Ultrasonic guided wave mode separation method based on frequency dispersion compensation and blind source separation

Abstract

The invention discloses an ultrasonic guided wave mode separation method based on frequency dispersion compensation and blind source separation, and relates to the field of ultrasonic guided wave mode separation and the field of ultrasonic guided wave nondestructive testing. The method comprises the following steps: extracting frequency dispersion characteristic parameters of a Lamb wave modal from response Lamb waves with known propagation distances through a particle swarm optimization algorithm; performing single-mode frequency dispersion compensation on the two actually measured signals according to the extracted parameters to enable the two signals to return to the same distance; lamb wave signals with the same distance and different superposition conditions are processed through a JADE blind source separation method; and performing sequential compensation and separation on different modes to obtain single-mode signals and realize multi-mode signal separation. According to the invention, the frequency dispersion compensation method and the blind source separation method are combined and applied to the research on the multi-mode Lamb wave signal mode separation problem, and the complex multi-mode Lamb wave signals can be effectively separated.

Description

Technical Field

[0001] The invention relates to the field of ultrasonic guided wave mode separation and ultrasonic guided wave nondestructive testing, and in particular to an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation. Background Art

[0002] Ultrasonic Lamb waves are widely used in nondestructive testing and structural health monitoring due to their long propagation distance and low attenuation. However, due to the multimodal and dispersive characteristics of Lamb waves, the received signals become complex, wave packets often overlap with each other, and characteristic information may be submerged in these overlapping signals, making them difficult to identify and extract, resulting in reduced accuracy of subsequent data analysis. Therefore, how to effectively separate these complex multimodal Lamb wave signals has become one of the focuses of current research.

[0003] Existing ultrasonic guided wave mode separation technologies mainly include traditional spectrum analysis and signal processing technology based on pattern recognition. The former usually relies on Fourier transform to analyze signal components, but due to the characteristics of Lamb wave signals themselves, this method often fails to achieve ideal separation effects; the latter attempts to achieve mode differentiation by learning signal features, which is theoretically feasible but performs poorly in the face of high-density signal superposition. Summary of the invention

[0004] The object of the present invention is to provide an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation to solve the problems raised in the prior art.

[0005] To achieve the above object, the present invention provides the following technical solution: an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation, the method comprising the steps of:

[0006] S10, extracting the dispersion characteristic parameters of the Lamb wave mode from the response Lamb wave of known propagation distance by particle swarm optimization algorithm;

[0007] S20, performing single-mode dispersion compensation on the two measured signals according to the extracted parameters, so that the two signals return to the same distance;

[0008] S30, processing Lamb wave signals with the same distance and different superposition conditions by using the JADE blind source separation method;

[0009] S40, sequentially compensating and separating different modes to obtain a single-mode signal, thereby achieving multi-mode signal separation.

[0010] According to the above solution, step S10 includes:

[0011] S11. In the Lamb wave-based structural health monitoring system, a Gaussian window burst signal is used as an excitation signal. The structural health monitoring system using the Gaussian window burst signal as an excitation signal can effectively improve the ability to evaluate the structural state, help identify potential damage or defects, and realize real-time monitoring. The Gaussian window burst signal formula is as follows:

[0012]

[0013] Where g0(t) is the Gaussian window burst signal at time t; t is time; t0 is the initial displacement of the excitation; σ is the bandwidth factor; f c It is expressed as the center frequency;

[0014] S12. When the distance from the excitation source is x and attenuation is not considered, the single-mode signal is represented by the spectrum of the excitation signal and the wave number of the specific Lamb wave. This representation method helps to analyze and understand the propagation behavior of Lamb waves in structural health monitoring and provides a basis for subsequent signal processing and defect identification. The representation formula is as follows:

[0015]

[0016] Among them, g(x,t) represents the single-mode response signal at the propagation distance x of the signal at time t; G0(ω) represents the spectrum of the excitation signal; ω represents the frequency of the excitation signal; k(ω) represents the wave number of the Lamb wave, which is a nonlinear function of ω; x represents the propagation distance of the signal; j represents the imaginary unit;

[0017] S13. The wave number of Lamb wave is Taylor expanded at the center frequency to obtain various coefficients; each coefficient provides important information about the variation of wave number with frequency, which helps to understand the propagation characteristics of Lamb wave and its application in structural health monitoring;

[0018] The center frequency is denoted as ω c =2πf c ; Among them, ω c Expressed as the center angular frequency; f c It is expressed as the center frequency;

[0019] The Taylor expansion formula is as follows:

[0020] k(ω)≈k0+k1(ω-ω c )+k2(ω-ω c ) 2 ;

[0021] Among them, k0, k1 and k2 represent the coefficients of Taylor expansion;

[0022] S14. Substituting the formula in step 13 into the formula in step 12, the single-mode response signal g(x, t) can be rewritten as g(τ, t), and the formula is as follows:

[0023]

[0024] Where τ = k1x represents the arrival time; β = 1 / (2σ 2 ) is expressed as a constant; Expressed as the amplitude component of the signal; Expressed as the phase component of the signal; φ′=(2πf c -k0 / k1)τ is represented as the phase shift term;

[0025] S15. Using the particle swarm optimization algorithm, improve the accuracy and efficiency of the dispersion characteristic parameter extraction of the Lamb wave mode; design the relative position of the excitation transducer and the receiving transducer to obtain the time domain response signal of the separated wave packet; perform the parameter estimation process for each individual wave component;

[0026] By combining particle swarm optimization algorithm, reasonable design of transducer layout and effective signal processing technology, the accuracy and efficiency of Lamb wave modal dispersion characteristic parameter extraction are significantly improved.

[0027] According to the above scheme, the observed data is (t i ,y i ), the model is g(Θ,t), where t i Represented as the observed value at the i-th time point; y i Represented as at time point t i The corresponding observation results at ;

[0028] And determine the objective function as:

[0029]

[0030] Where N represents the number of observed data points; Θ represents the independent characteristic parameter;

[0031] The independent characteristic parameters are estimated from the corresponding signal g(x0,t) with a propagation distance of x0; the independent characteristic parameters include the wave number, center frequency and attenuation constant of the Lamb wave.

[0032] According to the above scheme, in step S15, the particle swarm optimization algorithm includes:

[0033] Initialize the particle swarm and randomly generate the initial position and velocity of each particle; for each particle, calculate the corresponding fitness value F(Θ) according to the determined objective function;

[0034] When the fitness value of a particle is better than its historical best fitness value, the individual optimal position of the particle is updated; the particle with the best fitness value is found among all particles, and the global optimal position is updated;

[0035] Update speed, the formula is as follows:

[0036] v i new =w×v i old +c1×r1×(p i -x i )+c2×r2×(fx i );

[0037] Among them, v i new Expressed as the new velocity of particle i; v i old is the old velocity of particle i; w is the inertia weight; c1 is the individual learning factor, which determines the degree to which the particle learns from its individual optimal position; c2 is the social learning factor, which determines the degree to which the particle learns from the global optimal position; r1 and r2 are random numbers in the range of [0,1]; p i Represented as the individual optimal position of particle i; x i represents the current position of particle i; f represents the global optimal position;

[0038] Update the position, the formula is as follows:

[0039] x i new =x i old +v i new ;

[0040] Among them, x i new is represented by the new position of particle i; x i old Represented as the old position of particle i;

[0041] Determine whether the termination condition is met, wherein the termination condition includes reaching the maximum number of iterations or the fitness value of the global optimal solution reaching the standard; when the termination condition is met, the process ends, otherwise the fitness value of each particle is repeatedly calculated.

[0042] According to the above solution, step S20 includes:

[0043] S21. Perform dispersion compensation on the received Lamb wave signal according to the extracted parameters. The dispersion compensation is the inverse process of dispersion transformation, and the formula is as follows:

[0044]

[0045] Among them, H -1 It is represented as the dispersion compensation function; H(ω) is represented as the dispersion transformation; d is represented as the compensation distance; k(ω) is represented as the wave number of the Lamb wave, which is a nonlinear function of ω;

[0046] S22. After dispersion compensation, the dispersion-compensated Lamb wave signal is obtained to eliminate the dispersion effect caused by different propagation distances. The formula is as follows:

[0047]

[0048] Where y(t) represents the Lamb wave signal after dispersion compensation; G(ω) represents the spectrum of the original signal;

[0049] By applying dispersion compensation, the dispersion effect caused by different propagation distances can be effectively eliminated, thereby improving the clarity and accuracy of the signal.

[0050] According to the above solution, step S30 includes:

[0051] When the received mixed Lamb wave signal consists of dual-mode signals, and the dual-mode signals have different dispersion characteristics;

[0052] The mixed Lamb wave signals y1(t) and y2′(t) at positions a and b along the propagation path are measured, where the distance between a and b is e; at the same time, the two single-mode signals of the mixed Lamb wave signal at position a are x1(t) and x2(t) respectively;

[0053] The mixed Lamb wave signal at position b is compensated using the dispersion characteristics of the first mode, and the compensation distance is e. The compensated signal is expressed as y2(t), and the formula is as follows:

[0054]

[0055] in, is represented as the dispersion compensation function of the pth mode, and Y2′(ω) is represented as the spectrum of y2′(t);

[0056] The signal matrix is ​​set to Y(t) = [y1(t), y2(t)] T .

[0057] According to the above scheme, when both the Lamb wave signal and the propagation parameters are unknown, the JADE blind source separation algorithm retrieves each mode signal from the received multi-mode overlapping Lamb wave signal matrix Y(t).

[0058] According to the above scheme, the JADE blind source separation algorithm includes:

[0059] The signal matrix is ​​whitened, and the formula is as follows:

[0060] Z(t)=VY(t);

[0061] Wherein, V represents the whitening matrix, which is obtained by eigenvalue decomposition of the covariance matrix; Z(t) represents the data matrix after whitening;

[0062] Calculate the fourth-order cumulant matrix of Z(t). The fourth-order cumulant matrix formula of Z(t) is as follows:

[0063]

[0064] Among them, C represents the fourth-order cumulant matrix; Z represents the whitened data matrix; Z * It is represented as the conjugate of Z; H is represented as the conjugate transpose; It is represented by Kronecker product; E{} represents mathematical expectation;

[0065] Perform eigenvalue decomposition on the fourth-order cumulant matrix to obtain the characteristic matrix and the corresponding eigenvector; use the Givens rotation method to jointly approximate the diagonalization of the characteristic matrix to obtain the orthogonal matrix G;

[0066] The orthogonal matrix G is used to linearly transform the multi-mode overlapping Lamb wave signal matrix Y(t) to separate the Lamb wave single-mode signal. The formula is as follows:

[0067] S(t)=G T VY(t)

[0068] Wherein, S(t) represents the separated single-mode Lamb wave signal.

[0069] According to the above solution, step S40 includes:

[0070] Analyze the dispersion characteristics of the separated Lamb wave signal, identify and determine the specific Lamb wave mode corresponding to the Lamb wave signal; perform dispersion compensation and separation based on its unique dispersion characteristics;

[0071] The separation effect is verified by comparing the separated signal with the theoretical Lamb wave mode characteristics;

[0072] Output single-mode Lamb wave signal to complete multi-mode signal separation.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] 1. The present invention combines the dispersion compensation method with the blind source separation method and applies it to the study of the mode separation problem of multi-mode Lamb wave signals;

[0075] 2. The present invention can complete the compensation and separation of signals of different modes and enhance the ability to process complex signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 A schematic flow chart of an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to the present invention;

[0077] Figure 2 A flow chart of obtaining Lamb wave dispersion characteristic parameters by using a particle swarm optimization algorithm for an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to the present invention;

[0078] Figure 3 A flowchart of the present invention for obtaining a single-mode Lamb wave signal by blind source separation of an ultrasonic guided wave mode separation method JADE based on dispersion compensation and blind source separation;

[0079] Figure 4 It is a schematic diagram of a Comsol simulation model of an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation of the present invention;

[0080] Figure 5 This is a result diagram of estimating the dispersion characteristic parameters of A0 mode and S0 mode using a particle swarm optimization algorithm in an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to the present invention;

[0081] Figure 6 This is a result diagram of separating the A0 mode and the S0 mode by an ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation of the present invention. DETAILED DESCRIPTION

[0082] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0083] Example: Figure 1-Figure 6 As shown, the present invention provides a technical solution, a method for ultrasonic guided wave mode separation based on dispersion compensation and blind source separation. The method comprises the steps of:

[0084] S10, extracting the dispersion characteristic parameters of the Lamb wave mode from the response Lamb wave of known propagation distance by particle swarm optimization algorithm;

[0085] S11. In the Lamb wave-based structural health monitoring system, a Gaussian window burst signal is used as an excitation signal. The structural health monitoring system using the Gaussian window burst signal as an excitation signal can effectively improve the ability to evaluate the structural state, help identify potential damage or defects, and realize real-time monitoring. The Gaussian window burst signal formula is as follows:

[0086]

[0087] Where g0(t) is the Gaussian window burst signal at time t; t is time; t0 is the initial displacement of the excitation; σ is the bandwidth factor; f c It is expressed as the center frequency;

[0088] S12. When the distance from the excitation source is x and attenuation is not considered, the single-mode signal is represented by the spectrum of the excitation signal and the wave number of the specific Lamb wave. This representation method helps to analyze and understand the propagation behavior of Lamb waves in structural health monitoring and provides a basis for subsequent signal processing and defect identification. The representation formula is as follows:

[0089]

[0090] Among them, g(x,t) represents the single-mode response signal at the propagation distance x of the signal at time t; G0(ω) represents the spectrum of the excitation signal; ω represents the frequency of the excitation signal; k(ω) represents the wave number of the Lamb wave, which is a nonlinear function of ω; x represents the propagation distance of the signal; j represents the imaginary unit;

[0091] S13. The wave number of Lamb wave is Taylor expanded at the center frequency to obtain various coefficients; each coefficient provides important information about the variation of wave number with frequency, which helps to understand the propagation characteristics of Lamb wave and its application in structural health monitoring;

[0092] The center frequency is denoted as ω c =2πf c ; Among them, ω c Expressed as the center angular frequency; f c It is expressed as the center frequency;

[0093] The Taylor expansion formula is as follows:

[0094] k(ω)≈k0+k1(ω-ω c )+k2(ω-ω c ) 2 ;

[0095] Among them, k0, k1 and k2 represent the coefficients of Taylor expansion;

[0096] S14. Substituting the formula in step 13 into the formula in step 12, the single-mode response signal g(x, t) can be rewritten as g(τ, t), and the formula is as follows:

[0097]

[0098] Where τ = k1x represents the arrival time; β = 1 / (2σ 2 ) is expressed as a constant; Expressed as the amplitude component of the signal; Expressed as the phase component of the signal; φ′=(2πf c -k0 / k1)τ is represented as the phase shift term;

[0099] S15. Using the particle swarm optimization algorithm, improve the accuracy and efficiency of the dispersion characteristic parameter extraction of the Lamb wave mode; design the relative position of the excitation transducer and the receiving transducer to obtain the time domain response signal of the separated wave packet; perform the parameter estimation process for each individual wave component;

[0100] By combining particle swarm optimization algorithm, reasonable design of transducer layout and effective signal processing technology, the accuracy and efficiency of Lamb wave modal dispersion characteristic parameter extraction are significantly improved.

[0101] Initialize the particle swarm and randomly generate the initial position and velocity of each particle; for each particle, calculate the corresponding fitness value F(Θ) according to the determined objective function;

[0102] When the fitness value of a particle is better than its historical best fitness value, the individual optimal position of the particle is updated; the particle with the best fitness value is found among all particles, and the global optimal position is updated;

[0103] Update speed, the formula is as follows:

[0104] v i new =w×v i old +c1×r1×(p i -x i )+c2×r2×(fx i );

[0105] Among them, v i new Expressed as the new velocity of particle i; v i old is the old velocity of particle i; w is the inertia weight; c1 is the individual learning factor, which determines the degree to which the particle learns from its individual optimal position; c2 is the social learning factor, which determines the degree to which the particle learns from the global optimal position; r1 and r2 are random numbers in the range of [0,1]; p iRepresented as the individual optimal position of particle i; x i represents the current position of particle i; f represents the global optimal position;

[0106] Update the position, the formula is as follows:

[0107] x i new =x i old +v i new ;

[0108] Among them, x i new is represented by the new position of particle i; x i old Represented as the old position of particle i;

[0109] Determine whether the termination condition is met, wherein the termination condition includes reaching the maximum number of iterations or the fitness value of the global optimal solution reaching the standard; when the termination condition is met, the process ends, otherwise the fitness value of each particle is repeatedly calculated.

[0110] The observed data is (t i ,y i ), the model is g(Θ,t), where t i Represented as the observed value at the i-th time point; y i Represented as at time point t i The corresponding observation results at ;

[0111] And determine the objective function as:

[0112]

[0113] Where N represents the number of observed data points; Θ represents the independent characteristic parameter;

[0114] The independent characteristic parameters are estimated from the corresponding signal g(x0,t) with a propagation distance of x0; the independent characteristic parameters include the wave number, center frequency and attenuation constant of the Lamb wave.

[0115] S20, performing single-mode dispersion compensation on the two measured signals according to the extracted parameters, so that the two signals return to the same distance;

[0116] S21. Perform dispersion compensation on the received Lamb wave signal according to the extracted parameters. The dispersion compensation is the inverse process of dispersion transformation, and the formula is as follows:

[0117]

[0118] Among them, H -1It is represented as the dispersion compensation function; H(ω) is represented as the dispersion transformation; d is represented as the compensation distance; k(ω) is represented as the wave number of the Lamb wave, which is a nonlinear function of ω;

[0119] S22. After dispersion compensation, the dispersion-compensated Lamb wave signal is obtained to eliminate the dispersion effect caused by different propagation distances. The formula is as follows:

[0120]

[0121] Where y(t) represents the Lamb wave signal after dispersion compensation; G(ω) represents the spectrum of the original signal;

[0122] By applying dispersion compensation, the dispersion effect caused by different propagation distances can be effectively eliminated, thereby improving the clarity and accuracy of the signal.

[0123] S30, processing Lamb wave signals with the same distance and different superposition conditions by using the JADE blind source separation method;

[0124] When the received mixed Lamb wave signal consists of dual-mode signals, and the dual-mode signals have different dispersion characteristics;

[0125] The mixed Lamb wave signals y1(t) and y2′(t) at positions a and b along the propagation path are measured, where the distance between a and b is e; at the same time, the two single-mode signals of the mixed Lamb wave signal at position a are x1(t) and x2(t) respectively;

[0126] The mixed Lamb wave signal at position b is compensated using the dispersion characteristics of the first mode, and the compensation distance is e. The compensated signal is expressed as y2(t), and the formula is as follows:

[0127]

[0128] in, is represented as the dispersion compensation function of the pth mode, and Y2′(ω) is represented as the spectrum of y2′(t);

[0129] The signal matrix is ​​set to Y(t) = [y1(t), y2(t)] T .

[0130] When both the Lamb wave signal and the propagation parameters are unknown, the JADE blind source separation algorithm retrieves each mode signal from the received multi-mode overlapping Lamb wave signal matrix Y(t).

[0131] The JADE blind source separation algorithm includes: whitening the signal matrix, the formula is as follows:

[0132] Z(t)=VY(t);

[0133] Wherein, V represents the whitening matrix, which is obtained by eigenvalue decomposition of the covariance matrix; Z(t) represents the data matrix after whitening;

[0134] Calculate the fourth-order cumulant matrix of Z(t). The fourth-order cumulant matrix formula of Z(t) is as follows:

[0135]

[0136] Among them, C represents the fourth-order cumulant matrix; Z represents the whitened data matrix; Z * It is represented as the conjugate of Z; H is represented as the conjugate transpose; It is represented by Kronecker product; E{} represents mathematical expectation;

[0137] Perform eigenvalue decomposition on the fourth-order cumulant matrix to obtain the characteristic matrix and the corresponding eigenvector; use the Givens rotation method to jointly approximate the diagonalization of the characteristic matrix to obtain the orthogonal matrix G;

[0138] The orthogonal matrix G is used to linearly transform the multi-mode overlapping Lamb wave signal matrix Y(t) to separate the Lamb wave single-mode signal. The formula is as follows:

[0139] S(t)=G T VY(t)

[0140] Wherein, S(t) represents the separated single-mode Lamb wave signal.

[0141] S40, sequentially compensating and separating different modes to obtain a single-mode signal, thereby achieving multi-mode signal separation.

[0142] Analyze the dispersion characteristics of the separated Lamb wave signal, identify and determine the specific Lamb wave mode corresponding to the Lamb wave signal; perform dispersion compensation and separation based on its unique dispersion characteristics;

[0143] The separation effect is verified by comparing the separated signal with the theoretical Lamb wave mode characteristics;

[0144] Output single-mode Lamb wave signal to complete multi-mode signal separation.

[0145] like Figure 4 As shown, a finite element (FE) model of the composite structure is established in COMSOL to verify the feasibility of the method of this embodiment. Each layer of the composite laminate is connected together using a two-dimensional plane strain model, and each layer is modeled separately.

[0146] like Figure 1-Figure 6As shown, the present invention provides another technical solution, which uses a method based on dispersion compensation and blind source separation on a carbon fiber composite material plate to monitor potential structural damage. The carbon fiber composite material plate has orthogonal anisotropy and its ply direction is [0°\90°] 4s ;

[0147] Its performance parameters are as follows:

[0148] Density: ρ = 1630.4 kg / m 3 ,

[0149] Main elastic constants:

[0150] C 11 =54.55GPa; C 12 =7.01GPa; C 13 =6.38GPa; C 22 =52.16GPa; C 23 =6.31GPa; C 33 =9.22GPa; C 44 =3.07GPa; C 55 =2.98GPa;

[0151] Laying direction: [0 / 90 / 0 / 90]s, indicating four layers stacked, with a 90-degree rotation between every two layers;

[0152] Piezoelectric Sensors:

[0153] Size: 5mm long, 0.5mm thick;

[0154] Material: PZT-5H;

[0155] The piezoelectric element is connected to the composite laminate via a linear elastic thin layer condition;

[0156] Numerical model settings:

[0157] Node spacing: ensure that there are at least 10 nodes on the minimum wavelength;

[0158] Element growth rate: 1.25;

[0159] Time step resolution: The highest frequency is set to at least 20 points per cycle;

[0160] The dispersion characteristic parameters of Lamb wave modes are extracted from the response Lamb wave with known propagation distance through particle swarm optimization algorithm;

[0161] In the Lamb wave-based structural health monitoring system, a Gaussian window burst signal is used as an excitation signal. The structural health monitoring system using a Gaussian window burst signal as an excitation signal can effectively improve the ability to evaluate the structural state, help identify potential damage or defects, and realize real-time monitoring. The Gaussian window burst signal formula is as follows:

[0162]

[0163] Where g0(t) is the Gaussian window burst signal at time t; t is time; t0 is the initial displacement of the excitation; σ is the bandwidth factor; f c is represented by the center frequency; the center frequency is represented by ω c =2πf c ; Among them, ω c Expressed as the center angular frequency; f c It is expressed as the center frequency;

[0164] Initial displacement of excitation t0 = 0s; bandwidth factor σ = 0.1ms; center frequency f c =100kHz;

[0165] When the distance from the excitation source is x and attenuation is not considered, the single-mode signal is represented by the spectrum of the excitation signal and the wave number of the specific Lamb wave. This representation method helps to analyze and understand the propagation behavior of Lamb waves in structural health monitoring and provides a basis for subsequent signal processing and defect identification. The expression formula is as follows:

[0166]

[0167] Among them, g(x,t) represents the single-mode response signal at the propagation distance x of the signal at time t; G0(ω) represents the spectrum of the excitation signal; ω represents the frequency of the excitation signal; k(ω) represents the wave number of the Lamb wave, which is a nonlinear function of ω; x represents the propagation distance of the signal; j represents the imaginary unit;

[0168] The wave number of Lamb wave is Taylor expanded at the center frequency to obtain various coefficients; each coefficient provides important information about the variation of wave number with frequency, which helps to understand the propagation characteristics of Lamb wave and its application in structural health monitoring;

[0169] The Taylor expansion formula is as follows:

[0170] k(ω)≈k0+k1(ω-ω c )+k2(ω-ω c ) 2 ;

[0171] Among them, k0, k1 and k2 represent the coefficients of Taylor expansion;

[0172] Rewrite the single-mode response signal g(x,t) as g(τ,t), the formula is as follows:

[0173]

[0174] Where τ = k1x represents the arrival time; β = 1 / (2σ 2 ) is expressed as a constant; Expressed as the amplitude component of the signal; Expressed as the phase component of the signal; φ′=(2πf c -k0 / k1)τ is represented as the phase shift term;

[0175] The particle swarm optimization algorithm is used to improve the accuracy and efficiency of the dispersion characteristic parameter extraction of the Lamb wave mode; the relative positions of the excitation transducer and the receiving transducer are designed to obtain the time domain response signal of the separated wave packet; and the parameter estimation process is performed for each individual wave component;

[0176] By combining particle swarm optimization algorithm, reasonable design of transducer layout and effective signal processing technology, the accuracy and efficiency of Lamb wave modal dispersion characteristic parameter extraction are significantly improved. Figure 4 As shown, the waveguide signal received by the sensor 3 is used for the particle swarm optimization algorithm to obtain the dispersion characteristic parameters of the Lamb wave mode;

[0177] The particle swarm optimization algorithm includes: using the particle swarm optimization algorithm to extract the dispersion characteristic parameters k0, k1 and k2 from the response Lamb wave with a known propagation distance x0 = 1m; Figure 5 The figure shows the parameter results estimated by the particle swarm optimization algorithm, including the dispersion characteristic parameters k0, k1 and k2;

[0178] Initialize the particle swarm and randomly generate the initial position and velocity of each particle; for each particle, calculate the corresponding fitness value F(Θ) according to the determined objective function;

[0179] When the fitness value of a particle is better than its historical best fitness value, the individual optimal position of the particle is updated; the particle with the best fitness value is found among all particles, and the global optimal position is updated;

[0180] Update speed, the formula is as follows:

[0181] v i new =w×v i old +c1×r1×(p i -x i )+c2×r2×(fx i );

[0182] Among them, v inew Expressed as the new velocity of particle i; v i old is the old velocity of particle i; w is the inertia weight; c1 is the individual learning factor, which determines the degree to which the particle learns from its individual optimal position; c2 is the social learning factor, which determines the degree to which the particle learns from the global optimal position; r1 and r2 are random numbers in the range of [0,1]; p i Represented as the individual optimal position of particle i; x i represents the current position of particle i; f represents the global optimal position;

[0183] Update the position, the formula is as follows:

[0184] x i new =x i old +v i new ;

[0185] Among them, x i new is represented by the new position of particle i; x i old Represented as the old position of particle i;

[0186] Determine whether the termination condition is met, wherein the termination condition includes reaching the maximum number of iterations or the fitness value of the global optimal solution reaching the standard; when the termination condition is met, the process ends, otherwise the fitness value of each particle is repeatedly calculated.

[0187] The parameter estimation results obtained by particle swarm optimization algorithm are: k0 = 1.2 rad / m; k1 = 0.005 rad / m; k2 = -0.00002 rad / m;

[0188] The observed data is (t i ,y i ), the model is g(Θ,t), where t i Represented as the observed value at the i-th time point; y i Represented as at time point t i The corresponding observation results at ;

[0189] And determine the objective function as:

[0190]

[0191] Where N represents the number of observed data points; Θ represents the independent characteristic parameter;

[0192] The independent characteristic parameters are estimated from the corresponding signal g(x0,t) with a propagation distance of x0; the independent characteristic parameters include the wave number, center frequency and attenuation constant of the Lamb wave.

[0193] The single-mode dispersion compensation is performed on the two measured signals according to the extracted parameters, so that the two signals return to the same distance;

[0194] The received Lamb wave signal is subjected to dispersion compensation according to the extracted parameters. The dispersion compensation is the inverse process of dispersion transformation, and the formula is as follows:

[0195]

[0196] Among them, H -1 It is represented as the dispersion compensation function; H(ω) is represented as the dispersion transformation; d is represented as the compensation distance; k(ω) is represented as the wave number of the Lamb wave, which is a nonlinear function of ω;

[0197] After dispersion compensation, the dispersion-compensated Lamb wave signal is obtained, eliminating the dispersion effect caused by different propagation distances. The formula is as follows:

[0198]

[0199] Where y(t) represents the Lamb wave signal after dispersion compensation; G(ω) represents the spectrum of the original signal;

[0200] By applying dispersion compensation, the dispersion effect caused by different propagation distances can be effectively eliminated, thereby improving the clarity and accuracy of the signal.

[0201] Lamb wave signals with the same distance but different superposition situations are processed by JADE blind source separation method;

[0202] When the received mixed Lamb wave signal consists of dual-mode signals, and the dual-mode signals have different dispersion characteristics;

[0203] The mixed Lamb wave signals y1(t) and y2′(t) at positions a and b along the propagation path are measured, where the distance between a and b is e; at the same time, the two single-mode signals of the mixed Lamb wave signal at position a are x1(t) and x2(t) respectively;

[0204] The mixed Lamb wave signal at position b is compensated using the dispersion characteristics of the first mode, and the compensation distance is e. The compensated signal is expressed as y2(t), and the formula is as follows:

[0205]

[0206] in, is represented as the dispersion compensation function of the pth mode, and Y2′(ω) is represented as the spectrum of y2′(t);

[0207] The signal matrix is ​​set to Y(t) = [y1(t), y2(t)] T .

[0208] When both the Lamb wave signal and propagation parameters are unknown, the JADE blind source separation algorithm retrieves each mode signal from the received multi-mode overlapping Lamb wave signal matrix Y(t).

[0209] The JADE blind source separation algorithm includes: whitening the signal matrix, the formula is as follows:

[0210] Z(t)=VY(t);

[0211] Wherein, V represents the whitening matrix, which is obtained by eigenvalue decomposition of the covariance matrix; Z(t) represents the data matrix after whitening;

[0212] Calculate the fourth-order cumulant matrix of Z(t). The fourth-order cumulant matrix formula of Z(t) is as follows:

[0213]

[0214] Among them, C represents the fourth-order cumulant matrix; Z represents the whitened data matrix; Z * It is represented as the conjugate of Z; H is represented as the conjugate transpose; It is represented by Kronecker product; E{} represents mathematical expectation;

[0215] Perform eigenvalue decomposition on the fourth-order cumulant matrix to obtain the characteristic matrix and the corresponding eigenvector; use the Givens rotation method to jointly approximate the diagonalization of the characteristic matrix to obtain the orthogonal matrix G;

[0216] The orthogonal matrix G is used to linearly transform the multi-mode overlapping Lamb wave signal matrix Y(t) to separate the Lamb wave single-mode signal. The formula is as follows:

[0217] S(t)=G T VY(t)

[0218] Wherein, S(t) represents the separated single-mode Lamb wave signal.

[0219] Sequential compensation and separation of different modes, such as Figure 6 As shown, the separated A0 mode and S0 mode obtain a single-mode signal, thereby realizing multi-mode signal separation.

[0220] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. An ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation, characterized in that: The method comprises the steps of: S10, extracting the dispersion characteristic parameters of the Lamb wave mode from the response Lamb wave of known propagation distance by particle swarm optimization algorithm; S20, performing single-mode dispersion compensation on the two measured signals according to the extracted parameters, so that the two signals return to the same distance; S30, processing Lamb wave signals with the same distance and different superposition conditions by using the JADE blind source separation method; S40, sequentially compensating and separating different modes to obtain a single-mode signal, thereby achieving multi-mode signal separation.

2. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 1 is characterized in that: Step S10 includes: S11. In the Lamb wave-based structural health monitoring system, a Gaussian window burst signal is used as the excitation signal, and the formula is as follows: Where g0(t) is the Gaussian window burst signal at time t; t is time; t0 is the initial displacement of the excitation; σ is the bandwidth factor; f c It is expressed as the center frequency; S12. When the distance from the excitation source is x and attenuation is not considered, the single-mode signal is represented by the spectrum of the excitation signal and the wave number of the specific Lamb wave, and the formula is as follows: Among them, g(x,t) represents the single-mode response signal at the propagation distance x of the signal at time t; G0(ω) represents the spectrum of the excitation signal; ω represents the frequency of the excitation signal; k(ω) represents the wave number of the Lamb wave, which is a nonlinear function of ω; x represents the propagation distance of the signal; j represents the imaginary unit; S13, the wave number of Lamb wave is Taylor expanded at the center frequency to obtain various coefficients; The center frequency is denoted as ω c =2πf c ; Among them, ω c Expressed as the center angular frequency; f c It is expressed as the center frequency; The Taylor expansion formula is as follows: k(ω)≈k0+k1(ω-ω c )+k2(ω-ω c ) 2 ; Among them, k0, k1 and k2 represent the coefficients of Taylor expansion; S14. Substituting the formula in step 13 into the formula in step 12, the single-mode response signal g(x, t) can be rewritten as g(τ, t), and the formula is as follows: Wherein, T = k1x represents the arrival time; β = 1 / (2σ2) represents a constant; Expressed as the amplitude component of the signal; Expressed as the phase component of the signal; φ′=(2πf c -k0 / k1)τ is represented as the phase shift term; S15. Use the particle swarm optimization algorithm to improve the accuracy and efficiency of extracting the dispersion characteristic parameters of the Lamb wave mode; design the relative positions of the excitation transducer and the receiving transducer to obtain the time domain response signal of the separated wave packet; and perform the parameter estimation process for each individual wave component.

3. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 2 is characterized in that: The observed data is (t i ,y i ), the model is g(Θ, t), where t i Represented as the observed value at the i-th time point; y i Represented as at time point t i The corresponding observation results at ; And determine the objective function as: Where N represents the number of observed data points; Θ represents the independent characteristic parameter; The independent characteristic parameters are estimated from the corresponding signal g(x0,t) with a propagation distance of x0; the independent characteristic parameters include the wave number, center frequency and attenuation constant of the Lamb wave.

4. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 3 is characterized in that: In step S15, the particle swarm optimization algorithm includes: Initialize the particle swarm and randomly generate the initial position and velocity of each particle; for each particle, calculate the corresponding fitness value F(Θ) according to the determined objective function; When the fitness value of a particle is better than its historical best fitness value, the individual optimal position of the particle is updated; the particle with the best fitness value is found among all particles, and the global optimal position is updated; Update speed, the formula is as follows: v i new =w×v i old +c1×r1×(p i -x i )+c2×r2×(f-x i ); Among them, v i new Expressed as the new velocity of particle i; v i old is the old velocity of particle i; w is the inertia weight; c1 is the individual learning factor, which determines the degree to which the particle learns from its individual optimal position; c2 is the social learning factor, which determines the degree to which the particle learns from the global optimal position; r1 and r2 are random numbers in the range of [0,1]; p i Represented as the individual optimal position of particle i; x i represents the current position of particle i; f represents the global optimal position; Update the position, the formula is as follows: x i new =x i old +v i new ; Among them, x i new is represented by the new position of particle i; x i old Represented as the old position of particle i; Determine whether the termination condition is met, wherein the termination condition includes reaching the maximum number of iterations or the fitness value of the global optimal solution reaching the standard; when the termination condition is met, the process ends, otherwise the fitness value of each particle is repeatedly calculated.

5. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 1 is characterized in that: Step S20 includes: S21. Perform dispersion compensation on the received Lamb wave signal according to the extracted parameters. The dispersion compensation is the inverse process of dispersion transformation, and the formula is as follows: Among them, H -1 It is represented as the dispersion compensation function; H(ω) is represented as the dispersion transformation; d is represented as the compensation distance; k(ω) is represented as the wave number of the Lamb wave, which is a nonlinear function of ω; S22. After dispersion compensation, the dispersion-compensated Lamb wave signal is obtained to eliminate the dispersion effect caused by different propagation distances. The formula is as follows: Wherein, y(t) represents the Lamb wave signal after dispersion compensation; G(ω) represents the spectrum of the original signal.

6. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 1, characterized in that: Step S30 includes: When the received mixed Lamb wave signal consists of dual-mode signals, and the dual-mode signals have different dispersion characteristics; The mixed Lamb wave signals y1(t) and y2′(t) at positions a and b along the propagation path are measured, where the distance between a and b is e; at the same time, the two single-mode signals of the mixed Lamb wave signal at position a are x1(t) and x2(t) respectively; The mixed Lamb wave signal at position b is compensated using the dispersion characteristics of the first mode, and the compensation distance is e. The compensated signal is expressed as y2(t), and the formula is as follows: in, is represented as the dispersion compensation function of the pth mode, and Y2′(ω) is represented as the spectrum of y2′(t); The signal matrix is ​​set to Y(t) = [y1(t), y2(t)] T .

7. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 6 is characterized in that: When both the Lamb wave signal and the propagation parameters are unknown, the JADE blind source separation algorithm retrieves each mode signal from the received multi-mode overlapping Lamb wave signal matrix Y(t).

8. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 7 is characterized in that: The JADE blind source separation algorithm includes: The signal matrix is ​​whitened, and the formula is as follows: Z(t)=VY(t); Wherein, V represents the whitening matrix, which is obtained by eigenvalue decomposition of the covariance matrix; Z(t) represents the data matrix after whitening; Calculate the fourth-order cumulant matrix of Z(t). The fourth-order cumulant matrix formula of Z(t) is as follows: Among them, C represents the fourth-order cumulant matrix; Z represents the whitened data matrix; Z * It is represented as the conjugate of Z; H is represented as the conjugate transpose; It is represented by Kronecker product; E{} represents mathematical expectation; Perform eigenvalue decomposition on the fourth-order cumulant matrix to obtain the characteristic matrix and the corresponding eigenvector; use the Givens rotation method to jointly approximate the diagonalization of the characteristic matrix to obtain the orthogonal matrix G; The orthogonal matrix G is used to linearly transform the multi-mode overlapping Lamb wave signal matrix Y(t) to separate the Lamb wave single-mode signal. The formula is as follows: S(t)=G T VY(t) Wherein, S(t) represents the separated single-mode Lamb wave signal.

9. The ultrasonic guided wave mode separation method based on dispersion compensation and blind source separation according to claim 1, characterized in that: Step S40 includes: Analyze the dispersion characteristics of the separated Lamb wave signal, identify and determine the specific Lamb wave mode corresponding to the Lamb wave signal; perform dispersion compensation and separation based on its unique dispersion characteristics; The separation effect is verified by comparing the separated signal with the theoretical Lamb wave mode characteristics; Output single-mode Lamb wave signal to complete multi-mode signal separation.

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