A video vibration two-dimensional modal identification method and device based on a deep completion pyramid

Abstract

The application discloses a kind of video vibration two-dimensional modal identification method and equipment based on depth completion pyramid, belong to structural vibration measurement and modal identification technical field;First, the depth image sequence in the two-dimensional vibration process of measured structure is obtained;The sparse depth image of depth image sequence is directionally depth completed to construct Gaussian pyramid, and depth completion pyramid is constructed in combination with the Gaussian pyramid of adjacent scale, and the target layer is selected for fusion reconstruction;Then, the reconstructed depth sequence is sequentially subjected to difference amplification, transposition compression and direct current removal processing to construct a unified input matrix;Then, the input matrix is subjected to PDD method and H-DMD method to extract natural frequency, damping ratio and modal shape from two dimensions of frequency domain and time domain;Finally, the decomposition results of PDD method and H-DMD method are jointly checked, and the modal identification result of the structure is output.The two-dimensional structural vibration modal result obtained by the method is improved in terms of parameter integrity, spatial continuity and physical consistency.

Description

Technical Field

[0001] This invention belongs to the field of structural vibration measurement and modal recognition technology, specifically relating to a video vibration two-dimensional modal recognition method and device based on a depth-completed pyramid. Background Technology

[0002] Structural modal parameters, including natural frequencies, damping ratios, and mode shapes, are key indicators reflecting the dynamic characteristics of a structure and are of great significance in structural health monitoring, damage identification, and performance evaluation. Traditional modal identification mostly relies on contact sensors such as accelerometers and strain gauges. Although these sensors offer high measurement accuracy, they suffer from problems such as complex deployment, significant load effects, and limited spatial resolution, making them unsuitable for full-field two-dimensional plane vibration measurement of complex structures. Depth cameras, as a non-contact measurement method, can output depth information of the structural surface in the form of image sequences, providing high-density spatial sampling for full-field two-dimensional plane vibration response measurement. However, when using depth cameras for two-dimensional plane vibration modal identification, they typically face several challenges. The raw depth sequences commonly contain invalid pixels and local missing pixels, easily disrupting the spatial continuity of mode shapes. Simultaneously, depth measurements are affected by noise, quantization errors, and dynamic interference, increasing the spectral noise floor and making it difficult to stably separate weak higher-order modes. Furthermore, depth responses often contain static offset components; if directly analyzed in the frequency domain, strong peaks can easily form near zero frequency, affecting the stability of power spectral density matrix estimation and singular value decomposition. On the other hand, the two-dimensional full-field depth sequence itself has the characteristics of high dimensionality and large redundancy. If modal recognition is carried out directly without effective reconstruction and compression, not only will the amount of computation be large, but it will also easily cause discontinuous mode distribution and insufficient stability in the recognition results.

[0003] While existing depth vision-based two-dimensional planar vibration recognition schemes have made some progress in utilizing depth information, they still have limitations. Patent CN118196164A, focusing on depth completion and signal reconstruction, achieves overall mode shape extraction through steps such as depth completion, projection correction, moving average downsampling, polynomial fitting, Euler amplification, and Hankel dynamic mode decomposition. This approach can improve depth loss and signal distortion to some extent, but its technical approach mainly emphasizes post-completion reconstruction and single time-domain decomposition, without jointly extracting and cross-checking modal parameters from both frequency and time domains. It performs well on one-dimensional data, but its consideration of weak modal stability separation, damping information supplementation and identification, and mode shape spatial continuity optimization under two-dimensional full-field high-dimensional data conditions is still insufficient. The patent with publication number CN117522944A focuses on depth perception and adaptive region localization. It achieves two-dimensional structural vibration region localization and frequency measurement through effective pixel filtering, depth difference superposition, logical masking, connected component determination, region mean displacement extraction, and fast Fourier transform. Its advantages are simple process and low computational load. However, this method is mainly aimed at vibration region detection and single region frequency extraction. It does not carry out in-depth processing for full-field depth loss repair, two-dimensional high-dimensional response reconstruction, and joint identification of complete modal parameters such as natural frequency, damping ratio, and full-field mode shape. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a two-dimensional modal recognition method for video vibration based on a depth-completed pyramid. This method combines directional depth completion with a multi-scale image pyramid to achieve noise-resistant reconstruction of depth sequences. Then, differential amplification, transpose compression, and DC removal are used to construct a suitable two-dimensional input for modal recognition. Next, frequency domain decomposition (FDD) and Hankel dynamic mode decomposition (H-DMD) are combined to extract modal parameters. Finally, support vector regression is used to smooth the mode shapes, thereby achieving stable identification of vibration modal parameters for two-dimensional surface structures under conditions of missing depth, noise interference, and high-dimensional data.

[0005] This invention provides a method for two-dimensional modal recognition of video vibration based on a depth-completed pyramid, comprising the following steps:

[0006] Acquire a sequence of depth images during the two-dimensional vibration process of the structure under test;

[0007] Directional depth completion is performed on the sparse depth image of the region of interest in the depth image sequence to construct a Gaussian pyramid, and a depth completion pyramid is constructed by combining the Gaussian pyramids of adjacent scales. The target layer is selected for fusion and reconstruction.

[0008] The reconstructed depth sequence is then subjected to differential amplification, transpose compression, and DC removal in sequence to construct a unified input matrix suitable for frequency domain and time domain analysis.

[0009] The input matrix is ​​extracted from the natural frequency, damping ratio and mode shape in both the frequency domain and time domain using frequency domain decomposition and Hankel dynamic mode decomposition.

[0010] The decomposition results of the frequency domain decomposition method and the Hankel dynamic mode decomposition method are jointly verified, and the modal recognition results of the structure are output.

[0011] Furthermore, the depth image sequence The preprocessing involves effective pixel filtering and region of interest extraction. The region of interest extraction is performed by extracting a target region containing the main vibration information as the region of interest based on the spatial distribution of consecutive effective pixels in the first frame or a reference frame.

[0012] Furthermore, the Gaussian pyramid is obtained by low-pass filtering and smoothing downsampling on the depth-completed image;

[0013] in, This is the image after depth completion; For the first Image of a Gaussian pyramid; It is a two-dimensional Gaussian kernel. and These are the spatial pixel coordinates. Control the smoothness; This is a double downsampling process.

[0014] Furthermore, the depth-completed pyramid for:

[0015] in, For the first Layer depth completion of pyramid image; This is a double upsampling process; , and These are the upsampled pixel coordinates. and These are the pixel coordinates of the Gaussian pyramid. This is the interpolation kernel function.

[0016] Furthermore, choosing to deeply complete the pyramid... Layers are fused and reconstructed to obtain a reconstructed depth image. The The layers were determined through sensitivity analysis of the reconstructed layer parameters;

[0017] Furthermore, the input matrix is ​​used to extract features using frequency domain decomposition:

[0018] (1) The processed two-dimensional input matrix is ​​used as the multi-point response matrix, and the self-power spectrum and cross-power spectrum between the responses of each measurement point are calculated; they are then assembled into an output power spectral density matrix in matrix form. For the output power spectral density matrix Perform singular value decomposition:

[0019]

[0020] in, It is a singular value diagonal matrix; It is a singular vector matrix; It is a singular vector matrix with conjugate transpose;

[0021] (3) The natural frequency of the structure is determined by the peak position of the maximum singular value curve, and the initial mode shape is determined by the singular vector corresponding to the peak frequency.

[0022] (4) The damping ratio is calculated using the logarithmic decay method for the narrowband free decay response near the peak value.

[0023] Furthermore, the input matrix is ​​obtained by applying the Hankel dynamic mode decomposition method as follows:

[0024] (1) The processed two-dimensional input matrix is ​​used as the multi-point response matrix. The time-delay embedding is performed on the time-series response signals of each measurement point to construct the time-shifted enhanced observation matrix. ,

[0025]

[0026] in, As the normalization factor, For the first Enhanced observation matrix for each measurement point The last column;

[0027] (2) Enhanced observation matrix Perform singular value decomposition and truncate the first half of the result. Construct low-rank dynamic operators from principal components;

[0028]

[0029] in, for The time-shifted form; , and These are the truncated left singular matrix, singular value matrix, and right singular matrix, respectively.

[0030] (3) Perform eigenvalue decomposition on the low-rank dynamic operator to obtain discrete eigenvalues. And calculate continuous-time eigenvalues. :

[0031]

[0032] in, The sampling time interval;

[0033] (4) Calculate the natural frequency and damping ratio of each mode based on the continuous time eigenvalues, and recover the mode shape by combining the corresponding eigenvectors.

[0034] Furthermore, the joint verification specifically involves: when the output results of the frequency domain decomposition method and the Hankel dynamic modal decomposition method are consistent, the modal identification results of the structure are directly output; when the output results of the frequency domain decomposition method and the Hankel dynamic modal decomposition method are inconsistent, modal pairing is performed based on the proximity of natural frequencies, the proximity of damping ratios, and the similarity of mode shapes; if modal pairing is satisfied, the natural frequencies, damping ratios, and mode shape information are fused and output; if modal pairing is not satisfied, the natural frequencies are mainly determined by the frequency domain decomposition method, the damping ratios are mainly determined by the Hankel dynamic modal decomposition method, and the mode shape information is returned to the depth completion pyramid processing.

[0035] Furthermore, the discrete mode shape samples of the fused mode shape information The continuous mode shape function is constructed using support vector regression for the final output;

[0036]

[0037] in, Let these be the coordinates of the point to be determined. For the first Spatial coordinates of each measuring point; For the first Discrete mode shape values ​​at each measuring point; For kernel functions; These are the weighting coefficients; This is a bias term.

[0038] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the video vibration two-dimensional modal recognition method based on depth-completed pyramid described above.

[0039] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the video vibration two-dimensional modal recognition method based on depth-completed pyramid described above.

[0040] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the video vibration two-dimensional modal recognition method based on depth-completed pyramid described above.

[0041] The beneficial effects of this invention are as follows:

[0042] (1) Compared with methods that directly perform two-dimensional structural vibration mode identification based on the original depth sequence, the present invention does not only perform local repair of depth loss, but also constructs a depth completion pyramid through directional depth completion and multi-scale image pyramid, and combines differential amplification, transpose compression and DC removal preprocessing to simultaneously complete loss repair, noise suppression, static offset stripping and high-dimensional response reconstruction at the input end. As a result, the present invention not only improves the integrity and usability of the full-field depth response, but also improves the separability of weak higher-order modes, transforming the two-dimensional full-field depth sequence, which was originally constrained by loss, noise, zero-frequency strong peaks and data redundancy, into a stable input suitable for modal analysis, thereby enhancing the robustness of two-dimensional structural vibration mode identification under complex interference conditions.

[0043] (2) Compared with two-dimensional structural vibration mode identification methods that only use single frequency domain or single time domain analysis, the present invention performs joint time-frequency identification by combining frequency domain decomposition (FDD) and Hankel dynamic mode decomposition (H-DMD), and introduces support vector regression to process the mode shape continuity at the result end. This not only achieves the coordinated extraction of natural frequencies, damping ratios, and mode shapes, but also improves the reliability and consistency of modal parameter identification through mutual verification of frequency domain and time domain results. Furthermore, to address the problem of discrete fluctuations in two-dimensional full-field mode shapes due to noise and local missing data, the present invention performs smooth reconstruction of discrete mode shape results, thereby improving the parameter integrity, spatial continuity, and physical consistency of the final obtained two-dimensional structural vibration mode results. Attached Figure Description

[0044] Figure 1 This is an overall flowchart of the two-dimensional structural vibration mode identification method based on joint time-frequency depth reconstruction of the present invention;

[0045] Figure 2 This invention provides a more comprehensive flowchart of the pyramid construction and reconstruction process.

[0046] Figure 3 This is a comparison diagram of the spatial distribution of modal shapes identified by FDD and H-DMD in this invention;

[0047] Figure 4 This is a schematic diagram of the mode shape smoothing and result output of the present invention;

[0048] Figure 5This is a schematic diagram of the actual measurement system device of the present invention;

[0049] Figure 6 This is a diagram showing the actual measurement results of the present invention;

[0050] Figure 7 This is a graph showing the error data between the modal feature identification results and the true values ​​of the method of the present invention. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings. The embodiments are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0052] See Figures 1 to 6 This embodiment provides a method for identifying two-dimensional structural vibration modes based on joint time-frequency depth reconstruction. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0053] The method described in this invention takes a full-field depth image sequence acquired by a depth camera as input. First, it performs directional depth completion on depth-deficient regions and constructs a depth completion pyramid using a multi-scale image pyramid. Then, it performs differential amplification, transpose compression, and DC removal on the reconstructed depth sequence to construct a unified input matrix suitable for frequency and time domain analysis. Next, it uses Frequency Domain Decomposition (FDD) and Hankel Dynamic Mode Decomposition (H-DMD) to extract natural frequencies, damping ratios, and mode shapes from both the frequency and time domains. Finally, it uses support vector regression to smooth the discrete mode shapes and output the final modal parameters. The overall process is as follows: Figure 1 As shown.

[0054] This invention discloses a two-dimensional modal recognition method for video vibration based on a depth-completed pyramid, comprising the following steps:

[0055] Step 1: Use a depth camera to acquire a sequence of depth images during the two-dimensional vibration process of the structure under test;

[0056] Step 2: Perform effective pixel filtering and region of interest extraction on the acquired depth image sequence;

[0057] Step 3: Perform directional depth completion on the sparse depth image within the region of interest to obtain a dense depth image sequence;

[0058] Step 4: Construct a depth completion pyramid using a dense sequence of depth images, and select the target layer for fusion and reconstruction;

[0059] Step 5: Perform differential amplification on the reconstructed depth sequence to enhance the weak modal response components;

[0060] Step 6: Transpose and compress the differentially amplified depth sequence to construct a two-dimensional input matrix for modality recognition;

[0061] Step 7: Perform DC removal processing on the two-dimensional input matrix to suppress the strong zero-frequency peak caused by static offset;

[0062] Step 8: Extract the natural frequencies, damping ratios, and mode shapes of the structure from the preprocessed two-dimensional input matrix obtained in Step 7 using the frequency domain decomposition method;

[0063] Step 9: Use the Hankel dynamic mode decomposition method to extract the natural frequencies, damping ratios, and mode shapes of the structure from the preprocessed two-dimensional input matrix obtained in Step 7;

[0064] Step 10: Perform joint verification of the frequency domain decomposition results and Hankel dynamic mode decomposition results, smooth the mode shape results, and output the modal identification results of the structure.

[0065] In step 1, a series of continuous depth images are acquired using a depth camera during the two-dimensional vibration process of the structure under test to obtain the original depth response. ,in and These are spatial pixel coordinates. The image is a discrete-time index with an image resolution of M×N and a sequence of T frames. The depth image sequence is used to characterize the full-field two-dimensional structural vibration response of the structural surface and serves as the original input for subsequent depth reconstruction and modal recognition.

[0066] In step 2, effective pixel screening and region of interest extraction are specifically performed as follows: the effectiveness of the original depth image sequence is determined frame by frame, and an effective pixel mask is constructed. The value is 1, indicating that the corresponding pixel has a valid depth value at that moment, and 0, indicating that the corresponding pixel is a missing or invalid pixel. Based on the spatial distribution of consecutive valid pixels in the first frame or reference frame, the target region containing the main vibration information is extracted as the region of interest to reduce the interference of background and irrelevant regions on subsequent modal recognition.

[0067] The preprocessed two-dimensional input matrix obtained in step 7 is used as the multi-point synchronous response matrix, and a one-to-one correspondence between pixel measurement points and time series is established to provide a unified input for frequency domain analysis and time domain analysis.

[0068] To prepare for the frequency domain analysis in step 8, starting from the preprocessed multi-point response matrix, the self-power spectrum and cross-power spectrum between the responses of each measurement point are first calculated, and then assembled into an output power spectral density matrix in matrix form. This matrix is ​​then used as the direct input of the FDD to provide frequency domain input for the subsequent frequency domain decomposition method to extract natural frequencies, damping ratios and mode shapes.

[0069] To prepare for the time-domain analysis in step 9, time delay embedding is performed on the time-series signals at each measurement point to construct a Hankel-form enhanced observation matrix, providing time-domain input for the subsequent Hankel dynamic mode decomposition to extract natural frequencies, damping ratios, and mode shapes.

[0070] The frequency domain decomposition results obtained in step 8 are compared and their consistency is checked with the Hankel dynamic modal decomposition results obtained in step 9. When the frequency domain decomposition results are inconsistent with the Hankel dynamic modal decomposition results, modal pairing is first performed based on the proximity of natural frequencies, the proximity of damping ratios, and the similarity of mode shapes. Modal results that simultaneously satisfy the consistency of frequency, damping ratio, and mode shape are retained and then fused for output. If inconsistencies in modal results occur, they are processed in stages. The frequency is mainly based on FDD, and the damping is mainly based on H-DMD. For mode shape information, it is not directly output, but returns to the depth completion pyramid reconstruction in step 3 and the preprocessing stage in step 4 to reconstruct the modal recognition input data. Steps 8 and 9 are then re-executed to recalculate the mode shape information until the two-end mode shape results meet the consistency requirements before being used as the final mode shape output. If the mode shape results still cannot meet the consistency requirements after recalculation, the mode is marked as a low-confidence mode and does not participate in the final mode shape output.

[0071] Let the discrete mode shape sample be Continuous mode shape functions are constructed using support vector regression:

[0072]

[0073] This formula represents the discrete mode sample points. Based on this, continuous mode shape functions are constructed using support vector regression. .in, Indicates the first Spatial coordinates of each measuring point This represents the discrete mode shape value at the measuring point. The kernel function is used to characterize the point to be solved. Correlation between each sample point is the weight coefficient obtained during training, and b is the bias term. By weighted superposition of the kernel function responses of each sample point, continuous mode shape function values ​​can be obtained throughout the entire spatial region, thereby smoothly reconstructing the originally discrete mode shape results into a continuous mode shape distribution, thus improving the discreteness and local discontinuity problems in the spatial distribution of mode shapes.

[0074] Example 1

[0075] A video vibration two-dimensional modal recognition method based on depth-completed pyramids includes the following steps:

[0076] Step 1: Build the actual measurement system and acquire depth image sequences. In this embodiment, the experimental object is a steel plate. A magnetic fixing device is used to fix the bottom edge of the steel plate to the optical test platform, forming a cantilever-like support structure. A transient excitation force is applied by an impact hammer. A laser triangulation vibrometer is placed on the back of the steel plate to acquire the displacement time history signal of the plate's center point. The sampling frequency is set to 1000 Hz, and the total sampling time is set to 40 seconds. Simultaneously, a depth camera is set on the front of the steel plate to synchronously acquire the full-field vibration response. The pixel resolution is set to 848×480, and the video frame rate is set to 90 fps. The experimental setup is as follows: Figure 5 As shown. The original depth sequence acquired by the depth camera is denoted as: .in, These are spatial pixel coordinates. This is a discrete-time index.

[0077] Step 2: Extract the effective region and construct the full-field response input. The acquired raw depth image sequence is filtered frame by frame, removing invalid depth values ​​and background areas, retaining only the vibration region corresponding to the steel plate as the region of interest. To adapt to the subsequent modal recognition algorithm, the 3D depth sequence is organized into a two-dimensional matrix input form of "measurement point × time," that is, spatial pixels are expanded column-wise and mapped to one-dimensional measurement point indices, thus converting the M×N×T depth sequence into a K×T full-field response matrix.

[0078] Step 3: Perform directional depth completion on the sparse depth image within the region of interest. Let the original sparse depth image be... The completed dense depth image is then... :

[0079] in, For the deep completion process;

[0080] Step 4: Construct a depth-complete pyramid and perform multi-scale reconstruction;

[0081] Step 4.1: Based on the completed dense depth image Perform low-pass filtering and smoothing downsampling to construct a Gaussian pyramid;

[0082] in, For the first Image of the Gaussian pyramid It is a two-dimensional Gaussian kernel. Control the smoothness, This indicates a double downsampling process.

[0083] Step 4.2: Construct a depth-complete pyramid from Gaussian pyramid images at adjacent scales;

[0084] in, For the first Layer depth completion of pyramid image; This is a double upsampling process; , For interpolation kernel functions;

[0085] Step 4.3: Select depth-complete pyramid The layers are rebuilt. The layers were determined through sensitivity analysis of the reconstruction layer parameters. The selection principle prioritized middle layers of the pyramid to achieve a balance between data dimensionality reduction and modal detail preservation. Specific parameters were determined by comparing the recognition accuracy and operational efficiency under different layer selections, resulting in the reconstructed depth image. :

[0086] Right now This is the output image obtained after the depth-complete pyramid reconstruction described above. This step aims to strike a balance between detail preservation and data dimensionality reduction, providing low-redundancy input for subsequent modality recognition.

[0087] Step 5: Preprocess the reconstructed depth sequence. To enhance weak higher-order mode components and suppress static migration interference, preprocess the reconstructed depth sequence. Differential amplification, transpose compression, and DC removal are performed sequentially.

[0088] Step 5.1: Perform differential amplification on the reconstructed depth sequence; this step is used to improve the discriminability of weak modes.

[0089]

[0090] in, For the first The amplification factor corresponding to the first-order differential signal; and These are the reconstructed depth images at the reference time or the previous time, respectively.

[0091] Step 5.2: Use the transpose operation to adjust the data dimensions and compress it column-wise. Transform into a two-dimensional matrix form suitable for modality feature recognition This step is used to organize the entire field depth response into a "measurement point × time" matrix form required by subsequent modality recognition algorithms.

[0092]

[0093] in, This is the compressed row index; For time series indexing; and Differential magnified images Pixel coordinates;

[0094] Step 5.3: Since the static offset in the vibration response exhibits a strong peak at zero frequency in the frequency domain, it directly affects the calculation results of the power spectral density matrix in FDD and the reliability of singular value decomposition. Therefore, it is necessary to... DC removal is performed to obtain the normalized input matrix. ;

[0095]

[0096] After the above processing, the three-dimensional vibration data is effectively compressed and static offset is removed, while the higher-order modal components are enhanced, providing high-quality input data for subsequent frequency domain decomposition (FDD) and Hankel dynamic mode decomposition (H-DMD) methods, ensuring the reliability and accuracy of modal feature recognition.

[0097] In this embodiment, a two-dimensional input matrix with a size of 380×3760 is obtained after transpose compression, and the differential amplification factors are set to β2=2 and β3=3.

[0098] Step 6: Use FDD for frequency domain mode identification, construct the multi-point output response based on the preprocessed two-dimensional input matrix, and further form the output power spectral density matrix. Then, singular value decomposition is performed on the output power spectral density matrix at each discrete frequency point:

[0099]

[0100] in, It is a singular value diagonal matrix. It is a singular vector matrix. It is a singular vector matrix with conjugate transpose.

[0101] The natural frequency is determined by the peak position of the maximum singular value curve, the initial mode shape is determined by the singular vector corresponding to the peak frequency, and the damping ratio is calculated based on the narrowband free decay response near the peak. This step is used to extract the principal modal features from frequency domain stability.

[0102] Step 7: Use H-DMD for time-domain modal identification to decompose and extract the natural frequencies, damping ratios, and mode shapes of the tested structure, including the following steps:

[0103] Step 7.1 performs time-delay embedding on the time-series response signals at each measurement point to construct a Hankel-form enhanced observation matrix; this step is used to improve the separability of weak modes under low signal-to-noise ratio conditions. Assume the time-series response signal of the multi-degree-of-freedom system is... ,in Indicates the measurement point number, for the first... Construct a Hankel matrix with embedding dimension q for each measurement point:

[0104]

[0105] The time-shifted enhanced observation matrix is ​​constructed by combining the Hankel matrices of each measurement point (normalization scaling is required to ensure consistent weights for data at different time steps):

[0106]

[0107] in, As the normalization factor, For the first Enhanced observation matrix for each measurement point The last column;

[0108] Step 7.2: Perform singular value decomposition on the above enhanced observation matrix:

[0109]

[0110] Truncation of the front of the singular matrix Given principal components, construct a low-rank operator matrix as follows:

[0111]

[0112] in, for The time-shift form, , and These are the truncated left singular matrix, singular value matrix, and right singular matrix, respectively.

[0113] Step 7.3: Perform eigenvalue decomposition on the low-rank dynamic operator. To obtain discrete eigenvalues And calculate continuous-time eigenvalues. :

[0114]

[0115] in, The sampling time interval;

[0116] according to Calculate the natural frequencies and damping ratios of each mode, and recover the mode shapes using the corresponding eigenvectors. This step is used to extract complete modal parameters from the time domain.

[0117] In this embodiment, the Hankel matrix dimension of H-DMD is set to 15×3600, and the front is truncated. The principal components were screened based on their amounts.

[0118] Step 8: Jointly verify and smooth the output of the mode shape. Compare and verify the consistency between the frequency domain identification results obtained in Step 5 and the time domain identification results obtained in Step 6, and perform support vector regression smoothing on the discrete mode shape samples.

[0119] In this embodiment, a Gaussian kernel is selected as the kernel function for SVR, the kernel scale parameter is automatically adjusted, and the regularization coefficient is set to 1. The insensitive loss parameter is set to 0.01.

[0120] In this embodiment, Figure 3 The spatial distribution of modal shapes identified by FDD and H-DMD is compared. It can be seen that the modal shapes obtained by the two identification methods have good spatial consistency. Figure 6 The paper presents a comparison of the effects of the measured depth distribution map before and after processing by the method of this invention, demonstrating that under actual measurement conditions, missing pixels and noise interference in the original depth data can be effectively repaired. Figure 7 The data provided shows that the method of the present invention has relatively accurate identification. Furthermore, by comparing it with the benchmark results obtained by laser vibration measurement, the present invention can stably identify the first three modal parameters in actual steel plate experiments and maintain good frequency identification accuracy and mode shape consistency, thereby verifying the effectiveness of the method in actual two-dimensional structure vibration mode identification.

[0121] The disclosure and teachings in the foregoing specification are merely intended to aid in understanding the method and core ideas of this invention. This invention is not limited to the specific embodiments disclosed and described above, and those skilled in the art can make changes and modifications to the above embodiments. Some modifications and changes to this invention should fall within the protection scope of the claims of this invention, as well as other methods obtained using the same or similar steps, are all within the protection scope of this invention.

[0122] In particular, in some preferred embodiments of the present invention, a computer device is also provided, including a memory and a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the video vibration two-dimensional modal recognition method based on depth-completed pyramid described in any of the above embodiments.

[0123] In some other preferred embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the video vibration two-dimensional modal recognition method based on depth-completed pyramids described in any of the above embodiments.

[0124] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above embodiments of the video vibration two-dimensional modal recognition method based on depth-complete pyramid, which will not be repeated here.

[0125] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0126] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0127] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A video vibration two-dimensional modal recognition method based on depth-completed pyramids, characterized in that, Includes the following steps: Acquire a sequence of depth images during the two-dimensional vibration process of the structure under test; Directional depth completion is performed on the sparse depth image of the region of interest in the depth image sequence to construct a Gaussian pyramid, and a depth completion pyramid is constructed by combining the Gaussian pyramids of adjacent scales. The target layer is selected for fusion and reconstruction. The reconstructed depth sequence is then subjected to differential amplification, transpose compression, and DC removal in sequence to construct a unified input matrix suitable for frequency domain and time domain analysis. The input matrix is ​​extracted from the natural frequency, damping ratio and mode shape in both the frequency domain and time domain using frequency domain decomposition and Hankel dynamic mode decomposition. The decomposition results of the frequency domain decomposition method and the Hankel dynamic mode decomposition method are jointly verified, and the modal recognition results of the structure are output.

2. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 1, characterized in that, The depth image sequence The preprocessing involves effective pixel filtering and region of interest extraction. The region of interest extraction is performed by extracting a target region containing the main vibration information as the region of interest based on the spatial distribution of consecutive effective pixels in the first frame or a reference frame.

3. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 1, characterized in that, The Gaussian pyramid is obtained by low-pass filtering and smoothing downsampling on the depth-completed image. ； in, This is the image after depth completion; For the first Image of a Gaussian pyramid; It is a two-dimensional Gaussian kernel. and These are the spatial pixel coordinates. Control the smoothness; This is a double downsampling process.

4. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 3, characterized in that, The depth-completed pyramid is : ； in, For the first Layer depth completion of pyramid image; This is a double upsampling process; , and These are the upsampled pixel coordinates. and These are the pixel coordinates of the Gaussian pyramid. This is the interpolation kernel function.

5. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 4, characterized in that, Choose depth-completed pyramid Layers are fused and reconstructed to obtain a reconstructed depth image. The The layers were determined through sensitivity analysis of the reconstructed layer parameters; 。 6. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 1, characterized in that, The input matrix is ​​used to extract features using frequency domain decomposition: (1) The processed two-dimensional input matrix is ​​used as the multi-point response matrix, and the self-power spectrum and cross-power spectrum between the responses of each measurement point are calculated; they are then assembled into an output power spectral density matrix in matrix form. For the output power spectral density matrix Perform singular value decomposition: ； in, It is a singular value diagonal matrix; It is a singular vector matrix; It is a singular vector matrix with conjugate transpose; (3) The natural frequency of the structure is determined by the peak position of the maximum singular value curve, and the initial mode shape is determined by the singular vector corresponding to the peak frequency. (4) The damping ratio is calculated using the logarithmic decay method for the narrowband free decay response near the peak value.

7. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 1, characterized in that, The input matrix is ​​obtained using the Hankel dynamic mode decomposition method as follows: (1) The processed two-dimensional input matrix is ​​used as the multi-point response matrix. The time-delay embedding is performed on the time-series response signals of each measurement point to construct the time-shifted enhanced observation matrix. , ； in, As the normalization factor, For the first Enhanced observation matrix for each measurement point The last column; (2) Enhanced observation matrix Perform singular value decomposition and truncate the first half of the result. Construct low-rank dynamic operators from principal components; ； in, for The time-shifted form; , and These are the truncated left singular matrix, singular value matrix, and right singular matrix, respectively. (3) Perform eigenvalue decomposition on the low-rank dynamic operator to obtain discrete eigenvalues. And calculate continuous-time eigenvalues. : ； in, The sampling time interval; (4) Calculate the natural frequency and damping ratio of each mode based on the continuous time eigenvalues, and recover the mode shape by combining the corresponding eigenvectors.

8. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 1, characterized in that, The joint verification specifically involves the following steps: when the outputs of the frequency domain decomposition method and the Hankel dynamic modal decomposition method are consistent, the modal identification results of the structure are directly output; when the outputs of the frequency domain decomposition method and the Hankel dynamic modal decomposition method are inconsistent, modal pairing is performed based on the proximity of natural frequencies, the proximity of damping ratios, and the similarity of mode shapes; if modal pairing is satisfied, the natural frequencies, damping ratios, and mode shape information are fused and output; if modal pairing is not satisfied, the natural frequencies are primarily determined by the frequency domain decomposition method, the damping ratios are primarily determined by the Hankel dynamic modal decomposition method, and the mode shape information is returned to the depth completion pyramid processing.

9. The video vibration two-dimensional modal recognition method based on depth-completed pyramids according to claim 8, characterized in that, The discrete mode sample of the fused mode information The continuous mode shape function is constructed using support vector regression for the final output; ； in, Let these be the coordinates of the point to be determined. For the first Spatial coordinates of each measuring point; For the first Discrete mode shape values ​​at each measuring point; For kernel functions; These are the weighting coefficients; This is a bias term.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method as described in any one of claims 1 to 9.

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