Damage identification method for composite sandwich structure material based on bayesian fusion algorithm

Abstract

The application provides a composite sandwich structure material damage identification method based on a Bayesian fusion algorithm, and the method comprises the following steps: extracting the time of flight of a scattered wave signal based on continuous wavelet transform; wherein the time of flight refers to the time for which the scattered wave signal generated by an excitation sensor is transmitted to a receiving sensor; obtaining a likelihood function based on the time of flight and an elliptical positioning method; determining a correlation coefficient based on a damage signal and a reference signal; in a RAPID method, taking the correlation coefficient as a damage sensitivity characteristic to determine a prior probability density function of a damage position; performing Bayesian estimation based on the likelihood function and the prior probability density function to obtain a posterior probability density function of the damage position; and fitting a damage positioning image using a Markov Monte Carlo method (MCMC) based on the posterior probability density function of the damage position.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of composite materials, and particularly relates to a composite sandwich structure material damage identification method based on a Bayesian fusion algorithm. BACKGROUND

[0002] In a carbon fiber reinforced sandwich structure composite material, delamination defect is an important damage mode, and without early warning, it is easy to bring disastrous failure to the composite structure. Therefore, in order to avoid failure, the sandwich composite material is designed to be oversized or a periodic nondestructive testing method is used. In the past few decades, nondestructive testing is a reliable and effective delamination detection technology, but still faces many problems and challenges. Lamb wave, as a very important guided wave in ultrasonic wave, has been proved to be a promising guided wave technology in nondestructive testing. Lamb wave technology has significant advantages, such as strong penetration and low attenuation for long-distance propagation, and can be used in identification and positioning of various defects, such as delamination, debonding and crack.

[0003] The structural health monitoring technology includes an elliptical positioning method and a defect probability diagnosis reconstruction algorithm (Reconstruction Algorithm For Probabilistic Inspection Of Defects, RAPID) method. However, their resolution and sensitivity are highly dependent on the density and layout of the sensor array.

[0004] However, the application provides a method which can solve the problem that the elliptical positioning method and the RAPID method are highly dependent on the density and layout of the sensor array. SUMMARY

[0005] In view of the above technical problems, the application provides a composite sandwich structure material damage identification method based on a Bayesian fusion algorithm, which comprises the following steps:

[0006] Extracting the time of flight of the scattered wave signal based on continuous wavelet transform; wherein the time of flight refers to the time for the scattered wave signal generated by the excitation sensor to be transmitted to the receiving sensor;

[0007] Obtaining a likelihood function based on the time of flight and the elliptical positioning method;

[0008] Determining a correlation coefficient based on the damage and the reference signal;

[0009] In the RAPID method, the correlation coefficient is taken as a damage sensitivity feature to determine a prior probability density function of the damage position;

[0010] Performing Bayesian estimation based on the likelihood function and the prior probability density function to obtain a posterior probability density function of the damage position.

[0011] using Markov Monte Carlo method (MCMC) based on the posterior probability density function of the damage location

[0012] fitting the damage location image.

[0013] Preferably, the time of flight of the scattered wave signal based on the continuous wavelet transform comprises:

[0014] receiving the undamaged reference signal collected by the sensor, receiving the damaged signal collected by the sensor, and obtaining the scattered wave signal by subtracting the damaged signal from the reference signal.

[0015] transforming the obtained scattered wave time domain signal into a frequency domain signal based on the continuous wavelet transform, and taking the time of the first appearing wave peak on the time axis as the time of flight.

[0016] Preferably, the likelihood function based on the time of flight and the elliptical location method comprises:

[0017] The presence of the damage causes the scattering of the existing wave of the Lamb wave from P1 to P3, and the wave packet received by the P3 sensor includes the wave packet d as arriving at the damage region from P1 ad and the wave packet d ds arriving at P3 after scattering through the damage region; the total propagation distance d ad +d ds which can be calculated by the time of flight and the group velocity of the Lamb wave propagation; the elliptical equation formed by the P1 to P3 sensors is described as equation (1):

[0018]

[0019] In the formula, (x d , y d ) is the coordinate of the damage location, the coordinate of the excitation sensor is (x a , y a ), and the coordinate of the receiving sensor is (x s , y s ). v g is the group velocity of the Lamb wave, which is related to the thickness of the sample and the frequency of the excitation Lamb wave. The time of flight ToF is defined as the time difference between the signal generated from the excitation sensor and the damage scattered wave received by the receiving sensor. Since d ad +d ds in the elliptical equation d ad and d dsThere are numerous solutions, in order to determine the unique coordinate solution of the damage location, it is necessary to paste multiple sensor channels, the more the sensor channels, the more accurate the coordinate solution of the damage location. Each sensor channel can obtain an elliptic equation, therefore, according to the schematic diagram, three elliptic equations can determine the unique damage location coordinate;

[0020] Assuming that each grid intersection point is the damage location, the damage factor P(x, y) of each intersection point (x, y) can be defined as an exponential function in combination with the theoretical flight time ToF as equation (2):

[0021]

[0022] Wherein, N p is the total number of sensing paths, T i is the flight time ToF extracted from the scattered wave, τ0 is the delay factor set to 0.01, and P(x, y) is the maximum value of the predicted possible damage location coordinate;

[0023] The probability equation of the measured flight time (ToF) of the ith sensing channel is shown in equation (6):

[0024]

[0025] Wherein, is calculated using the theoretical flight time (ToF) and the actual damage location (xd, yd) in combination with equation (1);

[0026] The unknown parameters are taken as a vector θ = (x d , y d , σ), and the measured flight time (ToF) is taken as N p is the total number of sensing channels; and the likelihood function of the measured data is shown in equation (7):

[0027]

[0028] Preferably, before determining the correlation coefficient based on the damage and reference signals, it further comprises:

[0029] The RAPID method is used to determine the damage location, and the RAPID method is based on the fact that the propagation of Lamb waves will change significantly on the direct path between the sensor channels;

[0030] The damage location occurrence wave reduction amplification is increased as a direct wave; the damage location can affect the change of each sensor channel, and the linear sum of the changes of all sensor channels is taken as the damage location.

[0031] Preferably, the determining the correlation coefficient based on the damage signal and the reference signal comprises:

[0032] determining the correlation coefficient based on the damage signal and the reference signal comprises: k and Y k , μ is the corresponding data, and K is the number of corresponding data points.

[0033] Preferably, the determining the correlation coefficient based on the damage signal and the reference signal comprises:

[0034] The correlation coefficient is explained as follows: the smaller the correlation coefficient, the greater the probability of the corresponding damage location. If the two columns of signals are exactly the same, the correlation coefficient is close to 1.

[0035] The correlation coefficient is used as a damage sensitivity feature based on the RAPID method. The correlation coefficient can be expressed as function (3):

[0036]

[0037] Preferably, the determining the correlation coefficient based on the damage signal and the reference signal comprises:

[0038] The prior probability density function of the parameter vector can be expressed as:

[0039] P (θ|D)∝P (D|θ) P (θ) (8)

[0040] where P (θ) is the parameter of the prior probability density function, and the (x d , y d ) and σ of the prior probability density function can be obtained by the RAPID method. The prior probability density function of θ can be expressed as equation (9):

[0041]

[0042] Combining equation (8) and equation (9) can obtain the posterior distribution of θ as equation (10):

[0043]

[0044] Preferably, the determining the correlation coefficient based on the damage signal and the reference signal comprises:

[0045] The Markov Monte Carlo method (MCMC) can use the Matlab input command "mhsample" to substitute the posterior distribution equation P (θ|D) of θ into the relevant data to write an image processing program, so as to obtain the damage image.

[0046] Advantages of the present application:

[0047] The present application proposes a damage locating technology with high reliability and robustness for sandwich structure composite materials. The development of this technology is based on a new technology of probabilistic fusion of elliptical locating method and RAPID method in the Bayesian distribution theory system. Two damage features are extracted from Lamb waves, and the extracted features are used for signal processing by elliptical locating method and RAPID method respectively. The Bayesian probability is integrated into the elliptical locating method and RAPID method through the two damage features to obtain the probability density function of damage location.

[0048] BRIEF DESCRIPTION OF DRAWINGS

[0049] Fig. 1 Elliptical positioning schematic diagram provided by the embodiment of the present application;

[0050] Fig. 2 Bayesian fusion algorithm flowchart provided by the embodiment of the present application. DETAILED DESCRIPTION

[0051] Please refer to Figs. 1-2 In the embodiment of the present application, (1) the existence of Lamb wave from P1 to P3 is caused by the existence of damage, and the wave packet received by P3 sensor includes the wave packet d as from P1 to the damage area d ad and the wave packet d ds scattered after the damage area to P3. The total propagation distance d ad +d ds can be calculated by the time of flight and the group velocity of Lamb wave propagation. The elliptical equation formed by P1 to P3 sensor can be described as equation (1):

[0052]

[0053] In the formula, (x d , y d ) is the coordinate of the damage location, the coordinate of the excitation transducer is (x a , y a ), and the coordinate of the receiving transducer is (xs, ys). is the group velocity of Lamb wave. The time of flight ToF is defined as the time difference between the signal generated from the excitation sensor and the damage scattered wave received by the receiving sensor.

[0054] ​The group velocity is related to the thickness of the pattern template and the frequency of the applied excitation Lamb wave. Since there are infinitely many solutions for dad and dds in the elliptic equation dad + dds, multiple sensor channels are needed to determine the unique coordinates of the damage location. The more sensor channels, the more accurate the coordinates of the damage location. Each sensor channel yields an elliptic equation; therefore, according to the diagram, three elliptic equations are sufficient to determine the unique damage location coordinates.

[0055] To achieve probabilistic diagnostic localization, the sample to be tested needs to be divided into multiple discrete grids. Assuming the intersection of each grid is the damage location, then each intersection (x, y The damage factor P(x, ) y The theoretical time-of-flight (ToF) can be defined as a power function, as shown in equation (2):

[0056]

[0057] Where, N p T represents the total number of sensing paths. i The time-of-flight (ToF) extracted from the scattered wave is given by τ0, which is a delay factor set to 0.01, and P(x, y) is the maximum value of the predicted possible damage location coordinates.

[0058] In this embodiment, the RAPID method is based on the fact that the propagation of the Lamb wave will be significantly altered along the direct path between sensor channels due to damage. The reduction and amplification of the wave at the damage location is taken as an increase in the direct wave. The damage location can affect the change in each sensor channel, and the linear summation of the changes in all sensor channels is taken as the damage location. Based on this theory, the correlation coefficient is used as a damage sensitivity feature in the RAPID method. The correlation coefficient can be expressed as a function (3):

[0059]

[0060] In the formula, X k Y k These represent the baseline signal and the signal after passing through the damage location, respectively. μ is the corresponding data, and K is the number of corresponding data points. Theoretically, the smaller the correlation coefficient, the higher the probability of corresponding damage locations. If the two signals are completely identical, the correlation coefficient is close to 1. Considering the spatial distribution of damage locations, N is used. p As the number of participating sensing channels, the probability of the damage location coordinates (x, y) can be represented by equation (4):

[0061]

[0062] In the formula, Pr i(x, y), i = 1, 2,..., N p is the damage probability distribution for the ith sensor channel. p i is the correlation coefficient. is the spatial distribution function for the ith sensor channel. β is a parameter that controls the size of the distribution area for the RAPID method. i (x, y) is given by equation (5) as follows:

[0063]

[0064]

[0065] where (x ai , y ai ) and (x si , y si ) are the excitation sensor and the receiving sensor for the ith sensor channel. The parameter β is an empirical value based on a large number of experimental samples. Based on a large number of experimental samples, the parameter β can be defined as approximately 1.

[0066] Monitoring the damage location within the Bayesian distribution framework can reduce the uncertainty. This theory is to estimate the prior distribution using the RAPID method. In addition, the elliptical localization method can be used to determine the likelihood function. Using this method, the posterior distribution of the unknown parameters can be calculated using the test data combined with the Bayesian estimation. The error between the damage location predicted by the theory and the actual damage location can be represented by ε. The probability equation of the measured time of flight (ToF) for the ith sensor channel is shown in equation (6) as follows:

[0067]

[0068] where, is calculated using the theoretical time of flight (ToF) and the actual damage location (xd, yd) combined with equation (1).

[0069] The unknown parameters are represented as a vector θ = (xd, yd, σ), and the measured time of flight (ToF) is represented as D. N p is the total number of sensor channels. The likelihood function of the measured data is shown in equation (7) as follows:

[0070]

[0071] Using the Bayesian estimation, the prior probability density function of the parameter vector can be expressed as:

[0072] P(θ|D) ∝ P(D|θ) P(θ) (8)

[0073] where P(θ) is the prior probability density function of the parameter, and the posterior probability density function of the parameter is (xd , y d ) and σ can be calculated by the RAPID method. The prior probability density function of Θ can be expressed as equation (9):

[0074]

[0075] Combining equation (8) and equation (9) can obtain the posterior distribution of Θ as equation (10):

[0076]

[0077] It should be noted that the posterior distribution of Θ can be calculated using the MCMC algorithm. This damage identification method based on Bayesian estimation can reduce the positioning error.

[0078] Compared with the traditional ellipse positioning method and the RAPID method, this technology can effectively identify multiple damages, and more damage features can be integrated into the technology. It can solve the problem that the ellipse positioning method and the RAPID method are highly dependent on the density and layout of the sensor array. It can effectively reduce the positioning error, improve the damage sensitivity, and reduce the positioning error caused by the difference in damage position.

Claims

1. A method for damage identification of composite sandwich structure material based on Bayesian fusion algorithm, characterized in that, The method comprises: extracting the time of flight of the scattered wave signal based on the continuous wavelet transform; wherein the time of flight refers to the time of transmission of the scattered wave signal generated by the excitation sensor to the receiving sensor; obtaining a likelihood function based on the time of flight and the elliptical positioning method; determining a correlation coefficient based on the damage and reference signals; in the RAPID method, taking the correlation coefficient as a damage sensitivity feature to determine a prior probability density function of the damage position; performing Bayesian estimation based on the likelihood function and the prior probability density function to obtain a posterior probability density function of the damage position; fitting a damage positioning image using the Markov Monte Carlo method (MCMC) based on the posterior probability density function of the damage position; wherein the step of taking the correlation coefficient as a damage sensitivity feature to determine a prior probability density function of the damage position in the RAPID method comprises: based on the RAPID method, taking the correlation coefficient as a damage sensitivity feature, and the correlation coefficient is expressed as function (3): where X k and Y k represent the reference signal and the signal after the damage location, respectively, μ is the corresponding data, and K is the number of corresponding data points; in theory, the smaller the correlation coefficient, the greater the probability of the corresponding damage location; if the two columns of signals are exactly the same, the correlation coefficient is close to 1; considering the spatial distribution of the damage location, N p is used as the number of participating sensing channels, and the probability of the damage location coordinate (x, y) can be represented by equation (4): where Pr i (x,y),i = 1,2, …,N p is the damage probability distribution for the ith sensor channel; p i is the correlation coefficient, is the spatial distribution function for the ith sensor channel, β is a parameter that controls the size of the distribution area of the RAPID method, R i (x,y) is specifically shown in equation (5): wherein (x ai ,y ai ) and (x si ,y si ) are the excitation sensor and the receiving sensor of the ith sensing channel, and the parameter β is an empirical value based on a large number of test samples, and based on a large number of test samples, the parameter β is defined as 1. wherein the step of fitting a damage image using the Markov Monte Carlo method (MCMC) based on the posterior probability density function of the damage position comprises: the Markov Monte Carlo method (MCMC) can use the Matlab input command "mhsample", and the posterior distribution equation P(θ|D) of θ can be substituted into the relevant data to compile an image processing program to obtain the damage image; wherein the method further comprises, before the step of determining a correlation coefficient based on the damage and reference signals: determining the damage position using the RAPID method, which is based on the fact that the propagation of Lamb waves will change significantly on the direct path of the damage between sensor channels; reducing and amplifying the damage position-induced wave to increase the direct wave; the damage position can affect the change of each sensor channel, and the linear sum of the changes of all sensor channels is taken as the damage position; the step of obtaining a likelihood function based on the time of flight and the elliptical positioning method comprises: The presence of the damage causes the scattering of the Lamb wave from the direct wave from PI to P3, the wave packet received by the P3 sensor includes the wave packet d directly from PI to P3 as the wave packet d from PI to the damage region ad and the wave packet d scattered after passing through the damage region to P3 ds ; the total propagation distance d of the scattered wave ad +d ds The total propagation distance d of the scattered wave is calculated by the time of flight and the group velocity of the Lamb wave propagation; the ellipse equation formed by the PI to P3 sensors is described as equation (1): wherein (x d ,y d ) is the coordinate of the damage position, the coordinate of the excitation sensor is (x a ,y a ), and the coordinate of the receiving sensor is (x s ,y s ); is the group velocity of the Lamb wave, the group velocity is related to the thickness of the sample and the frequency of the excitation Lamb wave; the time of flight ToF is defined as the time difference between the signal generated from the excitation sensor and the damage scattered wave received by the receiving sensor; since there are infinite solutions for d ad and d ds in the elliptic equation d ad +d ds , in order to determine the unique coordinate solution of the damage position, multiple sensor channels need to be pasted, the more the sensor channels, the more accurate the coordinate solution of the damage position; each sensor channel can obtain an elliptic equation, and three elliptic equations can determine the unique coordinate of the damage position; assuming that the intersection point of each grid is the damage position, the damage factor P(x,y) of each intersection point (x,y) can be defined as an exponential function in combination with the theoretical time of flight ToF as equation (2): where N p is the total number of sensing paths, T i is the time of flight (ToF) extracted from the scattered wave, τ0is a time delay factor set to 0.01, and P(x, y) is the maximum value of the predicted possible damage location coordinates; the probability equation of the measured time of flight (ToF) of the ith sensor channel is shown as equation (6): wherein, is calculated using the theoretical time of flight (ToF) and the actual damage location (x d ,y d ) in conjunction with equation (1); Unknown parameters as a vector θ = (x d ,y d ,σ), measured time of flight (ToF) as N p is the total number of sensing channels; the likelihood function of the measurement data is shown in equation (7):

2. The method of claim 1, wherein, the step of extracting the time of flight of the scattered wave signal based on the continuous wavelet transform comprises: collecting an undamaged reference signal by the receiving sensor, collecting a damaged signal by the receiving sensor, and obtaining a scattered wave signal by subtracting the damaged signal from the reference signal, transforming the obtained scattered wave time-domain signal into a frequency-domain signal based on the continuous wavelet transform, and taking the time of the first appearing wave peak on the time axis as the time of flight.

3. The method of claim 2, wherein, the step of determining a correlation coefficient based on the damage and reference signals comprises: determining signals X representing the reference signal and the signal after the damage location, respectively k and Y k , μ is the corresponding data, K is the number of corresponding data points.

4. The method of claim 1, wherein, the step of performing Bayesian estimation based on the likelihood function and the prior probability density function to obtain a posterior probability density function of the damage position comprises: using Bayesian estimation, the prior probability density function of the parameter vector can be expressed as: P(θ|D)∝P(D|θ)P(θ) (8) where P(0) is the parameter of the prior probability density function, the prior probability density function of (x d ,y d ) and σ can be obtained by the RAPID method, and the prior probability density function of 0 can be expressed as equation (9): combining equation (8) and equation (9) to obtain the posterior distribution of θ as equation (10):

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