Double-array MUSIC beam forming damage positioning method and system

Abstract

The invention provides a double-array MUSIC beam forming damage positioning method and system, and relates to the technical field of material safety monitoring. Two symmetrically distributed linear piezoelectric sensor arrays are arranged on the surface of a plate-shaped structure, symmetric excitation is applied to excite S0 modal Lamb waves, and damage scattering signals are synchronously received by the double arrays; performing covariance matrix decomposition on the received signal by using a MUSIC algorithm, constructing a spatial spectrum in combination with noise subspace and steering vector orthogonality, generating a double-positioning map, performing cross validation and superposition fusion, and determining a final damage position; meanwhile, a beam forming technology is introduced, spatial filtering is carried out on array signals by adopting a time delay weighted summation method, the signal gain in the target direction is enhanced, clutter interference is suppressed, and the signal-to-noise ratio and the positioning resolution are improved. According to the method, high-precision and high-reliability damage positioning is realized, and the method is suitable for health monitoring of the plate-shaped structure in a complex environment.

Description

Technical Field

[0001] This application discloses a dual-array MUSIC beamforming damage localization method and system, which relates to the field of materials safety monitoring technology. Background Technology

[0002] High-speed trains, as a key component of modern transportation systems, are highly favored for their efficiency and speed. However, with increasing operating time and the influence of the external environment, high-speed train bodies inevitably suffer various types of damage, such as cracks, delamination, and corrosion. If these damages are not detected and addressed in a timely manner, they will seriously threaten the safe operation of the train and may even lead to major accidents. Therefore, regular or real-time damage monitoring and assessment of high-speed train bodies is particularly important. Traditional detection methods, such as visual inspection and impact testing, are not only inefficient but also difficult to detect minute damage. With the advancement of technology, non-destructive testing (NDT) techniques are increasingly being applied to damage monitoring of high-speed train bodies. Among these, Lamb wave-based damage imaging technology has attracted considerable attention due to its unique advantages.

[0003] In high-speed train body damage imaging research, key technologies such as finite element analysis (FEM), Lamb wave excitation technology, multiple signal input classification (MUSIC) algorithm, dual-sensor array cross-localization, and beamforming algorithm have played a crucial role. FEM is a powerful numerical analysis tool capable of simulating the mechanical behavior of complex structures and materials. In high-speed train body damage imaging research, FEM can be used to establish a three-dimensional model of the vehicle body and simulate damage under different operating conditions. This helps researchers understand the impact of damage on the vehicle structure, providing a theoretical basis for subsequent damage detection and assessment. Simultaneously, FEM can optimize sensor placement and excitation methods, improving the accuracy and efficiency of damage detection. Lamb waves are elastic waves propagating in plate-like structures, possessing advantages such as sensitivity to minor structural damage, long propagation distance, and ease of excitation and reception. In high-speed train body damage monitoring, by selecting appropriate excitation methods and sensor placement, Lamb wave signals can be excited and received. When Lamb waves encounter damage, reflection and scattering occur, leading to signal changes. By analyzing these changes, the location and size of the damage can be determined. To extract damage-related features, researchers used the Multiple Signal Input Classification (MUSIC) algorithm to process the signals captured by the sensor array. MUSIC is a high-resolution signal processing technique capable of identifying useful information from signals received from multiple sensors, providing accurate data support for damage localization.

[0004] To improve the accuracy and precision of damage localization, researchers employed a dual-sensor array for cross-localization. By simultaneously deploying two or more sensor arrays and comparing the differences in their received signals, precise determination of the damage location can be achieved. Furthermore, combining beamforming algorithms with spatial filtering of the array signals further reduces clutter interference, improving signal quality and localization accuracy. Beamforming is a signal processing technique that adjusts the phase and amplitude of the received signals from each sensor in the array, enhancing signals in specific directions while suppressing signals in other directions. This method has significant advantages and promising applications in high-speed train body damage imaging research.

[0005] Although Lamb wave-based damage imaging technology has achieved significant results in high-speed train body damage monitoring, several technical challenges remain. For example, the complex structure of high-speed train bodies and the varying types and degrees of damage in different parts necessitate the selection of appropriate excitation methods and sensor arrangements to improve the accuracy and efficiency of damage detection. Furthermore, in practical applications, environmental noise, temperature variations, and other factors can interfere with the propagation and reception of Lamb waves, affecting the accuracy of damage detection. Therefore, effectively reducing the impact of these interference factors is an important direction for future research. To overcome these challenges, researchers can further explore the propagation characteristics of Lamb waves in high-speed train bodies and optimize excitation methods and sensor arrangements. Simultaneously, combining other non-destructive testing techniques, such as ultrasonic testing and infrared thermal imaging, can form a multimodal damage monitoring system, improving the accuracy and reliability of damage detection. In addition, advanced technologies such as artificial intelligence and machine learning can be used to intelligently process and analyze the signals captured by the sensor array, enabling automatic damage identification and localization.

[0006] In conclusion, Lamb wave-based damage imaging technology has broad application prospects and significant research value in high-speed train body damage monitoring. Continuous optimization and improvement of related technologies can provide strong support for the safe operation of high-speed trains and promote the sustainable development of the transportation industry.

[0007] Currently, dual-array MUSIC beamforming damage localization methods only employ single-array MUSIC damage imaging methods. A proposed high-precision guided wave quantitative imaging method based on numerical approximation comprises the following steps: Step 1: Sequentially driving the PZT array elements of the linear array to generate guided waves, simultaneously acquiring the guided wave signals received by all other PZT array elements, and extracting the array difference signal between the damaged and healthy states, which is the damage scattering array signal; Step 2: Setting a scanning position (r, θ) within the monitoring area, and using the central array element of the linear array as the reference element, calculating the PZT of each excitation element. q represents the time delay from the reference element to the scanning position; by accumulating the delay, the response signal and the maximum value of the signal amplitude of each element in the array are obtained, and the sum of squares of the maximum value of the signal amplitude of each element in the array is calculated and recorded; Step 3: Repeat step 2 until the scanning of the monitoring area is completed, extract the search step with the largest sum of squares of the maximum value, and obtain the corresponding enhanced scattering array signal x′-p(t) that is focused on the damage location; Step 4: Calculate the covariance matrix of the enhanced damage scattering array signal; and perform eigenvalue decomposition on it to obtain the noise spanned by the eigenvectors corresponding to the small eigenvalues. Subspace; Step 5: Set a scanning position (r, θ) again, calculate the direction from the search position to each element in the array, and adaptively select the propagation velocity in the corresponding direction of each element to calculate the array manifold vector based on the pre-measured waveguide velocities on the structure; Step 6: Calculate the reciprocal of the magnitude of the product of the noise subspace and the array manifold vector at the scanning position, and record it as the spatial spectrum P(r, θ) of the scanning position; Step 7: Repeat steps 5-6 until the scanning of the monitoring area is completed; Draw an image with the spatial spectrum as pixel values, and the peak of the search image is the damage location. However, the main drawbacks of this technology are that its sensitivity to environmental factors may lead to positioning errors, its high requirements for hardware performance may increase the complexity and cost of the system, its computational complexity and real-time issues may affect the real-time monitoring capability of the system, its insufficient adaptability to complex structures may limit its promotion in practical applications such as high-speed trains, and its insufficient robustness to noise and interference may lead to a decrease in positioning accuracy. Therefore, future research needs to address these shortcomings to improve the overall performance and practicality of the system. Summary of the Invention

[0008] This application provides a dual-array MUSIC beamforming damage localization method and system to solve the technical problems of low positioning accuracy and poor robustness of existing Lamb wave-based damage localization technology in complex environments due to signal interference, noise effects, and insufficient spatial coverage of a single array.

[0009] Firstly, a dual-array MUSIC beamforming damage localization method includes: Two linear sensor arrays are symmetrically arranged on the surface of the plate-like structure under test. Each array consists of multiple piezoelectric sensing units that are evenly spaced. By applying a symmetrical excitation signal at a specific location on the structure, a single S0 mode Lamb wave is excited, which propagates within the plate and interacts with potential damage to generate a scattered signal; the response signal is received synchronously by two sensor arrays, and the time-domain waveform and frequency-domain characteristics of the signal are extracted respectively. A covariance matrix is ​​constructed from the received signal and eigenvalue decomposition is performed to separate the signal subspace and noise subspace. A spatial spectrum function is established based on the orthogonality between the noise subspace and the steering vector to generate their respective damage spatial spectra. The two sets of spatial spectrum results are cross-compared and superimposed to identify the spectral peak region with the highest overlap as the final damage location coordinates. At the same time, a beamforming algorithm is introduced in the signal processing process, and a time-delay weighted summation method is used to perform spatial filtering on the array signal.

[0010] In some implementations, the two sensor arrays are linear arrays, each array consisting of no fewer than 5 piezoelectric sensing units, which are equally spaced along a straight line. Two sensor arrays are symmetrically arranged on the surface of the structure under test, with their extension directions parallel and in a mirror-symmetric relationship with respect to the location of the excitation source; In some implementations, the spacing between adjacent elements in the sensor array is no greater than half the wavelength of the excited Lamb wave; The symmetrical excitation is applied to the vertical line between the two sensor arrays, specifically at the perpendicular bisector of the line connecting the two arrays, to excite the S0 mode Lamb wave that propagates bidirectionally along the plate plane. The excitation signal is a sinusoidal pulse signal with a center frequency of 160kHz, modulated by a Hanning window for 5 cycles.

[0011] In some implementations, by adjusting the frequency and waveform parameters of the excitation signal, the Lamb wave propagating in the structure under test is made to dominate in the S0 mode.

[0012] In some implementations, the covariance matrix is ​​constructed after sampling the received signal. The matrix is ​​then subjected to eigenvalue decomposition to separate the largest eigenvalue and its eigenvector corresponding to the signal subspace, and the smaller eigenvalue and its eigenvector corresponding to the noise subspace.

[0013] In some implementations, the step of constructing a covariance matrix of the received signal and performing eigenvalue decomposition to separate the signal subspace and noise subspace, and establishing a spatial spectrum function based on the orthogonality between the noise subspace and the steering vector to generate their respective damage spatial spectrum maps includes: The cross-correlation matrix of the received signal is , where H represents the conjugate transpose of the matrix; The signal matrix received by the array X(t) Substituting the values, we get:

[0014] In the formula: The signal correlation matrix; This is the noise correlation matrix; The variance of the noise signal; I It is an M×M identity matrix; Assuming the covariance matrix The eigenvalues ​​are { , , The corresponding feature vectors are { , , }; matrix The eigenvalues ​​are sorted in descending order to obtain... > >…> …> Among them, the M larger eigenvalues ​​correspond to the signal space, and the remaining MN smaller eigenvalues ​​correspond to the noise space; The eigenvectors corresponding to the signal eigenvalues ​​and noise eigenvalues ​​are the signal eigenvector and noise eigenvector, respectively; according to the definitions of eigenvalues ​​and eigenvectors:

[0015] For M < k < N, we have:

[0016] Riding on both sides have to

[0017] have to ,

[0018] The orthogonality between the noise feature vector and the array direction selection vector is obtained. By solving the noise feature vector corresponding to the cross-correlation matrix of the array signal, the azimuth of arrival of the signal source is searched to generate a spatial spectrum and perform direction of arrival estimation.

[0019] In some implementations, based on the orthogonality between the noise subspace and the steering vector, the spatial spectrum function is defined as:

[0020] in, The noise subspace matrix, The guide vector at a preset angle is obtained by scanning the entire field angle to obtain the position of the spectral peak as an estimate of the damage direction.

[0021] In some implementations, a time-delay weighted summation method is used to achieve beamforming, and the output signal is represented as:

[0022] In the formula: n is the array index; N is the number of array elements; θ is the pointing angle of the formed beam; f and c are the frequency and wave speed of the Lamb wave, respectively.

[0023] In some implementations, the spatial spectra generated by the two sensor arrays are superimposed or weighted and fused at the pixel level, and the coordinates of the joint spectrum peak are identified as the final damage localization result. When the results of independent positioning by the two arrays coincide within the preset tolerance range, the area is determined to be a reliable damage location; otherwise, a verification mechanism is initiated or an abnormal warning is issued.

[0024] Secondly, embodiments of this application provide a dual-array MUSIC beamforming damage localization device, comprising: The sensor module is used to symmetrically arrange two linear sensor arrays on the surface of the plate-shaped structure under test. Each array consists of multiple piezoelectric sensing units that are evenly distributed. The data acquisition module is used to excite a single S0 mode Lamb wave by applying a symmetrical excitation signal at a specific location on the structure, causing it to propagate within the plate and interact with potential damage to generate a scattered signal; the response signal is received synchronously by two sensor arrays, and the time-domain waveform and frequency-domain characteristics of the signal are extracted respectively. The positioning fusion module is used to construct a covariance matrix and perform eigenvalue decomposition on the received signal to separate the signal subspace and noise subspace. Based on the orthogonality between the noise subspace and the steering vector, a spatial spectrum function is established to generate their respective damage spatial spectrum maps. The two sets of spatial spectrum results are cross-compared and superimposed to identify the spectral peak region with the highest overlap as the final damage location coordinates. At the same time, a beamforming algorithm is introduced in the signal processing process, and a time-delay weighted summation method is used to perform spatial filtering on the array signal.

[0025] One or more embodiments of this application can bring at least the following beneficial effects: This application employs a dual-sensor array collaborative architecture, combining MUSIC high-resolution spatial spectrum estimation and beamforming signal enhancement techniques, to significantly improve the localization accuracy and anti-interference capability of minute damages in plate-like structures. Compared to traditional single-array methods, the dual-array design achieves spatial redundancy acquisition and cross-validation, effectively reducing the risk of mislocalization caused by local noise, signal attenuation, or path obstruction. The MUSIC algorithm can separate the noise subspace from the multi-channel received signals and utilize its orthogonality with the steering vector to construct a high-resolution spatial spectrum, accurately identifying the direction of the damage scattering source. Simultaneously, beamforming technology is introduced, which enhances the signal strength from the target area by performing time-delay weighted processing on the signals of each array element, suppressing clutter interference from non-interested directions, and further improving the signal-to-noise ratio and imaging clarity. Symmetrical excitation of S0-mode Lamb waves avoids the signal interpretation difficulties caused by multi-mode aliasing, ensuring the stability of propagation characteristics. The localization results of the two arrays are comprehensively judged through superposition fusion and consistency criteria, which not only improves localization reliability but also expands the coverage of the effective monitoring area. Experimental results show that this method can achieve sub-millimeter positioning accuracy, and is particularly suitable for engineering scenarios with extremely high structural safety requirements, such as high-speed trains and aerospace. It has good practicality, scalability and industrialization prospects. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0027] Figure 1 This is a schematic diagram of the linear array in this application; Figure 2 This is a schematic diagram of the finite element model of the aluminum plate provided in the embodiments of this application; Figure 3 This application provides a schematic diagram of sensor arrangement in an embodiment; Figure 4 A schematic diagram of the excitation signal provided in the embodiments of this application; Figure 5 The waveform diagram of array 1 provided in the embodiments of this application; Figure 6 The waveform diagram of array 2 provided in the embodiments of this application; Figure 7 This application provides a schematic diagram of the signal amplitude spectrum in an embodiment. Figure 8 This application provides a schematic diagram of the damage localization results for array 1 in an embodiment. Figure 9 This application provides a schematic diagram of the damage localization results for array 2 in an embodiment. Figure 10 This application provides a schematic diagram of the damage localization results in its embodiments. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0029] Explanation of related terms Finite element method (FEM): This is a numerical analysis method used to solve partial differential equations in complex engineering and physics problems. It involves dividing a continuum into a finite number of interconnected elements (such as triangles, quadrilaterals, tetrahedrons, etc.), applying approximate solutions to each element, and finally combining these to obtain the solution for the entire region. In structural analysis, the FEM is often used to predict the response of a structure under load, including stress, strain, and displacement.

[0030] Circular damage: In this application, circular damage refers to a simulated artificially created damage area in an aluminum plate, which is circular in shape and is used to study the propagation characteristics, reflection, and scattering phenomena of Lamb waves when they encounter damage.

[0031] Symmetrical excitation: Symmetrical excitation refers to applying the same or similar excitations (such as forces, vibrations, etc.) simultaneously on both sides of a structure to generate a specific waveform or mode. In this study, symmetrical excitation is used to excite the Lamb wave of the S0 mode, ensuring that the wave propagation has symmetry and consistency.

[0032] S0 mode Lamb wave: Lamb waves are elastic waves that propagate in plate structures. Depending on the wave propagation speed and the direction of particle vibration, they can be classified into various modes. The S0 mode is a type of Lamb wave, characterized by symmetrical particle vibration along the plate thickness direction and typically exhibiting a low propagation speed, making it suitable for structural health monitoring.

[0033] Multiple Signal Input Classification (MUSIC) Algorithm: MUSIC is a high-resolution signal processing technique based on matrix factorization and eigenvalue analysis, used to extract useful information from signals received from multiple sensors, especially when the number of signal sources is less than the number of sensors. In this study, the MUSIC algorithm is used to process signals captured by a sensor array to identify damage-related features.

[0034] Dual-sensor array: A dual-sensor array is an array consisting of two or more sensors used to simultaneously capture signals from different directions. In this study, a dual-sensor array was used for cross-localization, improving the accuracy of damage localization by comparing the differences in signals received by the two arrays.

[0035] Cross-location: Cross-location is a method that uses multiple sensors or arrays to simultaneously measure the position of a target. By comparing parameters such as the time difference and intensity difference of the signals received by different sensors, the position of the target can be calculated. In this study, cross-location was used to accurately determine the location of damage in an aluminum plate.

[0036] Beamforming Algorithm: Beamforming is a signal processing technique that adjusts the phase and amplitude of the received signals from each sensor in a sensor array to enhance signals in specific directions while suppressing signals in other directions. In this study, the beamforming algorithm is used to spatially filter the array signal, reducing clutter interference and improving signal quality and positioning accuracy.

[0037] Example 1: This application discloses a dual-array MUSIC beamforming damage localization method, including: S1, Two linear sensor arrays are symmetrically arranged on the surface of the plate-shaped structure to be tested. Each array consists of multiple piezoelectric sensing units that are equally spaced. S2, by applying a symmetrical excitation signal at a specific location on the structure, excites a single S0 mode Lamb wave, which propagates within the plate and interacts with potential damage to generate a scattered signal; the response signal is received synchronously by two sensor arrays, and the time-domain waveform and frequency-domain characteristics of the signal are extracted respectively; S3. A covariance matrix is ​​constructed for the received signal and eigenvalue decomposition is performed to separate the signal subspace and noise subspace. A spatial spectrum function is established based on the orthogonality between the noise subspace and the steering vector to generate their respective damage spatial spectrum maps. The two sets of spatial spectrum results are cross-compared and superimposed to identify the spectral peak region with the highest overlap as the final damage location coordinates. At the same time, a beamforming algorithm is introduced in the signal processing process, and a time-delay weighted summation method is used to perform spatial filtering on the array signal.

[0038] This application aims to achieve efficient and accurate imaging and assessment of damage in plate-like structures. Using the finite element method, a circular damage model was constructed in a three-dimensional aluminum plate to simulate damage under actual working conditions. To achieve this goal, a symmetrical excitation method was employed to generate Lamb waves in the S0 mode within the plate. This wave mode is suitable for structural health monitoring due to its propagation characteristics. Subsequently, an advanced multi-signal input classification (MUSIC) algorithm was used to meticulously process the signals captured by the sensor array to extract damage-related feature information. To further enhance positioning accuracy, a dual-sensor array cross-positioning strategy was designed, which effectively improved the ability to determine the location of potential damage in plate-like structures. Furthermore, a beamforming algorithm was introduced to spatially filter the array signals. This step significantly reduced clutter interference from other directions, further improving signal quality and positioning accuracy. Combining the above methods, the damage localization imaging algorithm constructed in this application has been verified to achieve high-precision positioning of damage in plate-like structures, providing an effective technical means for structural health monitoring and damage assessment.

[0039] For example, the plate-like structure to be tested is an aluminum alloy plate with geometric dimensions of 600mm × 600mm × 4mm. Material parameters include a density of 2700kg / m³, Young's modulus of 70.7GPa, and Poisson's ratio of 0.33. In actual processing, a three-dimensional finite element model of the plate-like structure is established, and explicit dynamic simulation is performed using ABAQUS software. The element type is C3D8R, the global mesh size is set to 1.0mm, the local mesh in the damaged area is refined to 0.05mm, the time step is 2ns, and the discretization accuracy requirement of containing 10–20 mesh elements within the minimum wavelength is met.

[0040] Optionally, the two sensor arrays described in this embodiment are linear arrays, each consisting of no fewer than five piezoelectric sensing units, evenly spaced along a straight line. The basic form and minimum size of the arrays meet the requirements of the MUSIC algorithm regarding the number and arrangement of elements, ensuring the effectiveness of spatial spectrum estimation. The two sensor arrays are symmetrically arranged on the surface of the structure under test, with parallel extension directions and mirror-symmetric relationships about the location of the excitation source. The core design concept of "dual-array symmetrical layout" enhances the spatial coverage and cross-validation effect of signal acquisition, improving positioning robustness. The spacing between adjacent elements in the sensor array is no greater than half the wavelength of the excited Lamb wave, preferably 5 mm at a center frequency of 160 kHz. This design avoids grating lobe interference caused by spatial undersampling, meets the spatial resolution requirements of beamforming and the MUSIC algorithm, and is a key constraint in array design. The symmetrical excitation is applied to the perpendicular bisector between the two sensor arrays, specifically at the perpendicular bisector of the line connecting the two arrays, to excite S0 mode Lamb waves propagating bidirectionally along the plate plane. This ensures good symmetry in the guided wave field, making the signals received by the two arrays comparable, which is beneficial for subsequent differential processing and fusion positioning.

[0041] Furthermore, the excitation signal is a sinusoidal pulse signal with a center frequency of 160kHz, modulated by a Hanning window for 5 cycles. This signal form can effectively excite a single S0 mode, suppress multi-mode aliasing, and also has good frequency domain concentration, which is beneficial to improving the signal-to-noise ratio and positioning accuracy.

[0042] By adjusting the frequency and waveform parameters of the excitation signal, the Lamb wave propagating in the structure under test is made to dominate in the S0 mode, significantly suppressing the energy proportion of other modal components such as A0. Focusing on a single mode simplifies the signal interpretation process, avoids the positioning ambiguity problem caused by multimodal coupling, and improves the stability and engineering practicality of the algorithm.

[0043] Furthermore, the covariance matrix is ​​constructed after sampling the received signal. The matrix is ​​then subjected to eigenvalue decomposition to separate the largest eigenvalue and its eigenvector corresponding to the signal subspace, and the smaller eigenvalues ​​and their eigenvectors corresponding to the noise subspace. Only by accurately separating the noise subspace can an effective spatial spectral function be constructed to achieve high-resolution direction-of-arrival estimation.

[0044] Based on the orthogonality between the noise subspace and the steering vector, the spatial spectral function is defined as:

[0045] in, The noise subspace matrix, The guide vector at a preset angle is obtained by scanning the entire field angle to obtain the position of the spectral peak as an estimate of the damage direction.

[0046] Beamforming is achieved using a time-delay weighted summation method, and the output signal is represented as follows: (11) In the formula: n is the array index; N is the number of array elements; θ is the pointing angle of the formed beam; f and c are the frequency and wave speed of the Lamb wave, respectively.

[0047] The spatial spectral maps generated by the two sensor arrays are pixel-level superimposed or weighted and fused to identify the coordinates of the joint spectral peak as the final damage localization result. This scheme is a key means of realizing dual-array information fusion, reducing the false positive rate through spatial redundancy verification and significantly improving localization reliability.

[0048] When the results of independent positioning by two arrays coincide within a preset tolerance range (e.g., ±1mm), the area is determined to be a reliable damage location; otherwise, a verification mechanism is activated or an anomaly warning is issued. By introducing a logical judgment mechanism, the system's self-diagnostic capability is enhanced, making it suitable for intelligent decision-making in automated monitoring systems. Circular through-holes with a diameter of 2mm to 4mm are set in the structure under test as artificial damage defects to simulate linear damage morphologies such as microcracks, delamination, or corrosion pits in actual engineering.

[0049] Therefore, the method of this application can be applied to health monitoring systems for plate structures such as high-speed train bodies, aerospace vehicle skins, bridge decks, or large pressure vessels to achieve real-time identification and precise location of early damage.

[0050] The steps in the above scheme are explained in detail below: The Music algorithm separates the signal subspace and noise subspace from the covariance matrix of the received signal from the array, and then uses the orthogonality between the signal direction vector and the noise subspace to construct a spatial scanning spectrum, thereby realizing the direction of arrival estimation of the signal.

[0051] Linear arrays are commonly used for modeling signal reception. Let the linear array consist of N arrays with a spacing of... d Composed of subarray elements, with far-field... M An unrelated information source, the angle formed between its direction and the normal direction of the array's first element. θ The incident angle. The signal matrix received by the array. X(t) This can be described by equation (1): (1) In the formula, A(θ) , A(t) and N(t) The expressions are as follows: (2) (3) (4) In the formula: A(0) is the direction matrix of the linear array; S(t) is the signal matrix emitted by M sources incident from the far field, and each source forms an angle with the normal direction of the first element of the array. N(t) is the noise matrix. Figure 1 This is a schematic diagram of a linear array.

[0052] The cross-correlation matrix of the received signal is , where H represents the conjugate transpose of the matrix. Assume the noise is uncorrelated, zero-mean additive Gaussian white noise. Substituting equation (1) into the equation, we get: (5) In the formula: The signal correlation matrix; This is the noise correlation matrix; The variance of the noise signal; I Let be an M×M identity matrix. Now assume the covariance matrix is... The eigenvalues ​​are { , , The corresponding feature vectors are { , , In the case of multiple incoherent sources and the number of sources M < N, It is positive semidefinite, and has M large eigenvalues ​​and NM values. The smaller eigenvalues. The matrix The eigenvalues ​​are sorted in descending order, i.e. > >…> …> In this equation, the M larger eigenvalues ​​correspond to the signal space, and the remaining MN smaller eigenvalues ​​correspond to the noise space. The eigenvectors corresponding to the signal eigenvalues ​​and noise eigenvalues ​​are the signal eigenvector and the noise eigenvector, respectively.

[0053] Based on the definitions of eigenvalues ​​and eigenvectors: (6) For M < k < N, we have: (7) At this point, multiply both sides of equation (6) achievable (8) achievable ,Right now: (9) Equation (9) shows that the noise eigenvector and the array direction selection vector are orthogonal. Utilizing this orthogonality, by solving for the noise eigenvector EN corresponding to the cross-correlation matrix of the array signal, the azimuth of arrival of the signal source is searched to generate a spatial spectrum, thereby realizing the direction of arrival estimation.

[0054] The spatial spectral function is defined as: (10) After receiving a signal, the linear array performs a series of processing steps, including delaying, weighting, and summing, on the data received by multiple array elements. This results in a signal with higher gain in a specified direction and lower gain in other directions, achieving spatial filtering. Traditional beamforming typically employs phase-shift beamforming or time-delay beamforming methods, selecting appropriate weighting signals to amplify the signal in a specified direction while attenuating the signal received in other directions. This is beneficial for extracting low-amplitude microcrack signals that are easily submerged in noise from the array signal.

[0055] This application uses a conventional beamforming (CBF) algorithm based on time delay weighted summation to achieve spatial filtering of microcrack signals and achieves beamforming of array signals through equation (11).

[0056] (11) In the formula: n is the array index; N is the number of array elements; The pointing angle of the formed beam is given by ; f and c are the frequency and velocity of the Lamb wave, respectively. This beamforming algorithm reduces interference from clutter in other directions within the array signal, ensuring the accuracy of nonlinear parameter evaluation methods and enabling array ultrasonic guided wave modeling of damaged signals.

[0057] A three-dimensional simulation model of an aluminum plate was established using the finite element software ABAQUS. The propagation of Lamb waves in the aluminum plate was analyzed using explicit dynamic analysis. The physical parameters of the aluminum plate are shown in Table 1, and its geometric parameters are 600 mm * 600 mm * 4 mm. Figure 2 As shown. Figure 2 This is a finite element model of an aluminum plate.

[0058] Table 1 Physical parameters of aluminum plates

[0059] Using the geometric center of the plate as the origin, the length and width directions are the x-axis and r-axis of the coordinate system, respectively, and the thickness direction is the z-axis. Two sensor arrays, A and B, each consisting of 7 elements, are established with point A1 at coordinates (-50, 50) and point B1 at coordinates (-50, -50) as the first array elements, and an element spacing of 5 mm. A symmetrical load is applied at coordinates (-50, 0) to excite a single S0 mode Lamb wave in the plate, as shown below. Figure 3 As shown. The excitation load signal is a sinusoidal signal with a center frequency of 160 kHz modulated by a 5-cycle Hanning window, and its time-domain waveform is as follows. Figure 4 As shown. Figure 3 This is a schematic diagram of the sensor arrangement. Figure 4 This is a schematic diagram of the excitation signal.

[0060] To ensure the accuracy and stability of the solution process and reduce computational complexity, the mesh size and time step need to meet certain conditions. Let λmin be the minimum wavelength of the signal frequency of interest, Lmax and Lmin be the maximum and minimum mesh cell sizes, respectively, Δt be the time step, and cg be the group velocity of the Lamb wave propagating in the plate. The following relationship needs to be satisfied:

[0061] The above formula indicates that a minimum wavelength contains 10-20 mesh elements; therefore, the maximum mesh size in this model is approximately 1.3 mm. Simultaneously, the local mesh size for damage within the board is subdivided to 0.05 mm, and the calculated maximum time step is approximately 9.6 ns. In this simulation, a global mesh size of 1.0 mm, a local mesh size of 0.05 mm, a time step of 2 ns, and a C3D8R mesh element type are used. Circular through-holes with diameters of 4 mm and 2 mm are used in the aluminum plate to simulate conventional linear damage, constructing regions containing this type of damage and embedding them into designated locations on the main board. The final results are as follows: Figures 5-10 As shown, where, Figure 5 The waveform diagram of array 1 provided in the embodiments of this application; Figure 6 The waveform diagram of array 2 provided in the embodiments of this application; Figure 7 This application provides a schematic diagram of the signal amplitude spectrum in an embodiment. Figure 8 This application provides a schematic diagram of the damage localization results for array 1 in an embodiment. Figure 9 This application provides a schematic diagram of the damage localization results for array 2 in an embodiment. Figure 10 The damage localization results provided in this application embodiment are shown in the following diagram (measured: (22.0 -3.0) actual: (22.5, -2.5)).

[0062] Ultimately, the positioning error was found to be only 0.5mm, demonstrating high precision.

[0063] In summary, this application proposes a dual-array MUSIC beamforming damage localization method. First, considering that single-array MUSIC methods may be affected by various factors (such as noise and wave velocity variations) during damage localization, resulting in limited accuracy, this application employs a dual-array design. Through the collaborative work of two or more sensor arrays, multiple acquisitions and cross-validations of damage signals can be achieved. This redundant design helps reduce errors that may be introduced by a single array, thereby improving the accuracy of damage localization. Second, the MUSIC algorithm itself has high resolution, enabling accurate identification of minute features in the signal. In this application, by combining it with a beamforming algorithm, the signal from the damage location can be further enhanced while suppressing interference signals from other directions. This dual effect of signal enhancement and interference suppression helps to accurately capture damage signals in complex noisy environments, improving the sensitivity and reliability of localization. Furthermore, the dual-array design also provides the system with greater flexibility and scalability. For example, the spacing, angle, and number of arrays can be adjusted according to actual needs to optimize the localization effect. In addition, through reasonable array layout and signal processing techniques, simultaneous localization of multiple damage locations can be achieved, improving detection efficiency. Finally, considering the dynamic and complex nature of real-world applications such as high-speed trains, This application utilizes a dual-array MUSIC beamforming method to achieve real-time monitoring and location of vehicle body damage. This helps in the timely detection of potential safety hazards and ensures the safe operation of trains. In summary, this application, by employing a dual-array design combined with MUSIC algorithms and beamforming technology, offers advantages such as improved damage location accuracy, sensitivity, and reliability, as well as enhanced system flexibility and scalability. These advantages make the solution applicable to fields such as high-speed train body damage monitoring.

[0064] Compared with the traditional single-array method, this application adopts a dual-array (or multi-array) design. This design not only increases the redundancy of signal acquisition and improves the reliability of data, but also reduces errors through cross-validation between arrays, thereby significantly improving the accuracy of damage localization.

[0065] The combination of MUSIC algorithm and beamforming technology: This application combines the high-resolution characteristics of the MUSIC algorithm with the signal enhancement and interference suppression capabilities of beamforming technology. The MUSIC algorithm can accurately identify minute features in the signal, while beamforming further enhances the signal from the damage location while suppressing interference from other directions. This combination enables this application to accurately capture damage signals even in complex noisy environments. Considering the dynamic and complex nature of practical applications such as high-speed trains, this application achieves real-time monitoring and location of vehicle body damage through optimized algorithm and hardware design. This capability is of great significance for timely detection of potential safety hazards and ensuring the safe operation of trains. The dual-array design provides greater flexibility and scalability. The spacing, angle, and number of arrays can be adjusted according to actual needs to optimize the positioning effect. In addition, through reasonable array layout and signal processing technology, simultaneous location of multiple damage locations can be achieved, improving detection efficiency.

[0066] Example 2: Secondly, embodiments of this application provide a dual-array MUSIC beamforming damage localization device, comprising: The sensor module is used to symmetrically arrange two linear sensor arrays on the surface of the plate-shaped structure under test. Each array consists of multiple piezoelectric sensing units that are evenly distributed. The data acquisition module is used to excite a single S0 mode Lamb wave by applying a symmetrical excitation signal at a specific location on the structure, causing it to propagate within the plate and interact with potential damage to generate a scattered signal; the response signal is received synchronously by two sensor arrays, and the time-domain waveform and frequency-domain characteristics of the signal are extracted respectively. The positioning fusion module is used to construct a covariance matrix and perform eigenvalue decomposition on the received signal to separate the signal subspace and noise subspace. Based on the orthogonality between the noise subspace and the steering vector, a spatial spectrum function is established to generate their respective damage spatial spectrum maps. The two sets of spatial spectrum results are cross-compared and superimposed to identify the spectral peak region with the highest overlap as the final damage location coordinates. At the same time, a beamforming algorithm is introduced in the signal processing process, and a time-delay weighted summation method is used to perform spatial filtering on the array signal.

[0067] Example 3: This embodiment also provides an electronic device, including a memory and a processor, wherein the memory is used to store one or more computer instructions, wherein the one or more computer instructions are executed by the processor to implement the method of Embodiment 1; In practical applications, the processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller unit (MCU), microprocessor, or other electronic components to execute the methods described in the above embodiments.

[0068] The method implemented in this embodiment is as shown in Embodiment 1.

[0069] Example 4: This embodiment also provides a computer storage medium, in which a computer program is stored, and when the computer program is executed by one or more processors, it implements the method of embodiment one. The computer-readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0070] The method implemented in this embodiment includes: The method implemented in this embodiment is as shown in Embodiment 1.

[0071] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can also be implemented in other ways. The system and method embodiments described above are merely illustrative.

[0072] It should be noted that in this application, the terms "first," "second," etc., in the specification and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0073] Although the embodiments disclosed in this application are as described above, the content described is only for the purpose of understanding the embodiments of this application and is not intended to limit this application.

Claims

1. A dual array MUSIC beamforming damage localization method, characterized in that, The method comprises the following steps: Two linear sensor arrays are symmetrically arranged on the surface of the plate-shaped structure to be measured, each array being composed of a plurality of piezoelectric sensing units distributed at equal intervals; A symmetric excitation signal is applied at a specific position of the structure to excite Lamb waves of a single S0 mode, which propagate in the plate and interact with potential damage to generate scattered signals; the two sensor arrays synchronously receive the response signals and extract the time-domain waveforms and frequency-domain features of the signals, respectively; A covariance matrix is constructed based on the received signals and eigenvalue decomposition is performed to separate the signal subspace and the noise subspace; a spatial spectrum function is established based on the orthogonality between the noise subspace and the steering vector to generate respective damage spatial spectrum graphs; the two sets of spatial spectrum results are cross-compared and superimposed and fused to identify the spectral peak region with the highest coincidence degree as the final damage position coordinates; meanwhile, a beamforming algorithm is introduced in the signal processing process, and a time delay weighted summation method is used to perform spatial filtering on the array signals.

2. The method of claim 1, wherein, The two sensor arrays are linear arrays, each array being composed of not less than 5 piezoelectric sensing units distributed at equal intervals along a straight line direction; The two sensor arrays are symmetrically arranged on the surface of the structure to be measured, and the extension directions thereof are parallel and mirror-symmetric about the position of the excitation source.

3. The method of claim 1, wherein, The distance between adjacent elements in the sensor array is not greater than half the wavelength of the excited Lamb wave; The symmetric excitation is applied on the perpendicular bisector between the two sensor arrays, specifically at the perpendicular bisector of the line connecting the two arrays, for exciting S0 mode Lamb waves propagating bidirectionally along the plane of the plate; The excitation signal is a sinusoidal pulse signal with a center frequency of 160 kHz and modulated by a 5-cycle Hanning window.

4. The method of claim 1, wherein, The frequency and waveform parameters of the excitation signal are adjusted to make the Lamb waves propagating in the structure to be measured dominated by the S0 mode.

5. The method of claim 1, wherein, Constructing a covariance matrix after sampling the received signal and performing eigenvalue decomposition on the matrix, separating out the largest eigenvalues and their eigenvectors corresponding to the signal subspace, and the smaller eigenvalues and their eigenvectors corresponding to the noise subspace.

6. The method of claim 5, wherein, The covariance matrix is constructed based on the received signals and eigenvalue decomposition is performed to separate the signal subspace and the noise subspace; a spatial spectrum function is established based on the orthogonality between the noise subspace and the steering vector to generate respective damage spatial spectrum graphs, comprising: The cross-correlation matrix of the received signals is where H denotes the conjugate transpose of a matrix. The signal matrix received by the array X(t) After substitution we get: wherein: is the signal correlation matrix; is the noise correlation matrix; is the variance of the noise signal; I is the M x M identity matrix; Assume the eigenvalues of the covariance matrix are , , , and the corresponding eigenvectors are , , , respectively. The eigenvalues of the matrix are sorted in descending order to obtain where the M larger eigenvalues correspond to the signal space and the remaining M-N smaller eigenvalues correspond to the noise space.​​​ The eigenvectors corresponding to the signal eigenvalues and the noise eigenvalues are signal eigenvectors and noise eigenvectors, respectively; the eigenvalues and the eigenvectors are defined as follows: For M < k < N, we have: Ride on both sides Available get , The noise eigenvectors and the array direction selection vectors are orthogonal to each other, the noise eigenvectors corresponding to the correlation matrix of the array signals are solved to search for the azimuth angle of the signal source, generate a spatial spectrum, and estimate the direction of arrival.

7. The method of claim 1, wherein, Based on the orthogonality between the noise subspace and the steering vector, the spatial spectrum function is defined as: wherein, is a noise subspace matrix, is a steering vector at a preset angle, and a spectrum peak position obtained by scanning a full field angle is taken as an estimated value of the damage direction.

8. The method of claim 1, wherein, The time delay weighted summation method is used to realize beamforming processing, and the output signal is represented as: In the formula, n is the serial number of the array; N is the number of elements of the array; is the pointing angle of the formed beam; f and c are the frequency and wave velocity of the Lamb wave, respectively.

9. The method of claim 1, wherein, The spatial spectrum graphs generated by the two sensor arrays are subjected to pixel-level superposition or weighted fusion processing, and the coordinate position of the joint spectral peak value is identified as the final damage positioning result; When the positioning results of the two arrays coincide within a preset tolerance range, the region is determined as a reliable damage position; otherwise, a review mechanism is started or an abnormal warning is prompted.

10. A dual-array MUSIC beamforming damage positioning device, comprising: A sensor module is used to arrange two linear sensor arrays symmetrically on the surface of the plate structure to be measured, each array consisting of a plurality of piezoelectric sensing units distributed at equal intervals; A data acquisition module is used to excite a single S0 mode Lamb wave by applying a symmetric excitation signal at a specific position of the structure, so that the Lamb wave propagates in the plate and interacts with potential damage to produce a scattering signal; the response signal is received synchronously by the two sensor arrays, and the time-domain waveform and frequency-domain features of the signal are extracted respectively; A positioning fusion module is used to construct a covariance matrix for the received signal and perform eigenvalue decomposition to separate the signal subspace and the noise subspace, establish a spatial spectrum function based on the orthogonality of the noise subspace and the steering vector, and generate respective damage spatial spectrum graphs; the two sets of spatial spectrum results are cross-compared and superimposed to identify the spectral peak region with the highest coincidence degree as the final damage position coordinates; meanwhile, a beamforming algorithm is introduced in the signal processing process, and a time delay weighted summation method is used to perform spatial filtering on the array signal.

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