Lamb wave double-frequency fusion imaging method based on covariance matrix reconstruction

Abstract

The invention belongs to the technical field of metal structure damage imaging, and particularly relates to a Lamb wave double-frequency fusion imaging method based on covariance matrix reconstruction. According to the method, a Lamb wave damage imaging uniform linear array signal model is adopted, aiming at the problem that the PZT size limits the highest frequency of a narrow-band excitation signal, a dual-frequency fusion damage imaging method is adopted, the grating lobe effect generated by high-frequency imaging is compensated through a low-frequency imaging result, the influence of the grating lobe effect on self-adaptive imaging is avoided, and the imaging precision is improved. The advantage of narrow main lobe in the grating lobe effect is reserved; in order to solve the problem that the imaging quality is influenced by significant errors existing between a sampling covariance matrix and an ideal covariance matrix, an interference and noise covariance matrix is reconstructed by adopting an iterative covariance matrix estimation method, and imaging is carried out by utilizing a result of the reconstruction, so that high-quality and high-resolution damage imaging is realized. Experiments show that the method provided by the invention can effectively improve the positioning precision, suppress sidelobe artifacts occurring under a high-frequency condition, avoid grating lobe interference and improve the imaging contrast.

Description

Technical Field

[0001] This invention belongs to the field of metal structure damage imaging technology, specifically relating to a Lamb wave dual-frequency fusion imaging method. Background Technology

[0002] In critical sectors such as aerospace and military industries, there is a significant demand for plate-shaped metal structures. If defects or damage are left untreated, it can compromise their safe operation. Phased array-based Lamb wave damage imaging technology, as an effective non-destructive testing method, is widely used in damage detection and imaging.

[0003] When using phased array technology for Lamb wave damage imaging, the spacing between receiving array elements must be less than or equal to half the wavelength of the narrowband excitation signal to satisfy the spatial sampling theorem. Increasing the excitation signal frequency reduces the wavelength, resulting in higher angular resolution. However, the size of piezoelectric transducer (PZT) array elements is limited by practical constraints. When the element diameter exceeds half the wavelength of the excitation signal, a grating lobe effect occurs. The grating lobe effect degrades the performance of adaptive beamforming damage imaging algorithms, potentially leading to a decrease in image quality and severely impacting the imaging results. Furthermore, significant errors between the sampling covariance matrix and the ideal covariance matrix in adaptive beamforming methods can also affect image quality. Summary of the Invention

[0004] The purpose of this invention is to provide a Lamb wave dual-frequency fusion imaging method based on covariance matrix reconstruction with good imaging quality and high resolution, so as to overcome the problem that the array element size limits the excitation frequency and the problem that sampling covariance mismatch affects the imaging quality.

[0005] The Lamb wave dual-frequency fusion imaging method based on covariance matrix reconstruction provided by this invention addresses the limitation of PZT size on the highest frequency of narrowband excitation signals. It employs a dual-frequency fusion damage imaging method to compensate for the grating lobe effect generated by high-frequency imaging through low-frequency imaging results, thereby avoiding the influence of the grating lobe effect on adaptive imaging and retaining the advantage of narrow main lobe in the grating lobe effect. To address the problem that the sampling covariance matrix and the ideal covariance matrix may have significant errors affecting imaging quality, an iterative covariance matrix estimation method is used to reconstruct the interference plus noise covariance matrix, and the result is used for imaging, achieving high-quality, high-resolution damage imaging.

[0006] In this invention, the area to be detected is divided into small grids, and a Lamb wave damage imaging uniform linear array signal model is used. (See [link to relevant documentation]). Figure 1As shown in the figure. That is, a uniform linear array composed of M PZT sensors is installed on a plate-like metal structure. The signal model of this linear array is based on the far-field assumption. The spacing between adjacent sensors is d. It is assumed that the angle of incidence of the scattered signal on the uniform linear array is θ, where θ ∈ (0, π).

[0007] The working principle of damage detection imaging is as follows: First, a narrowband excitation signal with a center frequency of f is applied to the PZT excitation sensor to generate Lamb wave signals in the plate-like structure. The Lamb waves propagate in the plate-like structure and are scattered when encountering damage. Then, the scattered signals are respectively received by the receiving sensors S1, S2,..., S M Receive. Then, subtract the received scattered echo signal from the reference echo signal collected from the plate-like structure in the healthy state to obtain the damage scattered signal containing damage information. Finally, use the array signal processing technology to process the obtained damage scattered signal for damage imaging.

[0008] The specific steps of the present invention are as follows:

[0009] In the first step, based on the one-dimensional uniform linear array signal model, two excitation frequencies are denoted as f1 and f2 respectively, and f1 < f2. There is no grating lobe effect at the low frequency f1, and there is a grating lobe effect at the high frequency f2. In this case, the Lamb wave transmit-receive signals of the healthy plate-like structure are collected respectively:

[0010] Under the far-field condition, the received signal of the i-th array element can be expressed as:

[0011] x i (t) = a i (θ)s(t) + n i (t). (1)

[0012] Where, a i (θ) is the steering vector of the i-th array element, s(t) is the damage scattered signal, and n i (t) is the noise signal received by the i-th array element;

[0013] Express the received signals of the above linear array in matrix form:

[0014] X(t) = a(θ)S(t) + N(t). (2)

[0015] Where:

[0016] X(t) = [x1(t), x2(t),..., x M (t)] T , (3)

[0017] a(θ) = [a1(θ), a2(θ),..., a M (θ)] T , (4)

[0018] N(t) = [n1(t), n2(t), ..., n M (t)] T (5)

[0019] superscript T This indicates the matrix transpose.

[0020] The second step involves acquiring Lamb wave transmission-reception signals of the damaged plate structure at two different excitation frequencies based on a one-dimensional uniform linear array signal model. These signals are then compared with the signals of the healthy plate at the corresponding frequencies to obtain a pure scattered echo signal.

[0021] The third step involves scanning each grid point (x, y) within the imaging region for the scattered echo signal under two excitation frequencies, iteratively solving the power spectrum and covariance matrix, and using the reconstructed interference plus noise covariance matrix to calculate the weighting coefficients of the MVDR beamformer in each direction.

[0022] Assume the sampled signal covariance matrix of the array is:

[0023]

[0024] The superscript H indicates conjugate transpose.

[0025] To estimate the power spectrum The following covariance matrix fitting criteria are used to estimate the parameters:

[0026]

[0027] Where ||·|| denotes the Frobenius norm of the matrix, R -1 / 2 R represents a positive definite matrix. -1 The square root of.

[0028] The equivalent function g of function f is expressed as follows:

[0029]

[0030] Where K represents the number of angles that divide the incoming wave direction (range from -90° to 90°) that the linear array may receive.

[0031] Minimizing the g function is an SDP problem. Solving SDP problems is computationally too expensive. Therefore, minimizing g is formulated as a constrained minimization problem:

[0032]

[0033] in,

[0034] Solving equation (9) under the above constraints yields the final solution.

[0035] Furthermore, a fitting iterative method is specifically adopted. The specific process is as follows: first, the power spectrum estimation is initialized by time averaging.

[0036]

[0037] After completing the initial estimation, repeat the following iterative process until convergence:

[0038]

[0039] Where R(i) represents the result of the previous iteration. Constructed To update the newly obtained covariance matrix.

[0040] The fourth step involves traversing the grid points within each imaging region at excitation frequencies f1 and f2. Based on the delay time of the array received signal and the weighting coefficients calculated in the previous step, the pixel value of each grid point is determined, and all grid points are normalized for imaging to obtain imaging results Y1(x,y) and Y2(x,y) at the two frequencies.

[0041] The fifth step involves performing dual-frequency fusion imaging by multiplying the imaging results from the two frequencies to obtain the dual-frequency fusion imaging result:

[0042] Y(x,y)=Y1(x,y)·Y2(x,y)., (12)

[0043] Experiments show that the method of the present invention can effectively improve positioning accuracy, suppress side lobe artifacts that occur at high frequencies, avoid grid lobe interference, and improve imaging contrast. Attached Figure Description

[0044] Figure 1 This is a diagram illustrating the one-dimensional uniform linear array signal model of the present invention.

[0045] Figure 2 This is a schematic diagram of the experimental platform.

[0046] Figure 3 For comparison of damage imaging results. Detailed Implementation

[0047] The invention will be further illustrated below with experimental examples and accompanying drawings.

[0048] This invention designs and builds an experimental platform (such as...) Figure 3The experiment (shown) consists of an aluminum plate, a PZT piezoelectric sensor, a signal generator, a power amplifier, an oscilloscope, and a computer. The excitation signal is generated by an Agilent 33220A arbitrary function generator and controlled by the host computer. An Aigtek ATA-2021B high-voltage amplifier is used to amplify the excitation signal. Data recording is performed using an Agilent MSO6052A oscilloscope with a sampling frequency of 1 MHz. In the experiment, the excitation Lamb signal was selected as the excitation frequency for the low-frequency phase, with a center frequency of 40 kHz and a five-cycle Hanning window tone burst, at which point no grating lobe effect occurs. A five-cycle Hanning window tone burst with a center frequency of 100 kHz was selected as the excitation frequency for the high-frequency phase, at which point a grating lobe effect occurs. A cylindrical mass block with a diameter of 2 cm was used to simulate damage to the aluminum plate, and different damage locations were simulated by changing the position of the mass block.

[0049] In the experiment, the uniform linear array consisted of 6 elements (M=6), distributed at equal intervals of 12 mm between (470 mm, 0 mm) and (530 mm, 0 mm); the simulated damage was set at the position of (500 mm, 300 mm).

[0050] Figure 3 The dual-frequency fusion imaging results of the DAS algorithm, MVDR algorithm, and the Lamb wave damage imaging algorithm based on covariance matrix reconstruction of this invention are presented. In this case, for the DAS algorithm, (a) the localization error is 26.25 mm; (b) the localization error is 36.22 mm; and (c) the localization error is 25.71 mm. For the MVDR algorithm, (d) the localization error is 24.70 mm; (e) due to the grating lobe effect affecting damage localization, the localization error is 395.30 mm, which is extremely large; and (f) the localization error is 23.54 mm. For the algorithm of this invention, (g) the localization error is 24.33 mm; (h) the localization error is 64.67 mm; and (i) the localization error is 21.37 mm. The localization results of the dual-frequency fusion imaging algorithm of this invention are more accurate and have smaller localization errors than those of the DAS and MVDR algorithms. As can be seen from the figure, the present invention not only effectively improves the positioning accuracy, but also suppresses side lobe artifacts that occur at high frequencies, avoids grid lobe interference, and improves the imaging contrast.

Claims

1. A Lamb wave dual-frequency fusion imaging method based on covariance matrix reconstruction, characterized in that, The area to be detected is divided into small grids, and a uniform linear array signal model for Lamb wave damage imaging is adopted. This involves installing a uniform linear array of M PZT sensors on a plate-shaped metal structure. This linear array signal model is based on the far-field assumption. The spacing between adjacent sensors is d, and the angle at which the scattered signal is incident on the uniform linear array is assumed to be θ, where θ∈(0,π). The working principle of damage detection imaging is as follows: First, a narrowband excitation signal with a center frequency of f is applied to the PZT excitation sensor, exciting a Lamb wave signal in the plate-shaped structure. The Lamb wave propagates in the plate-shaped structure and is scattered when it encounters damage. Then, the scattered signal is received by the receiving sensors S1, S2, ..., S... in the array. M The received scattered echo signal is then subtracted from the reference echo signal acquired from the healthy plate structure to obtain the damage scattered signal containing damage information. Finally, the damage scattered signal is processed using array signal processing technology to perform damage imaging. The specific steps are as follows: First step, apply two excitation frequencies, denoted as f1 and f2, and f1 < f2. There is no grating lobe effect at the low frequency f1, and there is a grating lobe effect at the high frequency f2. In this case, collect the Lamb wave emission-reception signals of the healthy plate-like structure respectively: Under the far-field condition, the received signal of the i-th element is expressed as: x i (t)=a i (θ)s(t)+n i (t). (1) Among them, a i (θ) is the guiding vector of the i-th array element, s(t) is the damage scattering signal, and n i (t) represents the noise signal received by the i-th array element; Express the received signals of the above linear array in matrix form: X(t) = a(θ)S(t) + N(t). (2) Where: X(t)=[x1(t),x2(t),...,x M (t)] T , (3) a(θ)=[a1(θ),a2(θ),...,a M (i)] T , (4) N(t)=[n1(t),n2(t),...,n M (t)] T , (5) superscript T Indicates matrix transpose; Second step, collect the Lamb wave emission-reception signals of the damaged plate-like structure at the two excitation frequencies respectively, and subtract them from the healthy plate signals at the corresponding frequencies to obtain pure scattered echo signals; Third step, at the two excitation frequencies, for the scattered echo signals, scan each grid point (x, y) in the imaging area, iteratively solve the power spectrum and covariance matrix, and use the reconstructed interference plus noise covariance matrix to calculate the weight coefficients of the MVDR beamformer in each direction; Assume that the covariance matrix of the sampled signals of the array is: Where, the superscript H represents the conjugate transpose; To estimate the power spectrum The following covariance matrix fitting criteria are used to estimate the parameters: Where ||·|| denotes the Frobenius norm of the matrix, R -1 / 2 R represents a positive definite matrix. -1 The square root of; The expression of the equivalent function g of the f function is as follows: Where, K represents the number of angles divided from the range of the incoming wave directions -90° to 90° that the linear array may receive; The minimization problem of the g function is a SDP problem, and the computational complexity of solving the SDP problem is too large. Therefore, the problem of minimizing g is expressed as the following constrained minimization problem: in, Solve the equation (9) under the above constraints to obtain the final solution.

2. The Lamb wave dual-frequency fusion imaging method based on covariance matrix reconstruction according to claim 1, characterized in that, Specifically, the fitting iteration method is adopted, and the specific process is as follows: First, initialize the power spectrum estimation through time averaging: After completing the initialization estimation, repeat the following iterative process until convergence: Where R(i) represents the result of the previous iteration. Constructed To update the newly obtained covariance matrix; Traverse each grid point in the imaging area at the two excitation frequencies f1 and f2. According to the delay time of the array received signal and the weight coefficients calculated in the previous step, determine the pixel value of each grid point, and perform normalized imaging on all grid points to obtain the imaging results Y1(x, y) and Y2(x, y) at the two frequencies; Perform dual-frequency fusion imaging on the imaging results at the two frequencies in a dot-multiplication manner to obtain the dual-frequency fusion imaging result: Y(x, y) = Y1(x, y)·Y2(x, y) (12).

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