Wave number domain compressed sensing damage detection method suitable for plate-shaped structure

Abstract

The invention relates to a wavenumber domain compressed sensing damage detection method suitable for a plate-shaped structure. The method comprises the following steps: S1, constructing a compressed sensing equation; s2, solving the compressed sensing equation, and reconstructing to obtain a wave number domain signal of a full wave field; and S3, selecting a threshold value for the reconstructed wavenumber domain data for filtering, returning to a spatial domain through inverse Fourier transform, and carrying out merging processing on results by adopting a root mean square method to obtain a damage morphology graph. According to the method, the sparse basis matrix meeting the compressed sensing requirement is constructed by optimizing the sparse representation of the signal, so that the precision of full-wave field signal reconstruction is remarkably improved; the number of sampling points is greatly reduced, the full-wave-field data acquisition efficiency is improved, and the potential of breaking through the limitation of the Nyquist sampling law is achieved; the position and the shape of the damage are detected, the detection effect is good, and the detection efficiency is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of nondestructive testing, relates to damage position and morphology detection of plate-like structures, and particularly to a wavenumber domain compressed sensing damage detection method suitable for plate-like structures. Background Art

[0002] Plate structures are a widely used structural form in industries such as aerospace, petroleum engineering, and transportation. Due to long-term environmental factors and cyclic loads, these structures may suffer damage, including but not limited to corrosion caused by weather changes and cracks caused by fatigue. If these damages are not detected and repaired in time, they may pose potential risks to the integrity and safety of the plate structures, leading to safety accidents. Therefore, the development of efficient and accurate detection technologies is crucial to ensure the reliability of these critical structures and extend their service life.

[0003] For practical engineering, when performing damage detection on plate-like structures, it should be ensured that no new damage will be caused to the plate-like structures. Therefore, considering the reusability of the structure, non-destructive testing methods should be used for damage detection. Common non-destructive testing methods include: X-ray testing, magnetic particle testing, eddy current testing, infrared thermal imaging, ultrasonic testing, etc. Ultrasonic testing has become one of the most widely used and most studied methods due to its high sensitivity, strong applicability, and harmlessness to the human body. In particular, ultrasonic guided waves can propagate over long distances in plate-like structures with low attenuation, thereby achieving large-scale detection. It is known as one of the most promising non-destructive testing and evaluation (NDT&E) and structural health monitoring (SHM) methods for plate-like structures.

[0004] In order to further improve the efficiency and accuracy of plate structure health monitoring and maintenance, researchers are developing advanced signal processing algorithms, such as applying compressed sensing technology to optimize the damage detection process, thereby providing more scientific and professional technical support for continuous monitoring and timely maintenance of structures.

[0005] At present, the Scanning Laser Doppler Vibrometer (SLDV) based on the Doppler principle has become an effective tool for collecting full-wavefield signals of ultrasonic guided waves, and has received increasing attention in the field of non-destructive testing. However, the acquisition of SLDV is limited by the Nyquist sampling theorem, that is, the spatial sampling interval is less than half a wavelength, which makes the number of measurement points in space huge, resulting in the process of SLDV obtaining full-wavefield data being very time-consuming. The Compressed Sensing (CS) method can break through the limitations of the Nyquist sampling theorem, undersample the sparse signal, and accurately restore the original high-dimensional signal through the reconstruction algorithm.

[0006] In recent years, the application of compressed sensing technology in the field of ultrasonic guided wave testing has made significant progress. Based on the compressed sensing theory, a sparse reconstruction method of the guided wave field is established, so that the complete wave field signal can be accurately reconstructed with a small number of measurement points, which can not only ensure the detection quality, but also greatly reduce the number of measurement points and improve the damage detection efficiency. Therefore, the application of compressed sensing methods in non-destructive testing systems can improve the efficiency of SLDV in collecting full wave field signals without sacrificing the detection quality. Summary of the invention

[0007] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a wavenumber domain compressed sensing damage detection method suitable for plate-like structures, with the goal of significantly reducing the number of sampling points, extracting and processing the guided wave changes caused by damage to the plate-like structure, and achieving more accurate damage location and morphology detection.

[0008] The present invention solves the technical problem by the following technical solutions:

[0009] A wavenumber domain compressed sensing damage detection method suitable for plate-like structures, the method first constructs a sparse basis matrix that can be used in a compressive sensing equation, then constructs an observation matrix containing distance information of measurement points and reconstruction points, the observation matrix satisfies the finite isometry property, and the sparse basis matrix and the observation matrix are multiplied to form a sensing matrix in the compressed sensing equation; wave field data v(x, y, ω) of a small number of measurement points are measured by SLDV, and the compressed sensing equation is solved by a basis pursuit BP algorithm to reconstruct the wavenumber domain data of the full wavefield; an imaging algorithm WFA of wavenumber threshold filtering is used to filter the reconstructed wavenumber domain data, and then the filtered data is converted back to the spatial domain through an inverse Fourier transform, and the root mean square RMS method is used to merge the results to finally obtain a damage morphology map.

[0010] Furthermore, the steps of the method are:

[0011] S1. Constructing compressed sensing equations

[0012] a) Determine the sparse representation of the full wavefield signal and construct a sparse basis matrix Ψ

[0013] For compressed sensing theory, the reconstructed signal must meet the sparsity requirement. The full wavefield signal is converted into the wavenumber domain through two-dimensional Fourier transform to obtain the wavenumber domain signal w(k x ,k y ,ω), if the wave number domain signal is to be reconstructed, a two-dimensional inverse Fourier transform matrix is ​​required as the sparse basis matrix Ψ∈C N×N :

[0014]

[0015] Where: u and v are the indices in the frequency domain, x and y are the wave numbers in the spatial domain, and N is the number of sample points in each dimension;

[0016] b) Construct the measurement matrix Φ containing the distance information of the measured points and the reconstructed points

[0017] The reconstruction area is discretized into N randomly distributed pixels at equal intervals, and these pixels are regarded as assumed sources, namely "potential sources". The potential sources are the reconstruction points. Assuming that all potential sources are scattered uniformly in all directions and the number of measurement points is M, the observation matrix Φ∈C is constructed. M×N :

[0018]

[0019] Where: d m,n is the distance between the mth measurement point and the nth potential source, is the wave number of the μ mode in the direction from the mth measurement point to the nth potential source;

[0020] c) Constructing the sensing matrix A

[0021] Multiply the sparse basis matrix Ψ and the observation matrix Φ to obtain the sensing matrix A∈C M×N :

[0022] A=Φ×Ψ

[0023] d) Constructing compressed sensing equation

[0024] v(x,y,ω)=Aw(k x ,k y ,ω);

[0025] S2, using ultrasonic transducer to excite ultrasonic guided wave, using SLDV to collect a small amount of measurement point data v(x, y, ω), and using BP algorithm to solve the compressed sensing equation to reconstruct the wave number domain signal w(k x ,k y ,ω);

[0026] S3. The imaging algorithm using wavenumber threshold filtering first selects a threshold to filter the reconstructed wavenumber domain data, then returns to the spatial domain through inverse Fourier transform, and uses the root mean square method to merge the results to finally obtain the damage morphology map.

[0027] The positive effects that the present invention can produce are:

[0028] 1. This invention proposes for the first time an innovative method for compressed sensing in the wavenumber domain. This method optimizes the sparse representation of the signal, constructs a sparse basis matrix that meets the requirements of compressed sensing, and significantly improves the accuracy of full wavefield signal reconstruction.

[0029] 2. The present invention can significantly reduce the number of sampling points, improve the efficiency of full-wavefield data acquisition, and has the potential to break through the limitations of Nyquist sampling theorem.

[0030] 3. The present invention can detect the location and morphology of damage at the same time, and has good detection effect and high detection efficiency.

[0031] 4. The present invention is universal for defect detection of plate-like structures and is applicable to ultrasonic guided wave signals excited by various lasers, air-coupled air-coupled sensor excitations and other excitation sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of the present invention;

[0033] Figure 2 is a schematic diagram of a test piece of the present invention;

[0034] Figure 3 It is a schematic diagram of the arrangement of measurement points and reconstruction points of the present invention;

[0035] Figure 4 An average wavenumber diagram for reconstructing wavenumber domain data of the present invention;

[0036] Figure 5 This is the WFA damage imaging diagram of the present invention. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below through specific examples. The following examples are only illustrative and not restrictive, and the protection scope of the present invention cannot be limited thereto.

[0038] like Figure 1 The present invention provides a wave number domain compressed sensing damage detection method applicable to plate-like structures, the innovation of which lies in: the steps of the method are:

[0039] 1. Generate measurement point and reconstruction point coordinates

[0040] The test piece used in the present invention is an aluminum plate whose length and width are much larger than the damage size. The damage is a square surface defect with a side length of 10 mm and a depth of 1.5 mm. The damage is located in the center of the aluminum plate. A measurement area is selected in the test piece, such as Figure 2 Determine the sparse sampling network. In this example, the sparse measurement range selected is 40mm×40mm, and the spacing between two adjacent measurement points is 2mm.

[0041] Determine the potential source area and try to cover all defects. Set a uniform grid in this area. In this example, the potential source area selected is 60mm×60mm, and the grid spacing is 1mm. In each grid, randomly select points based on the grid center point to generate potential point coordinates, such as Figure 3 In the signal reconstruction process, these potential points are regarded as the reconstruction points corresponding to the grid center.

[0042] 2. Constructing the compressed sensing equation

[0043] a) Determine the sparse representation method of the full wavefield signal and construct the sparse basis matrix Ψ

[0044] According to the sparsity analysis of the signals in each domain of the full wavefield data, it is decided to perform compressed sensing in the wavenumber domain with better sparsity, that is, to reconstruct the wavenumber domain signal of the full wavefield through compressed sensing. The transformation of the spatial domain signal to the wavenumber domain requires a two-dimensional Fourier transform, so the sparse basis matrix Ψ∈C N×N It is expressed as:

[0045]

[0046] Among them, u and v are indices in the frequency domain, x and y are indices in the spatial domain, and N is the number of sample points in each dimension.

[0047] b) Construct the measurement matrix Φ containing the distance information of the measured points and the reconstructed points

[0048] Assuming that the excitation functions of all potential sources are uniformly excited in all directions, construct the transfer matrix Φ∈C from the assumed source to the measurement point M×N , where M = 441 and N = 3600 represent the number of sparse measurement points and the number of potential sources, respectively. The number of sampling points of the present invention can be reduced by 87.75%. Under the excitation frequency selected in the experiment, the A0 mode is the main mode in the plate, so only the A0 mode is considered. When only the A0 mode is considered, the transfer function of the excitation signal propagating from the mth row and nth column element of Φ to the nth potential source to the mth measurement point is expressed as:

[0049]

[0050] Among them, d m,n is the distance between the mth measurement point and the nth potential source, is the wave number of the A0 mode in the direction from the mth measurement point to the nth potential source.

[0051] c) Constructing the sensing matrix A

[0052] Multiply the measurement matrix Φ and the sparse basis matrix Ψ to obtain the sensor matrix A∈C M×N :

[0053] A=Φ×Ψ

[0054] d) Constructing compressed sensing equation

[0055] v(x,y,ω)=Aw(k x ,k y ,ω);

[0056] 3. Use ultrasonic transducers to excite ultrasonic guided waves, and use SLDV produced by Polytec to collect 441 measurement point data v(x, y, ω). Then use the BP algorithm to solve the compressed sensing equation y = Aw and reconstruct the wavenumber domain signal w(k x ,k y ,ω), the signal w(k x ,k y ,ω) to make an average wave number diagram, such as Figure 4 shown.

[0057] 4. Use the imaging algorithm of wave number threshold filtering to perform damage imaging on the reconstructed wave number domain signal:

[0058] The candidate threshold that can make 5% of the elements in the filter function matrix equal to 0 is selected as the final experimental threshold to implement threshold filtering; the wave field data after each threshold filtering is subjected to two-dimensional Fourier inverse transform to obtain the wave field signal in the time and space domain after filtering; the above process is repeated for all wave field data and all filtered data are merged by the root mean square method to obtain the imaging image of the damage morphology, such as Figure 5 As shown, the present invention can effectively detect the location and morphology of damage to a plate-like structure.

[0059] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will appreciate that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A wavenumber domain compressed sensing damage detection method applicable to plate-like structures, characterized in that: The method first constructs a sparse basis matrix that can be used in the compressed sensing equation, and then constructs an observation matrix containing the distance information of the measurement points and the reconstruction points. The observation matrix satisfies the finite isometry property, and the sparse basis matrix and the observation matrix are multiplied to form a sensing matrix in the compressed sensing equation; the wave field data v(x, y, ω) of a small number of measurement points are measured by SLDV, and the basis pursuit BP algorithm is used to solve the compressed sensing equation to reconstruct the wave number domain data of the full wave field; the imaging algorithm WFA of wave number threshold filtering is used to filter the reconstructed wave number domain data, and then the filtered data is converted back to the spatial domain through inverse Fourier transform, and the root mean square RMS method is used to merge the results to finally obtain the damage morphology map.

2. The wavenumber domain compressed sensing damage detection method applicable to plate-like structures according to claim 1, characterized in that: The steps of the method are: S1. Constructing compressed sensing equations a) Determine the sparse representation of the full wavefield signal and construct the sparse basis matrix Ψ For compressed sensing theory, the reconstructed signal must meet the sparsity requirement. The full wavefield signal is converted into the wavenumber domain through two-dimensional Fourier transform to obtain the wavenumber domain signal w(k x ,k y ,ω), if the wave number domain signal is to be reconstructed, a two-dimensional inverse Fourier transform matrix is ​​required as the sparse basis matrix Ψ∈C N×N : Where: u and v are the indices in the frequency domain, x and y are the wave numbers in the spatial domain, and N is the number of sample points in each dimension; b) Construct the measurement matrix Φ containing the distance information of the measured points and the reconstructed points The reconstruction area is discretized into N randomly distributed pixels at equal intervals, and these pixels are regarded as assumed sources, namely "potential sources". The potential sources are the reconstruction points. Assuming that all potential sources are scattered uniformly in all directions and the number of measurement points is M, the observation matrix Φ∈C is constructed. M×N : Where: d m,n is the distance between the mth measurement point and the nth potential source, is the wave number of the μ mode in the direction from the mth measurement point to the nth potential source; c) Constructing the sensing matrix A Multiply the sparse basis matrix Ψ and the observation matrix Φ to obtain the sensing matrix A∈C M×N : A=Φ×Ψ d) Constructing compressed sensing equation v(x,y,ω)=Aw(k x ,k y ,ω); S2, using ultrasonic transducer to excite ultrasonic guided wave, using SLDV to collect a small amount of measurement point data v(x, y, ω), and using BP algorithm to solve the compressed sensing equation to reconstruct the wave number domain signal w(k x ,k y ,ω); S3. The imaging algorithm using wavenumber threshold filtering first selects a threshold to filter the reconstructed wavenumber domain data, then returns to the spatial domain through inverse Fourier transform, and uses the root mean square method to merge the results to finally obtain the damage morphology map.

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