Multilayer medium ultrasonic super-resolution imaging method based on time reversal operator

Abstract

The invention provides a multilayer medium ultrasonic super-resolution imaging method based on a time reversal operator for the blank of a multilayer medium super-resolution imaging technology, and belongs to the technical field of ultrasonic detection. The method specifically comprises the following steps: step 1, placing an ultrasonic phased array probe on the surface of a detected workpiece, and utilizing ultrasonic phased array transceiver equipment to carry out ultrasonic detection on the surface of the detected workpiece; collecting one-transmitting full-receiving data of the N-array-element ultrasonic phased array to obtain full-matrix collection data E; 2, performing singular value decomposition on the collected full-matrix data E in a frequency domain, and selecting a corresponding signal subspace threshold to obtain a signal subspace singular value and a singular vector; 3, calculating an improved Green function GI between the image sampling point and the position of the transducer; 4, the TR-MUSIC super-resolution imaging factor is combined with the TFM imaging factor to obtain a defect image pixel value of the target imaging point Xi, and multi-layer medium ultrasonic super-resolution imaging is completed.

Description

Technical Field

[0001] The invention relates to a multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator, and belongs to the technical field of ultrasonic detection. Background Art

[0002] Ultrasonic nondestructive testing can achieve high-sensitivity identification of internal defects without destroying the object being tested, and is widely used in industrial production. The ultrasonic phased array is composed of multiple piezoelectric chips arranged in an array, and can achieve arbitrary deflection and focusing of the sound beam by controlling the excitation and reception delay of the piezoelectric signal. The time-domain delay superposition algorithm is used in conjunction with the multi-channel echo data collected by the phased array to achieve defect imaging in the tested area of ​​the workpiece. In order to increase the resolution of ultrasonic phased array imaging, a common method is to increase the ultrasonic frequency of the phased array or increase the number of phased array elements; however, on the one hand, the ultrasonic attenuation coefficient increases with the increase of frequency, so that the ultrasonic detection range decreases with the increase of frequency. On the other hand, the increase in the ultrasonic frequency or the number of array elements of the phased array is subject to the manufacturing process and processing cost of the probe, so the probe frequency and the number of array elements cannot be increased indefinitely. In order to use low-frequency ultrasonic waves with longer propagation distances to achieve higher-resolution ultrasonic imaging of defects, it is necessary to develop corresponding ultrasonic super-resolution imaging algorithms.

[0003] The existing ultrasonic super-resolution imaging algorithms have the following shortcomings: 1. Deconvolution super-resolution imaging technology based on defect sparsity prior. This method takes the prior condition of defect sparse distribution in ultrasonic images as the L1 regularization term, and uses the relevant optimization algorithm to solve the least squares expression containing the L1 regularization term to obtain a super-resolution image of the defect. This method requires setting multiple hyperparameters in the optimization solution process, and the resolution ability depends on the prediction of the point spread function; 2. Ultrasonic super-resolution imaging technology based on deep learning. This method learns the complex mapping relationship between low-resolution images and real images by training multiple sets of different measured data, thereby achieving super-resolution imaging. This method requires a large number of data sets, and its application effect and generalization ability are closely related to the selection of data sets and the setting of training networks, making it difficult to use for large-scale production; 3. Ultrasonic super-resolution imaging technology based on time reversal multi-signal classification, using the principle of time reversal, by repeatedly inverting the received signal to achieve sound field focusing at the defect. The non-zero eigenvalues ​​of the received signal frequency response correspond one-to-one to the defect distribution. This method is simple to operate and does not require additional hyperparameter settings, and is expected to be applied in actual detection. 4. Current research on ultrasonic super-resolution algorithms focuses on defect imaging in single-layer isotropic media. The objects to be tested in industrial production, such as welds, water immersion detection, wedge detection, and "sandwich" structures, are all multi-layer media, and their internal sound field propagation is more complex. Therefore, the corresponding ultrasonic super-resolution imaging technology needs further research. Summary of the invention

[0004] The present invention aims at the blank of multi-layer medium super-resolution imaging technology, and further proposes a multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator, which specifically includes:

[0005] Step 1: Place the ultrasonic phased array probe on the surface of the workpiece to be measured, and use the ultrasonic phased array transceiver to collect the one-send-all-receive data of the N-element ultrasonic phased array to obtain the full matrix collection data E;

[0006] Step 2: Perform singular value decomposition on the collected full matrix data E in the frequency domain, select the corresponding signal subspace threshold, and obtain the signal subspace singular value and singular vector;

[0007] Step 3: Calculate the improved Green's function GI between the image sampling point and the transducer position;

[0008] Step 4: Use the TR-MUSIC super-resolution imaging factor combined with the TFM imaging factor to obtain the target imaging point X i The defect image pixel value is calculated to complete the ultrasonic super-resolution imaging of multi-layer media.

[0009] Preferably, in step 1, the frequency of the ultrasonic phased array probe is f0, the number of array elements is N, the array element spacing is s, and the sampling frequency is f s , the sampling point is M, and the full matrix acquisition data is E(t,m,n), where t is the sampling time, n is the serial number of the transmitting array element, m is the serial number of the receiving array element, (m,n)=1, 2,…,N.

[0010] Preferably, step 2 specifically includes:

[0011] Step 2.1: Perform a one-dimensional fast Fourier transform on the full matrix data E(t,m,n) according to the time dimension t to obtain

[0012]

[0013] Step 2.2: Use the singular value classification algorithm to Perform singular value decomposition and obtain the singular value σ i and the singular vector V i , where V i is an N-dimensional column vector, i = 1, 2, ..., N;

[0014] Step 2.3: Set the threshold of the signal subspace, when the singular value σ i When the threshold is exceeded, the corresponding singular value σ i As the singular value σ of the signal subspace k , and the corresponding singular vector is used as the signal subspace singular vector V k ;

[0015] The expression is:

[0016]

[0017] The singular value decomposition expression is:

[0018]

[0019] In formula (2), V(ω)=[V1(ω)V2(ω)…V N (ω)] T ;

[0020] The calculation formula of signal subspace singular values ​​and singular vectors is:

[0021] σs(ω)=[σs1(ω)σs2(ω)…σs k (ω)] T (3);

[0022] Vs(ω)=[V1(ω)V2(ω)…V k (ω)] T (4).

[0023] Preferably, step 3 specifically includes:

[0024] Step 3.1: For the specified piezoelectric array element m and the second layer target imaging point X i , the ultrasonic beam excited by the piezoelectric array element is set to enter the second layer of medium through the interface point A and reach the target imaging point X i , obtain the expression of the propagation time of the sound beam in the multilayer medium;

[0025] Step 3.2: Divide the incident interface into p incident points A with equal spacing i , i = 1, 2, ..., p, calculate the i When it is the incident point, it propagates from the piezoelectric array element m to the target imaging point X i The acoustic beam travel time t i ;

[0026] Step 3.3: Set the minimum beam travel time t i As propagated from the piezoelectric array element m to the target imaging point X i When the sound

[0027] Step 3.4: Based on the propagation from the piezoelectric array element m to the target imaging point X i The improved Green's function GI between the image sampling point and the transducer position is obtained by using the acoustic time;

[0028] The expression of the sound beam propagation time in multilayer media is:

[0029]

[0030] In formula (5), d is the Euclidean distance between two points, c1 is the longitudinal wave sound speed of the first layer of medium, and c2 is the longitudinal wave sound speed of the second layer of medium;

[0031] Acoustic beam travel time t i The calculation formula is:

[0032]

[0033] Minimum sound beam travel time t i The calculation formula is:

[0034]

[0035] The expression of improved Green's function GI is:

[0036]

[0037] In formula (8), H0 is the first kind of zero-order Hankel function, j is an imaginary unit, f0 is the center frequency of the ultrasonic transducer, and R m is the direction vector of the mth piezoelectric array element of the piezoelectric transducer, X i is the direction vector of the target imaging point, t(R m ,X i ) is the distance from the mth piezoelectric array element to the target sampling point X i The sound beam propagation time.

[0038] Preferably, step 4 specifically includes:

[0039] Step 4.1: According to the principle of forward propagation of the acoustic field, the reflection amplitude of the defect scatterer in the workpiece under test is set to ρ i , i = 1, 2, ..., k, calculate the frequency domain response of the received sound field Theoretical expression of

[0040] Step 4.2: Decompose the singular value expression and By comparing with the theoretical expression of , it can be obtained that the Green function GI is orthogonal to the singular vectors of the non-signal subspace, and the defect characteristics of the target imaging point are obtained, where the defect characteristics of the target imaging point are that for any target imaging point, when there is a defect scatterer at the corresponding target imaging point, the sum of the inner products of all the singular vectors of the signal subspace and the Green function is 1;

[0041] Step 4.3: Based on the defect characteristics of the target imaging point, the TR-MUSIC (GI) super-resolution imaging factor is obtained. i When there is a defect at the location, the amplitude of the imaging factor is infinite;

[0042] Step 4.4: Obtain the target imaging point X based on the TR-MUSIC (GI) super-resolution imaging factor and the TFM imaging factor i The pixel value of the defective image;

[0043] Sound field frequency response The theoretical expression is:

[0044]

[0045] The expression of TR-MUSIC(GI) super-resolution imaging factor is:

[0046]

[0047] Target imaging point X i The expression of the pixel value of the defect image is:

[0048]

[0049] In formula (11), V i is the signal subspace singular vector obtained in step 2, ΓI(X i ,ω) is when the target imaging point is X i When the Green's function of the array, ΓI(X i ,ω) is:

[0050] ΓI(X i ,ω)=[GI(R1,X i ,ω)GI(R2,X i ,ω)…GI(R N ,X i ,ω)] T (12).

[0051] The beneficial effects of the present invention are:

[0052] The present invention proposes a multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator, which fills the gap in the ultrasonic phased array imaging method in the field of super-resolution ultrasonic detection of multi-layer medium defects. The present invention uses an improved Green's function factor to expand the traditional super-resolution imaging technology to multi-layer anisotropic media, and realizes the quantification of sub-wavelength size defects; at the same time, the full focusing imaging factor is weighted into the multi-layer medium super-resolution imaging factor, which effectively reduces the axial artifacts of the image and realizes axial precise positioning. The present invention is expected to be applied to industrial ultrasonic non-destructive testing such as industrial weld detection, aircraft composite material detection, and water immersion ultrasonic detection to improve the detection resolution capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1A flowchart of a multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator provided by the present invention;

[0054] Figure 2 A diagram of an ultrasonic super-resolution defect imaging device for a multi-layer structure provided by the present invention. DETAILED DESCRIPTION

[0055] Combination Figure 1 and Figure 2 To illustrate this embodiment, Figure 1 As shown, the steps of a multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator described in this embodiment include:

[0056] S1: Select ultrasonic phased array probe;

[0057] The frequency of the ultrasonic phased array probe selected in this embodiment is f0, the number of array elements is N, the array element spacing is s, and the sampling frequency is f s , the sampling point is M.

[0058] S2: Collect full matrix data E using ultrasonic phased array transceiver equipment;

[0059] In this embodiment, the ultrasonic super-resolution defect imaging device is as follows: Figure 2 As shown, the array probe is placed on the surface of the workpiece to be measured, and a commercial ultrasonic phased array transceiver is used to collect the one-transmit-all-receive data of the N-element ultrasonic phased array, and the full matrix acquisition data is obtained as E(t,m,n), where t is the sampling time, n is the serial number of the transmitting array element, and m is the serial number of the receiving array element (m,n=1,2,…,N);

[0060] S3: Perform one-dimensional Fourier transform on the full matrix acquisition data E to obtain

[0061] One-dimensional Fourier transform As shown in formula (1):

[0062]

[0063] S4: Perform singular value decomposition to obtain the signal subspace singular values ​​and singular vectors;

[0064] S401: Using the singular value decomposition (SVD) algorithm Perform singular value decomposition, as shown in formula (2), and obtain the singular value σ i and the singular vector V i (V i is an N-dimensional column vector), where i = 1, 2, ..., N;

[0065]

[0066] In formula (2), V(ω)=[V1(ω)V2(ω)…V N (ω)] T ;

[0067] S402: Set the threshold of the signal subspace to 10%, that is, when the singular value σ i When it is greater than 10% of the maximum singular value, it belongs to the signal subspace singular value σ k , the corresponding singular vector is called the signal subspace singular vector V k , the corresponding singular values ​​and singular vectors are shown in formula (3) and formula (4);

[0068] σs(ω)=[σs1(ω)σs2(ω)…σs k (ω)] T (3);

[0069] Vs(ω)=[V1(ω)V2(ω)…V k (ω)] T (4).

[0070] S5: Calculate the improved Green's function factor GI;

[0071] S501: For the specified piezoelectric array element m and the second layer target imaging point X i , the ultrasonic beam excited by the piezoelectric array element is set to enter the second layer of medium through the interface point A and reach the target imaging point X i , obtain the expression of the propagation time of the sound beam in the multilayer medium;

[0072] The expression of the sound beam propagation time in multilayer media is:

[0073]

[0074] In formula (5), d is the Euclidean distance between two points, c1 is the longitudinal wave sound speed of the first layer of medium, and c2 is the longitudinal wave sound speed of the second layer of medium;

[0075] S502: To determine the incident point A, this embodiment divides the incident interface into p incident points A at equal intervals. i , i = 1, 2, ..., p, calculate A i When it is the incident point, it propagates from the piezoelectric array element m to the target imaging point X i The acoustic beam travel time t i ;

[0076] Acoustic beam travel time t i The calculation formula is:

[0077]

[0078] S503: Set the minimum acoustic beam travel time t i As propagated from the piezoelectric array element m to the target imaging point X i When the sound

[0079] Minimum sound beam travel time t i The calculation formula is:

[0080]

[0081] S504: Based on the propagation from the piezoelectric array element m to the target imaging point X i The improved Green's function GI between the image sampling point and the transducer position is obtained by using the acoustic time;

[0082] The expression of improved Green's function GI is:

[0083]

[0084] In formula (8), H0 is the first kind of zero-order Hankel function, j is an imaginary unit, f0 is the center frequency of the ultrasonic transducer, and R m is the direction vector of the mth piezoelectric array element of the piezoelectric transducer, X i is the direction vector of the target imaging point, t(R m ,X i ) is the distance from the mth piezoelectric array element to the target sampling point X i The sound beam propagation time.

[0085] S6: Calculate the pixel value of the defect image;

[0086] S601: According to the principle of forward propagation of the acoustic field, the reflection amplitude of the defect scatterer contained in the workpiece under test is set to ρ i , i = 1, 2, ..., k, calculate the frequency domain response of the received sound field Theoretical expression of

[0087] Sound field frequency response The theoretical expression is:

[0088]

[0089] S602: Comparing the theoretical expression of with formula (2), it can be obtained that the Green function GI is orthogonal to the singular vectors of the non-signal subspace. Therefore, for any target imaging point, when there is a defect scatterer at that point, the sum of the inner products of all the singular vectors of the signal subspace and the Green function should be 1;

[0090] S603: Obtaining TR-MUSIC (GI) super-resolution imaging factor based on the defect characteristics of the target imaging point. iWhen there is a defect at the location, the amplitude of the imaging factor is infinite;

[0091] The expression of TR-MUSIC(GI) super-resolution imaging factor is:

[0092]

[0093] S604: Obtain the target imaging point X based on the TR-MUSIC (GI) super-resolution imaging factor and the TFM imaging factor i The pixel value of the defective image;

[0094] Target imaging point X i The expression of the pixel value of the defect image is:

[0095]

[0096] In formula (11), V i is the signal subspace singular vector obtained in step 2, ΓI(X i ,ω) is when the target imaging point is X i When the Green's function of the array, ΓI(X i ,ω) is:

[0097] ΓI(X i ,ω)=[GI(R1,X i ,ω)GI(R2,X i ,ω)…GI(R N ,X i ,ω)] T (12).

[0098] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. A multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator, characterized in that: The method for multi-layer medium ultrasonic super-resolution imaging based on a time reversal operator comprises the following steps: Step 1: Place the ultrasonic phased array probe on the surface of the workpiece to be measured, and use the ultrasonic phased array transceiver to collect the one-send-all-receive data of the N-element ultrasonic phased array to obtain the full matrix collection data E; Step 2: Perform singular value decomposition on the collected full matrix data E in the frequency domain, select the corresponding signal subspace threshold, and obtain the signal subspace singular value and singular vector; Step 3: Calculate the improved Green's function GI between the image sampling point and the transducer position; Step 4: Use the TR-MUSIC super-resolution imaging factor combined with the TFM imaging factor to obtain the target imaging point X i The defect image pixel value is calculated to complete the ultrasonic super-resolution imaging of multi-layer media.

2. The multi-layer medium ultrasonic super-resolution imaging method based on time reversal operator according to claim 1, characterized in that: In step 1, the frequency of the ultrasonic phased array probe is f0, the number of array elements is N, the array element spacing is s, and the sampling frequency is f s , the sampling point is M, and the full matrix acquisition data is E(t,m,n), where t is the sampling time, n is the serial number of the transmitting array element, m is the serial number of the receiving array element, (m,n)=1, 2,…,N.

3. The multi-layer medium ultrasonic super-resolution imaging method based on time reversal operator according to claim 1, characterized in that: Step 2 specifically includes: Step 2.1: Perform a one-dimensional fast Fourier transform on the full matrix data E(t,m,n) according to the time dimension t to obtain Step 2.2: Use the singular value decomposition algorithm to Perform singular value decomposition and obtain the singular value σ i and the singular vector V i , where V i is an N-dimensional column vector, i = 1, 2, ..., N; Step 2.3: Set the threshold of the signal subspace, when the singular value σ i When the threshold is exceeded, the corresponding singular value σ i As the singular value σ of the signal subspace k , and the corresponding singular vector is used as the signal subspace singular vector V k ; The expression is: In formula (1), e -jωt is a complex function, e is the natural logarithm, ω is the angular frequency, and t is the time; The singular value decomposition expression is: In formula (2), V(ω)=[V1(ω)V2(ω)…V N (ω)] T ; The calculation formula of signal subspace singular values ​​and singular vectors is: σs(ω)=[σs1(ω)σs2(ω)…σs k (oh)] T (3); Vs(ω)=[V1(ω)V2(ω)…V k (oh)] T (4)。 4. The multi-layer medium ultrasonic super-resolution imaging method based on time reversal operator according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1: For the specified piezoelectric array element m and the second layer target imaging point X i , the ultrasonic beam excited by the piezoelectric array element is set to enter the second layer of medium through the interface point A and reach the target imaging point X i , obtain the expression of the propagation time of the sound beam in the multilayer medium; Step 3.2: Divide the incident interface into p incident points A with equal spacing i , i = 1, 2, ..., p, calculate the i When it is the incident point, it propagates from the piezoelectric array element m to the target imaging point X i The acoustic beam travel time t i ; Step 3.3: Set the minimum beam travel time t i As propagated from the piezoelectric array element m to the target imaging point X i When the sound Step 3.4: Based on the propagation from the piezoelectric array element m to the target imaging point X i The improved Green's function GI between the image sampling point and the transducer position is obtained by using the acoustic time; The expression of the sound beam propagation time in multilayer media is: In formula (5), d is the Euclidean distance between two points, c1 is the longitudinal wave sound speed of the first layer of medium, and c2 is the longitudinal wave sound speed of the second layer of medium; Acoustic beam travel time t i The calculation formula is: Minimum sound beam travel time t i The calculation formula is: The expression of improved Green's function GI is: In formula (8), H0 is the first kind of zero-order Hankel function, j is an imaginary unit, f0 is the center frequency of the ultrasonic transducer, and R m is the direction vector of the mth piezoelectric array element of the piezoelectric transducer, X i is the direction vector of the target imaging point, t(R m ,X i ) is the distance from the mth piezoelectric array element to the target sampling point X i The sound beam propagation time.

5. The multi-layer medium ultrasonic super-resolution imaging method based on time reversal operator according to claim 1, characterized in that: Step 4 specifically includes: Step 4.1: According to the principle of forward propagation of the acoustic field, the reflection amplitude of the defect scatterer in the workpiece under test is set to ρ i , i = 1, 2, ..., k, calculate the frequency domain response of the received sound field Theoretical expression of Step 4.2: Decompose the singular value expression and By comparing with the theoretical expression of , it can be obtained that the Green function GI is orthogonal to the singular vectors of the non-signal subspace, and the defect characteristics of the target imaging point are obtained, where the defect characteristics of the target imaging point are that for any target imaging point, when there is a defect scatterer at the corresponding target imaging point, the sum of the inner products of all the singular vectors of the signal subspace and the Green function is 1; Step 4.3: Based on the defect characteristics of the target imaging point, the TR-MUSIC (GI) super-resolution imaging factor is obtained. i When there is a defect at the location, the amplitude of the imaging factor is infinite; Step 4.4: Obtain the target imaging point X based on the TR-MUSIC (GI) super-resolution imaging factor and the TFM imaging factor i The pixel value of the defective image; Sound field frequency response The theoretical expression is: The expression of TR-MUSIC(GI) super-resolution imaging factor is: Target imaging point X i The expression of the pixel value of the defect image is: In formula (11), V i is the signal subspace singular vector obtained in step 2, ΓI(X i ,ω) is when the target imaging point is X i When the Green's function of the array, ΓI(X i ,ω) is: ΓI(X i ,ω)=[GI(R1,X i ,ω)GI(R2,X i ,ω)…GI(R N ,X i ,oh)] T (12)。

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