A multi-layered medium ultrasonic super-resolution imaging method based on time reversal operator

Abstract

Aiming at the gap in multi-layer medium super-resolution imaging technology, the present invention proposes a multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator, which belongs to the field of ultrasonic detection technology. Specifically, the method comprises the following steps: step 1: placing an ultrasonic phased array probe on the surface of a workpiece to be measured, and using an ultrasonic phased array transceiver to collect all-received data of an N-element ultrasonic phased array to obtain full-matrix collected data E; step 2: performing singular value decomposition on the collected full-matrix data E in the frequency domain, selecting the corresponding signal subspace threshold, and obtaining the signal subspace singular value and singular vector; step 3: calculating the improved Green's function GI between the image sampling point and the transducer position; step 4: using 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.

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 (NDT) can achieve highly sensitive identification of internal defects without damaging the object being tested, and is widely used in industrial production. An ultrasonic phased array, composed of multiple piezoelectric chips, can arbitrarily deflect and focus the acoustic beam by controlling the excitation and reception delays of the piezoelectric signals. Using a time-domain delay superposition algorithm combined with multi-channel echo data collected by the phased array, defect imaging can be achieved in the test area of ​​the workpiece. To increase the resolution of ultrasonic phased array imaging, a common approach is to increase the ultrasonic frequency or the number of elements in the phased array. However, the ultrasonic attenuation coefficient increases with frequency, resulting in a decrease in the ultrasonic detection range. Furthermore, increasing the ultrasonic frequency or the number of elements in the phased array is limited by the probe manufacturing process and processing costs, so the probe frequency and number of elements cannot be increased indefinitely. To achieve higher-resolution ultrasonic defect imaging using low-frequency ultrasound waves with longer propagation distances, corresponding ultrasonic super-resolution imaging algorithms need to be developed.

[0003] 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 the sparse distribution of defects in the ultrasonic image 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 the training network, making it difficult to use for large-scale production; 3. Ultrasonic super-resolution imaging technology based on time-reversal multi-signal classification. It uses the time reversal principle to achieve sound field focusing at the defect by repeatedly inverting the received signal. The non-zero eigenvalues ​​of the received signal frequency response correspond one-to-one with the defect distribution. This method is simple to operate, 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 being tested in industrial production, such as welds, water immersion inspections, wedge block inspections, and "sandwich" structures, are all multi-layer media with more complex internal sound field propagation. Therefore, the corresponding ultrasonic super-resolution imaging technology requires further research. Summary of the Invention

[0004] The present invention addresses the gap in multi-layer medium super-resolution imaging technology and 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 N The ultrasonic phased array element receives all data at once, obtaining full matrix acquisition data E ;

[0006] Step 2: Collect the full matrix data E Perform singular value decomposition 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, the frequency of the ultrasonic phased array probe in step 1 is f 0, the number of array elements is N , the array element spacing is s , the sampling frequency is f s , the sampling point is M， The full matrix acquisition data is E ( t , m , n ),in t is the sampling time, n is the serial number of the transmitting element, m is the serial number of the receiving element, m , n = 1, 2, …, N .

[0010] Preferably, step 2 specifically includes:

[0011] Step 2.1: Full matrix data E ( t , m , n ) Perform one-dimensional fast Fourier transform according to the time dimension t, and get ；

[0012] Step 2.2: Use the singular value classification algorithm to Perform singular value decomposition to obtain singular values si and the singular vector V i , where V i for N dimensional column vector, i =1, 2, ..., N ;

[0013] Step 2.3: Set the threshold of the signal subspace, when the singular value s i When the threshold is exceeded, the corresponding singular value s i As the singular values ​​of the signal subspace s k , and the corresponding singular vector is used as the signal subspace singular vector V k ;

[0014] The expression is:

[0015] (1);

[0016] The singular value decomposition expression is:

[0017] (2);

[0018] In formula (2), ;

[0019] The calculation formula of the signal subspace singular value and singular vector is:

[0020] (3);

[0021] (4).

[0022] Preferably, step 3 specifically includes:

[0023] 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 an expression for the propagation time of an acoustic beam in a multilayer medium;

[0024] Step 3.2: Divide the incident interface into equal intervals p The incident point A i , i = 1, 2, …, p , calculated with A i When the incident point is m Propagate to the target imaging point X iThe sound beam travel time t i ;

[0025] Step 3.3: Set the minimum beam time t i As a piezoelectric array element m Propagate to the target imaging point X i When the sound

[0026] Step 3.4: Based on the piezoelectric array element m Propagate 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 the acoustic time;

[0027] The expression of the sound beam propagation time in multilayer media is:

[0028] (5);

[0029] In formula (5), d is the Euclidean distance between two points, c 1 is the longitudinal wave speed of the first layer of medium, c 2 is the longitudinal wave speed of the second layer of medium;

[0030] Acoustic beam travel time t i The calculation formula is:

[0031] (6);

[0032] Minimum beam travel time t i The calculation formula is:

[0033] (7);

[0034] The expression of the improved Green's function GI is:

[0035] (8);

[0036] In formula (8), H0 is the first-order zero-order Hankel function, j is the imaginary unit, f 0 is the center frequency of the ultrasonic transducer, R m For piezoelectric transducers m The direction vector of the piezoelectric array element, X i is the direction vector of the target imaging point, t (R m ,X i ) is from m piezoelectric array element to the target sampling point X i The sound beam travel time.

[0037] Preferably, step 4 specifically includes:

[0038] Step 4.1: According to the principle of forward propagation of the acoustic field, set the reflection amplitude of the defect scatterer in the workpiece to be r i , i =1, 2, …, k , calculate the frequency domain response of the sound field it receives Theoretical expression of

[0039] 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. Among them, 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;

[0040] Step 4.3: Get the TR-MUSIC(GI) super-resolution imaging factor based on the defect characteristics of the target imaging point. i When there is a defect at , the imaging factor amplitude is infinite;

[0041] 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 defect image;

[0042] Sound field frequency domain response The theoretical expression is:

[0043] (9);

[0044] The expression of TR-MUSIC(GI) super-resolution imaging factor is:

[0045] (10);

[0046] Target imaging point X i The expression of the pixel value of the defect image is:

[0047] (11);

[0048] In formula (11), V i is the signal subspace singular vector obtained in step 2, ΓI(X i , oh ) is when the target imaging point is X i When the Green's function of the array, ΓI(X i, oh ) is:

[0049] (12).

[0050] The beneficial effects of the present invention are:

[0051] 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 field of super-resolution ultrasonic detection of multi-layer medium defects by ultrasonic phased array imaging methods. The present invention uses an improved Green's function factor to expand the traditional super-resolution imaging technology to multi-layer anisotropic media, realizing 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, effectively reducing the axial artifacts of the image and realizing 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

[0052] Figure 1 A flowchart of a multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator provided by the present invention;

[0053] Figure 2 A diagram of the ultrasonic super-resolution defect imaging device for multi-layer structures provided by the present invention. DETAILED DESCRIPTION

[0054] Combine Figure 1 and Figure 2 This embodiment is described as follows. 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:

[0055] S1: Select ultrasonic phased array probe;

[0056] The frequency of the ultrasonic phased array probe selected in this embodiment is f 0, the number of array elements is N , the array element spacing is s , the sampling frequency is f s , the sampling point is M .

[0057] S2: Using ultrasonic phased array transceiver equipment to collect full matrix data E ;

[0058] 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 commercial ultrasonic phased array transceiver equipment is used to collect NThe array element ultrasonic phased array receives all data at once, and the full matrix acquisition data is obtained as follows: E ( t , m , n ),in t is the sampling time, n is the serial number of the transmitting element, m The serial number of the receiving element m , n =(1,2,…, N );

[0059] S3: Collect data for the entire matrix E Perform a one-dimensional Fourier transform to obtain ;

[0060] One-dimensional Fourier transform As shown in formula (1):

[0061] (1);

[0062] S4: Perform singular value decomposition to obtain the signal subspace singular values ​​and singular vectors;

[0063] S401: Using the singular value decomposition (SVD) algorithm Perform singular value decomposition, as shown in formula (2), to obtain the singular value s i and the singular vector V i (V i for N -dimensional column vector), where i =1, 2, ..., N ;

[0064] (2);

[0065] In formula (2), ;

[0066] S402: Set the threshold of the signal subspace to 10%, that is, when the singular value s i When it is greater than 10% of the maximum singular value, it belongs to the signal subspace singular value s 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);

[0067] (3);

[0068] (4).

[0069] S5: Calculate the improved Green's function factor GI;

[0070] 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 an expression for the propagation time of an acoustic beam in a multilayer medium;

[0071] The expression of the sound beam propagation time in multilayer media is:

[0072] (5);

[0073] In formula (5), d is the Euclidean distance between two points, c 1 is the longitudinal wave speed of the first layer of medium, c 2 is the longitudinal wave speed of the second layer of medium;

[0074] S502: To determine the incident point A, this embodiment divides the incident interface into equal intervals. p The incident point A i , i = 1, 2, …, p , calculated with A i When the incident point is m Propagate to the target imaging point X i The sound beam travel time t i ;

[0075] Acoustic beam travel time t i The calculation formula is:

[0076] (6);

[0077] S503: Set the minimum acoustic beam time t i As a piezoelectric array element m Propagate to the target imaging point X i When the sound

[0078] Minimum beam travel time t i The calculation formula is:

[0079] (7);

[0080] S504: Based on the piezoelectric array element m Propagate to the target imaging point X iThe improved Green's function GI between the image sampling point and the transducer position is obtained by the acoustic time;

[0081] The expression of the improved Green's function GI is:

[0082] (8);

[0083] In formula (8), H0 is the first-order zero-order Hankel function, j is the imaginary unit, f 0 is the center frequency of the ultrasonic transducer, R m For piezoelectric transducers m The direction vector of the piezoelectric array element, X i is the direction vector of the target imaging point, t (R m ,X i ) is from m piezoelectric array element to the target sampling point X i The sound beam travel time.

[0084] S6: Calculate the pixel value of the defect image;

[0085] S601: According to the principle of forward propagation of the sound field, the reflection amplitude of the defect scatterer in the workpiece to be tested is set to r i , i =1, 2, …, k , calculate the frequency domain response of the sound field it receives Theoretical expression of

[0086] Sound field frequency domain response The theoretical expression is:

[0087] (9);

[0088] 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;

[0089] S603: Based on the defect characteristics of the target imaging point, the TR-MUSIC (GI) super-resolution imaging factor is obtained. When the target imaging point X i When there is a defect at , the imaging factor amplitude is infinite;

[0090] The expression of TR-MUSIC(GI) super-resolution imaging factor is:

[0091] (10);

[0092] 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 defect image;

[0093] Target imaging point X i The expression of the pixel value of the defect image is:

[0094] (11);

[0095] In formula (11), V i is the signal subspace singular vector obtained in step 2, ΓI(X i , oh ) is when the target imaging point is X i When the Green's function of the array, ΓI(X i , oh ) is:

[0096] (12).

[0097] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection 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 N The ultrasonic phased array element receives all data at once, obtaining full matrix acquisition data E ; Step 2: Collect the full matrix data E Perform singular value decomposition 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 3 specifically includes: Step 3.1: For the specified m piezoelectric array elements 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 on the second layer. i ， Obtain an expression for the propagation time of an acoustic beam in a multilayer medium; Step 3.2: Divide the incident interface into equal intervals p The incident point A i , i = 1, 2, …, p , calculated with A i When it is the incident point, m The piezoelectric array elements propagate to the second layer target imaging point X i The sound beam travel time t i ; Step 3.3: Set the minimum beam time t i As from m The piezoelectric array elements propagate to the second layer target imaging point X i When the sound Step 3.4: Based on the m The piezoelectric array elements propagate to the second layer target imaging point X i The improved Green's function GI between the image sampling point and the transducer position is obtained by the acoustic time; The expression of the sound beam propagation time in multilayer media is: （5）； In formula (5), d is the Euclidean distance between two points, c 1 is the longitudinal wave speed of the first layer of medium, c 2 is the longitudinal wave speed of the second layer of medium; Acoustic beam travel time t i The calculation formula is: （6）； Minimum beam travel time t i The calculation formula is: （7）； The expression of the improved Green's function GI is: （8）； In formula (8), H0 is the first-order zero-order Hankel function, j is the imaginary unit, f 0 is the center frequency of the ultrasonic transducer, R m For piezoelectric transducers m The direction vector of the piezoelectric array element, t (R m , X i ) is from m piezoelectric array elements to the second layer target imaging point X i The sound beam travel time; Step 4: Use the TR-MUSIC super-resolution imaging factor combined with the TFM imaging factor to obtain the second layer target imaging point X i The defect image pixel value is calculated to complete the multi-layer medium ultrasonic super-resolution imaging; Step 4 specifically includes: Step 4.1: According to the principle of forward propagation of the acoustic field, set the reflection amplitude of the defect scatterer in the workpiece to be ρ i , i =1, 2, …, k , calculate the frequency domain response of the sound field it receives 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's function GI is orthogonal to the singular vectors of the non-signal subspace, and the defect characteristics of the second-layer target imaging point are obtained. Among them, the defect characteristics of the second-layer target imaging point are that for any second-layer target imaging point, when there is a defect scatterer at the corresponding second-layer target imaging point, the sum of the inner products of all signal subspace singular vectors and the Green's function is 1; Step 4.3: Based on the defect characteristics of the second-layer target imaging point, the TR-MUSIC (GI) super-resolution imaging factor is obtained. When the second-layer target imaging point X i When there is a defect at , the imaging factor amplitude is infinite; Step 4.4: Obtain the second layer 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 defect image; Sound field frequency domain response The theoretical expression is: （9）； The expression of TR-MUSIC(GI) super-resolution imaging factor is: （10）； The second layer target imaging point X i The expression of the pixel value of the defect image is: （11）； In formula (11), V i is the signal subspace singular vector obtained in step 2, ΓI(X i , ω ) is when the second layer target imaging point is X i When the Green's function of the array, ΓI(X i , ω ) is: （12）。 2. The multi-layer medium ultrasonic super-resolution imaging method based on a time reversal operator according to claim 1, characterized in that: The frequency of the ultrasonic phased array probe in step 1 is f 0, the number of array elements is N , the array element spacing is s , the sampling frequency is f s , the sampling point is M， The full matrix acquisition data is E ( t , m , n ),in t is the sampling time, n is the serial number of the transmitting element, m is the serial number of the receiving 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: Collect data from the entire matrix E ( t , m , n ) Perform one-dimensional fast Fourier transform according to the time dimension t, and get ； Step 2.2: Use the singular value decomposition algorithm to Perform singular value decomposition to obtain singular values σ i and the singular vector V i , where V i for 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 values ​​of the signal subspace σ k , and the corresponding singular vector is used as the signal subspace singular vector V k ; The expression is: （1）； In formula (1), is a complex function, e is the natural logarithm, ω is the angular frequency, t For time; The singular value decomposition expression is: （2）； In formula (2), ; The calculation formula of the signal subspace singular value and singular vector is: （3）； （4）。

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