Non-reference damage imaging method based on nonlinear Lamb wave and Bayesian inference

Abstract

The invention provides a non-reference damage imaging method based on nonlinear Lamb waves and Bayesian inference, and relates to the field of damage imaging, and the method specifically comprises the following steps: collecting nonlinear Lamb wave signals of a plurality of propagation paths; an enhanced second harmonic signal is obtained through a pulse inversion technology; extracting a flight time feature of the envelope signal; the frequency spectrum of the nonlinear Lamb wave signal is obtained through fast Fourier transform, and nonlinear coefficient damage index features are obtained through calculation; feature level fusion is carried out based on Bayesian estimation; and solving a posterior probability density function of the damage position parameter by using Hamiltonian Monte Carlo sampling, and carrying out damage probability imaging positioning according to posterior probability distribution. According to the technical scheme, the problems that in the prior art, a large number of sensors usually need to be deployed, and the dual requirements for high-precision damage detection and sensor number minimization in engineering practice are difficult to meet are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of damage imaging, and in particular to a non-reference damage imaging method based on nonlinear Lamb waves and Bayesian inference. BACKGROUND

[0002] Under the harsh working conditions of long-term high load operation, stress concentration and chemical corrosion, the surface and interior of engineering structures are prone to cracks, corrosion, delamination and debonding and other damage forms. Timely and accurate detection and identification of these potential defects are of great engineering significance for preventing catastrophic accidents and ensuring structural safety. Ultrasonic Lamb waves have become an important technical means in the field of structural health monitoring and nondestructive evaluation due to their long propagation distance and sensitivity to internal defects.

[0003] Nonlinear Lamb wave technology has shown significant technical advantages in early damage detection of structures due to its unique ability to capture nonlinear effects such as high-order harmonics and mixing modulation. In addition, this technology breaks through the dependence on reference data in traditional linear Lamb wave damage detection methods. However, current nonlinear Lamb wave damage imaging methods still have obvious shortcomings in the use of feature information: existing researches are mostly limited to single nonlinear feature damage imaging, such as trajectory imaging based on the time difference of second harmonic and defect probability detection reconstruction algorithm based on nonlinear coefficient damage index, which fails to effectively integrate multiple nonlinear feature information, resulting in limited damage imaging resolution. In addition, existing methods usually require the deployment of a large number of sensors, which is difficult to meet the dual needs of high-precision damage detection and minimization of the number of sensors in engineering practice.

[0004] Therefore, there is a need for a non-reference damage imaging method based on nonlinear Lamb waves and Bayesian inference that can improve the accuracy and reliability of damage detection without the need for deploying a large number of sensors. SUMMARY

[0005] The main purpose of the present application is to provide a non-reference damage imaging method based on nonlinear Lamb waves and Bayesian inference to solve the problem that a large number of sensors are usually required in the prior art, which is difficult to meet the dual needs of high-precision damage detection and minimization of the number of sensors in engineering practice.

[0006] To achieve the above-mentioned purpose, the present application provides a non-reference damage imaging method based on nonlinear Lamb waves and Bayesian inference, which specifically comprises the following steps: S1, deploying a sparse piezoelectric sensor network on the surface of the structure to be tested, all sparse piezoelectric sensors are alternately excited and received to form several damage detection paths, and nonlinear Lamb wave signals of multiple propagation paths are collected.

[0007] S2, obtaining enhanced second harmonic signals by pulse inversion technology.

[0008] S3, filtering noise signals in the second harmonic signal by continuous Shannon wavelet transform, and calculating the filtered envelope signal by applying Hilbert transform, and further extracting the time-of-flight feature of the envelope signal.

[0009] S4, obtaining the frequency spectrum of the nonlinear Lamb wave signal by using fast Fourier transform, and calculating the nonlinear coefficient damage index feature.

[0010] S5, constructing a likelihood function by using the time-of-flight difference feature combined with the trajectory imaging positioning principle, constructing a prior probability density function by using the nonlinear coefficient damage index feature combined with the defect probability detection reconstruction algorithm principle, and constructing a posterior probability density function of the damage location parameter according to Bayes' theorem for feature level data fusion.

[0011] S6, solving the posterior probability density function of the damage location parameter by using Hamilton Monte Carlo sampling, and performing damage probability imaging positioning according to the posterior probability distribution.

[0012] Further, step S2 specifically includes the following steps: S2.1, due to the existence of nonlinear damage, the excitation and response of the system are simplified as: (1) ; wherein, represents the excitation signal, is the system response, , and are the amplitude coefficients of the fundamental wave, the second harmonic wave and the third harmonic wave respectively.

[0013] S2.2, based on the pulse inversion technique, first excite the sensor array with positive phase and collect the response signal; then excite the sensor array with negative phase, and superimpose the two acquired time domain signals; assuming that the positive phase excitation is , and the negative phase excitation is , then the responses obtained by the two excitations are respectively: (2) ; wherein, and represent the positive phase response signal and the negative phase response signal respectively, and the superposition of the two response signals is: (3).

[0014] Further, step S3 specifically includes the following steps: S3.1, filtering noise signals in the second harmonic signal by continuous Shannon wavelet transform, for the second harmonic signal in real number space The continuous Shannon wavelet transform WT of is defined as follows: (4); wherein is a scale factor, is a shift factor; denotes the real space, and " " denotes the conjugate, is a Shannon mother wavelet function: (5); wherein denotes the imaginary unit, denotes time, denotes the bandwidth of the mother wavelet, is the center frequency of the Shannon mother wavelet.

[0015] S3.2, the relationship between the center frequency of the second harmonic signal and the scale factor is as follows: (6); wherein is the center frequency of the second harmonic, is the sampling frequency of the nonlinear Lamb wave signal, is the scale factor.

[0016] S3.3, the Hilbert transform is applied to calculate the envelope of the second harmonic signal: (7); wherein is the second harmonic signal, is the Hilbert transform of is the corresponding envelope signal.

[0017] S3.4, the time-of-flight feature of the second harmonic is extracted according to the peak value of the envelope signal.

[0018] Further, step S4 is specifically: The frequency spectrum of the positive-phase excitation nonlinear Lamb wave response signal is obtained by using the fast Fourier transform, and the nonlinear coefficient damage index feature NCDI is calculated according to the following formula: (8); wherein is the fundamental amplitude in the frequency spectrum, is the second harmonic amplitude in the frequency spectrum.

[0019] Further, step S5 specifically includes the following steps: S5.1, assuming that the center coordinates of the damage are Two different receiving sensors corresponding to the same exciter are taken as a group, and there are a total of​ group; according to the trajectory imaging method, the second harmonic for the first group two sensors, sensor and The time-of-flight difference theoretical value of : (9); wherein, and are the coordinates of the sensor and , respectively, and are the group velocities of the second harmonic in the direction of the sensor and .

[0020] S5.2, the measured time-of-flight difference is expressed as : (10); wherein, is the uncertainty, subject to a Gaussian distribution with a mean of 0 and a variance of .

[0021] S5.3, according to the measured second harmonic time-of-flight difference characteristic data and formula (9), a likelihood function is constructed: (11); wherein, is an exponential function.

[0022] Further, step S5 further comprises the following steps: S5.4, constructing the prior distribution of the damage location parameter according to the defect probability detection reconstruction algorithm : (12); wherein, is the nonlinear coefficient damage index of the first excitation receiving path, is the total number of excitation receiving paths; is an elliptical distribution function: (13); wherein, is an elliptical shape control parameter, the expression is: (14); wherein, the coordinates of the excitation sensor and the receiving sensor are and .

[0023] S5.5, according to Bayes' theorem, the posterior distribution of the damage location parameter satisfies: (15); wherein, represents proportional to.

[0024] obtain the posterior distribution of the damage location parameter : (16).

[0025] Further, the step S6 is specifically: The probability distribution of the damage location in the monitoring area is written in the standard form of two-dimensional normal distribution : (17); wherein, is the mean vector of the damage location parameter ; is the covariance matrix; is the determinant of the covariance matrix ; The coordinates corresponding to the maximum value are the predicted damage location.

[0026] The present application has the following beneficial effects: (1) The present application uses pulse inversion technology and continuous Shannon wavelet transform technology, which not only enhances the second harmonic component but also reduces the interference of noise on damage identification.

[0027] (2) The present application considers the uncertainty in the feature measurement of the nonlinear Lamb wave signal and the damage location identification process, which enhances the reliability and robustness of damage positioning.

[0028] (3) The present application makes full use of the characteristic information of nonlinear Lamb wave, and has excellent damage positioning accuracy compared with traditional methods under the condition of deploying a small amount of sensors.

[0029] (4) The present application does not need to measure the health reference signal of the structure in advance as a reference, and can overcome the challenge brought by the time-varying characteristics of the actual service environment of the engineering structure. BRIEF DESCRIPTION OF DRAWINGS

[0030] In order to make the specific embodiment of the present application or the technical solution in the prior art clearer, the drawings needed in the specific embodiment or the prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings. In the drawings: Figure 1 A flow chart of a non-reference damage imaging method based on nonlinear Lamb wave and Bayesian inference is shown.

[0031] Figure 2 A schematic diagram of trajectory imaging principle is shown.

[0032] Figure 3 A schematic diagram of defect probability detection reconstruction algorithm principle is shown.

[0033] Figure 4 A schematic diagram of a sensor array of a structure to be measured and damage is shown.

[0034] Figure 5 A phase velocity dispersion curve of the 0° direction of the structure to be measured is shown.

[0035] Figure 6 A schematic diagram of a sensor excitation signal is shown.

[0036] Figure 7 A time domain corresponding signal when the 0° phase is excited is shown.

[0037] Figure 8 A frequency spectrum of the response signal when the 0° phase is excited is shown.

[0038] Figure 9 A time domain corresponding signal when the 180° phase is excited is shown.

[0039] Figure 10 A frequency spectrum of the response signal when the 180° phase is excited is shown.

[0040] Figure 11 A 0° and 180° superimposed time domain signal is shown.

[0041] Figure 12 A 0° and 180° superimposed frequency spectrum is shown.

[0042] Figure 13 A schematic diagram of time-of-flight feature extraction is shown.

[0043] Figure 14 A group velocity profile of the second harmonic is shown.

[0044] Figure 15 A posterior distribution of the damage position parameter x-axis direction is shown.

[0045] Figure 16 The posterior distribution of the damage location parameter y-axis direction is shown.

[0046] Figure 17 The error map of the trajectory imaging method for damage imaging positioning is shown.

[0047] Figure 18 The error map of the defect probability detection reconstruction method for damage imaging positioning is shown.

[0048] Figure 19 The error map of the method proposed by the present application for damage imaging positioning is shown. DETAILED DESCRIPTION

[0049] The technical solutions of the present application will be described clearly and completely below in conjunction with the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0050] As Figure 1 shown in a non-linear Lamb wave and Bayesian inference based non-reference damage imaging method, specifically comprising the following steps: S1, deploying a sparse piezoelectric sensor network on the surface of the structure to be measured, all sparse piezoelectric sensors taking turns to excite and receive, forming several damage detection paths, and collecting non-linear Lamb wave signals of multiple propagation paths.

[0051] S2, obtaining enhanced second harmonic signals by pulse inversion technology.

[0052] S3, filtering noise signals in the second harmonic signals by continuous Shannon wavelet transform, and calculating the envelope signal after filtering by applying Hilbert transform, and then extracting the time-of-flight feature of the envelope signal.

[0053] S4, obtaining the frequency spectrum of the non-linear Lamb wave signal by using fast Fourier transform, and calculating the non-linear coefficient damage index feature.

[0054] S5, using the time-of-flight difference feature to construct a likelihood function in combination with the trajectory imaging positioning principle, using the non-linear coefficient damage index feature to construct a prior probability density function in combination with the defect probability detection reconstruction algorithm principle, and constructing a posterior probability density function of the damage location parameter according to the Bayesian theorem for feature-level data fusion. That is, Bayesian feature-level fusion.

[0055] S6, solving the posterior probability density function of the damage location parameter by using Hamilton Monte Carlo sampling, and performing damage probability imaging positioning according to the posterior probability distribution.

[0056] In particular, step S2 specifically comprises the following steps: S2.1, due to the existence of nonlinear damage, the excitation and response of the system are simplified as: (1); wherein, represents the excitation signal, is the system response, , and are the amplitude coefficients of the fundamental wave, the second harmonic wave and the third harmonic wave respectively.

[0057] S2.2, based on the pulse inversion technique, the sensor array is first excited with a positive phase (phase angle of 0°) (i.e. a sparse piezoelectric sensor network is deployed on the surface of the structure to be measured) and the response signal is collected; then the excitation signal is excited in reverse phase (phase angle of 180°), and the two time domain signals obtained are superimposed; assuming that the positive phase excitation is and the reverse phase excitation is , then the responses obtained from the two excitations are respectively: (2); wherein, and represent the positive phase response signal and the reverse phase response signal respectively, and the superposition of the two response signals is: (3).

[0058] Therefore, through the pulse inversion technique, the second harmonic signal can be significantly enhanced. The amplitude of the high-order harmonic wave above the fourth order is much lower than the second harmonic wave and can be ignored.

[0059] In particular, step S3 specifically comprises the following steps: S3.1, the noise signal in the second harmonic signal is filtered by continuous Shannon wavelet transform, and for the continuous Shannon wavelet transform WT of the second harmonic signal in the real number space is defined as follows: (4); wherein, is a scale factor, is a translation factor; represents the real number space, and " " represents the conjugate, is the Shannon mother wavelet function: (5); wherein, represents the imaginary unit, represents time, represents the bandwidth of the mother wavelet, is the center frequency of the Shannon mother wavelet.

[0060] S3.2, a more pure second harmonic signal is extracted by using continuous Shannon wavelet transform, and the relationship between the center frequency of the second harmonic signal and the scale factor is as follows: (6) ; wherein, is the center frequency of the second harmonic, is the sampling frequency of the nonlinear Lamb wave signal, is the scale factor.

[0061] Therefore, by adjusting the scale factor , the center frequency of the mother wavelet and the bandwidth of the mother wavelet , a more pure second harmonic signal can be extracted.

[0062] S3.3, the Hilbert transform is applied to calculate the envelope of the second harmonic signal: (7) ; wherein, is the second harmonic signal, is the Hilbert transform of , and is the corresponding envelope signal.

[0063] S3.4, the time-of-flight feature of the second harmonic is extracted according to the peak value of the envelope signal.

[0064] Specifically, step S4 is specifically: The frequency spectrum of the positive phase excitation nonlinear Lamb wave response signal is obtained by using fast Fourier transform, and the nonlinear coefficient damage index feature NCDI is calculated according to the following formula: (8) ; wherein, is the fundamental amplitude in the frequency spectrum, is the second harmonic amplitude in the frequency spectrum.

[0065] Specifically, step S5 specifically includes the following steps: S5.1, as shown in Figure 2 , assuming that the center coordinates of the damage are , two different receiving sensors corresponding to the same exciter are a group, and there are groups in total; according to the trajectory imaging method, for the second harmonic of the two sensors of the group, the theoretical calculation value of the time-of-flight difference of the sensors and is : (9) ; wherein, and are the coordinates of the sensors and respectively, and are the group velocities of the second harmonic in the directions of the sensors and respectively.

[0066] S5.2, due to the existence of random errors and systematic errors, the measured time-of-flight difference has an uncertainty, the measured time-of-flight difference is expressed as : (10); wherein, is the uncertainty, which is subject to a Gaussian distribution with a mean of 0 and a variance of .

[0067] S5.3, according to the measured second harmonic time-of-flight difference characteristic data and formula (9), a likelihood function is constructed: (11); wherein, is an exponential function.

[0068] Specifically, step S5 further comprises the following steps: S5.4, as shown in Figure 3 , it is a schematic diagram of the principle of the defect probability detection reconstruction algorithm. It is assumed that the coordinate distribution of the excitation sensor and the receiving sensor is and . It can be seen from Figure 3 that when the nonlinearity coefficient damage index in the excitation-receiving path is significant, the probability of damage occurring on the direct propagation path is the largest. At the same time, as the distance between the path and the direct propagation path increases, the probability of damage occurring presents a gradually decreasing trend. According to the defect probability detection reconstruction algorithm, the prior distribution of the damage location parameter is constructed: (12); wherein, is the nonlinearity coefficient damage index of the th excitation-receiving path, is the total number of excitation-receiving paths; is an elliptical distribution function: (13); wherein, is an elliptical shape control parameter, which is obtained by experience as 1.015. The expression is: (14); The coordinates of the excitation sensor and the receiving sensor are respectively... and .

[0069] S5.5, According to Bayes' theorem, the posterior distribution of the damage location parameters is... satisfy: (15); in, It represents a direct proportion to.

[0070] The posterior distribution of the damage location parameters was obtained. : (16); Therefore, according to formula (16), feature-level data fusion of two nonlinear Lamb wave features, namely flight time difference and nonlinear coefficient damage index, was achieved.

[0071] Specifically, step S6 is as follows: The probability distribution of the damage location within the monitoring area can be written in the standard form of a two-dimensional normal distribution. : (17); in, Damage location parameters The mean vector; It is the covariance matrix: ; Covariance matrix The determinant of; The coordinates corresponding to the maximum value are the predicted damage location.

[0072] To verify the effectiveness of the method of this invention, nonlinear Lamb wave detection data for delamination damage in composite material plate structures were generated using numerical simulation. The dimensions of the structure under test, sensor layout, and damage settings are as follows: Figure 4 As shown. Figure 4 T1, T2, T3, and T4 are piezoelectric sensors. The composite material plate has a geometric dimension of 400 mm × 400 mm × 2 mm. The composite material type is AS4M3502, and the layup is [0° / 90°]. 2s Each layer is 0.25 mm thick, and the center of the delamination damage is located at (200 mm, 150 mm), between the bottommost single-layer board and the second-to-last single-layer board. For example... Figure 5The phase velocity dispersion curve of the composite plate is shown, and according to the dispersion curve, it can be known that only A0 and S0 modes exist in a relatively low frequency range, and there is a nonlinear cumulative effect of the S0 mode. Figure 6 As shown in the figure, the excitation signal adopts a 10-period sine wave signal modulated by a Hanning window with a center frequency of 150 kHz. As shown in the figure, Figures 7-12 As shown in the figure, the pulse inversion technique is used to significantly enhance the second harmonic component. In addition, the continuous Shannon wavelet transform is applied to filter the second harmonic signal to reduce the interference of noise. As shown in the figure, Figure 13 As shown in the figure, the Hilbert transform is used to calculate the envelope signal and extract the time of flight, and then the time of flight difference feature is obtained. The fast Fourier transform is used to obtain the frequency spectrum of the nonlinear Lamb wave signal, and the nonlinear coefficient damage index feature is calculated according to formula (8). As shown in the figure, Figure 14 As shown in the figure, the group velocity profile of the second harmonic is shown, and the anisotropy of the composite material is considered, and the posterior probability density function of the damage location parameter is established according to formula (16), and the nonlinear feature data fusion is completed. As shown in the figure, Figure 15 and Figure 16 As shown in the figure, the Hamilton Monte Carlo sampling is used to solve formula (16) to obtain the posterior distribution result of the damage location parameter. Finally, the damage location probability distribution result obtained according to formula (17) is obtained, and compared with the traditional method as shown in the figure, Figures 17-19 As shown in the figure, the trajectory imaging positioning error is 14.6 mm, the defect probability detection reconstruction algorithm positioning error is 36.4 mm, and the error of the method of the application is only 3.0 mm, which shows that the damage positioning accuracy of the method of the application is higher.

[0073] Of course, the above description is not a limitation of the application, and the application is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the scope of the application should also be within the protection scope of the application.

Claims

1. A non-linear Lamb wave and Bayesian inference based reference-free damage imaging method, characterized in that, Specifically comprising the following steps: S1, deploying sparse piezoelectric sensor network on the surface of the structure to be tested, all sparse piezoelectric sensors are stimulated and received in turn to form several damage detection paths, and the nonlinear Lamb wave signals of multiple propagation paths are collected; S2, obtaining enhanced second harmonic signals through pulse inversion technology; S3, filtering noise signals in the second harmonic signals through continuous Shannon wavelet transform, and calculating the envelope signal after filtering by applying Hilbert transform, and then extracting the time-of-flight feature of the envelope signal; S4, obtaining the frequency spectrum of the nonlinear Lamb wave signal by using fast Fourier transform, and calculating the nonlinear coefficient damage index feature; S5, constructing a likelihood function by using the time-of-flight difference feature combined with the trajectory imaging positioning principle, constructing a prior probability density function by using the nonlinear coefficient damage index feature combined with the defect probability detection reconstruction algorithm principle, and constructing a posterior probability density function of the damage position parameter according to Bayes theorem for feature level data fusion; S6, solving the posterior probability density function of the damage position parameter by using Hamilton Monte Carlo sampling, and performing damage probability imaging positioning according to the posterior probability distribution.

2. The non-linear Lamb wave and Bayesian inference based reference-free damage imaging method according to claim 1, characterized in that, Step S2 specifically comprises the following steps: S2.1, due to the existence of nonlinear damage, the excitation and response of the system are simplified as: （1）； wherein, represents the excitation signal, is the system response, , and are the amplitude coefficients of the fundamental, second and third harmonic, respectively. S2.2, based on the pulse inversion technique, first excite the sensor array with positive phase and collect the response signal; then excite the sensor array with negative phase, and superimpose the two time-domain signals obtained. Assuming that the positive phase excitation is and the negative phase excitation is , then the responses obtained from the two excitations are respectively: （2）； wherein and respectively represent the positive phase response signal and the inverted phase response signal, and the two response signals are superimposed to obtain: （3）。 3. The non-linear Lamb wave and Bayesian inference based reference-free damage imaging method of claim 1, wherein, Step S3 specifically comprises the following steps: S3.1, filtering noise signals in the second harmonic signal by a continuous Shannon wavelet transform, for the continuous Shannon wavelet transform WT of the second harmonic signal in the real number space is defined as follows: （4）； where is a scale factor, is a translation factor; denotes the real space, " " denotes the conjugate, is the Shannon mother wavelet function: （5）； wherein, denotes the imaginary unit, denotes time, denotes the bandwidth of the mother wavelet, is the center frequency of the Shannon mother wavelet; S3.2, the relationship between the center frequency of the second harmonic signal and the scale factor is as follows: （6）； wherein, is the center frequency of the second harmonic, is the sampling frequency of the nonlinear Lamb wave signal, is a scaling factor; S3.3, the envelope of the second harmonic signal is calculated by applying Hilbert transform: （7）； wherein is a second harmonic signal, is is a Hilbert transform of is a corresponding envelope signal; S3.4, the time-of-flight feature of the second harmonic is extracted according to the peak value of the envelope signal.

4. The non-linear Lamb wave and Bayesian inference based reference-free damage imaging method of claim 1, wherein, Step S4 is specifically: The frequency spectrum of the positive phase excitation nonlinear Lamb wave response signal is obtained by using fast Fourier transform, and the nonlinear coefficient damage index feature NCDI is calculated according to the following formula: （8）； wherein, is the fundamental amplitude in the frequency spectrum, is the second harmonic amplitude in the frequency spectrum.

5. The non-linear Lamb wave and Bayesian inference based reference-free damage imaging method of claim 1, wherein, Step S5 specifically comprises the following steps: S5.1, assuming the center coordinates of the lesion are Two different receiving sensors corresponding to the same exciter are a group, and there are groups in total; according to the trajectory imaging method, the second harmonic for the two sensors of the group, the time difference of the flight of the sensors and is theoretically calculated as : （9）； wherein and are the coordinates of the sensor and respectively, and are the group velocities of the second harmonic in the direction of the sensor and respectively. S5.2, the measured time-of-flight difference is expressed as : （10）； wherein, is an uncertainty, subject to a Gaussian distribution with mean 0 and variance . S5.3, the measured second harmonic time-of-flight difference characteristic data and equation (9) to construct a likelihood function : （11）； wherein is an exponential function.

6. The non-linear Lamb wave and Bayesian inference based reference-free damage imaging method of claim 5, wherein, Step S5 further comprises the following steps: S5.

4. Constructing the prior distribution of damage location parameters from the defect probability detection reconstruction algorithm : （12）； wherein, is the number of the first nonlinear coefficient impairment index of the mth is the total number of the excitation receiving paths; is an elliptic distribution function: （13）； wherein is an elliptical shape control parameter, The expression is: （14）； wherein the coordinates of the excitation sensor and the receiving sensor are respectively and ; S5.5, According to Bayes' theorem, the posterior distribution of the damage location parameter satisfies: （15）； wherein proportional to; obtaining a posterior distribution of the damage location parameter : （16）。 7. The non-linear Lamb wave and Bayesian inference based reference-free damage imaging method of claim 1, wherein, Step S6 is specifically: The probability distribution of the location of the lesion within the monitoring region is written in the standard form of a two-dimensional normal distribution : （17）； wherein, is the mean vector of the damage location parameters ; is the covariance matrix: is the determinant of the covariance matrix ; The coordinates corresponding to the maximum value are the predicted damage location.

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