural modal analysis. In Eulerian-based motion processing, unlike linear methods that increase noise power, phase-based methods are less susceptible to image noise interference. However, they are computationally inefficient, and when using large magnification factors, the reconstructed video may exhibit artifacts. Summary of the Invention

[0004] The present invention aims to address the shortcomings of the existing technology by proposing a structural mode shape visualization method based on an Euler-Lagrange hybrid frame. This method aims to better achieve global spatial motion decoupling and improve the accuracy of the motion field, thereby reducing the complexity of the algorithm and improving the quality of the visualized structural mode shape.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] The present invention provides a method for visualizing structural vibration modes based on an Euler-Lagrange hybrid frame, characterized by the following steps:

[0007] Step 1: Acquire a set of motion video data D of the beam structure using a camera, and divide the beam structure in the image plane at the first time t1 in the set of motion video data D into m discrete regions {r j(t)|j=1,2,…,m;t=0,1,2,…,t1}, where r j (t) represents the j-th discrete region divided by the beam structure in the image plane at time t, and m represents the number of discrete regions;

[0008] Using a sub-pixel precision image matching algorithm, all m discrete regions {r j The vibration signals {δ(r)|j=1,2,…,m;t=0,1,2,…,t1} of m discrete regions coupled in the time domain are processed to obtain the vibration signals {δ(r)|j=1,2,…,m;t=0,1,2,…,t1} of m discrete regions. j ,t)|j=1,2,…,m;t=0,1,2,…,t1}, where δ(r j ,t) represents the j-th discrete region r j (t) Subpixel displacement at time t;

[0009] Step 2, using the motion processing method based on the Lagrange perspective shown in equation (1) to process the coupled vibration signal {δ(r j The vibration signal is characterized by {j = 1, 2, ..., m; t = 0, 1, 2, ..., t1}, and then the blind source separation algorithm is used to solve for the characterized vibration signal, thereby obtaining the mixing matrix A and the decoupled first k modal response signals {δ} of the beam structure at the first t1 time step. i (t)|i=1,2,…,k; t=0,1,2,…,t1};

[0010]

[0011] In equation (1), k represents the number of activated modes; δ i (t) represents the i-th modal response signal of the beam structure at time t;

[0012] Step 3: Based on the modal superposition principle, the relationship between spatial motion and structural pixel grayscale changes is constructed using the motion processing method based on the Euler perspective shown in equation (2). Equation (2) is then solved to obtain the spatial weights of the beam structure in the image plane.

[0013]

[0014] In equation (2), ω i (x n ) represents the nth pixel x in the image plane n Spatial weighting coefficients related to the i-th mode of the beam structure at different locations; f(x) n ) represents the nth pixel x in the image plane n The initial displacement equation at the position; Represents the nth pixel x in the image plane nThe spatial weights of the i-th modal response of the beam structure at its position; N represents the total number of pixels in the image plane; B(x n (,t) represents the nth pixel x at time t in the image plane. n Position and the nth pixel x at the initial time n The grayscale difference between positions;

[0015] Step 4: Calculate the nth pixel x in the image plane at time t according to equation (3). n Image grayscale values ​​related to the i-th mode of the beam structure at different locations This yields the image grayscale values ​​of all N pixel locations within the image plane at time t1 that are related to the first k modes of the beam structure.

[0016]

[0017] In equation (3), I(x) n (,0) represents the nth pixel x in the image plane at the initial moment. n Image grayscale at location;

[0018] Step 5: Optimize the Demons algorithm by using convolution smoothing and mask construction. Use the optimized Demons algorithm to process the image grayscale values ​​{I(x)} at all N pixel locations within the image plane at the initial time step. n The image grayscale values ​​of the first k modes of the beam structure at time t1 and the relationship between the n=1, 0)|n=1,2,…,N} are also considered. The process yields the inter-frame dense motion field associated with a single mode in the first k modes of the beam structure. This represents the dense motion field between frames that is only related to the i-th mode of the beam structure.

[0019] Step 6, based on the dense motion field between frames Using a motion compensation algorithm, the image grayscale values ​​{I(x)} at all N pixel locations within the image plane at the initial time are calculated. n The image is processed to obtain the image grayscale values ​​of all N pixel positions in the image plane at time t1, which are related to the first k modes of the beam structure. in, x represents the nth pixel in the image plane at time t. n The image grayscale value at the position related to the i-th mode of the beam structure.

[0020] The structural mode visualization method based on the Euler-Lagrange hybrid frame described in this invention is characterized in that step 5 includes:

[0021] Step 5.1 Define the current iteration number as g and initialize g = 1; define the maximum iteration number as g.max Define the inter-frame dense motion field associated with the i-th mode of the beam structure in the g-th iteration as: and initialize It is a zero vector field with the same dimension as the image plane;

[0022] Step 5.2 Solve for the updated motion field in the g-th iteration by calculating the minimum value of equation (4).

[0023]

[0024] In equation (4), σ represents the cost function for the i-th mode in the g-th iteration; p Indicates image noise; σ x Indicates spatial uncertainty parameters; Represents a mapping operation; ||·|| represents a norm;

[0025] Step 5.3 Update the motion field for the g-th iteration according to equation (5). Perform a Gaussian convolution operation to obtain the updated motion field after regularization in the g-th iteration.

[0026]

[0027] In equation (5), G represents the Gaussian convolution operation; G represents the Gaussian kernel.

[0028] Step 5.4 Obtain the inter-frame motion field related to the i-th mode of the beam structure after removing background motion interference in the g-th iteration according to equation (6).

[0029]

[0030] In equation (6), M represents the image mask constructed based on the beam structure; D represents the convolution kernel; and * represents the multiplication operation.

[0031] Step 5.5 Determine if g > g max Check if the condition is met. If it is, proceed to step 5.6; otherwise, proceed to the next step. Assign to After assigning g+1 to g, return to step 5.2 and execute sequentially;

[0032] Step 5.6 According to equation (7) Perform Gaussian convolution operation to output the optimal motion field. As an inter-frame dense motion field that is only related to the i-th order mode of the beam structure:

[0033]

[0034] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program that supports the processor in executing the structural mode visualization method, and the processor is configured to execute the program stored in the memory.

[0035] The present invention discloses a computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, performs the steps of the structural mode visualization method.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] 1. This invention utilizes structural modal response as a medium for interaction between Eulerian and Lagrange motion descriptions, thereby better achieving global spatial motion decoupling.

[0038] 2. This invention utilizes the optimized Demons algorithm to obtain dense motion fields between frames related to a single mode of the structure, thereby improving the accuracy of the motion fields, reducing the complexity of the algorithm, and enhancing the quality of the visualized structural vibration modes. Attached Figure Description

[0039] Figure 1 This is a flowchart of a structural mode visualization method based on an Euler-Lagrange hybrid frame according to the present invention;

[0040] Figure 2 This is a structural diagram of the beam under test in which targets are arranged in a discrete region according to the present invention.

[0041] Figure 3 This is a diagram of the coupled vibration signal extracted from the discrete region of the beam structure according to the present invention;

[0042] Figure 4 The present invention provides the decoupled modal response signal and its spectrum related to a single mode.

[0043] Figure 5 This is a mask diagram of the present invention;

[0044] Figure 6 This is a visualization of the structural vibration mode diagram of the present invention. Detailed Implementation

[0045] In this embodiment, a method for visualizing structural vibration modes based on an Euler-Lagrange hybrid frame is described, such as... Figure 1 As shown, it includes the following steps:

[0046] Step 1: Acquire a set of motion video data D of the beam structure using a camera. Based on the assumption of local structural rigidity, divide the beam structure in the image plane at the first time t1 in the motion video data set D into m discrete regions {rj (t)j=1,2,…,m; t=0,1,2,…,t1}, such as Figure 2 As shown, targets are arranged in discrete regions on the beam structure under test to extract vibration signals, where r j (t) represents the j-th discrete region divided by the beam structure in the image plane at time t, and m represents the number of discrete regions;

[0047] Using a sub-pixel precision image matching algorithm, all m discrete regions {r j The vibration signals {δ(r)j=1,2,…,m;t=0,1,2,…,t1} of m discrete regions are processed to obtain the time-domain coupled vibration signals {δ(r)j=1,2,…,m;t=0,1,2,…,t1} of m discrete regions. j ,t)j=1,2,…,m; t=0,1,2,…,t1}, such as Figure 3 As shown, Figure 3 Part (a) of the text Figure 3 Part (b) of the text Figure 3 Part (c) shows the vibration signals extracted from the first three discrete regions of the beam structure. It can be observed that the vibration signals are coupled at this point, where δ(r j ,t) represents the j-th discrete region r j (t) is the subpixel displacement at time t;

[0048] Step 2: In practical applications, the vibration of the beam structure can be expressed as a linear combination of modal responses according to equation (1):

[0049]

[0050] In equation (1), i represents the modal order; k represents the number of activated modes; w i (x n ) represents the nth pixel x in the image plane n Spatial weighting coefficients related to the i-th order mode of the beam structure at their location; δ i (t) represents the i-th modal response signal of the beam structure at time t; ∑ represents the summation symbol.

[0051] In a Lagrange perspective, pixels can be viewed as particles, and the motion of a beam structure can be tracked by capturing the trajectories of these particles. In practical applications, tracking the trajectories of all particles on an image and then decoupling those trajectories would consume a significant amount of computational resources and time. Therefore, the modal response signals of the beam structure can be calculated using vibration signals from discrete regions on the beam structure.

[0052] The motion processing method based on the Lagrange perspective shown in equation (2) is used to process the coupled vibration signal {δ(r)}. jThe vibration signal is characterized by {j = 1, 2, ..., m; t = 0, 1, 2, ..., t1}, and then the blind source separation algorithm is used to solve for the characterized vibration signal, thereby obtaining the mixing matrix A and the decoupled first k modal response signals {δ} of the beam structure at the first t1 time step. i (t)|i=1,2,…,k; t=0,1,2,…,t1}, such as Figure 4 As shown, Figure 4 The first column represents the modal response signal. Figure 4 The second column is the spectrum diagram corresponding to the first column. Figure 4 Part (a) of the text Figure 4 Part (b) of the text Figure 4 Part (c) shows the modal response signals and their spectra of the first three orders of the beam structure. It can be observed that the modal response signals are uncoupled at this time.

[0053]

[0054] Step 3, based on the motion processing method of Euler's perspective, the temporal pixel grayscale changes can characterize the spatial motion of the image plane structure, and therefore can be expressed according to equation (3):

[0055] I(x n ,t)=f(x n +δ(x n ,t)) (3)

[0056] In equation (3), I(x) n (,t) represents the nth pixel x in the image plane at time t. n Image grayscale at position; δ(x) n (,t) represents the nth pixel x of the beam structure in the image plane at time t. n Displacement at position; f(x) n +δ(x n ,t)) represents the nth pixel x of the beam structure in the image plane at time t. n The displacement equation at the position.

[0057] Equation (3) can also be approximated by a first-order Taylor expansion, as shown in equation (4):

[0058]

[0059] In equation (4), f(x) represents the remainder term of the first-order Taylor expansion. n ) represents the nth pixel x in the image plane n The initial displacement equation at the position.

[0060] Therefore, the relationship between spatial motion and structural pixel grayscale changes can be expressed by equation (5), and by solving equation (5), the spatial weights of the beam structure in the image plane can be obtained.

[0061]

[0062] In equation (5), Represents the nth pixel x in the image plane n The spatial weights of the i-th modal response of the beam structure at its position; N represents the total number of pixels in the image plane; {B(x n The expression `x,t)|n=1,2,…,N;t=0,1,2,…,t1}` represents the nth pixel x in the image plane at time t1 before the current time. n Position and the nth pixel x at the initial time n All grayscale differences between positions;

[0063] B(x n (,t) represents the nth pixel x at time t in the image plane. n Position and the nth pixel x at the initial time n The grayscale difference between positions;

[0064] Step 4: Calculate the nth pixel x in the image plane at time t according to equation (6). n Image grayscale values ​​related to the i-th mode of the beam structure at different locations This yields the image grayscale values ​​of all N pixel locations within the image plane at time t1 that are related to the first k modes of the beam structure.

[0065]

[0066] In equation (6), I(x) n (,0) represents the nth pixel x in the image plane at the initial moment. n Image grayscale at location;

[0067] Step 5: The Demons algorithm is optimized using convolutional smoothing and mask construction. Convolutional smoothing filters out high-frequency noise in the image, while mask construction removes background motion interference. The optimized Demons algorithm is then used to process the image grayscale values ​​{I(x)} at all N pixel locations within the image plane at the initial time step. n The image grayscale values ​​of the first k modes of the beam structure at time t1 and the relationship between the n=1, 0)|n=1,2,…,N} are also considered. The process yields the inter-frame dense motion field associated with a single mode in the first k modes of the beam structure. This represents the dense motion field between frames that is only related to the i-th mode of the beam structure.

[0068] Step 5.1 Define the current iteration number as g and initialize g = 1; define the maximum iteration number as g. max Define the inter-frame dense motion field associated with the i-th mode of the beam structure in the g-th iteration as: and initialize It is a zero vector field with the same dimension as the image plane;

[0069] Step 5.2 Solve for the updated motion field in the g-th iteration by calculating the minimum value of equation (7).

[0070]

[0071] In equation (7), σ represents the cost function for the i-th mode in the g-th iteration; p Indicates image noise; σ x Indicates spatial uncertainty parameters; Represents a mapping operation; ||·|| represents a norm;

[0072] Step 5.3 Update the motion field for the g-th iteration according to equation (8). Perform a Gaussian convolution operation to obtain the updated motion field after regularization in the g-th iteration.

[0073]

[0074] In equation (5), G represents the Gaussian convolution operation; G represents the Gaussian kernel.

[0075] Step 5.4 Obtain the inter-frame motion field related to the i-th mode of the beam structure after removing background motion interference in the g-th iteration according to equation (9).

[0076]

[0077] In equation (9), M represents the image mask, such as Figure 5 As shown, a mask is constructed based on the shape of the beam structure; D represents the convolution kernel; * represents the multiplication operation;

[0078] Step 5.5 Determine if g > g max Check if the condition is met. If it is, proceed to step 5.6; otherwise, proceed to the next step. Assign to After assigning g+1 to g, return to step 5.2 and execute sequentially;

[0079] Step 5.6 According to equation (7) Perform Gaussian convolution operation to output the optimal motion field. As an inter-frame dense motion field that is only related to the i-th order mode of the beam structure

[0080]

[0081] Step 6, based on the dense motion field between frames By selecting an appropriate magnification factor α, and using a motion compensation algorithm, the image grayscale values ​​{I(x)} at all N pixel locations within the image plane at the initial time are calculated. n The image is processed to obtain the image grayscale values ​​of all N pixel positions in the image plane at time t1, which are related to the first k modes of the beam structure. like Figure 6 As shown, Figure 6 Part (a) of the text Figure 6 Part (b) of the text Figure 6 Part (c) shows a comparison between the initial image of the beam structure and its first three visualized structural modes. It can be observed that the visualized structural modes obtained using the method of this invention produce virtually no artifacts, and the image quality is high. x represents the nth pixel in the image plane at time t. n The image grayscale value at the position related to the i-th mode of the beam structure.

[0082] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described structural mode visualization method. The processor is configured to execute the program stored in the memory.

[0083] In this embodiment, a computer-readable storage medium stores a computer program, which, when run by a processor, executes the steps of the above-described structural mode visualization method.

Claims

1. A method for visualizing structural vibration modes based on an Euler-Lagrange hybrid frame, characterized in that, Includes the following steps: Step 1: Acquire a set of motion video data D of the beam structure using a camera, and divide the beam structure in the image plane at the first time t1 in the set of motion video data D into m discrete regions {r j (t)|j=1,2,…,m;t=0,1,2,…,t1}, where r j (t) represents the j-th discrete region divided by the beam structure in the image plane at time t, and m represents the number of discrete regions; Using a sub-pixel precision image matching algorithm, all m discrete regions {r j The vibration signals {δ(r)|j=1,2,…,m;t=0,1,2,…,t1} of m discrete regions coupled in the time domain are processed to obtain the vibration signals {δ(r)|j=1,2,…,m;t=0,1,2,…,t1} of m discrete regions. j ,t)|j=1,2,…,m;t=0,1,2,…,t1}, where δ(r j ,t) represents the j-th discrete region r j (t) is the subpixel displacement at time t; Step 2, using the motion processing method based on the Lagrange perspective shown in equation (1) to process the coupled vibration signal {δ(r j The vibration signal is characterized by {j = 1, 2, ..., m; t = 0, 1, 2, ..., t1}, and then the blind source separation algorithm is used to solve for the characterized vibration signal, thereby obtaining the hybrid matrix A and the decoupled first k-th order modal response signal {δ} of the beam structure at the first t1 time. i (t)|i=1,2,…,k; t=0,1,2,…,t1}; In equation (1), k represents the number of activated modes; δ i (t) represents the i-th modal response signal of the beam structure at time t; Step 3: Based on the modal superposition principle, the relationship between spatial motion and structural pixel grayscale changes is constructed using the motion processing method based on the Euler perspective shown in equation (2). Equation (2) is then solved to obtain the spatial weights of the beam structure in the image plane. In equation (2), ω i (x n ) represents the nth pixel x in the image plane n Spatial weighting coefficients related to the i-th mode of the beam structure at different locations; f(x) n ) represents the nth pixel x in the image plane n The initial displacement equation at the position; Represents the nth pixel x in the image plane n The spatial weights of the i-th modal response of the beam structure at its position; N represents the total number of pixels in the image plane; B(x n (,t) represents the nth pixel x at time t in the image plane. n Position and the nth pixel x at the initial time n The grayscale difference between positions; Step 4: Calculate the nth pixel x in the image plane at time t according to equation (3). n Image grayscale values ​​related to the i-th mode of the beam structure at different locations This yields the image grayscale values ​​of all N pixel locations within the image plane at time t1 that are related to the first k modes of the beam structure. In equation (3), I(x) n (,0) represents the nth pixel x in the image plane at the initial moment. n Image grayscale at location; Step 5: Optimize the Demons algorithm by using convolution smoothing and mask construction. Use the optimized Demons algorithm to process the image grayscale values ​​{I(x)} at all N pixel locations within the image plane at the initial time step. n The image grayscale values ​​of the first k modes of the beam structure at time t1 and the relationship between the n=1, 0)|n=1,2,…,N} are also considered. The process yields the inter-frame dense motion field associated with a single mode in the first k modes of the beam structure. This represents the dense motion field between frames that is only related to the i-th mode of the beam structure. Step 6, based on the dense motion field between frames Using a motion compensation algorithm, the image grayscale values ​​{I(x)} at all N pixel locations within the image plane at the initial time are calculated. n The image is processed to obtain the image grayscale values ​​of all N pixel positions in the image plane at time t1, which are related to the first k modes of the beam structure. in, x represents the nth pixel in the image plane at time t. n The image grayscale value at the position related to the i-th mode of the beam structure.

2. The structural mode visualization method based on the Euler-Lagrange hybrid frame according to claim 1, characterized in that, Step 5 includes: Step 5.1 Define the current iteration number as g and initialize g = 1; define the maximum iteration number as g. max Define the inter-frame dense motion field associated with the i-th mode of the beam structure in the g-th iteration as: and initialize It is a zero vector field with the same dimension as the image plane; Step 5.2 Solve for the updated motion field in the g-th iteration by calculating the minimum value of equation (4). In equation (4), σ represents the cost function for the i-th mode in the g-th iteration; p Indicates image noise; σ x Indicates spatial uncertainty parameters; Represents a mapping operation; ||·|| represents a norm; Step 5.3 Update the motion field for the g-th iteration according to equation (5). Perform a Gaussian convolution operation to obtain the updated motion field after regularization in the g-th iteration. In equation (5), G represents the Gaussian convolution operation; G represents the Gaussian kernel. Step 5.4 Obtain the inter-frame motion field related to the i-th mode of the beam structure after removing background motion interference in the g-th iteration according to equation (6). In equation (6), M represents the image mask constructed based on the beam structure; D represents the convolution kernel; and * represents the multiplication operation. Step 5.5 Determine if g > g max Check if the condition is met. If it is, proceed to step 5.6; otherwise, proceed to the next step. Assign to After assigning g+1 to g, return to step 5.2 and execute sequentially; Step 5.6 According to equation (7) Perform Gaussian convolution operation to output the optimal motion field. As an inter-frame dense motion field that is only related to the i-th order mode of the beam structure:

3. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the structural mode visualization method of claim 1 or 2, and the processor is configured to execute the programs stored in the memory.

4. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when run by a processor, executes the steps of the structural mode visualization method as described in claim 1 or 2.

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