A guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement

Abstract

The application discloses a guided wave phase velocity dispersion reconstruction method based on spectrum decomposition and phase spectrum enhancement, comprising the following steps: measuring adjacent guided wave signals at two non-overlapping positions by using an oscilloscope; performing spectrum decomposition on the guided wave signals to obtain a set number of filtered guided wave signal components; performing phase spectrum expansion processing on the guided wave signal components by using a phase spectrum enhancement technology to obtain phase differences between the guided wave signals; reconstructing phase velocities and frequencies of guided wave modes to obtain a reconstructed dispersion curve; obtaining parameters representing mechanical properties of a composite material, the parameters including a layer direction, an elastic matrix and material density; establishing a theoretical model of Lamb wave propagation in a composite material plate by using a semi-analytical finite element method to obtain a theoretical dispersion curve of Lamb wave propagation in the composite material plate; and comparing the reconstructed dispersion curve with the theoretical dispersion curve to verify the effectiveness of the application. The application provides certain support for analysis and research on non-stationary guided wave signals.

Description

Technical Field

[0001] This invention relates to the fields of ultrasonic guided wave signal processing and ultrasonic guided wave nondestructive testing technology, specifically to a guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement. Background Technology

[0002] Lamb waves have been widely used in nondestructive testing and structural health monitoring for locating and quantitatively detecting structural damage in various objects. However, Lamb waves possess unique propagation characteristics, such as dispersion, multimodality, mode interleaving, and mode splitting caused by edges. These factors often make the received Lamb wave signal exceptionally complex. Dispersion can be considered one of the main characteristics of Lamb waves, further complicating the analysis and processing of the wave signal.

[0003] Lamb wave signal packets consist of components of different frequencies propagating at different speeds, characterized by phase velocity and group velocity as described by the dispersion curve. Dispersion typically affects the duration of signal spread and reduces signal amplitude with distance. For Lamb waves used in applications, signal processing techniques capable of assessing dispersion phenomena and relating frequency to phase and group velocities should be employed. Existing dispersion reconstruction methods mostly require deploying multiple sensor arrays to simultaneously acquire signals, followed by spectral analysis to reconstruct the Lamb wave dispersion. This method is costly and complex, especially in large or irregular structures, where deployment is difficult and efficient measurement is challenging. It also involves significant computational demands and requires sophisticated signal processing algorithms. Achieving broadband reconstruction of the dispersion curve often requires multiple excitations with varying excitation signals, a cumbersome and time-consuming process. Therefore, an improved method is urgently needed to enhance the accuracy, bandwidth, efficiency, and applicability of dispersion curve reconstruction, enabling its better application in practical engineering testing. Summary of the Invention

[0004] The purpose of this invention is to provide a guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement. By improving the sensitivity of small amplitude components through spectral decomposition, the phase shift between signals is estimated, and phase velocity reconstruction is performed on specific frequency components corresponding to the peak value of the amplitude spectrum, thereby realizing broadband reconstruction of the dispersion curve.

[0005] The present invention adopts the following technical solution:

[0006] A guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement includes the following steps:

[0007] S1. Measure the adjacent guided wave signals u at two non-overlapping positions x1 and x2 at time t using an oscilloscope. x1 (t) and u x2 (t).

[0008] S2. Perform spectral decomposition on the signal obtained in step S1 to obtain a set number of filtered guided wave signal components.

[0009] S3. Using phase spectrum enhancement technology, the signal components in step S2 are subjected to phase spectrum expansion processing to obtain the phase difference between the guided wave signals.

[0010] S4. Reconstruct the phase velocity and frequency of the guided wave mode to obtain the reconstructed dispersion curve.

[0011] Furthermore, in step S2, the obtained guided wave signal components include the following:

[0012] S201. Calculate the spectrum of the signal, using the following formula:

[0013] U x1 (f)=FT[u x1 (t)]

[0014] U x2 (f)=FT[u x2 (t)]

[0015] Among them, U x1 (f) represents u x1 The spectrum of (t), U x2 (f) represents u x2 The spectrum of (t), where FT represents the Fourier transform and f represents the frequency.

[0016] S202. Filter the spectrum obtained in step S201. The specific formula is as follows:

[0017] U x1,i (f)=U x1 (f)·B i (f)

[0018] U x2,i (f)=U x2 (f)·B i (f)

[0019] Among them, U x1,i (f) represents U after filtering by the i-th Gaussian filter. x1 (f) sub-spectrum; U x2,i (f) represents U after filtering by the i-th Gaussian filter. x2 (f) sub-spectrum; B i (f) represents the i-th Gaussian filter. i = 1, 2, ..., I, where I represents the total number of Gaussian filters, f LdB represents the minimum value of the sliding range of the center frequency of the Gaussian filter, ΔB represents the filter bandwidth, and df represents the frequency domain shift step between the center frequencies of two adjacent Gaussian filters. df = (f H -f L ) / (I-1), f H This represents the maximum value of the sliding range of the center frequency of the Gaussian filter.

[0020] S203. Using the inverse Fourier transform, reconstruct the sub-spectrum obtained in step S202 into the time domain. The specific formula is as follows:

[0021] u x1,i (t) = IFT.U x1,i (f) /

[0022] u x2,i (t) = IFT.U x2,i (f) /

[0023] Where IFT represents the inverse Fourier transform, u x1,i (t) represents the i-th frequency domain component U x1,i (f) Reconstruct the signal components back to the time domain, u x2,i (t) represents the i-th frequency domain component U x2,i (f) Reconstruct the signal components back to the time domain.

[0024] Furthermore, in step S3, the phase difference between the guided wave signals is obtained as follows:

[0025] S301. Under moderate dispersion, calculate u based on the maximum value of the Hilbert envelope. x1,i (t) and u x2,i The offset of (t) is given by the following formula:

[0026] e x1,i (t)=u x1,i (t+t m1 )

[0027] e x2,i (t)=u x2,i (t+t m2 )

[0028] Among them, e x1,i (t) represents u x1,i (t) is a time-shifted signal; e x2,i (t) represents u x2,i The time-shifted signal of (t); t m1 Indicate u x1,i The offset time of (t), HT represents the time corresponding to the maximum value of the Hilbert envelope, and HT represents the Hilbert transform; t m2Indicate u x2,i The offset time of (t),

[0029] S302. Calculate the complex spectrum of the time-shifted signal. The specific formula is as follows:

[0030] E x1,i (f)=FT[e x1,i (t)]

[0031] E x2,i (f)=FT[e x2,i (t)]

[0032] Among them, E x1,i (f) represents e x1,i The complex spectrum of E(t), x2,i (f) represents e x2,i The complex spectrum of (t).

[0033] S303, Calculate the phase difference between time-shifted signals. The specific formula is as follows:

[0034]

[0035] Where, α x1,i (f) represents e x1,i The phase of (t), arctan[] denotes the arctangent function, Im denotes the real part of the spectrum, and Re denotes the imaginary part of the spectrum; α x2,i (f) represents e x2,i The phase of (t),

[0036]

[0037] Furthermore, in step S4, the reconstructed dispersion curve includes the following:

[0038] The formula for calculating phase velocity is:

[0039]

[0040] Among them, c p (i) represents phase velocity; f i Represents the amplitude spectrum |E x1,i (f)| Peak-to-peak frequency; d represents the distance between the two guided wave signals, d = x2 - x1.

[0041] f i Corresponding to the amplitude spectrum |E x1,i The frequency of the peak-to-peak value of (f)|.

[0042] The reconstructed dispersion curve represents the frequency and phase velocity. i ,c p (i) / The set of scattered points.

[0043] Furthermore, step S5 is included: verifying the accuracy of the dispersion curve reconstructed in step S4.

[0044] Furthermore, verifying accuracy includes the following:

[0045] S501. Obtain parameters characterizing the mechanical properties of composite materials, including layup direction, elastic matrix, and material density.

[0046] S502. Using the semi-analytical finite element method, the theoretical dispersion curve of Lamb wave propagation in composite material plate is obtained.

[0047] S503. Compare the reconstructed dispersion curve in step S4 with the theoretical dispersion curve in step S502. When the overlap rate between the reconstructed dispersion curve and the theoretical dispersion curve reaches more than 90%, it indicates that the reconstructed dispersion curve meets the requirements.

[0048] Furthermore, in step S502, the theoretical dispersion curve obtained includes the following:

[0049] To model the composite material, an orthogonal three-dimensional global coordinate system xyz is established for the anisotropic composite laminate, where the x-axis is parallel to the thickness direction of the laminate. An orthogonal material coordinate system x′y′z′ is also established, where the y-axis is parallel to the fiber orientation. The angle between the composite laminate and the orientation of a single fiber layer relative to the global coordinate system is set to θ. Ignoring the viscoelasticity of the material, the elastic modulus of the composite material is expressed as:

[0050] in,

[0051] s = sin(θ), c = cos(θ);

[0052] C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32 C 33 C 44 C 55 C 66 Both represent elastic constants, C 12 =C 21 C 13 =C 31 C 23 =C32 .

[0053] The wave vector K of the guided wave in an anisotropic plate structure is related to the propagation direction β of the guided wave, specifically expressed as:

[0054]

[0055] Where k represents the wave number and β represents the wave propagation angle. and This represents the corresponding unit direction vector.

[0056] The nodal displacement u is a function of time and space, specifically expressed as:

[0057] u(x,y,z,t)=Nq (e) exp{j[ωt+ksin(β)y-kcos(β)z]}

[0058] in, N represents the interpolation matrix composed of shape functions. Let q represent the nth shape function. (e) represents the column vector of nodal displacement components within the spectral element, e represents the element label, ω represents the angular frequency, exp{} represents the natural exponential function, and j represents the imaginary unit.

[0059] The strain field ε within the spectral unit is expressed as:

[0060] ε=[B1-jk y B2-jk z B3]q (e) exp[j(ωt+ksin(β)y-kcos(β)z)]

[0061] Where, B1 = L x N x , N x B² represents the derivative of N in the x-direction; y N, B3 = L z N, k y Represents the wavenumber component in the y-direction; k z This represents the wavenumber component in the z-direction.

[0062] Based on C θ We obtain the mass matrix M and the stiffness matrix K. mn The specific expression is:

[0063]

[0064] Where, m (e) =∫(e) N T ρNdx,N T This represents the transpose of N, and ρ represents the material density; n e Indicates the number of spectral units;

[0065] Extending Hamilton's variational principle to the entire domain, we combine the attributes of all units into a global attribute matrix, resulting in the global governing equations, specifically expressed as:

[0066] [A-γB]Q=0

[0067] in, ss=sin(β), cc=cos(β); Q = [q γq] T , γ=jk.

[0068] Given the relevant material parameters, the wavenumber variations of all guided wave modes within the corresponding frequency range are obtained by solving the global control equations, thus yielding the theoretical phase velocity. The specific formula is as follows:

[0069]

[0070] Among them, c p ′ represents the theoretical phase velocity; phase velocity refers to the propagation speed of a wave packet at a fixed phase point in the propagation direction.

[0071] This allows us to obtain the theoretical dispersion curve of guided wave propagation in composite materials.

[0072] Furthermore, the present invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement.

[0073] Furthermore, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the described guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement.

[0074] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0075] 1. This invention combines spectral decomposition technology and enhanced phase spectrum technology to improve the sensitivity of small amplitude components and realize broadband reconstruction of phase velocity dispersion curves.

[0076] 2. The reconstruction accuracy of this invention is high, it is easy to use, and it is inexpensive, making it very suitable for industrial applications.

[0077] 3. This invention can be used for ultrasonic non-destructive evaluation of industrial facilities, aerospace equipment, and structural health monitoring. Attached Figure Description

[0078] Figure 1 This is a flowchart illustrating the overall implementation of the present invention.

[0079] Figure 2 This is a flowchart illustrating the implementation of the guided wave phase velocity dispersion reconstruction method of the present invention.

[0080] Figure 3 This is a schematic diagram of the COMSOL simulation model according to an embodiment of the present invention.

[0081] Figure 4 This is a schematic diagram of the semi-analytical finite element model of the composite material of the present invention.

[0082] Figure 5 This is a numerical simulation reconstruction result diagram of an embodiment of the present invention. Detailed Implementation

[0083] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0084] To achieve the above objectives, this invention proposes a guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement, and verifies the reconstructed curve. It can reconstruct velocity values ​​over a wide bandwidth and consists of signal measurement, spectral decomposition, phase spectrum enhancement, and dispersion reconstruction. Figure 1 As shown, the specific steps are as follows:

[0085] Among them, such as Figure 2 As shown, obtaining the reconstructed dispersion curve includes steps S1-S4:

[0086] S1. Measure the adjacent guided wave signals u at two non-overlapping positions x1 and x2 at time t using an oscilloscope. x1 (t) and u x2 (t).

[0087] The simulation model created in the simulation software COMSOL is as follows: Figure 3 As shown, the system includes a composite laminate, actuators, and sensors. Each layer of the composite laminate is connected using a two-dimensional plane strain model, with each layer modeled individually. The lower surfaces of the actuators and sensors are grounded and connected to the composite laminate via a thin linear elastic adhesive layer. The actuators are used to apply a voltage signal to excite guided waves, and the two sensors are used to receive signals from two adjacent guided waves.

[0088] In this embodiment, a carbon fiber composite material plate with orthogonal anisotropy is used, and its layup direction is [0°\90°].4s The main mechanical properties are as follows:

[0089] Density: ρ = 1630.4 kg / m³ 3 Main elastic constant: C 11 =54.55GPa, C 12 =7.01 GPa, C 13 =6.38GPa, C 22 =52.16 GPa, C 23 =6.31 GPa, C 33 =9.22 GPa, C 44 =3.07 GPa, C 55 =2.98 GPa, C 66 =3.59 GPa.

[0090] This model simulates the generation of two signals received from deployed piezoelectric sensors. The piezoelectric elements are connected to a composite laminate via linear elastic thin-layer conditions. Each piezoelectric element is 5 mm long and 0.5 mm thick, made of PZT-5H. Typically, the accuracy of the numerical model depends on the temporal and spatial resolution of the analysis. The node spacing in the composite laminate model is set to ensure at least 10 nodes at the minimum wavelength, and an element growth rate of 1.25. For the time step resolution, the highest frequency is set to at least 20 points per period.

[0091] The excitation signal is a cosine pulse modulated by a Gaussian window, expressed as follows:

[0092]

[0093] Where G = 1, f c =200kHz, t0=12.5μs, σ=3.5×10 -6 .

[0094] S2. Perform spectral decomposition on the signal obtained in step S1 to obtain a predetermined number of filtered guided wave signal components; the specific content is as follows:

[0095] S201. Calculate the spectrum of the signal, using the following formula:

[0096] U x1 (f)=FT[u x1 (t)]

[0097] U x2 (f)=FT[u x2 (t)]

[0098] Among them, U x1 (f) represents u x1 The spectrum of (t), U x2(f) represents u x2 The spectrum of (t), where FT represents the Fourier transform and f represents the frequency.

[0099] S202. Filter the spectrum obtained in step S201. The specific formula is as follows:

[0100] U x1,i (f)=U x1 (f)·B i (f)

[0101] U x2,i (f)=U x2 (f)·B i (f)

[0102] Among them, U x1,i (f) represents U after filtering by the i-th Gaussian filter. x1 (f) sub-spectrum; U x2,i (f) represents U after filtering by the i-th Gaussian filter. x2 (f) sub-spectrum; B i (f) represents the i-th Gaussian filter. i = 1, 2, ..., I, where I represents the total number of Gaussian filters, f L dB represents the minimum value of the sliding range of the center frequency of the Gaussian filter, ΔB represents the filter bandwidth, and df represents the frequency domain shift step between the center frequencies of two adjacent Gaussian filters. df = (f H -f L ) / (I-1), f H This represents the maximum value of the sliding range of the center frequency of the Gaussian filter.

[0103] S203. Using the inverse Fourier transform, reconstruct the sub-spectrum obtained in step S202 into the time domain. The specific formula is as follows:

[0104] u x1,i (t) = IFT.U x1,i (f) /

[0105] u x2,i (t) = IFT.U x2,i (f) /

[0106] Where IFT represents the inverse Fourier transform, u x1,i (t) represents the i-th frequency domain component U x1,i (f) Reconstruct the signal components back to the time domain, u x2,i (t) represents the i-th frequency domain component U x2,i (f) Reconstruct the signal components back to the time domain.

[0107] S3. Using phase spectrum enhancement technology, the signal components in step S2 are subjected to phase spectrum expansion processing to obtain the phase difference between the guided wave signals; the specific content is as follows:

[0108] S301, Signal Time Shift. To avoid uncertainties during phase expansion, each waveform u... x1,i (t) and u x2,i (t) will be offset by t in the time domain m1 and t m2 In the case of moderate dispersion, u is calculated based on the maximum value of the Hilbert envelope. x1,i (t) and u x2,i The offset of (t) is given by the following formula:

[0109] e x1,i (t)=u x1,i (t+t m1 )

[0110] e x2,i (t)=u x2,i (t+t m2 )

[0111] Among them, e x1,i (t) represents u x1,i (t) is a time-shifted signal; e x2,i (t) represents u x2,i The time-shifted signal of (t); t m1 Indicate u x1,i The offset time of (t), HT represents the time corresponding to the maximum value of the Hilbert envelope, and HT represents the Hilbert transform; t m2 Indicate u x2,i The offset time of (t), The offset time corresponds to the maximum value of the Hilbert envelope to compensate for the signal delay caused by the phase velocity.

[0112] S302. Calculation of the complex spectrum of the time-shifted signal. The specific formula for calculating the complex spectrum of the time-shifted signal is as follows:

[0113] E x1,i (f)=FT[e x1,i (t)]

[0114] E x2,i (f)=FT[e x2,i (t)]

[0115] Among them, E x1,i (f) represents e x1,i The complex spectrum of E(t), x2,i (f) represents e x2,i The complex spectrum of (t).

[0116] S303. Phase Difference Calculation. Calculate the phase difference between time-shifted signals. The specific formula is as follows:

[0117]

[0118] Where, α x1,i (f) represents e x1,i The phase of (t), arctan[] denotes the arctangent function, Im denotes the real part of the spectrum, and Re denotes the imaginary part of the spectrum; α x2,i (f) represents e x2,i The phase of (t),

[0119]

[0120] Phase α x1,i (f) and α x2,i (f) is calculated within the range of [-π, π] radians. If the phase exceeds the limit of ±π radians, some discontinuities will occur. Therefore, the phase α x1,i (f) and α x2,i (f) must be expanded.

[0121] S4. Reconstruct the phase velocity and frequency of the guided wave mode to obtain the reconstructed dispersion curve; the specific content is as follows:

[0122] The formula for calculating phase velocity is:

[0123]

[0124] Among them, c p (i) represents phase velocity; f i Represents the amplitude spectrum |E x1,i (f)| Peak-to-peak frequency; d represents the distance between the two guided wave signals, d = x2 - x1.

[0125] f i Corresponding to the amplitude spectrum |E x1,i The frequency of the peak-to-peak value of (f)|.

[0126] The reconstructed dispersion curve represents the frequency and phase velocity. i ,c p (i) / The set of scattered points.

[0127] S5. Verify the accuracy of the reconstructed dispersion curve in step S4. The specific steps are as follows:

[0128] S501. Obtain parameters characterizing the mechanical properties of composite materials, including layup direction, elastic matrix, and material density.

[0129] S502. Using the semi-analytical finite element method, the theoretical dispersion curve of Lamb wave propagation in composite material plates is obtained; the specific content is as follows:

[0130] To model the composite material, an orthogonal three-dimensional global coordinate system xyz is established for the anisotropic composite laminate, where the x-axis is parallel to the thickness direction of the laminate. An orthogonal material coordinate system x′y′z′ is also established, where the y-axis is parallel to the fiber orientation. The angle between the composite laminate and the orientation of a single fiber layer relative to the global coordinate system is set to θ. Ignoring the viscoelasticity of the material, the elastic modulus of the composite material is expressed as:

[0131] in,

[0132] s = sin(θ), c = cos(θ), C 12 =C 21 C 13 =C 31 C 23 =C 32 .

[0133] The wave vector K of the guided wave in an anisotropic plate structure is related to the propagation direction β of the guided wave, specifically expressed as:

[0134]

[0135] Where k represents the wave number and β represents the wave propagation angle. and This represents the corresponding unit direction vector.

[0136] The nodal displacement u is a function of time and space, specifically expressed as:

[0137] u(x,y,z,t)=Nq (e) exp{j[ωt+ksin(β)y-kcos(β)z]}

[0138] in, N represents the interpolation matrix composed of shape functions. Let q represent the nth shape function, where the shape function is a Lagrange interpolation polynomial with Gauss-Lobatto-Legendre nodes. (e) represents the column vector of nodal displacement components within the spectral element, e represents the element label, ω represents the angular frequency, exp{} represents the natural exponential function, and j represents the imaginary unit.

[0139] The strain field ε within the spectral unit is expressed as:

[0140] ε=[B1-jk yB2-jk z B3]q (e) exp[j(ωt+ksin(β)y-kcos(β)z)]

[0141] Where, B1 = L x N x , N x B² represents the derivative of N in the x-direction; y N, B3 = L z N, k y Represents the wavenumber component in the y-direction; k z This represents the wavenumber component in the z-direction.

[0142] Based on C θ We obtain the mass matrix M and the stiffness matrix K. mn The specific expression is:

[0143]

[0144] Where, m (e) =∫ (e) N T ρNdx,N T This represents the transpose of N, and ρ represents the material density; n e Indicates the number of spectral units;

[0145] Extending Hamilton's variational principle to the entire domain, we combine the attributes of all units into a global attribute matrix, resulting in the global governing equations, specifically expressed as:

[0146] [A-γB]Q=0

[0147] in, ss=sin(β), cc=cos(β); Q = [q γq] T , γ=jk.

[0148] Given the relevant material parameters, the wavenumber variations of all guided wave modes within the corresponding frequency range are obtained by solving the global control equations, thus yielding the theoretical phase velocity. The specific formula is as follows:

[0149]

[0150] Among them, c p ′ represents the theoretical phase velocity; phase velocity refers to the propagation speed of a wave packet at a fixed phase point in the propagation direction.

[0151] This allows us to obtain the theoretical dispersion curve of guided wave propagation in composite materials.

[0152] S503. Compare the reconstructed dispersion curve in step S4 with the theoretical dispersion curve in step S502. When the overlap rate between the reconstructed dispersion curve and the theoretical dispersion curve reaches more than 90%, it indicates that the reconstructed dispersion curve meets the requirements.

[0153] Figure 4 This is a schematic diagram of a semi-analytical finite element model. The semi-analytical finite element method is used to obtain the phase velocity dispersion curve of guided wave propagation theory.

[0154] Compare the theoretical curve with a series of scatter points reconstructed by the method proposed in this invention, such as... Figure 5 As shown, the theoretical dispersion curve is very close to the reconstructed dispersion curve, with a high overlap rate, indicating the correctness and feasibility of the method.

[0155] This invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. It should be noted that when the processor executes the computer program, it corresponds to the specific steps of the method provided in this invention, possessing the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in this invention.

[0156] This invention also proposes a computer-readable storage medium storing a computer program. It should be noted that when the computer program is executed by a processor, it corresponds to the specific steps of the method provided in this invention, possessing the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in this invention.

[0157] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for reconstructing the phase velocity dispersion of guided waves based on spectral decomposition and phase spectrum enhancement, characterized in that, include: S1. Measure the adjacent guided wave signals u at two non-overlapping positions x1 and x2 at time t using an oscilloscope. x1 (t) and u x2 (t); S2. Perform spectral decomposition on the signal obtained in step S1 to obtain a predetermined number of filtered guided wave signal components; specifically: S201. Calculate the spectrum of the signal, using the following formula: U x1 (f)=FT[u x1 (t)] U x2 (f)=FT[u x2 (t)] Among them, U x1 (f) represents u x1 The spectrum of (t), U x2 (f) represents u x2 The spectrum of (t), where FT represents the Fourier transform and f represents the frequency; S202. Filter the spectrum obtained in step S201. The specific formula is as follows: U x1,i (f)=U x1 (f)·B i (f) U x2,i (f)=U x2 (f)·B i (f) Among them, U x1,i (f) represents U after filtering by the i-th Gaussian filter. x1 (f) sub-spectrum; U x2,i (f) represents U after filtering by the i-th Gaussian filter. x2 (f) sub-spectrum; B i (f) represents the i-th Gaussian filter. I represents the total number of Gaussian filters, f L dB represents the minimum value of the sliding range of the center frequency of the Gaussian filter, ΔB represents the filter bandwidth, and df represents the frequency domain shift step between the center frequencies of two adjacent Gaussian filters. df = (f H -f L ) / (I-1), f H This represents the maximum value of the sliding range of the center frequency of the Gaussian filter; S203. Using the inverse Fourier transform, reconstruct the sub-spectrum obtained in step S202 into the time domain. The specific formula is as follows: u x1,i (t)=IFT9U x1,i (f)0 u x2,i (t)=IFT9U x2,i (f)0 Where IFT represents the inverse Fourier transform, u x1,i (t) represents the i-th frequency domain component U x1,i (f) Reconstruct the signal components back to the time domain, u x2,i (t) represents the i-th frequency domain component U x2,i (f) Reconstruct the signal components back to the time domain; S3. Using phase spectrum enhancement technology, the signal components in step S2 are subjected to phase spectrum expansion processing to obtain the phase difference between the guided wave signals; specifically: S301. Under moderate dispersion, calculate u based on the maximum value of the Hilbert envelope. x1,i (t) and u x2,i The offset of (t) is given by the following formula: e x1,i (t)=u x1,i (t+t m1 ) e x2,i (t)=u x2,i (t+t m2 ) Among them, e x1,i (t) represents u x1,i (t) is a time-shifted signal; e x2,i (t) represents u x2,i The time-shifted signal of (t); t m1 Indicate u x1,i The offset time of (t), HT represents the time corresponding to the maximum value of the Hilbert envelope, and HT represents the Hilbert transform; t m2 Indicate u x2,i The offset time of (t), S302. Calculate the complex spectrum of the time-shifted signal. The specific formula is as follows: E x1,i (f)=FT[e x1,i (t)] E x2,i (f)=FT[e x2,i (t)] Among them, E x1,i (f) represents e x1,i The complex spectrum of E(t), x2,i (f) represents e x2,i The complex spectrum of (t), where FT represents the Fourier transform; S303, Calculate the phase difference between time-shifted signals. The specific formula is as follows: Where, α x1,i (f) represents e x1,i The phase of (t), arctan[] denotes the arctangent function, Im denotes the real part of the spectrum, and Re denotes the imaginary part of the spectrum; α x2,i (f) represents e x2,i The phase of (t), S4. Reconstruct the phase velocity and frequency of the guided wave mode to obtain the reconstructed dispersion curve; specifically: The formula for calculating phase velocity is: Among them, c p (i) represents phase velocity; f i Represents the amplitude spectrum |E x1,i (f) | Peak-to-peak frequency; d represents the distance between the two guided wave signals, d = x2 - x1; f i Corresponding to the amplitude spectrum |E x1,i (f)| has peak-to-peak frequency, i = 1, 2, ... I, where I represents the total number of Gaussian filters; The reconstructed dispersion curve is the frequency and phase velocity (f) i c p (i)) The set of scattered points; S5. Verify the accuracy of the reconstructed dispersion curve in step S4, specifically as follows: S501. Obtain parameters characterizing the mechanical properties of composite materials, including layup direction, elastic matrix, and material density. S502. Using the semi-analytical finite element method, the theoretical dispersion curve of Lamb wave propagation in composite material plate is obtained. S503. Compare the reconstructed dispersion curve in step S4 with the theoretical dispersion curve in step S502. When the overlap rate between the reconstructed dispersion curve and the theoretical dispersion curve reaches more than 90%, it indicates that the reconstructed dispersion curve meets the requirements.

2. The guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement according to claim 1, characterized in that, In step S502, the theoretical dispersion curve obtained includes the following: To model the composite material, an orthogonal three-dimensional global coordinate system xyz is established for the anisotropic composite laminate, where the x-axis is parallel to the thickness direction of the laminate. An orthogonal material coordinate system x′y′z′ is also established, where the y-axis is parallel to the fiber orientation. The angle between the composite laminate and the orientation of a single fiber layer relative to the global coordinate system is set to θ. Ignoring the viscoelasticity of the material, the elastic modulus of the composite material is expressed as: in, s = sin(θ), c = cos(θ); C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32 C 33 C 44 C 55 C 66 Both represent elastic constants, C 12 =C 21 C 13 =C 31 C 23 =C 32 ; The wave vector K of the guided wave in an anisotropic plate structure is related to the propagation direction β of the guided wave, specifically expressed as: Where k represents the wave number and β represents the wave propagation angle. and This represents the corresponding unit direction vector; The nodal displacement u is a function of time and space, specifically expressed as: u(x,y,z,t)=Nq (e) exp{j[ωt+ksin(β)y-kcos(β)z]} in, N represents the interpolation matrix composed of shape functions. Let q represent the nth shape function. (e) represents the column vector of nodal displacement components within the spectral element, e represents the element label, ω represents the angular frequency, exp{} represents the natural exponential function, and j represents the imaginary unit; The strain field ε within the spectral unit is expressed as: ε=[B1-jk y B2-jk z B3]q (e) exp[j(ωt+ksin(β)y-kcos(β)z)] Where, B1 = L x N x , N x B² represents the derivative of N in the x-direction; y N, B3 = L z N, k y Represents the wavenumber component in the y-direction; k z This represents the wavenumber component in the z-direction; Based on C θ We obtain the mass matrix M and the stiffness matrix K. mn The specific expression is: Where, m (e) =∫ (e) N T ρN dx,N T This represents the transpose of N, and ρ represents the material density; n e Indicates the number of spectral units; m, n = 1, 2, 3; Extending Hamilton's variational principle to the entire domain, we combine the attributes of all units into a global attribute matrix, resulting in the global governing equations, specifically expressed as: [A-γB]Q=0 Among them, ss=sin(β), cc=cos(β); Q=[q γq] T ,γ=jk; Given the relevant material parameters, the wavenumber variations of all guided wave modes within the corresponding frequency range are obtained by solving the global control equations, thus yielding the theoretical phase velocity. The specific formula is as follows: Among them, c p ′ represents the theoretical phase velocity; phase velocity refers to the propagation speed of a wave packet at a fixed phase point in the propagation direction; This allows us to obtain the theoretical dispersion curve of guided wave propagation in composite materials.

3. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement as described in any one of claims 1 to 2.

4. A computer-readable storage medium storing a computer program, characterized in that, The computer program, when executed by the processor, performs the guided wave phase velocity dispersion reconstruction method based on spectral decomposition and phase spectrum enhancement as described in any one of claims 1 to 2.

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