An ultrasonic guided wave equifractional staggered conformal array design method for pipeline damage imaging

Abstract

The application belongs to the technical field of structural health monitoring and imaging signal processing, and discloses a design method of an ultrasonic guided wave equidifferent staggered conformal array for pipeline damage imaging, and proposes an equidifferent staggered conformal array (ASCA) structure, which comprehensively improves the spatial imaging resolution by performing physical topology optimization such as axial arrangement and circumferential staggering of the array. Meanwhile, the application introduces polarization matching weight, directivity weight and nonlinear coherent enhancement mechanism in combination with an improved DAS imaging algorithm, breaks the spatial symmetry limitation of the traditional array, effectively overcomes problems such as polarization distortion and color band artifacts, highly matches the pipeline curved wave characteristics, and greatly improves the signal noise ratio and the accuracy of damage imaging.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring and imaging signal processing technology, specifically relating to a design method for an ultrasonic guided wave staggered conformal array for pipeline damage imaging. Background Technology

[0002] Pipelines, as core transportation carriers in oil and gas, chemical, and urban hot water supply sectors, are subject to long-term corrosion, fatigue loads, and third-party damage, making them prone to hidden damage such as cracks, thinning, and holes. If these defects are not accurately located, they can easily lead to safety accidents such as leaks and pipe bursts. Array technologies such as phased arrays based on ultrasonic guided waves have attracted much attention in pipeline structural health monitoring due to their wide-range and high-efficiency detection capabilities. Among them, conformal arrays arranged circumferentially along the pipe wall are a typical sensor configuration for realizing full-circumferential defect monitoring of pipelines. Theoretically, circumferential defect localization imaging can be achieved through beamforming and coherent superposition.

[0003] However, in practical applications, the detection performance of conformal arrays is severely limited by the physical polarization effect caused by the curved surface of the pipe. Due to the uniaxial sensing characteristic of the normal piezoelectric sensor, the guided wave undergoes strong spatial polarization projection attenuation when propagating along the curved surface. This microscopic polarization distortion manifests macroscopically as a severe deformation of the conformal array's directivity, significantly reducing the system's ability to resolve the orientation of circumferential defects.

[0004] To address the aforementioned issues, existing research has attempted to improve imaging quality through array layout optimization algorithms, but the following shortcomings remain: First, the lack of axial dimension leads to forward and backward blurring; in traditional single-ring arrays, all sensors are located on the same axial coordinate, and sound path measurement relies solely on circumferential phase difference, making it impossible to distinguish between front and rearward ( (direction) and rear ( The echo signal (direction); during time delay superposition (DAS) coherent superposition, equal amplitudes will inevitably be calculated on both sides of the array, resulting in the energy not being able to be focused unidirectionally in the axial direction. Second, spatial undersampling causes severe grating lobe effect; limited by the pipe size and sensor physical size, the element spacing of a single-ring array often cannot strictly satisfy the spatial Nyquist sampling theorem (i.e., spacing). When high-frequency shortwave guided waves are incident, insufficient spatial sampling can lead to coherent enhancement of the wavefield reconstruction in directions of non-real defects, forming high-energy sidelobes or grating lobes. Third, cylindrical spiral multipath interference; the scattering path of guided waves in a pipe is not a single generatrix direction, but also a complex path that spirals multiple times along the pipe wall to reach the receiving array element. Traditional single-ring arrays lack three-dimensional spatial modulation capabilities and cannot effectively solve and delay-align multipath signals of different spiral orders, causing these signals to interfere unintended and unconstructively at incorrect pixel points.

[0005] The aforementioned defects manifest in the imaging results as typical “color banding artifacts”: the focused bright spot corresponding to the real damage is severely broadened or elongated, forming radial false color stripes along the circumference or axis; spurious color bands of equal energy appear at the axially symmetrical position of the real defect; the entire imaging background presents water ripples or cross-grid color noise, causing low-scattering energy damage such as early micro-cracks to be completely submerged by artifacts, and the system loses its ability to identify weak defects.

[0006] In summary, existing conformal array design methods fail to organically combine the three-dimensional spatial topology of the pipeline, the mechanical characteristics of guided wave propagation, and the spatial sampling constraints of the array, resulting in difficulties in synergistically improving array directivity, axial resolution, and multipath suppression capabilities. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a design method for an ultrasonic guided wave staggered conformal array for pipeline damage imaging. By optimizing the physical topology of the phased array through axial arrangement and circumferential misalignment design, an staggered conformal array (ASCA) structure is constructed. Then, by introducing polarization matching weights, directional weights, and a nonlinear coherence enhancement mechanism into the DAS imaging algorithm, polarization distortion of the conformal array is effectively compensated, and color banding is eliminated. This significantly improves the high-precision extraction and accurate imaging of pipeline damage features.

[0008] The present invention discloses a method for designing an ultrasonic guided wave staggered conformal array for pipeline damage imaging, comprising the following steps: Step S1-a: Based on the traditional single-ring uniformly distributed phased array structure, spatial expansion is carried out in the axial dimension of the pipeline to construct a multi-ring array topology composed of M rings; Step S2-a: Introduce an arithmetic misalignment mechanism in the circumferential dimension, causing the sensor of the i-th ring to rotate around the pipe axis, generating a size of The circumferential offset angles create a staggered distribution; where i = 1, 2, 3, ..., M; Step S3-a: Introduce the Euler rotation method and realize the mapping and unification of the sensor's local coordinate system and the pipeline's global coordinate system by constructing a spatial coordinate transformation matrix; Step S4-a: Combine the array topological coordinates and the guided wave characteristics of the pipeline surface to establish a three-dimensional arithmetic staggered conformal array mathematical model that integrates the polarization effect and spatial directivity characteristics of the guided wave on the pipeline surface.

[0009] Furthermore, step S1-a specifically includes: There are N sensors, evenly distributed across the cross-sections of M circular rings. Each ring contains n sensors. Construct an axial multi-ring array topology consisting of M rings; define the axial coordinate of the i-th ring on the pipe as Z. iThe axial spacing between each ring is set to be equidistant or non-equidistant according to the detection wavelength.

[0010] Furthermore, step S2-a specifically includes: The n sensors within each ring are evenly distributed at equal angles, meaning the central angle distance between adjacent sensors within the same ring is constant. ; Taking the first ring as the circumferential phase reference, that is Each of the remaining rings (i≥2) is assigned an independent overall rotation angle about the axis, called the circumferential misalignment angle. The circumferential misalignment angle of the i-th ring is... ; After staggered arrangement, the circumferential angular coordinates of the j-th sensor on the i-th ring are defined as follows: , Where j = 1, 2, 3, ..., n; The spatial coordinates of all sensors are: They form an arithmetic progression staggered conformal array; S ij R represents an independent physical node in a multi-ring array topology; R is the distance from the origin of the global coordinate system.

[0011] Furthermore, step S3-a specifically includes: Define the composite rotation matrix R(U, V, W) for a conformal array: , in, This represents the first rotation, which rotates around the original z-axis of the current coordinate system, changing only the direction of the xy-axis in the zOy plane, while the z-axis remains unchanged; Represents the second rotation, around The rotation of the new x-axis only changes the direction of the yz axis in the yOz plane, while the new x-axis remains unchanged. Represents the third rotation, around The rotation of the new z-axis only changes the orientation of the new x-axis and the new y-axis in the new xOy plane; the coordinates of the new z-axis remain unchanged. The sensor's coordinates in the local coordinate system are transformed to the pipeline's global coordinate system using a composite rotation matrix, thus obtaining the coordinates in the global coordinate system and achieving the mapping and unification between the sensor's local coordinate system and the pipeline's global coordinate system.

[0012] In step S4-a, the three-dimensional arithmetic alternating conformal array mathematical model (three-dimensional ASCA mathematical model) is as follows: , Where X(t) is the snapshot data vector, S(t) is the incident signal vector, and n(t) is the noise vector. This is the guiding vector. Due to the orientation of conformal array elements and the polarization characteristics of ultrasound, different elements respond differently to the incident signal. Therefore, in addition to the spatial guiding vector caused by the path difference, the conformal array should also include the element response vector to the ultrasound polarization. It can be represented as: , in, The final response of each array element is the product of the spatial phase and polarization response; These represent the azimuth angle, elevation angle, degree of polarization, and phase difference of polarization direction for a single array element.

[0013] This invention also provides an improved DAS imaging method for imaging pipe damage using an ultrasonic guided wave staggered conformal array, comprising the following steps: Step S1-b: Collect the original vibration signals x of the pipeline under healthy and damaged conditions respectively. health (t) and x defect (t); Step S2-b: Average and reduce noise on the original vibration signal, and use the reference subtraction method to remove the defect scattering signal. ; Step S3-b: Bandpass filter the signal obtained in step S2-b using a Butterworth filter, and extract the analytical envelope using a Hilbert transform. Step S4-b: Initialize the spatial coordinates of each sensor in the conformal misalignment array, and perform 3D meshing on the cylindrical surface of the pipe to determine the imaging pixels. Where Z is the axial coordinate and θ is the circumferential angular coordinate; Step S5-b: Calculate the flight time of the signal from the transmitter to the receiver through the target pixel based on the spiral path analysis; Step S6-b: Based on the calculated flight time, extract the analytical envelope data at the corresponding time and perform energy nonlinear pre-amplification on it; Step S7-b: Calculate the dual physical weighting, including the directional spatial filter weights. and adaptive polarization matching weights ; Step S8-b: Perform spatial joint physical weighting, multiply the nonlinear pre-amplified energy with the dual physical weighting weights, and complete the coherent superposition integration to obtain the imaging amplitude of the pixel. Step S9-b: Construct a global imaging matrix based on the imaging amplitude of all pixels, and perform normalization and contrast enhancement processing on the global imaging matrix. The final output is 3D solid envelope imaging (3D Iso-surface Rendering) and 2D unfolded surface imaging (C-scan Mapping).

[0014] Further, step S2-b specifically involves: using the reference subtraction method to remove the weak defect scattering signal. : , in, The ultrasonic signals collected from the pipeline under healthy operating conditions. The ultrasonic signals of the pipeline under damaged conditions were collected.

[0015] Furthermore, step S3-b specifically involves: applying the Hilbert transform to extract the analytic envelope E. i (t): , in, This is a Hilbert transform operation.

[0016] Further, step S4-b specifically involves: dividing the cylindrical surface of the pipe into a 3D mesh to determine the imaging pixels. ,in, Let Z be a 3D pixel on the cylindrical surface of the pipe, where Z is the axial coordinate. These are circumferential angular coordinates.

[0017] Further, step S5-b specifically involves: calculating the time of flight (TOF) of the signal from the transmitter to the receiver through the target pixel based on helical acoustic path analysis. , Among them, T TOF It is the total theoretical flight time of the guided wave from the transmitter, through the target pixel P, to the receiver; d tx d is the spiral acoustic path propagation distance from the transmitter to the target pixel P; rx C is the helical acoustic path propagation distance from the target pixel P to the receiver; g This represents the group velocity of a specific guided wave mode in this frequency band.

[0018] Furthermore, step S6-b specifically includes: Step S6-b-1: Based on the calculated flight time, extract the analytical envelope data A corresponding to the time point. , Where A represents the calculated flight time T TOFAt the corresponding moment, from the parsed envelope E i The amplitude extracted from (t); Step S6-b-2, perform energy nonlinear pre-amplification on the analytical envelope data A: , Among them, A sq This represents the amplitude after nonlinear energy pre-amplification via squaring.

[0019] Furthermore, step S7-b specifically includes: Step S7-b-1: Calculate the directional spatial filter weights W dir : , in, The angle between the propagation direction from the transmitter to the pixel and the direction of the main sound beam from the transmitter. It is the angle between the propagation direction of the pixel to the receiver and the main sensing direction of the receiver.

[0020] In pipe guided wave imaging, since the sound waves propagate along the curved surface of the cylindrical shell (helical path) rather than in a straight line in three-dimensional space, the definition of the principal direction and the calculation of the included angle must be analyzed on a two-dimensional plane (or local tangent plane) unfolded on the pipe surface.

[0021] The cylindrical surface of the pipe is unfolded into a two-dimensional plane along the axis. After (among them) For axial coordinates, Let circumferential arc length coordinates be used. ), defining the unit vector of the principal direction. This invention introduces The angular dimensions of the three can be unified into the dimension of length (arc length), thus allowing them to be unfolded in a two-dimensional plane. Accurately construct the sound path propagation vector and .

[0022] The unit vector of the main sound beam direction at the transmitting end is set to If it points to the positive axis, then The unit vector of the main sensing direction at the receiving end is set to... If the reception is in the same direction, then If there is a specific preset deflection angle ,but .

[0023] To calculate the propagation direction, it is necessary to extract the coordinates of the transmitter, pixels, and receiver on the 2D unfolded plane: Transmitter coordinates: ,in Target pixel coordinates: ,in Receiver coordinates: ,in ;in, These are the axial coordinates of the transmitter, the target imaging pixel, and the receiver on the pipe, respectively. These are the respective circumferential arc length coordinates obtained by unfolding the cylindrical surface; The initial circumferential angle position of the sensor currently acting as the transmitter in the cylindrical coordinate system of the pipe (i.e., the circumferential angle corresponding to the array element). ); For the target imaging pixel points to be reconstructed Circumferential grid angle coordinates in the circumferential direction of the pipe; This represents the initial circumferential angular position of the sensor, which is currently acting as the receiving end, in the cylindrical coordinate system of the pipe.

[0024] Subsequently, a spatial vector representing the actual propagation path of the sound wave is constructed: Propagation vector from transmitter to pixel : , Propagation vector from pixel to receiver : , Due to the circumferential continuity of the cylindrical surface (waves can propagate multiple times around the pipe wall), the difference in circumferential arc length needs to consider the shortest helical path, i.e., the difference in circumferential coordinates. Take the modulus to ensure its range is within Between, then multiply by the radius The circumferential coordinate difference refers to the relative circumferential angle between two different network locations, such as the relative angular distance between the transmitter and a pixel, or between a pixel and a receiver, used to calculate the actual shortest sound path (propagation path) of the sound wave propagating along the pipe wall; the calculation formula is: , Using the dot product formula of vectors The cosine of the angle between the propagation vector and the principal direction vector can be directly calculated, and then the angle can be obtained.

[0025] Transmitter sound field divergence angle , is the direction of the emitted sound beam With actual transmission path The angle between them; , Therefore, we can conclude that: ; Receiver sensitivity deflection It is the path of the scattered wave to the receiver. With the receiver's main sensitive direction The angle between them; , Therefore, we can conclude that: ; In actual DAS algorithm programming, since the weight formula itself is... The dot product obtained above can be directly calculated. and Substituting into the fourth power calculation eliminates the need to call computationally more expensive methods. Determining the specific angle by inverse solution can significantly improve the computational efficiency of 3D pixel mesh traversal.

[0026] Step S7-b-2, calculate the adaptive polarization matching weight W pol : , in, This represents the difference in polarization angle before and after the guided wave is scattered at the pixel.

[0027] In ultrasonic guided wave nondestructive testing, the difference in polarization angle before and after scattering of the guided wave at the pixel point is calculated. The physical essence of this is to determine the scattering angle of the sound wave. For commonly used guided wave modes, the direction of particle vibration (polarization) is usually consistent with the direction of wave propagation. Therefore, the difference in polarization angle can be equivalent to the difference between the incident wave propagation vector and the scattered wave propagation vector at the pixel point. The spatial angle at the point. The steps to calculate this angle difference on the two-dimensional unfolded surface of the pipe are as follows: 1) Construct the incident and scattering vectors at pixel P; Unfold the cylindrical surface into a two-dimensional plane. coordinate system ( For axial coordinates, (Circumferential arc length coordinates) Incident wave vector Represents guided waves from the transmitting end Reach the target pixel The direction of propagation, its vector direction is from point to : , Scattered wave vector Represents the waveguide at the pixel. After defect scattering occurs, it propagates to the receiver. The direction of , its vector direction is from point to : , Due to the circumferential closed nature of the pipeline, calculation and When doing so, the shortest spiral arc length on the cylindrical surface must be taken, meaning the angle difference is limited to a certain value. Multiply by the radius within the range .

[0028] 2) Calculate the polarization angle difference using vector dot product ; The angle between the incident vector and the scattered vector is the polarization angle difference. Using the dot product formula The cosine value of that angle can be calculated: , Expanding it into an algebraic form with specific coordinates: , When calculating the adaptive polarization matching weights, the above formula can be directly substituted into... In the middle, no inverse solution is needed. This improves the algorithm's traversal efficiency. The processing speed of pixel grids.

[0029] Further, step S8-b specifically involves multiplying the nonlinearly pre-amplified energy with the double weights to complete the coherent superposition integration and obtain the imaging amplitude I(P) of the pixel: , Where I(P) represents the final imaging amplitude of the target pixel P, i.e., the damage probability.

[0030] Further, step S9-b specifically involves: normalizing and enhancing the contrast of the global imaging results. , Among them, I norm is the normalized global imaging amplitude matrix, typically ranging from (0,1); I is the set containing all pixels I(P), i.e., the unnormalized global imaging matrix; max(I) is the maximum amplitude value in the global imaging matrix I.

[0031] The beneficial effects of this invention are as follows: The method described in this invention constructs an arithmetic staggered conformal array (ASCA) structure by axially arranging and circumferentially misaligning a traditional phased array. This breaks the inherent spatial symmetry limitations of traditional arrays at the physical topology level, achieving a full-range improvement in imaging resolution. It also avoids the decreased monitoring efficiency caused by low array directivity in complex working conditions of traditional ring arrays. It effectively optimizes the spatial topology parameters of the sensor array and eliminates guided wave scattering and polarization distortion interference caused by the complex and harsh environment of the pipeline. By introducing polarization matching weights, directivity weights, and nonlinear coherence enhancement mechanisms, the traditional DAS algorithm is improved, resulting in an improved DAS imaging method that avoids common problems in traditional imaging methods such as polarization distortion and color banding artifacts. Simultaneously, this method can better adapt to the characteristics of curved guided waves in pipelines, improving the signal-to-noise ratio and thus more accurately extracting damage features. Furthermore, it can better integrate mechanical and axial characteristic information of the pipeline, achieving high-precision damage reconstruction and accurate imaging through the improved DAS algorithm. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of sensor topology optimization; Figure 2 This is a logical structure diagram of the DAS imaging algorithm; Figure 3 This is a schematic diagram of Euler rotation; Figure 4 This is a schematic diagram of the experimental equipment; Figure 5 These are ultrasonic signal diagrams corresponding to different working conditions; Figure 6 These are spatial polar coordinate directivity diagrams of the array's energy reception at different azimuth angles; Figure 7 It is the directional beammap at the location of spatial damage in the imaging. Figure 8 It is a comparison of the circumferential unfolded surface imaging of different arrays; Figure 9 It is a 3D imaging reconstruction that satisfies polarization and directional characteristics; Figure 10 This is a flowchart of the ultrasonic guided wave equal arithmetic staggered conformal array design method for pipeline damage imaging; Figure 11 This is a flowchart of an improved DAS imaging method using an ultrasonic guided wave staggered conformal array for pipeline damage imaging. Detailed Implementation

[0033] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0034] like Figure 10 As shown, the ultrasonic guided wave staggered conformal array design method for pipeline damage imaging according to the present invention includes the following steps: Step S1-a: Based on the traditional single-ring uniformly distributed phased array structure, spatial expansion is carried out in the axial dimension of the pipeline to construct a multi-ring array topology composed of M rings; Step S2-a: Introduce a misalignment mechanism in the circumferential dimension, causing the sensor of the i-th ring to rotate around the pipe axis, generating a size of The circumferential offset angle, thus forming a misaligned distribution; Step S3-a: Introduce the Euler rotation method and realize the mapping and unification of the sensor's local coordinate system and the pipeline's global coordinate system by constructing a spatial coordinate transformation matrix; Step S4-a: Combine the array topological coordinates and the guided wave characteristics of the pipeline surface to establish a three-dimensional arithmetic staggered conformal array mathematical model that integrates the polarization effect and spatial directivity characteristics of the guided wave on the pipeline surface.

[0035] In this embodiment, the influence of polarization on the received signal from the curved surface of the pipe is simulated by the amplitude of the sensor signal received in different circumferential directions. Since the conformal array elements are uniformly distributed along the circumference of the pipe, the directional main lobe is kept aligned with the damaged area during the experiment. By sequentially selecting array elements at different circumferential positions for reception, the rotation of the receiving sensitive direction is effectively achieved. By comparing the signal amplitudes of array elements at different angles, the array element direction corresponding to the largest amplitude is the optimal polarization sensitive direction, thus completing the polarization direction determination and polarization matching.

[0036] Arithmetic progression refers to rotating sequentially around the first ring of reference elements as the 0° direction, with each subsequent ring rotating in a fixed angle relative to the previous ring. For example, the second ring rotates by 11.25°, the third ring by 22.5°, and the fourth ring by 33.75°. The difference between the angle of rotation in each ring and the angle of rotation in the previous ring is always 11.25°.

[0037] like Figure 1 As shown, Figure 1 (a) is a traditional array layout for pipelines, where the sensors are evenly arranged in a ring along the outer edge of the pipeline, resulting in low axial resolution; Figure 1 (b) shows a conformal array layout for the pipeline, which effectively improves the axial resolution of the array detection. Figure 1 (c) is a pipe equal-arithmetic staggered conformal array layout, which has good axial and circumferential resolution and eliminates detection blind spots.

[0038] like Figure 3 As shown, step S3-a specifically involves achieving a composite transformation effect through the right multiplication of the three fundamental rotation matrices.

[0039] (1) The fundamental rotation matrix of a single coordinate axis; A single rotation around different coordinate axes corresponds to a fixed-form 3×3 orthogonal matrix. Furthermore, it satisfies... That is, the vector magnitude remains unchanged after rotation, and the orthogonality remains unchanged.

[0040] 1) Rotation matrix around the z-axis When rotating about the z-axis, the x-axis and y-axis rotate in the xOy plane, while the z-axis coordinate remains unchanged. Its matrix form is: ; 2) Rotation matrix around the y-axis When rotating about the y-axis, the x-axis and z-axis rotate in the xOz plane, while the y-axis coordinate remains unchanged. Its matrix form is: ; 3) Rotation matrix around the x-axis When rotating about the x-axis, the y-axis and z-axis rotate in the yOz plane, while the x-axis coordinate remains unchanged. Its matrix form is: , Where c, k, and g are the rotation angles about the z-axis, y-axis, and x-axis, respectively, with the counterclockwise direction being positive, following the right-hand screw rule.

[0041] In order to unify the local coordinate system of the sensors located on the pipeline surface with the global coordinate system set according to the pipeline, the local coordinate system is adjusted by three rotations so that the coordinate axes are aligned with the global coordinate axes.

[0042] Define a composite rotation matrix R(U, V, W) for a conformal array as a right-multiplied combination of three fundamental rotations, with the rotation order from right to left, performing the rotation of the right-hand matrix first. , in, This represents the first rotation, which rotates around the original z-axis of the current coordinate system, changing only the direction of the xy-axis in the zOy plane, while the z-axis remains unchanged; Represents the second rotation, around The new "x-axis" generated after rotation only changes the direction of the yz axis in the yOz plane, while the new x-axis remains unchanged; Represents the third rotation, around The rotation of the newly generated "z-axis" only changes the orientation of the new x and y axes in the new xOy plane; the coordinates of the new z-axis remain unchanged.

[0043] After matrix multiplication, the composite rotation matrix obtained based on Euler rotation is: , Substituting the three fundamental matrices and expanding them, we obtain a combination of trigonometric functions U, V, and W. matrix.

[0044] (3) Coordinate system transformation of vectors; If the coordinates of a vector in the initial coordinate system (such as a local rectangular coordinate system) are... By using the composite rotation matrix R(U,V,W), its coordinates in the target coordinate system (such as the global Cartesian coordinate system) can be obtained. .

[0045] like Figure 2 and Figure 11 As shown, the improved DAS imaging method for pipeline damage imaging using an ultrasonic guided wave staggered conformal array according to the present invention includes the following steps: Step S1-b: Collect the original vibration signals x of the pipeline under healthy and damaged conditions respectively. health (t) and x defect (t); Step S2-b: Average and reduce noise on the original vibration signal, and use the reference subtraction method to remove the defect scattering signal. ; Step S3-b: Bandpass filter the signal obtained in step S2-b using a Butterworth filter, and extract the analytical envelope using a Hilbert transform. Step S4-b: Initialize the spatial coordinates of each sensor in the conformal misalignment array, and perform 3D meshing on the cylindrical surface of the pipe to determine the imaging pixels. Where Z is the axial coordinate and θ is the circumferential angular coordinate; Step S5-b: Calculate the flight time of the signal from the transmitter to the receiver through the target pixel based on the spiral path analysis; Step S6-b: Based on the calculated flight time, extract the analytical envelope data at the corresponding time and perform energy nonlinear pre-amplification on it; Step S7-b: Calculate the dual physical weighting, including the directional spatial filter weights. and adaptive polarization matching weights ; Step S8-b: Perform spatial joint physical weighting, multiply the nonlinear pre-amplified energy with the dual physical weighting weights, and complete the coherent superposition integration to obtain the imaging amplitude of the pixel. Step S9-b: Construct a global imaging matrix based on the imaging amplitude of all pixels, and perform normalization and contrast enhancement processing on the global imaging matrix. The final output is 3D solid envelope imaging (3D Iso-surface Rendering) and 2D unfolded surface imaging (C-scan Mapping).

[0046] In this embodiment, the collected data is processed according to the steps described above to achieve accurate imaging of pipeline damage.

[0047] The experiment was divided into two parts: signal acquisition under healthy pipeline conditions and signal acquisition under damaged pipeline conditions. The experimental system consisted of an experimental pipeline, piezoelectric sensors, signal acquisition boards, signal transceivers, and a control terminal. Ultrasonic signals were transmitted into the pipeline by fixed sensors. Receiving sensors were arranged in an ASCA topology to acquire guided wave signals from the pipeline under healthy and damaged conditions. The experimental equipment included… Figure 4 As shown, the ultrasonic signal is amplified, bandpass filtered, and converted from analog to digital by the board and signal transceiver equipment before being transmitted to the control terminal.

[0048] Step S2-b specifically involves stripping away the weak defect scattering signal using a reference subtraction method, such as... Figure 5 As shown, where, Figure 5 (a) is the original waveform acquired in the healthy pipeline. Figure 5 (b) shows the original waveform acquired in the damaged pipe. Figure 5 (c) is the superimposed waveform of the waveform acquired from the healthy pipeline and the waveform acquired from the damaged pipeline. Figure 5 (d) is Figure 5 The waveform obtained by subtracting the two waveforms in (c) represents the extracted ultrasonic scattering signal that will be processed later. Figure 5 (a) and Figure 5 As shown in (b), the scattering energy of the real defect is extremely weak. Figure 5 In the superposition comparison of (c), it can be observed that the macroscopic waveforms of the two sets of signals highly overlap, with the high-energy direct wave and initial clutter dominating, completely masking the defect characteristics. After applying the reference subtraction, as shown... Figure 5 As shown in (d), the dominant direct wave background was successfully suppressed. A magnified view clearly shows that the high-frequency defect scattering wave packets, originally hidden under strong background noise, were precisely extracted.

[0049] Step S4-b specifically involves: dividing the cylindrical surface of the pipe into a 3D mesh to determine the imaging pixels. .in, Let Z be a 3D pixel on the cylindrical surface of the pipe, where Z is the axial coordinate. These are circumferential angular coordinates.

[0050] Mesh division is based on the minimum effective wavelength in the detected signal. Divide into sections.

[0051] Standards for setting imaging grid density: Lower bound of the spatial Nyquist criterion: In order to fully reconstruct the scattered wave field of the defect in the spatial domain without spatial aliasing, the physical step size of the mesh must be satisfied. .

[0052] The specific steps for 3D mesh generation: 1) Determine the minimum wavelength; Based on the highest frequency of the excitation signal (For example, in the 60-100kHz frequency band, take 80kHz) and the group velocity of a specific guided wave mode. Calculate the minimum wavelength of the guided wave in the pipe material: , 2) Set the axial mesh step size ; Based on the expected positioning accuracy and computer memory limitations, select a reasonable subdivision scaling factor. (Usually 4 to 10 are selected): ; 3) Set the circumferential angle step size ; To ensure the isotropy of pixels in 3D space (i.e., the physical dimensions of pixels are approximately the same in the axial and circumferential directions), the circumferential arc length... It should be equal to the axial step size. ; Utilizing the outer diameter of the pipe Calculate the corresponding circumferential angle step size (in radians): ; 4) Generate the global pixel matrix; Based on the total axial length of the pipeline The number of axial nodes is divided into Based on the characteristics of a cylindrical surface, the number of circumferential nodes is divided into: The algorithm will traverse the Each pixel is coherently superimposed and integrated.

[0053] Step S5-b specifically involves: calculating the time of flight (TOF) of the signal from the transmitter to the receiver through the target pixel based on helical acoustic path analysis. , Among them, T TOF d is the total theoretical flight time of the guided wave from the transmitter, through the target pixel P, to the receiver. tx Let d be the helical acoustic path propagation distance from the transmitter to the target pixel P. rx C is the helical acoustic path propagation distance from the target pixel P to the receiver; g This represents the group velocity of a specific guided wave mode in this frequency band.

[0054] Step S6-b specifically includes: Step S6-b-1: Based on the calculated flight time, extract the analytical envelope data A corresponding to the time point. , Where A represents the calculated flight time T TOF At the corresponding moment, from the parsed envelope E i The amplitude extracted from (t); Step S6-b-2, perform energy nonlinear pre-amplification on the analytical envelope data A: , Where Asq represents the amplitude after nonlinear energy pre-amplification through squaring.

[0055] Traditional DAS algorithms typically perform coherent superposition of the extracted signal amplitudes (or envelope amplitudes), a linear process that reflects the spatial superposition of sound pressure amplitudes. This invention squares the amplitudes before superposition, shifting the algorithm from amplitude calculation to energy calculation. This results in: 1) At the focal point of coherent superposition (i.e., the actual defect location), the multi-channel signals are in phase. After squaring, the high amplitude of the actual signal is non-linearly amplified; while background noise and incoherent clutter amplitudes are usually small, and squaring them further reduces their size, effectively amplifying strong signals and suppressing weak noise; 2) In the imaging image, the defect appears as a high-energy main lobe. The energy squaring operation makes the main lobe steeper and sharper (sharpened), resulting in clearer defect boundary contours in 3D or 2D imaging, thus improving spatial resolution.

[0056] Due to limitations in array aperture and sensor spacing, traditional DAS algorithms inevitably produce sidelobe or grating lobe artifacts at non-defect locations. This invention effectively reduces these artifacts by using nonlinear energy amplification combined with subsequent multiplicative weights.

[0057] Step S7-b is as follows: Step S7-b-1: Calculate the directional spatial filter weights W dir : , in, The angle between the propagation direction from the transmitter to the pixel and the direction of the main sound beam from the transmitter. It is the angle between the propagation direction of the pixel to the receiver and the main sensing direction of the receiver.

[0058] like Figure 6 As shown, Figure 6 (a) is the sensor in Radial and tangential signal amplitudes (directly facing the defect); Figure 6 (b) is the sensor in Radial and tangential signal amplitudes in the polarization dead zone; Figure 6 (c) is the sensor in (Radial and tangential signal amplitudes at the back of the pipe); Figure 6 (d) is the spatial polar coordinate pointing map of the array's received energy. The spatial polar coordinate pointing map of the array's received energy produces a "dumbbell" shape. This indicates that the array has the highest sensitivity near 0° and 180° when receiving energy, while severe polarization blind zones appear near 90° and 270°. Therefore, due to the inherent spatial anisotropy of the curved conformal array during reception, a polarization matching processing mechanism needs to be introduced in the later data processing to ensure a balanced distribution of imaging energy.

[0059] Step S7-b-2, calculate the adaptive polarization matching weight W pol : , in, This represents the difference in polarization angle before and after the guided wave is scattered at the pixel.

[0060] like Figure 7 As shown, Figure 7 (a) is a comparison of the log-scale normalized point spread function (PSF) of different array topologies at the defect center (Z=350mm); Figure 7 (b) is a circumferential directional profile (showing the side lobe suppression capability); Figure 7 (c) is an axial resolution profile (demonstrating spatial focusing capability). For example... Figure 7 As shown in (a), the decisive influence of the array's spatial topology on beamforming can be observed. First, due to spatial aliasing, traditional single-ring arrays generate extremely high-level grating lobes in multiple non-target directions, with some grating lobe levels even approaching the main lobe. This means that in complex tube wall wavefields, this array is highly susceptible to misinterpreting circumferential background noise as defects, leading to severe imaging artifacts. Second, while the multi-ring aligned array significantly narrows the main lobe width at 0°, the strict axial alignment of its elements fails to break the periodicity of spatial sampling. Therefore, this array still retains a significant sidelobe leakage of approximately -20dB near 90° and 270°. The misaligned arrangement breaks the array's circumferential symmetry. In addition to maintaining high-purity energy focusing in the 0° defect direction, this array deeply and uniformly suppresses the sidelobe levels across the entire circumference (non-target region) into a low-noise region of -20dB to -30dB. Figure 7As shown in (b), in the circumferential slice, the traditional single-ring array exhibits significant grating lobes in non-defect directions due to spatial aliasing caused by uniform sampling. Multi-ring aligned arrays and equal-arithmetic staggered conformal arrays have a significant suppressive effect on circumferential grating lobes. It can be observed from the figure that within the circumferential range of 90° to 270°, the curve of the equal-arithmetic staggered conformal array tends to be flatter, with energy concentrated in the main beam, and its sidelobe levels are significantly suppressed. Figure 7 In (c), in the axial slice, the main lobes of the multi-ring aligned array and the equal-arithmetic staggered conformal array are significantly narrower than those of the traditional single-ring array, and the main lobe energy is closer to the actual defect location. Furthermore, due to... Figure 7 As shown in (c) axial slices, traditional single-ring arrays, lacking axial spatial sampling, exhibit extremely wide main lobes, leading to severe axial energy tailing. Introducing a multi-ring arrangement significantly narrows the axial full width at half maximum (FWHM) at -6 dB. This indicates that expanding the axial aperture fundamentally improves the system's axial spatial resolution.

[0061] In terms of circumferential spatial filtering performance, different topologies exhibit significant differences. For example... Figure 7 As shown in (a), the uniform sampling of a single-ring array in the circumferential direction easily induces spatial aliasing, resulting in strong grating lobes near 45° and 230°. These high-level sidelobes create strong artifacts in the final 2D imaging. In contrast, the multi-ring structure effectively suppresses these coherent noises. In particular, the circumferential background noise floor of the arithmetic staggered conformal array is more smoothly and uniformly maintained in the extremely low level range of -20dB to -25dB.

[0062] Step S8-b specifically involves multiplying the nonlinearly pre-amplified energy by the double weights to complete the coherent superposition integration and obtain the imaging amplitude I(P) of the pixel. , Where I(P) represents the final imaging amplitude of the target pixel P, i.e., the damage probability.

[0063] Step S9-b specifically involves: normalizing and enhancing the contrast of the global imaging results. , Among them, I norm is the normalized global imaging amplitude matrix, typically ranging from (0,1); I is the set containing all pixels I(P), i.e., the unnormalized global imaging matrix; max(I) is the maximum amplitude value in the global imaging matrix I.

[0064] Under a unified DAS differential imaging algorithm, the imaging quality of the three arrays exhibits significant differences determined by the hardware spatial topology. For example... Figure 8 As shown, Figure 8 (a) represents a schematic diagram of a traditional pipeline array arrangement. Figure 8 (b) represents a schematic diagram of the conformal array arrangement of pipes. Figure 8 (c) represents a schematic diagram of the conformal array arrangement of pipelines with equal and alternating arithmetic progressions. From Figure 8 As can be seen in (a), traditional single-ring arrays, due to the lack of axial synthetic aperture and circumferential periodic sampling, suffer from severe "V"-shaped spatial aliasing and raster lobe artifacts; from Figure 8 As can be seen in (b), although the conformal multi-ring array effectively compresses the axial tail of the focal point by expanding the axial aperture, it still retains obvious radial side lobes in the circumferential direction because it does not break the spatial symmetry. In contrast, Figure 8 In (c), ASCA imaging yielded the best results, with extremely sharp defect focal points and a clean background across the entire field. Because the staggered arrangement completely disrupts the spatial periodicity of the array, it induces destructive interference of non-target direction interference noise at the physical level. This result effectively demonstrates that even using the most basic equal-weighted superposition algorithm, this arithmetic staggered conformal array topology can achieve high-contrast, high-precision imaging of weak damage in complex tube wall wavefields.

[0065] like Figure 9 As shown, Figure 9 (a) represents the measured data of the pipe cylindrical surface unfolding imaging and 3D reconstruction imaging (polarization matching only). Figure 9 (b) represents the measured data of the unfolded imaging of the cylindrical surface of the pipe (only for optimization). Figure 9 (c) represents the unfolded imaging of the cylindrical surface of the pipe (directivity optimization + polarization matching). From the unfolded cylindrical surface image and the 3D reconstructed imaging results, as shown... Figure 9 (a) Single polarization matching or as Figure 9 While single-directivity optimization (b) can initially indicate the circumferential and axial positions of defects, it suffers from significant energy dissipation and spatial soft scattering artifacts, resulting in unclear physical boundaries of the defects. In contrast, from Figure 9 (c) shows that when both directivity optimization and polarization matching mechanisms are satisfied, spatial clutter and sidelobe interference are completely suppressed, and reflected energy is realized in the real defect region. High-intensity convergence within )

[0066] The above description is merely a preferred embodiment of the present invention and is not intended to further limit the present invention. All equivalent changes made based on the description and drawings of the present invention are within the protection scope of the present invention.

Claims

1. A method for designing an ultrasonic guided wave staggered conformal array for pipeline damage imaging, characterized in that, Includes the following steps: Step S1-a: Based on the traditional single-ring uniformly distributed phased array structure, spatial expansion is carried out in the axial dimension of the pipeline to construct a multi-ring array topology composed of M rings; Step S2-a: Introduce an arithmetic misalignment mechanism in the circumferential dimension, causing the sensor of the i-th ring to rotate around the pipe axis, generating a size of The circumferential offset angles create a staggered distribution; where i = 1, 2, 3, ..., M; Step S3-a: Introduce the Euler rotation method and realize the mapping and unification of the sensor's local coordinate system and the pipeline's global coordinate system by constructing a spatial coordinate transformation matrix; Step S4-a: Combine the array topological coordinates and the guided wave characteristics of the pipeline surface to establish a three-dimensional arithmetic staggered conformal array mathematical model that integrates the polarization effect and spatial directivity characteristics of the guided wave on the pipeline surface.

2. The ultrasonic guided wave staggered conformal array design method for pipeline damage imaging according to claim 1, characterized in that, Step S1-a specifically includes: There are N sensors, evenly distributed across the cross-sections of M circular rings. Each ring contains n sensors. Construct an axial multi-ring array topology consisting of M rings; Let the axial coordinate of the i-th ring on the pipe be Z. i The axial spacing between each ring is set to be equidistant or non-equidistant according to the detection wavelength.

3. The ultrasonic guided wave staggered conformal array design method for pipeline damage imaging according to claim 2, characterized in that, Step S2-a specifically includes: The n sensors within each ring are evenly distributed at equal angles, meaning the central angle distance between adjacent sensors within the same ring is constant. ; Taking the first ring as the circumferential phase reference, that is Each of the remaining rings is given an independent overall rotation angle about the axis, called the circumferential misalignment angle. The circumferential misalignment angle of the i-th ring is... ; After staggered arrangement, the circumferential angular coordinates of the j-th sensor on the i-th ring are defined as follows: ， Where j = 1, 2, 3, ..., n; The spatial coordinates of all sensors are: They form an arithmetic progression staggered conformal array; S ij R represents an independent physical node in a multi-ring array topology; R is the distance from the origin of the global coordinate system.

4. The ultrasonic guided wave staggered conformal array design method for pipeline damage imaging according to claim 1, characterized in that, Step S3-a specifically includes: Define the composite rotation matrix R(U, V, W) for a conformal array: ， in, This represents the first rotation, which rotates around the original z-axis of the current coordinate system, changing only the direction of the xy-axis in the zOy plane, while the z-axis remains unchanged; Represents the second rotation, around The rotation of the new x-axis only changes the direction of the yz axis in the yOz plane, while the new x-axis remains unchanged. Represents the third rotation, around The rotation of the new z-axis only changes the orientation of the new x-axis and the new y-axis in the new xOy plane; the coordinates of the new z-axis remain unchanged. The sensor's coordinates in the local coordinate system are transformed to the pipeline's global coordinate system using a composite rotation matrix, thus obtaining the coordinates in the global coordinate system and achieving the mapping and unification between the sensor's local coordinate system and the pipeline's global coordinate system.

5. An improved DAS imaging method using an ultrasonic guided wave staggered conformal array for pipeline damage imaging, characterized in that, Includes the following steps: Step S1-b: Collect the original vibration signals x of the pipeline under healthy and damaged conditions respectively. health (t) and x defect (t); Step S2-b: Average and reduce noise on the original vibration signal, and use the reference subtraction method to remove the defect scattering signal. ; Step S3-b: Bandpass filter the signal obtained in step S2-b using a Butterworth filter, and extract the analytical envelope using a Hilbert transform. Step S4-b: Initialize the spatial coordinates of each sensor in the arithmetic progression staggered conformal array, and perform 3D meshing on the cylindrical surface of the pipe to determine the imaging pixels. Where Z is the axial coordinate and θ is the circumferential angular coordinate; Step S5-b: Calculate the flight time of the signal from the transmitter to the receiver through the target pixel based on the spiral path analysis; Step S6-b: Based on the calculated flight time, extract the analytical envelope data corresponding to the time from the analytical envelope and perform energy nonlinear pre-amplification on it; Step S7-b: Calculate the dual physical weighting, including the directional spatial filter weights. and adaptive polarization matching weights ; Step S8-b: Perform spatial joint physical weighting, multiply the nonlinear pre-amplified energy with the dual physical weighting weights, and complete the coherent superposition integration to obtain the imaging amplitude of the pixel. Step S9-b: Construct a global imaging matrix based on the imaging amplitude of all pixels, normalize and enhance the contrast of the global imaging matrix, and finally output 3D solid envelope imaging and 2D unfolded surface imaging.

6. An improved DAS imaging method for pipe damage imaging using an ultrasonic guided wave equal-aberration staggered conformal array according to claim 5, characterized in that, Step S5-b specifically involves: Based on the analytical calculation of the helical acoustic path, the flight time of the signal from the transmitter to the receiver through the target pixel is calculated as follows: ， Among them, T TOF It is the total theoretical flight time of the guided wave from the transmitter, through the target pixel P, to the receiver; d tx d is the spiral acoustic path propagation distance from the transmitter to the target pixel P; rx C is the helical acoustic path propagation distance from the target pixel P to the receiver; g This represents the group velocity of a specific guided wave mode in this frequency band.

7. An improved DAS imaging method for pipe damage imaging using an ultrasonic guided wave staggered conformal array according to claim 5, characterized in that, Step S6-b specifically includes: Step S6-b-1: Based on the calculated flight time, extract the analytical envelope data A corresponding to the time point. ， Where A represents the calculated flight time T TOF At the corresponding moment, from the parsed envelope E i The amplitude extracted from (t); Step S6-b-2: Perform energy nonlinear pre-amplification on the analytical envelope data A: ， Among them, A sq This represents the amplitude after nonlinear energy pre-amplification via squaring.

8. An improved DAS imaging method for pipe damage imaging using an ultrasonic guided wave staggered conformal array according to claim 5, characterized in that, Step S7-b is as follows: Step S7-b-1: Calculate the directional spatial filter weights. : ， in, The angle between the propagation direction from the transmitter to the pixel and the direction of the main sound beam from the transmitter. The angle between the propagation direction of the pixel to the receiver and the main sensing direction of the receiver; Step S7-b-2: Calculate the adaptive polarization matching weights : ， in, This represents the difference in polarization angle before and after the guided wave is scattered at the pixel.

9. An improved DAS imaging method for pipe damage imaging using an ultrasonic guided wave equal-aberration staggered conformal array according to claim 5, characterized in that, Step S8-b specifically includes: The nonlinearly pre-amplified energy is multiplied by the double weights, and coherent superposition integration is performed to obtain the imaging amplitude I(P) of the pixel: ， Where I(P) represents the final imaging amplitude of the target pixel P, i.e., the damage probability; Indicates the directional spatial filter weights; Indicates the adaptive polarization matching weight; This represents the amplitude after nonlinear energy pre-amplification via squaring.

10. An improved DAS imaging method for pipe damage imaging using an ultrasonic guided wave equal-aberration staggered conformal array according to claim 5, characterized in that, Step S9-b is as follows: The global imaging results are normalized and contrast enhanced. ， in, is the normalized global imaging amplitude matrix; I is the set containing the imaging amplitudes I(P) of all pixels, i.e., the unnormalized global imaging matrix; max(I) is the maximum amplitude value in the global imaging matrix I.

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