A method for inversion of ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning

Abstract

A method for inverting the dispersion curve of ultrasonic guided waves based on complex sparse Bayesian learning relates to the technical field of ultrasonic non-destructive testing. The present invention is to solve the problem that when ultrasonic guided waves propagate in a plate-like thin-walled structure, the dispersion characteristics generate wave packet distortion, which makes it difficult to accurately extract damage information in the guided wave signal. The present invention converts the guided wave frequency response model into a sparse linear model, and converts the complex sparse linear model into a real linear model and uses the same hyperparameters to control the real and imaginary parts of the sparse vector to ensure the sparse consistency of the real and imaginary parts, thereby improving the sparse Bayesian learning effect. When the present invention performs complex sparse Bayesian learning, the Laplace prior is used for the unknown weight coefficient, which promotes the sparsity of the wave number weight vector and improves the accuracy of guided wave wave number identification. Based on the identification of dispersion curves by randomly arranged sensors, the problem of wave packet distortion caused by dispersion characteristics when ultrasonic guided waves propagate in thin-walled structures is overcome.

Description

Technical Field

[0001] The invention belongs to the technical field of ultrasonic nondestructive testing, and in particular relates to the inversion of ultrasonic guided wave dispersion curves. Background Art

[0002] Ultrasonic guided waves are widely used to detect thin-walled structures such as flat plates, pipelines, oil tanks, aircraft, and fans due to their advantages such as sensitivity to tiny damage, reduced energy attenuation, and ability to detect a wide range. When ultrasonic waves propagate in thin plates, transverse waves and longitudinal waves are reflected and converted multiple times by the plate surface, forming a new wave packet that propagates forward stably. The wave packet has multiple modes. The phase velocity and group velocity of these modes will change with frequency, that is, dispersion will occur. Therefore, ultrasonic guided waves with a certain bandwidth will deform during propagation due to different propagation speeds, and the waveform distortion will become more and more serious as the propagation distance increases. Although the ultrasonic guided waves used in general detection are signals with a narrow frequency range, some modes of the guided waves will also produce obvious waveform distortion during propagation, making it difficult to accurately extract damage information from the guided wave signal. If the dispersion curve of the thin plate to be detected is estimated before damage identification, the ultrasonic guided wave signal can be analyzed based on the dispersion curve, thereby improving the effectiveness and reliability of ultrasonic guided wave damage detection. Summary of the invention

[0003] The present invention aims to solve the problem that when ultrasonic guided waves propagate in a plate-like thin-walled structure, it is difficult to accurately extract damage information in the guided wave signal due to wave packet distortion caused by dispersion characteristics. A method for inverting the dispersion curve of ultrasonic guided waves based on complex sparse Bayesian learning is provided.

[0004] A method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning comprises the following steps:

[0005] Step 1: Use n ultrasonic sensors to transmit signals to each other, where when one ultrasonic sensor is used as the excitation end of the ultrasonic guided wave signal, the remaining n-1 ultrasonic sensors are used as the receiving ends of the ultrasonic guided wave signal, and the total number of propagation paths of the ultrasonic guided wave signal and the total number of effective ultrasonic guided wave signals are both N, N = n(n-1) / 2;

[0006] Step 2: Calculate the frequency response signal of each propagation path at each frequency using the waveguide frequency response model. The waveguide frequency response model is:

[0007]

[0008] Among them, y(r i ,ω) is the frequency response signal of the ith propagation path at frequency ω, r i is the propagation distance of the i-th propagation path, i=1,2,...,N, L is y(ri ,ω), l=1,2,...,L,k l is the wave number of the lth guided wave mode, c l (ω) is the response coefficient of the lth guided wave mode;

[0009] Step 3: Average the frequency response signals of all propagation paths at each frequency to obtain the average response amplitude at each frequency, collect the waveguide response contained in the ultrasonic guided wave signal at the frequency corresponding to the average response amplitude greater than the noise energy, and use the frequencies corresponding to all waveguide responses to form the main energy distribution frequency set [ω1,ω2,...,ω F ], F is the total number of elements in the main energy distribution frequency set;

[0010] Step 4: Establish the fth element ω in the main energy distribution frequency set f The frequency response signal vector Y(ω) of all propagation paths under f ), f=1,2,...,F, the Y(ω f )=[y1(r1,ωf),y2(r2,ω f ),...,y N (r N ,ω f )], where y N (r N ,ω f ) is the frequency ω f The frequency response signal of the Nth propagation path;

[0011] Step 5: Discretize the wavenumber range of all frequency response signals in the estimated main energy distribution frequency set, so that the wavenumber density in the discretized wavenumber range is much larger than the wavenumber density of each frequency response signal in the main energy distribution frequency set. Then, establish the complex overcomplete dictionary matrix D about the discretized wavenumber according to the waveguide frequency response model:

[0012]

[0013] Among them, k M is the Mth wave number after discretization, j is the imaginary unit;

[0014] Step 6: Use the complex overcomplete dictionary matrix D to calculate the frequency response signal vector Y(ω f ) is sparsely represented and decomposed to obtain D and Y(ω f ) real matrix;

[0015] Step 7: Perform bi-norm normalization on each column of the real number matrix of the complex overcomplete dictionary matrix D to obtain the normalized real number classic primitive corresponding to each column, and then form a primitive matrix with the normalized real number classic primitives corresponding to all columns;

[0016] Step 8: Use the complex sparse Bayesian learning algorithm to solve the posterior probability distribution of the weight coefficient vector under the same sparse constraints for the real and imaginary parts, so as to obtain the frequency ω f The wave number of the guided wave mode contained in the lower frequency response signal;

[0017] Step 9: Determine whether f≥F, if yes, execute step 10, otherwise set f=f+1, and then return to step 4;

[0018] Step 10: Draw a discretized ultrasonic guided wave dispersion curve using the wave number of the frequency response signal at F frequencies in the main energy distribution frequency set.

[0019] Furthermore, in the above step 3, the frequency response signals of all propagation paths at each frequency are averaged using the following formula:

[0020]

[0021] Where y(ω) is the average response amplitude at frequency ω, y N (r N ,ω) is the frequency response signal of the Nth propagation path at frequency ω, |y N (r N ,ω)| is y N (r N ,ω) amplitude.

[0022] Furthermore, in the above step 4, Y(ω f ) is in the form of:

[0023]

[0024] Among them, [c1(ω f ),c2(ω f ),...,c R (ω f )] is the response coefficient vector, R is the frequency ω f The total number of waves in the frequency response signal.

[0025] Further, the above step 6 obtains Y(ω f ) is as follows:

[0026] After sparse representation, Y(ω f ) and the complex overcomplete dictionary matrix D have the following relationship:

[0027] Y(ω f )=Dc(ω f ) Formula 1,

[0028] Among them, c(ω f ) is the weight coefficient vector after sparse representation,

[0029] Y(ω f ) and the real and imaginary parts of D are disassembled, and then the disassembled real and imaginary parts are combined into a matrix form, so that Formula 1 is rewritten as:

[0030]

[0031] Among them, Re(Y) and Im(Y) are Y(ω f ), Re(D) and Im(D) are the real and imaginary parts of D, Re(c) and Im(c) are the real and imaginary parts of c(ω f ),

[0032] Extract the real matrix of each matrix in formula 2 to obtain:

[0033] X=Bw,

[0034] Where X is Y(ω f ), B is the real matrix of D, w is the real matrix of c(ω f ) is a real matrix.

[0035] Furthermore, the method for obtaining the primitive matrix in the above step 7 is:

[0036] Use the following formula to perform bi-norm normalization on each column of the real matrix B of D:

[0037]

[0038] Among them, B ε is the normalized real number primitive in the εth column of B, b ε is the εth column in B, ε=1,2,...,2M,

[0039] Create a primitive matrix using normalized real-valued canonical primitives corresponding to all columns:

[0040] Φ=[B1,B2,...,B 2M ],

[0041] Convert X=Bw to X=Φw.

[0042] Furthermore, in the above step eight, the specific method of using the complex sparse Bayesian learning algorithm to solve the posterior probability distribution of the weight coefficient vector under the same sparse constraint conditions for the real part and the imaginary part is:

[0043] Weight coefficient vector c(ω f The prior distribution p(w|σ) of the real matrix w of ) is:

[0044] p(w|σ)=N(w|0,σ) Formula 3,

[0045] Where σ is the covariance matrix of the multivariate Gaussian distribution, σ=diag(σ1,σ2,...,σ M ,σ1,σ2,...,σ M ),

[0046] According to the principle of maximum information entropy, the Gaussian likelihood function is used to characterize the likelihood between Φw and X:

[0047] p(X|w,β)=N(X|Φw,β -1 I) Formula 4,

[0048] Among them, β is the error accuracy parameter of all weight coefficients, I is the unit matrix of 2N×2N,

[0049] Formula 3 and Formula 4 are used to obtain the posterior probability distribution of the weight coefficient vector under the same sparse constraints for the real and imaginary parts:

[0050]

[0051] in, is the optimal estimation result of σ under the Gamma super prior, μ is the posterior mean vector, ψ is the covariance matrix, μ = βψΦ T X,

[0052] Furthermore, the wave number corresponding to the non-zero term in the posterior mean vector μ is taken as the frequency ω f The wave number of the guided wave mode contained in the frequency response signal below.

[0053] The beneficial effects of the present invention are:

[0054] The present invention provides an ultrasonic guided wave dispersion curve inversion method based on complex sparse Bayesian learning, according to which the guided wave frequency response model is converted into a sparse linear model, and the complex sparse linear model is converted into a real linear model and the same hyperparameter is used to control the real and imaginary parts of the sparse vector, so as to ensure the sparse consistency of the real and imaginary parts, thereby improving the sparse Bayesian learning effect. The present invention adopts Laplace prior to the unknown weight coefficient when performing complex sparse Bayesian learning, promotes the sparsity of the wave number weight vector, and improves the accuracy of guided wave wave number identification. Based on the identification of dispersion curves by randomly arranged sensors, the problem of wave packet distortion caused by dispersion characteristics when ultrasonic guided waves propagate in thin-walled structures is overcome. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The figure is a schematic diagram of the inversion of the dispersion curve of the ultrasonic guided wave signal involved in the present invention, wherein 1 is a signal generator, 2 is an amplifier, 3 is an oscilloscope, 4 is a computer, 5 is a thin plate to be detected, and 6 is a sensor;

[0056] Figure 2 are the excitation signals and their spectrum diagrams, where (a) is the time domain excitation signal; (b) is the spectrum obtained by Fourier transform of the time domain signal;

[0057] Figure 3 The average spectrum obtained by Fourier transforming multiple time domain signals;

[0058] Figure 4 It is a discrete dispersion curve diagram identified by using the ultrasonic guided wave dispersion curve inversion method of the present invention. DETAILED DESCRIPTION

[0059] The following will be combined with the accompanying 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, rather than 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 belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0060] The dispersion curve is a nonlinear equation solved based on the constitutive equation, the governing equation and the geometric equation, and the nonlinear equation has multiple solutions, corresponding to multiple ultrasonic guided wave modes. In recent years, with the rapid development of computer technology, the nonlinear problem of the dispersion curve can be solved by sparse Bayesian learning (SBL). First, the statically determinate nonlinear problem is converted into an underdetermined linear sparse problem according to the frequency response signal, and then the SBL algorithm is used to find the optimal solution of the unknown parameters in the linear model, so that the model output is as close to the actual data as possible. The specific process is that the SBL algorithm assumes the prior distribution of the unknown parameters in the model based on past experience, and then uses the Gaussian likelihood function to simulate the prediction error, and finally uses the Bayesian theorem to obtain the posterior probability distribution of the unknown model parameters. Compared with the deterministic method, SBL does not require the manual selection of regularization parameters, avoiding the deviation caused by inaccurate parameter selection. In addition, it can make full use of data information and quantify the uncertainty of the posterior recognition results. Since the frequency response signal of ultrasonic guided waves is a complex number, the real and imaginary parts of the complex response have the same sparsity, so the complex sparse Bayesian learning (CSBL) is used to invert the dispersion curve. The algorithm can use the same hyperparameters to control the real and imaginary parts, thereby ensuring the sparse consistency and improving the accuracy of the recognition results, providing key information for structural damage recognition based on ultrasonic guided waves. Specifically, this embodiment is to apply the present invention to the inversion of the guided wave dispersion curve in the aluminum plate, Figure 2 The excitation signal used in the experiment is a broadband Chirp signal with a duration of 8 μs, a starting frequency of 0 Hz and a bandwidth of 2 MHz.

[0061] The ultrasonic guided wave dispersion curve inversion method based on complex sparse Bayesian learning described in this embodiment includes the following steps:

[0062] Step 1: If Figure 1 As shown, n ultrasonic sensors are used to transmit signals to each other, and specifically, in this embodiment, n=15. When one ultrasonic sensor is used as the excitation end of the ultrasonic guided wave signal, the remaining 14 ultrasonic sensors are used as the receiving ends of the ultrasonic guided wave signal, so the 15 ultrasonic sensors can transmit n(n-1)=210 ultrasonic guided wave signals to each other, and these ultrasonic guided wave signals are transmitted through N=n(n-1) / 2=105 propagation paths and obtain 105 effective ultrasonic guided wave signals.

[0063] Step 2: Calculate the frequency response signal of each propagation path at each frequency using the waveguide frequency response model. The waveguide frequency response model is:

[0064]

[0065] Among them, y(r i ,ω) is the frequency response signal of the ith propagation path at frequency ω, r iis the propagation distance of the i-th propagation path, i=1,2,...,N, L is y(r i ,ω), l=1,2,...,L,k l is the wave number of the lth guided wave mode, c l (ω) is the response coefficient of the lth guided wave mode.

[0066] Step 3: Use the following formula to average the frequency response signals of all propagation paths at each frequency to obtain the average response amplitude at each frequency:

[0067]

[0068] Where y(ω) is the average response amplitude at frequency ω, y N (r N ,ω) is the frequency response signal of the Nth propagation path at frequency ω, |y N (r N ,ω)| is y N (r N ,ω) amplitude.

[0069] The larger the average response amplitude at a certain frequency, the greater the signal energy at that frequency. When the average response amplitude is greater than the noise signal energy, it is considered that the ultrasonic guided wave signal contains a guided wave response. At this time, the average response amplitude greater than the noise energy is collected to obtain the guided wave response contained in the ultrasonic guided wave signal at the frequency corresponding to these average response amplitudes. The frequencies corresponding to all guided wave responses are used to form the main energy distribution frequency set of the ultrasonic guided wave signal [ω1,ω2,...,ω F ], where F is the total number of elements in the main energy distribution frequency set. Figure 3 As shown, the frequency range of the main energy distribution is [0,400] kHz.

[0070] Step 4: Establish the fth element ω in the main energy distribution frequency set f The frequency response signal vector Y(ω) of all propagation paths under f ), f=1,2,...,F. f ) is expressed in the following form:

[0071]

[0072] Among them, y N (r N ,ω f ) is the frequency ω f The frequency response signal of the Nth propagation path is:

[0073] [c1(ω f ),c2(ωf ),...,c R (ω f )] is the response coefficient vector,

[0074] R is the frequency ω f The total number of waves in the frequency response signal.

[0075] Step 5: Discretize the wavenumber range of all frequency response signals in the estimated main energy distribution frequency set, so that the wavenumber density in the discretized wavenumber range is much larger than the wavenumber density of each frequency response signal in the main energy distribution frequency set, and obtain the wavenumber vector k = [k1, k2, ..., k M ].

[0076] In this embodiment, [0.5, 2000] m -1 Discretized to: [0.5, 1, 1.5, 2, 2.5, …, 2000] m -1 .

[0077] Then, the complex over-complete dictionary matrix D of the discretized wave number is established according to the waveguide frequency response model:

[0078]

[0079] Among them, k M is the M=4000th wave number after discretization, and j is an imaginary unit.

[0080] Step 6: Since M>>R, Y(ω f ) is padded with 0 if the number of elements less than D is less than D, that is, the complex overcomplete dictionary matrix D is used for the frequency response signal vector Y(ω f ) is sparsely represented. After sparse representation, Y(ω f ) and the complex overcomplete dictionary matrix D have the following relationship:

[0081] Y(ω f )=Dc(ω f ) Formula 1,

[0082] Among them, c(ω f ) is the weight coefficient vector after sparse representation.

[0083] The real and imaginary parts of the complex frequency response signal have the same consistency, so the same hyperparameters can be used to control the real and imaginary parts, and the above complex linear model can be modified into a real linear model. That is: change Y(ω f ) and the real and imaginary parts of D are disassembled, and then the disassembled real and imaginary parts are combined into a matrix form, so that Formula 1 is rewritten as:

[0084]

[0085] Among them, Re(Y) and Im(Y) are Y(ω f ), Re(D) and Im(D) are the real and imaginary parts of D, Re(c) and Im(c) are the real and imaginary parts of c(ω f )'s real and imaginary parts.

[0086] Extract the real matrix of each matrix in formula 2 to obtain:

[0087] X=Bw,

[0088] Where X is Y(ω f ), B is the real matrix of D, w is the real matrix of c(ω f ) is a real matrix.

[0089] Step 7: In order to improve the computational efficiency of sparse Bayesian learning, each column of the real number matrix B of the complex overcomplete dictionary matrix D is normalized by the bi-norm to obtain the normalized real number dictionary primitive corresponding to each column:

[0090]

[0091] Among them, B ε is the normalized real number primitive in the εth column of B, b ε is the εth column in B. Since the dimensions of all matrices double after the complex numbers are converted into real number matrices, ε = 1, 2, ..., 2M. In this embodiment, ε = 1, 2, ..., 8000.

[0092] Then, the normalized real number primitives corresponding to all columns form a primitive matrix Φ = [B1, B2, ..., B 2M ], thereby converting the sparse representation model X=Bw into X=Φw.

[0093] Step 8: Weight coefficient vector c(ω f The prior distribution p(w|σ) of the real matrix w of ) is:

[0094] p(w|σ)=N(w|0,σ) Formula 3,

[0095] Where σ is the covariance matrix of the multivariate Gaussian distribution, σ=diag(σ1,σ2,...,σ M ,σ1,σ2,...,σ M ), thereby imposing the same sparse constraints on the real weight coefficient vector Re(c) and the imaginary weight coefficient vector Im(c).

[0096] According to the principle of maximum information entropy, the Gaussian likelihood function is used to characterize the likelihood between Φw and X:

[0097] p(X|w,β)=N(X|Φw,β -1 I) Formula 4,

[0098] Among them, β is the error accuracy parameter of all weight coefficients, and I is the 2N×2N unit matrix.

[0099] Formula 3 and Formula 4 are used to obtain the posterior probability distribution of the weight coefficient vector under the same sparse constraints for the real and imaginary parts:

[0100]

[0101] in, is the optimal estimation result of σ under the Gamma super prior, μ is the posterior mean vector, ψ is the covariance matrix, μ = βψΦ T X,

[0102] Furthermore, in this step, the following formula is used to apply the Gamma hyper-prior to each element in the covariance matrix:

[0103]

[0104] Among them, p(σ m |λ) is the mth hyperparameter σ m The Gamma hyper-prior result, m = 1, 2, ..., M, λ / 2 is the inverse scale parameter of the Gamma distribution,

[0105] The Gamma super prior expression of the covariance matrix σ is:

[0106]

[0107] Finally, the wave number corresponding to the non-zero term in the posterior mean vector μ is taken as the frequency ω f The wave number of the guided wave mode contained in the frequency response signal below.

[0108] Step 9: Determine whether f≥F, if yes, execute step 10, otherwise set f=f+1, and then return to step 4;

[0109] Step 10: Draw a discretized ultrasonic guided wave dispersion curve using the wave number of the frequency response signal at F frequencies in the main energy distribution frequency set.

[0110] like Figure 4 As shown in the figure, the identified dispersion curve is very close to the theoretically calculated dispersion curve. In addition, since the propagation distance of the boundary reflection wave packet is not considered in the overcomplete dictionary matrix, there are some outliers in the recognition result, which can be eliminated by singular value detection, so the impact on the recognition result is small.

[0111] This embodiment constructs an overcomplete dictionary matrix related to wave number according to the frequency response model. Since the number of wave numbers contained in the dictionary matrix is ​​much larger than the number of guided wave modes in the frequency response, complex sparse Bayesian learning is used to perform sparse decomposition on all frequency responses at each frequency, thereby identifying the wave number of guided wave modes at each frequency. Complex sparse Bayesian learning is performed on the frequency responses at all valid frequencies to obtain discrete dispersion curves.

[0112] In summary, this embodiment provides an ultrasonic guided wave dispersion curve inversion method based on complex sparse Bayesian learning, which uses n(n-1) / 2 effective guided wave signals collected by n sensors to perform Fourier transform to obtain a complex frequency response signal; then based on the discretized wave number vector k=[k1,k2,...,k M ] Establish a complex overcomplete dictionary matrix D for all response signals Y(ω f )=[y1(r1,ω f ),y2(r2,ω f ),...,y N (r N ,ω f )] for sparse decomposition; complex sparse Bayesian learning is used to invert the guided wave dispersion curve, and the Laplace prior formed by the Gaussian prior and the Gamma prior is used to promote sparsity. Then, the accuracy of the recognition result is improved by sharing the hyperparameters of the real and imaginary parts, so as to obtain the wave number of each guided wave mode; complex sparse Bayesian learning is performed on the response signals at all effective frequencies to obtain discrete dispersion curves.

[0113] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning, characterized in that: The following steps are involved: Step 1: Use n ultrasonic sensors to transmit signals to each other, where when one ultrasonic sensor is used as the excitation end of the ultrasonic guided wave signal, the remaining n-1 ultrasonic sensors are used as the receiving ends of the ultrasonic guided wave signal, and the total number of propagation paths of the ultrasonic guided wave signal and the total number of effective ultrasonic guided wave signals are both N, N = n(n-1) / 2; Step 2: Calculate the frequency response signal of each propagation path at each frequency using the waveguide frequency response model. The waveguide frequency response model is: Among them, y(r i ,ω) is the frequency response signal of the ith propagation path at frequency ω, r i is the propagation distance of the i-th propagation path, i=1,2,...,N, L is y(r i ,ω), l=1,2,...,L,k l is the wave number of the lth guided wave mode, c l (ω) is the response coefficient of the lth guided wave mode; Step 3: Average the frequency response signals of all propagation paths at each frequency to obtain the average response amplitude at each frequency, collect the waveguide response contained in the ultrasonic guided wave signal at the frequency corresponding to the average response amplitude greater than the noise energy, and use the frequencies corresponding to all waveguide responses to form the main energy distribution frequency set [ω1,ω2,...,ω F ], F is the total number of elements in the main energy distribution frequency set; Step 4: Establish the fth element ω in the main energy distribution frequency set f The frequency response signal vector Y(ω) of all propagation paths under f ), f=1,2,...,F, the Y(ω f )=[y1(r1,ω f ),y2(r2,ω f ),...,y N (r N ,ω f )], where y N (r N ,ω f ) is the frequency ω f The frequency response signal of the Nth propagation path; Step 5: Discretize the wavenumber range of all frequency response signals in the estimated main energy distribution frequency set, so that the wavenumber density in the discretized wavenumber range is much larger than the wavenumber density of each frequency response signal in the main energy distribution frequency set. Then, establish the complex overcomplete dictionary matrix D about the discretized wavenumber according to the waveguide frequency response model: Among them, k M is the Mth wave number after discretization, j is the imaginary unit; Step 6: Use the complex overcomplete dictionary matrix D to calculate the frequency response signal vector Y(ω f ) is sparsely represented and decomposed to obtain D and Y(ω f ) real matrix; Step 7: Perform bi-norm normalization on each column of the real number matrix of the complex overcomplete dictionary matrix D to obtain the normalized real number classic primitive corresponding to each column, and then form a primitive matrix with the normalized real number classic primitives corresponding to all columns; Step 8: Use the complex sparse Bayesian learning algorithm to solve the posterior probability distribution of the weight coefficient vector under the same sparse constraints for the real and imaginary parts, so as to obtain the frequency ω f The wave number of the guided wave mode contained in the lower frequency response signal; Step 9: Determine whether f≥F, if yes, execute step 10, otherwise set f=f+1, and then return to step 4; Step 10: Draw a discretized ultrasonic guided wave dispersion curve using the wave number of the frequency response signal at F frequencies in the main energy distribution frequency set; In step eight, the specific method of using the complex sparse Bayesian learning algorithm to solve the posterior probability distribution of the weight coefficient vector under the same sparse constraint conditions for the real part and the imaginary part is: Weight coefficient vector c(ω f ) is: p(w|σ)=N(w|0,σ) Formula 3, Where σ is the covariance matrix of the multivariate Gaussian distribution, σ=diag(σ1,σ2,...,σ M ,σ1,σ2,...,σ M ), According to the principle of maximum information entropy, the Gaussian likelihood function is used to characterize the likelihood between Φw and X: p(X|w,β) = N(X|Φw,β -1 I) Equation Four, Among them, β is the error accuracy parameter of all weight coefficients, I is the 2N×2N unit matrix, X is Y(ω f ), Φ=[B1,B2,...,B 2M ], Formula 3 and Formula 4 are used to obtain the posterior probability distribution of the weight coefficient vector under the same sparse constraints for the real and imaginary parts: in, is the optimal estimation result of σ under the Gamma super prior, μ is the posterior mean vector, ψ is the covariance matrix, μ = βψΦ T X, Take the wave number corresponding to the non-zero term in the posterior mean vector μ as the frequency ω f The wave number of the guided wave mode contained in the frequency response signal below.

2. The method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning according to claim 1, characterized in that: In step 3, the frequency response signals of all propagation paths at each frequency are averaged using the following formula: Where y(ω) is the average response amplitude at frequency ω, y N (r N ,ω) is the frequency response signal of the Nth propagation path at frequency ω, |y N (r N ,ω)| is y N (r N ,ω) amplitude.

3. The method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning according to claim 1, characterized in that: In step 4, Y(ω f ) is in the form of: Among them, [c1(ω f ),c2(ω f ),...,c R (ω f )] is the response coefficient vector, R is the frequency ω f The total number of waves in the frequency response signal.

4. The method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning according to claim 3, characterized in that: Since the wave number density in the discretized wave number range is much larger than the wave number density of each frequency response signal in the main energy distribution frequency set, M>>R, Y(ω f ) is padded with 0 to achieve Y(ω f ) is a sparse representation of .

5. The method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning according to claim 4, characterized in that: Step 6: Get Y(ω f ) is as follows: After sparse representation, Y(ω f ) and the complex overcomplete dictionary matrix D have the following relationship: Y(ω f )=Dc(ω f ) Formula 1, Among them, c(ω f ) is the weight coefficient vector after sparse representation, Y(ω f ) and the real and imaginary parts of D are disassembled, and then the disassembled real and imaginary parts are combined into a matrix form, so that Formula 1 is rewritten as: Among them, Re(Y) and Im(Y) are Y(ω f ), Re(D) and Im(D) are the real and imaginary parts of D, Re(c) and Im(c) are the real and imaginary parts of c(ω f ), Extract the real matrix of each matrix in formula 2 to obtain: X=Bw, Where X is Y(ω f ), B is the real matrix of D, w is the real matrix of c(ω f ) is a real matrix.

6. The method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning according to claim 1, characterized in that: The method to obtain the primitive matrix in step 7 is: Use the following formula to perform bi-norm normalization on each column of the real matrix B of D: Among them, B ε is the normalized real number primitive in the εth column of B, b ε is the εth column in B, ε=1,2,...,2M, Create a primitive matrix using normalized real-valued canonical primitives corresponding to all columns: Φ=[B1,B2,...,B 2M ], Convert X=Bw to X=Φw.

7. The method for inverting ultrasonic guided wave dispersion curves based on complex sparse Bayesian learning according to claim 1, characterized in that: The Gamma hyper-prior is applied to each element of the covariance matrix using the following formula: Among them, p(σ m |λ) is the mth hyperparameter σ m The Gamma hyper-prior result, m = 1, 2, ..., M, λ / 2 is the inverse scale parameter of the Gamma distribution, The Gamma super prior expression of the covariance matrix σ is:

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