Plate-shaped structure damage morphology imaging method under sub-Nyquist sampling condition

Abstract

The invention discloses a plate-shaped structure damage morphology imaging method under a sub-Nyquist sampling condition. The method comprises the following steps: designing and optimizing a ring filter to obtain a sub-Nyquist sampling adaptive wave number filter; obtaining a frequency-wavenumber domain signal; obtaining filtered wave number domain data; and obtaining an imaging picture of the damage morphology and the like. The method has the advantages that under the condition that the distance between the measuring points does not meet the Nyquist sampling theorem, the damaged morphology can be accurately imaged, and the detection efficiency can be remarkably improved. By filtering the direct wave signal and enhancing the damage information of the wave number domain, accurate damage morphology imaging can be realized, and meanwhile, the position of the damage is positioned. The method is suitable for all isotropic and anisotropic plate-shaped structures, and has high universality. The method is suitable for various types of excitation sensors, and has universality for detecting various types of defects of a plate-shaped structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of non-destructive testing, and in particular relates to a method for imaging the damage morphology of a plate-like structure under sub-Nyquist sampling conditions. Background Art

[0002] Currently, with the rapid development of industries such as aerospace, shipbuilding, and rail transportation, new high-performance materials such as high-strength, lightweight composites and corrosion-resistant alloys are being widely used. Although these materials possess excellent mechanical properties and resistance to environmental corrosion, they may still suffer damage from factors such as fatigue and corrosion during long-term service. To ensure the safety and reliability of structures, they must be regularly inspected to promptly identify potential safety hazards. Because traditional destructive testing can damage the components themselves, non-destructive testing (NDT) has become the preferred solution in this field due to its non-invasive and repeatable advantages.

[0003] Among numerous nondestructive testing methods, ultrasonic-based methods hold a prominent position in industrial damage detection due to their unique advantages, including high sensitivity, low implementation cost, excellent detection efficiency, and lack of ionizing radiation hazards. Ultrasonic guided wave technology offers significant advantages, particularly for inspecting plate-like structures. Its low attenuation enables long-distance detection, while its sensitivity to minute damage makes it invaluable for visually detecting hidden damage. These advantages have led to its widespread application and widespread acceptance in the field of industrial nondestructive testing.

[0004] Wavenumber-domain filtering imaging, a key technique in ultrasonic guided wave testing, is based on the interaction between guided waves and damage as they propagate through plate-like structures. Damage in the guided wave propagation path produces significant wavefield disturbances, including but not limited to amplitude attenuation, reflection generation, mode conversion, and changes in wave velocity and wavenumber parameters. These characteristics exhibit distinct distribution differences in the wavenumber domain. By separating the incident wave from the altered ultrasonic wave caused by the damage, quantitative imaging of structural damage can be achieved.

[0005] However, existing ultrasonic damage detection technology based on full-wavefield scanning faces significant bottlenecks in engineering applications, the main limiting factor being the low efficiency of data acquisition. This technical bottleneck stems from the rigid requirement of the Nyquist sampling theorem, which states that the sampling interval must be less than 1 / 2 of the minimum excitation wavelength, making the detection process time-consuming and the data transmission and storage costs high. However, it is worth noting that experimental research results have confirmed that even under sub-Nyquist sampling conditions, the collected wavenumber domain data still retains key damage feature information. By developing specific wavenumber domain signal processing algorithms, it is possible to effectively extract damage features from these sub-sampled data and realize visualization of damage morphology. Summary of the Invention

[0006] In order to solve the above problems, the object of the present invention is to provide a method for imaging the damage morphology of a plate-like structure under sub-Nyquist sampling conditions.

[0007] To achieve the above-mentioned object, the present invention provides a method for imaging the damage morphology of a plate structure under sub-Nyquist sampling conditions, comprising the following steps performed in sequence:

[0008] 1) Based on the dispersion characteristics of the plate-like structural material, a ring filter is designed and optimized to obtain an adaptive wavenumber filter with sub-Nyquist sampling;

[0009] 2) Using ultrasonic transducer as the excitation source, the full wave field data w(x, y, ω) of different sampling intervals are measured by laser Doppler vibrometer, and then the full wave field data w(x, y, ω) is transformed into the frequency-wave number domain by two-dimensional Fourier transform to obtain the frequency-wave number domain signal W(k x ,k y ,ω);

[0010] 3) The above frequency-wavenumber domain signal W(k x ,k y ,ω) is extracted, and then the frequency-wavenumber domain signal of each frequency point is filtered using the SNWA filter designed in step 1), and the direct wave signal with a significant amplitude is filtered out to enhance the weak scattered signal caused by damage, and the filtered wavenumber domain data is obtained.

[0011] 4) The wave number domain data after the above filtering Perform two-dimensional inverse Fourier transform and convert it to the spatial domain to obtain the spatial wave field signal Then, the root mean square method is used in the spatial domain to analyze the spatial wave field signal. After merging, the images of the damage morphology are finally obtained.

[0012] In step 1), the method of designing and optimizing a ring filter based on the dispersion characteristics of the plate-like structural material to obtain a sub-Nyquist sampling adaptive wavenumber filter is as follows:

[0013] 1.2) Design a wavenumber domain ring filter based on the dispersion characteristics;

[0014] For isotropic materials, the wavenumber values ​​k0 in different directions at the same center frequency are the same, and the distribution is approximately a ring. Based on experience, the width of the ring is set to 0.2, and the annular filter in the wavenumber domain is:

[0015]

[0016] For anisotropic materials, the wave number distribution in different directions at the same center frequency is approximately an elliptical ring. The wave number values ​​in the directions of 0° and 90° are k0, Wave value k0, are half of the minor axis and major axis of the ellipse respectively; according to experience, the width of the elliptical ring is set to 0.2, then the annular filter M(k x ,k y )for:

[0017]

[0018] Where θ is the angle between the waveguide propagation direction and the x-axis, k θ is the wave value in the direction of the angle θ between the propagation direction of the guided wave and the x-axis;

[0019] 1.2) Optimizing the above wavenumber domain ring filter to obtain a sub-Nyquist sampling adaptive wavenumber filter;

[0020] Sampling interval dx in the x direction and wavenumber domain range The relationship is:

[0021]

[0022] When k xs -k 0max <k 0max When the sampling interval in two-dimensional space does not satisfy the Nyquist sampling theorem, aliasing will occur after two-dimensional Fourier transform;

[0023] Similarly, the sampling interval dy in the y direction is related to the wavenumber domain range The relationship is:

[0024]

[0025] in, are the maximum absolute values ​​of the wave numbers in the x and y directions, respectively;

[0026] Therefore, according to the characteristics of aliasing, the above wavenumber domain ring filter is optimized to a SNWA filter:

[0027]

[0028] in, sgn is the sign function;

[0029]

[0030] In step 2), the full wavefield data w(x, y, ω) is transformed into the frequency-wavenumber domain by two-dimensional Fourier transform to obtain the frequency-wavenumber domain signal W dxdy (k x ,k y ,ω) is as follows:

[0031]

[0032] Where ω is the frequency.

[0033] In step 3), the frequency-wavenumber domain signal W dxdy (k x ,k y ,ω) is extracted, and then the frequency-wavenumber domain signal of each frequency point is filtered using the SNWA filter designed in step 1) to obtain the filtered wavenumber domain data with significantly enhanced damage information. The formula is as follows:

[0034]

[0035] In step 4), the wavenumber domain data after filtering is Perform two-dimensional inverse Fourier transform and convert it to the spatial domain to obtain the spatial wave field signal The formula is as follows:

[0036]

[0037] The spatial wave field signal is analyzed by using the root mean square method in the spatial domain. The formula for merging is:

[0038]

[0039] The plate-like structure damage morphology imaging method under sub-Nyquist sampling conditions provided by the present invention has the following beneficial effects:

[0040] 1. The present invention breaks through the limitations of the Nyquist sampling theorem and can accurately image the morphology of damage even when the distance between measurement points does not meet the Nyquist sampling theorem, thereby significantly improving detection efficiency.

[0041] 2. The present invention filters out the direct wave signal and enhances the damage information in the wavenumber domain, thereby achieving more accurate damage morphology imaging and locating the position of the damage.

[0042] 3. The present invention is applicable to all isotropic and anisotropic plate structures and has high universality.

[0043] 4. The present invention is applicable to various types of excitation sensors and is also universally applicable to the detection of various types of defects in plate-like structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of the method for imaging damage morphology of plate-like structures under sub-Nyquist sampling conditions provided by the present invention;

[0045] Figure 2 is a wave number diagram in each direction at the center frequency of the composite material plate calculated in the present invention;

[0046] Figure 3 This is the principle diagram of wave number aliasing under sub-Nyquist sampling conditions;

[0047] Figure 4 Figures 1 and 2 show the center frequency wavenumber spectra and corresponding SNWA filters at different sampling intervals in the present invention. (a) The sampling interval is 2 mm; (b) The sampling interval is 3.125 mm; (c) The sampling interval is 4 mm; and (d) The sampling interval is 5 mm. (e)-(f) The corresponding SNWA filters at these different sampling intervals.

[0048] Figure 5 To verify the imaging results of composite material delamination damage at different sampling intervals of the present invention: (a) sampling interval is 2mm; (b) sampling interval is 3.125mm; (c) sampling interval is 4mm; (d) sampling interval is 5mm. DETAILED DESCRIPTION

[0049] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] like Figure 1 As shown, the method for imaging the damage morphology of a plate structure under sub-Nyquist sampling conditions provided by the present invention includes the following steps performed in sequence:

[0051] 1) Based on the dispersion characteristics of the plate-like structural material, a ring filter is designed and optimized to obtain a sub-Nyquist sampling adaptive wavenumber filter (SNWA filter);

[0052] 1.1) Design a wavenumber domain ring filter based on the dispersion characteristics;

[0053] The composite material plate specimen used in this embodiment is CFRP material, composed of 16 layers of carbon fiber [+45 / -45 / 0 / 0]2s, with a total thickness of 2mm. The characteristic parameters are shown in the following table.

[0054] <![CDATA[ρ(kg / m 3 )]]> <![CDATA[E1(GPa)]]> <![CDATA[E2(GPa)]]> <![CDATA[E3(GPa)]]> <![CDATA[G 12 (GPa)]]> <![CDATA[G 13 (GPa)]]> <![CDATA[G 23 (GPa)]]> <![CDATA[v 12 ]]> <![CDATA[v 13 ]]> <![CDATA[v23]]> 1600 172 11.6 11.6 7.8 7.8 3.9 0.36 0.36 0.55

[0055] The dispersion curves of the 16-layer composite plate in various directions were calculated using the finite element simulation method. The center frequency selected in the experiment was 200kHz, and the wave number diagrams in various directions were obtained at this frequency. Figure 2 .

[0056] For this anisotropic composite material plate, the wave number distribution in different directions at the same center frequency can be considered to be approximately an elliptical ring. The wave number values ​​in the directions of 0° and 90° are selected as k0, Wave value k0, are half of the minor and major axes of the ellipse respectively;

[0057] Damage will cause the wavenumber of the guided wave to change, causing the wavenumber distribution outside the original guided wave main mode (the elliptical ring area near the ellipse) to change. By filtering out the signal components within the passband of the elliptical ring, the wavenumber domain disturbance characteristics caused by the damage can be effectively separated. According to experience, the width of the elliptical ring is set to 0.2, then the wavenumber domain ring filter M(k x ,k y )for:

[0058]

[0059] Where θ is the angle between the waveguide propagation direction and the x-axis, k θ is the wave value in the direction of the angle θ between the propagation direction of the guided wave and the x-axis;

[0060] 1.2) Optimizing the above wavenumber domain ring filter to obtain a sub-Nyquist sampling adaptive wavenumber filter;

[0061] Sampling interval dx in the x direction and wavenumber domain range The relationship is:

[0062]

[0063] When k xs -k 0max <k 0max When the sampling interval in two-dimensional space does not satisfy the Nyquist sampling theorem, aliasing will occur after two-dimensional Fourier transform. Figure 3 ;

[0064] Similarly, the sampling interval dy in the y direction is related to the wavenumber domain range The relationship is:

[0065]

[0066] in, are the maximum absolute values ​​of the wave numbers in the x and y directions, respectively;

[0067] Therefore, according to the characteristics of aliasing, the above wavenumber domain ring filter can be optimized into a SNWA filter, see Figure 4 :

[0068]

[0069] in, sgn is the sign function;

[0070]

[0071] 2) The present invention constructs a finite element simulation model of the above-mentioned 16-layer composite material plate, uses an ultrasonic transducer as an excitation source, and uses a laser Doppler vibrometer to measure the full wavefield data w(x, y, ω) at different sampling intervals. The full wavefield data w(x, y, ω) is then transformed into the frequency-wavenumber domain by a two-dimensional Fourier transform to obtain the frequency-wavenumber domain signal W dxdy (k x ,k y ,ω), the formula is as follows:

[0072]

[0073] 3) The above frequency-wavenumber domain signal W dxdy (k x ,k y ,ω) is extracted, and then the frequency-wavenumber domain signal of each frequency point is filtered using the SNWA filter designed in step 1), and the direct wave signal with a significant amplitude advantage is filtered out to enhance the weak scattered signal caused by damage, and obtain the filtered wavenumber domain data with significantly enhanced damage information. The formula is as follows:

[0074]

[0075] 4) The wave number domain data after the above filtering Perform two-dimensional inverse Fourier transform and convert it to the spatial domain to obtain the spatial wave field signal The formula is as follows:

[0076]

[0077] Then, the root mean square method is used in the spatial domain to analyze the spatial wave field signal. After merging, the image of the damage morphology is obtained. Figure 5 .

[0078] The root mean square method is used to analyze the spatial wave field signal The formula for merging is:

[0079]

[0080] Although the specific embodiments of the present invention have been described and illustrated in detail above, it should be pointed out that those skilled in the art can make various equivalent changes and modifications to the above embodiments in accordance with the spirit of the present invention, and the functional effects produced thereby should be within the scope of protection of the present invention as long as they do not exceed the spirit covered by the description and drawings.

Claims

1. A method for imaging damage morphology of plate-like structures under sub-Nyquist sampling conditions, characterized by: The method for imaging the damage morphology of a plate-like structure under sub-Nyquist sampling conditions comprises the following steps performed in sequence: 1) Based on the dispersion characteristics of the plate-like structural material, a ring filter is designed and optimized to obtain an adaptive wavenumber filter with sub-Nyquist sampling; 2) Using ultrasonic transducer as the excitation source, the full wave field data w(x, y, ω) of different sampling intervals are measured by laser Doppler vibrometer, and then the full wave field data w(x, y, ω) is transformed into the frequency-wave number domain by two-dimensional Fourier transform to obtain the frequency-wave number domain signal W(k x ,k y ,ω); 3) The above frequency-wavenumber domain signal W(k x ,k y ,ω) is extracted, and then the frequency-wavenumber domain signal of each frequency point is filtered using the SNWA filter designed in step 1), and the direct wave signal with a significant amplitude is filtered out to enhance the weak scattered signal caused by damage, and the filtered wavenumber domain data is obtained. 4) The wave number domain data after the above filtering Perform two-dimensional inverse Fourier transform and convert it to the spatial domain to obtain the spatial wave field signal Then, the root mean square method is used in the spatial domain to analyze the spatial wave field signal. After merging, the images of the damage morphology are finally obtained.

2. The method for imaging damage morphology of plate-like structures under sub-Nyquist sampling conditions according to claim 1, characterized in that: In step 1), the method of designing and optimizing a ring filter based on the dispersion characteristics of the plate-like structural material to obtain a sub-Nyquist sampling adaptive wavenumber filter is as follows: 1.1) Design a wavenumber domain ring filter based on the dispersion characteristics; For isotropic materials, the wavenumber values ​​k0 in different directions at the same center frequency are the same, and the distribution is approximately a ring. Based on experience, the width of the ring is set to 0.2, and the annular filter in the wavenumber domain is: For anisotropic materials, the wave number distribution in different directions at the same center frequency is approximately an elliptical ring. The wave number values ​​in the directions of 0° and 90° are k0, Wave value k0, are half of the minor axis and major axis of the ellipse respectively; according to experience, the width of the elliptical ring is set to 0.2, then the annular filter M(k x ,k y )for: Where θ is the angle between the waveguide propagation direction and the x-axis, k θ is the wave value in the direction of the angle θ between the propagation direction of the guided wave and the x-axis; 1.2) Optimizing the above wavenumber domain ring filter to obtain a sub-Nyquist sampling adaptive wavenumber filter; Sampling interval dx in the x direction and wavenumber domain range The relationship is: When k xs -k 0max <k 0max When the sampling interval in two-dimensional space does not satisfy the Nyquist sampling theorem, aliasing will occur after two-dimensional Fourier transform; Similarly, the sampling interval dy in the y direction is related to the wavenumber domain range The relationship is: in, are the maximum absolute values ​​of the wave numbers in the x and y directions, respectively; Therefore, according to the characteristics of aliasing, the above wavenumber domain ring filter is optimized to a SNWA filter: in, sgn is the sign function; 3. The method for imaging damage morphology of plate-like structures under sub-Nyquist sampling conditions according to claim 1, characterized in that: In step 2), the full wavefield data w(x, y, ω) is transformed into the frequency-wavenumber domain by two-dimensional Fourier transform to obtain the frequency-wavenumber domain signal W dxdy (k x ,k y ,ω) is as follows: Where ω is the frequency.

4. The method for imaging damage morphology of plate-like structures under sub-Nyquist sampling conditions according to claim 1, characterized in that: In step 3), the frequency-wavenumber domain signal W dxdy (k x ,k y ,ω) is extracted, and then the frequency-wavenumber domain signal of each frequency point is filtered using the SNWA filter designed in step 1) to obtain the filtered wavenumber domain data with significantly enhanced damage information. The formula is as follows:

5. The method for imaging damage morphology of plate-like structures under sub-Nyquist sampling conditions according to claim 1, characterized in that: In step 4), the wavenumber domain data after filtering is Perform two-dimensional inverse Fourier transform and convert it to the spatial domain to obtain the spatial wave field signal The formula is as follows: The spatial wave field signal is analyzed by using the root mean square method in the spatial domain. The formula for merging is:

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