CN115856101A - Ultrasonic frequency domain full focusing method based on sparse matrix - Google Patents

Abstract

The invention provides an ultrasonic frequency domain full focusing method based on a sparse matrix, and belongs to the field of nondestructive testing. Using full matrix signals collected by a phased array probe as original data, sequentially calculating weighted amplitudes of single-transmission full-receiving array signals, constructing sparse coefficients by combining the center frequency, sampling frequency, array element number and spacing of the probe, screening sparse arrays according to weights and implementing Fourier transform; calculating migration factors by utilizing the transverse wave number and the longitudinal wave number to obtain extrapolated wave fields at different depths and obtain weighted full-focus sub-images; and linearly superposing and averaging the sub-images corresponding to each sparse array, and finally realizing ultrasonic imaging in the detection area. The method uses less data to carry out full-focusing imaging, has faster imaging efficiency while ensuring imaging quality, and has certain real-time full-focusing application prospect.

Description

A Sparse Matrix-Based Ultrasonic Frequency-Domain Total Focusing Method

technical field

The invention relates to an ultrasonic frequency-domain total focusing method based on a sparse matrix, which belongs to the field of non-destructive testing.

Background technique

The total focusing method is an ultrasonic imaging detection technology based on full matrix data capture, which can perform virtual focusing on any point in the imaging area. Compared with the phased array ultrasonic detection technology, it has higher imaging resolution and spatial consistency. At present, most of the omni-focusing methods are based on time-domain delay superposition, by defining a high-density grid, and performing point-by-point focusing processing and imaging on the detection area. However, the time-domain imaging algorithm using full matrix data has high complexity and low imaging efficiency, which limits its practical application. In order to improve imaging efficiency, sparse arrays can be applied to data processing and algorithm optimization, while ensuring imaging quality, and using less data to achieve full-focus imaging (Hu Hongwei, et al. Two-layer dielectric ultrasonic phased array full-focus imaging based on sparse matrix Focus imaging [J]. Chinese Journal of Mechanical Engineering).

The time-domain total focusing method based on sparse arrays still uses delay and superposition processing, and the imaging efficiency is improved to a certain extent, but the improvement effect is limited. In contrast, the wavenumber domain method, as an emerging ultrasonic imaging technology, uses layer-by-layer extrapolation of the wave field to replace the point-by-point delay stacking process in the time domain, and improves the efficiency of defect imaging detection through fast Fourier transform (Z.Zhuang , et al, Comparison of time domain and frequency-wavenumber domain ultrasonic array imaging algorithms for non-destructive evaluation[J].Sensors). In this method, the two-dimensional matrix data emitted by a single array element and received by all array elements are used to form an omni-focus sub-image, and then omni-focus imaging is performed by linear superposition. In this process, the number of transmitting array elements only affects the number of superimpositions and has little effect on the range of imaging wavenumbers. Reducing the number of transmitting array elements is still expected to maintain better imaging quality and improve imaging efficiency. Accordingly, the present invention proposes an ultrasonic frequency-domain total focusing method based on a sparse matrix, which performs sparse processing at the signal transmitting end, constructs sparse coefficients, calculates weighted amplitudes, uses less data to perform imaging, and further improves total focus imaging. efficiency.

Contents of the invention

The present invention provides an ultrasonic frequency-domain total focusing method based on a sparse matrix, the purpose of which is to combine the existing frequency-domain total focusing method to calculate the weighted amplitude of the array signal, construct a sparse coefficient to reduce the signal dimension, and obtain the signal from the full matrix signal according to the weight Sparse arrays are screened in the medium to further improve imaging efficiency while ensuring imaging quality.

The technical scheme adopted by the present invention is: use the full matrix signal collected by the phased array probe as the original data, sequentially calculate the weighted amplitude of the single-shot and full-receive array signal, and combine the probe center frequency, sampling frequency, array element number and spacing to construct Sparse coefficients, filter sparse arrays according to weights and implement Fourier transform; use horizontal and vertical wavenumbers to calculate migration factors, obtain extrapolated wave fields at different depths, and obtain weighted fully focused sub-images; linearize the sub-images corresponding to each sparse array superposition, and finally realize the ultrasonic imaging in the detection area; the specific steps of the method are as follows:

(a) Determination of detection parameters

Select the appropriate phased array probe type, number of array elements n, array element spacing L, sampling frequency fs and number of sampling points Nt according to the material, size and area to be inspected of the workpiece to be inspected;

(b) Obtain full matrix signal

Place the selected probe above the area to be detected for signal acquisition, and obtain a full matrix signal M of dimension Nt×n×n, the matrix is composed of n ² time domain signals; the A-scan of transmitting array element i and receiving array element j The uth point in the signal is expressed as M _ij (u), where 1≤u≤Nt, 1≤i≤n, 1≤j≤n;

(c) Full matrix signal sparse processing

Divide M into n two-dimensional sub-matrices, where the sub-matrix signals transmitted by array element i and received by all array elements are defined as M _i , and the data dimension is Nt×n; weighted calculation of the amplitude of all A-scan signals in each sub-matrix The sum of squares S _i , as shown in formula (1):

Calculate the S _i corresponding to each sub-matrix, and construct the sparse full matrix signal M _new by taking the first kn M _i according to its weight, k represents the sparse coefficient related to the probe center frequency, sampling frequency, array element number and spacing, 0<k≤1 , the dimension of the sparse full matrix signal is Nt×n×kn;

(d) Ultrasonic frequency-domain all-focus imaging

Use the sparse full-matrix signal M _new as the imaging data, where the sub-matrix signal transmitted by the array element a and received by all array elements is defined as M _a , 1≤a≤kn; the center position of the first array element of the phased array probe is taken as the origin Establish a Cartesian coordinate system, the abscissa is x, and the depth is z; determine the longitudinal wavenumber ω and transverse wavenumber k _x according to the array element spacing L, sparse coefficient k and sampling frequency fs, where the value range of ω is (-πfs, πfs) , the value range of k _x is (-π/kL, π/kL); the two-dimensional Fourier transform is used to transform _Ma into the wavenumber domain, and the array spectrum FM _a is obtained; the migration factor F is calculated according to the transverse and longitudinal wavenumbers, combined with The time-domain extrapolated wave field expression M _az at depth z can be obtained by inverse Fourier transform:

The sound wave is emitted by the array element a, and the time required to reach point (x, z) is expressed as N _a (x, z). The all-focus sub-image P _az at each depth can be obtained by weighting the amplitude PM of each point at the depth, As shown in formula (3) and formula (4) respectively:

PM=M _az (x,fs×N _a (x,z))(3)

In the formula, cov means variance operation;

Repeat the process of formulas (2)-(4) within the depth range of the detection area to obtain the fully focused sub-image P _a in the detection area emitted by the array element a and received by all array elements; for the sparse full matrix signal M _new Repeat the above steps for all sub-matrices to obtain kn omni-focus sub-images and perform linear superposition and averaging to obtain a complete omni-focus image, as shown in formula (5):

Read the position of the strongest peak in the image as the defect location, and perform defect detection and quantification in the -6dB range.

The beneficial effects of the present invention are: the ultrasonic frequency-domain full-focus imaging method based on sparse matrix performs sparse processing on the collected full-matrix signal at the transmitting end, calculates the weighted amplitude of the array signal and screens the sparse array according to the weight, and utilizes fast Fusion The Lie transform performs wave field extrapolation and sub-image superposition to further improve the efficiency of all-focus imaging in the frequency domain.

Description of drawings

Figure 1 is a schematic diagram of the ultrasonic testing system used.

Fig. 2 is a schematic diagram of an aluminum alloy test block processed with adjacent horizontal through holes.

Figure 3 is the imaging result of adjacent cross-vias using the original full-matrix signal.

Figure 4 shows the imaging results of adjacent cross-vias using sparse full-matrix signals.

Detailed ways

The specific implementation manners of the present invention will be further described below in conjunction with the accompanying drawings and technical solutions.

The ultrasonic frequency-domain total focusing method based on sparse matrix, the ultrasonic detection system used is shown in Figure 1, and the specific detection and processing steps are as follows:

(a) The tested block is an aluminum alloy with a thickness of 40mm, and the sound velocity of the longitudinal wave of the test block v=6350m/s. Two horizontal through holes with a diameter of 2mm, a depth of 14mm at the upper end point, and a distance between centers of 3.8mm are processed inside the test block, as shown in Figure 2.

(b) Using the full-focus signal acquisition system, a phased array probe with a center frequency of 2.25MHz, the number of array elements n=32, and the distance between array elements L=0.6mm is placed directly above the defect for full-matrix signal acquisition, and the sampling frequency fs= 100MHz, the number of sampling points Nt=2000, the M dimension of the obtained full matrix signal is 2000×32×32.

(c) Divide the collected full matrix signal into 32 two-dimensional sub-matrix signals M _i of single-shot and full-receive, and the dimension of M _i is 2000×32. Set the sparse coefficient to k=0.25, compared with the original full-matrix signal of dimension 2000×32×32, the dimension of the sparse array is reduced to 2000×32×8, calculate the sum of squares of the signal amplitude of each sub-matrix, and select in turn The 8 sub-matrices with the highest weight are used as the sparse full-matrix signal M _new .

(d) Obtain the sub-matrix signal M _a received by all the array elements transmitted by a single array element in the sparse full-matrix signal, and obtain the two-dimensional spectrum FM _a after Fourier transform; according to the sampling frequency, the number of array elements and the distance between array elements Calculate the transverse and longitudinal wave numbers, and then obtain the migration factor F. On this basis, the wave number domain form of the wave field at depth z is obtained, and after Fourier inverse transform, the amplitude of each focal point is calculated and weighted to obtain an all-focus image.

(e) Fig. 3 and Fig. 4 show the frequency-domain all-focus imaging results using the original full-matrix signal M (that is, the sparse coefficient k=1) and the sparse full-matrix signal M _new respectively. API is used to characterize the coverage of defects in the image, and the smaller the value, the higher the imaging resolution. The results show that when using M imaging, the API value is 0.29, the imaging time is 38.3s, and the measured values of the depth and center distance of the transverse through hole are 13.8mm and 4.2mm respectively; when using M _new for imaging, the API value is 0.25, and the imaging time is 38.3s. The time is 7.0s, and the measured values of the depth of the horizontal through hole and the distance between centers are 13.8mm and 4.2mm, respectively. It can be seen from the comparison that when the sparse full matrix data is used for imaging, the API value is reduced by 13.8%, and the imaging efficiency is increased by 4.5 times. The imaging quality is better than the original full matrix data imaging, and the imaging time is greatly shortened.

The descriptions presented above of the exemplary embodiments are for illustration only and are not intended to be exhaustive or to limit the invention to the precise forms described. Obviously, many modifications and variations are possible to those skilled in the art based on the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application, thereby enabling others skilled in the art to understand, implement and utilize the various exemplary embodiments of the invention and various alternatives thereof and modified form. It is intended that the scope of the invention be defined by the appended claims and their equivalents.

Claims (1)

1. An ultrasonic frequency domain full focusing method based on a sparse matrix, using the full matrix signal collected by the phased array probe as the original data, and sequentially calculating the weighted amplitude of the single-shot full-receive array signal, combined with the center frequency of the probe and the sampling frequency , the number of array elements and the spacing to construct the sparse coefficient, and filter the sparse array according to the weight and implement Fourier transform; use the transverse and longitudinal wave numbers to calculate the migration factor, obtain the extrapolated wave field at different depths, and obtain the weighted fully focused sub-image; The sparse array corresponds to the sub-images for linear superposition and averaging, and finally realizes the ultrasonic imaging in the detection area; it is characterized in that the specific steps are as follows: (a) Determination of detection parameters Select the appropriate phased array probe type, number of array elements n, array element spacing L, sampling frequency fs and number of sampling points Nt according to the material, size and area to be inspected of the workpiece to be inspected; (b) Obtain full matrix signal Place the selected probe above the area to be detected for signal acquisition, and obtain a full matrix signal M of dimension Nt×n×n, the full matrix signal M is composed of n ² time domain signals; the array element i is transmitted, and the array element j is received The uth point in the A-scan signal of is expressed as M _ij (u), where 1≤u≤Nt, 1≤i≤n, 1≤j≤n; (c) Full matrix signal sparse processing Divide the full matrix signal M into n two-dimensional sub-matrices, in which the array element i is transmitted, and the sub-matrix signal received by all array elements is defined as M _i , and the data dimension is Nt×n; weighted calculation of all A-scans in each sub-matrix Signal amplitude square sum S _i , as shown in formula (1):

Calculate the S _i corresponding to each sub-matrix, and construct the sparse full matrix signal M _new by taking the first kn M _i according to its weight, k represents the sparse coefficient related to the probe center frequency, sampling frequency, array element number and spacing, 0<k≤1 , the dimension of the sparse full matrix signal is Nt×n×kn; (d) Ultrasonic frequency-domain all-focus imaging Use the sparse full-matrix signal M _new as the imaging data, where the sub-matrix signal transmitted by the array element a and received by all array elements is defined as M _a , 1≤a≤kn; the center position of the first array element of the phased array probe is taken as the origin Establish a Cartesian coordinate system, the abscissa is x, and the depth is z; determine the longitudinal wavenumber ω and transverse wavenumber k _x according to the array element spacing L, sparse coefficient k and sampling frequency fs, where the value range of ω is (-πfs, πfs) , the value range of k _x is (-π/kL, π/kL); the two-dimensional Fourier transform is used to transform _Ma into the wavenumber domain, and the array spectrum FM _a is obtained; the migration factor F is calculated according to the transverse and longitudinal wavenumbers, combined with The time-domain extrapolated wavefield expression M _az at depth z is obtained by inverse Fourier transform:

The sound wave is emitted by the array element a, and the time required to reach point (x, z) is denoted as N _a (x, z), and the all-focus sub-image P _az at each depth is obtained by weighting the amplitude PM of each point at the depth, As shown in formula (3) and formula (4) respectively: PM=M _az (x,fs×N _a (x,z))(3)

In the formula, cov means variance operation; Repeat the process of formula (2)-(4) within the depth range of the detection area, that is, the all-focus sub-image P _a in the detection area emitted by the array element a and received by all array elements is obtained; for all the sparse full matrix signal M _new The sub-matrix repeats the above steps to obtain kn omni-focus sub-images and perform linear superposition and averaging to obtain a complete omni-focus image, as shown in formula (5):

Read the position of the strongest peak in the image as the defect location, and perform defect detection and quantification in the -6dB range.

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