A Guided Wave Imaging Method for Aircraft Curved Skin Damage

Abstract

This invention discloses a guided wave damage imaging method for curved aircraft skin, relating to the fields of structural health monitoring and ultrasonic guided wave non-destructive testing. First, using the flight time of the direct wave from the healthy baseline, algebraic reconstruction techniques are employed to calibrate the path-scale equivalent slowness field, reducing probability map defocusing and peak shift caused by the global fixed wave velocity assumption. Second, path reliability is evaluated based on the healthy repeating signal, and path classification compensation and coverage density balancing are implemented using reliability-weighted sensitivity to enhance credible weak responses and suppress spurious probability accumulation in densely populated areas. Finally, D-S evidence theory with reliability discounting and spatial support gating is used to perform pixel-level fusion of signal difference coefficients and flight time characteristics. Experiments show that for a through-hole defect with a radius of 5 mm, the proposed method reduces the average positioning error by 65.4% compared to the traditional RAPID method, and the spatial standard deviation in high-probability areas is reduced to 1.39 mm, demonstrating good imaging focus and adaptability to curved structures.

Description

Technical Field

[0001] This application relates to the fields of structural health monitoring and ultrasonic guided wave nondestructive testing, and in particular to a guided wave damage imaging method for aircraft curved skin. Background Technology

[0002] In the development of the modern aerospace industry, the safety and reliability of aircraft structures and the economic efficiency of operation and maintenance throughout their entire life cycle have always been the underlying driving forces for core technological innovation. Under the influence of long-term alternating loads, corrosive environments, and foreign object impacts, aircraft skin may develop fatigue cracks, localized corrosion, and porosity damage. If such damage is not detected in time, it may reduce the structural load-bearing capacity and service reliability, and in severe cases, even endanger flight safety.

[0003] To achieve online monitoring and rapid assessment of damage to aircraft skin structures, a piezoelectric sensor network is typically deployed on the surface of the monitored area of ​​the curved skin. A transmitter-receiver separation layout is used, with the transmitter array and receiver array positioned on opposite sides of the monitoring area. The transmitter piezoelectric sensor excites ultrasonic guided waves, which propagate along the thin skin structure. The receiver piezoelectric sensor picks up the propagated guided wave signal. In the sensor network, a specific transmitter-receiver combination from a transmitter to a receiver is defined as a sensing path. Multiple transmitter-receiver combinations constitute multiple sensing paths, each providing effective information covering a specific spatial range within the monitored area. During wave propagation, if damage exists along the propagation path, the guided wave will be reflected, scattered, and attenuated, resulting in a measurable change in the received signal compared to the signal under healthy conditions.

[0004] The existing reconstruction damage detection algorithm RAPID (Reconstruction Algorithm for Probabilistic Inspection of Damage / Defects) is one of the most representative methods in the field of guided wave damage imaging. This method usually focuses on the sensor transmitter and receiver, uses the difference between the healthy state and the current state of the guided wave signal to construct a single type of damage index, and maps the damage index of each path from the transmitter to the receiver to a spatial elliptical probability distribution, and then forms a damage probability map by superimposing multiple paths.

[0005] However, different damage features have significant differences in their sensitivity to noise and their spatial constraint capabilities. If the single damage probabilities of each path are directly superimposed linearly or fused with fixed weights, the false responses of low-confidence features in densely packed areas will be amplified, while the true contribution of weak scattering paths may be submerged. This makes it difficult to effectively leverage the complementary advantages of the two types of features, ultimately leading to a decrease in the positioning accuracy and focus of the damage probability map, and even the appearance of spurious peaks that significantly deviate from the true defects under certain working conditions. Summary of the Invention

[0006] Therefore, it is necessary to provide a method for imaging guided wave damage in aircraft curved skin to address the aforementioned technical problems.

[0007] The following technical solution is adopted in this specification: This specification provides a method for imaging guided wave damage in aircraft curved skin, including: Acquire multiple sets of healthy baseline guided wave signals of the aircraft curved skin and the current guided wave signal under the state to be detected, and extract the flight time of the healthy direct wave from the healthy baseline guided wave signals; The propagation time of each sensing path is calibrated based on the time-of-flight of the health direct wave, and a time-of-flight constrained probability map is constructed based on the calibrated propagation time. Based on the multiple sets of healthy baseline guided wave signals and the current guided wave signal, the sensing path is subjected to sensitivity classification compensation and coverage density equalization to generate a compensated signal differential coefficient probability map. Using the compensated SDC probability map as primary evidence and the TOF constrained probability map as secondary evidence, and based on the consistency between the secondary evidence and the primary evidence, the reliability of the secondary evidence is discounted to obtain the discounted TOF reliability. Spatial support gating is constructed using the spatial distribution characteristics of the primary evidence to constrain the secondary evidence, resulting in a controlled TOF auxiliary map. Finally, based on the primary evidence, the discounted TOF reliability, and the controlled TOF auxiliary map, the two types of evidence are fused at the pixel level using evidence theory to obtain the fused damage quality distribution. Based on the fused damage quality distribution, a final surface skin damage probability imaging map is generated.

[0008] Furthermore, the calibration of the propagation time of each sensing path based on the time-of-flight of the health direct wave includes: The flight time of the healthy direct wave is iteratively inverted using algebraic reconstruction techniques to obtain the equivalent slowness field at the path scale. The propagation time of each sensor path is recalculated using the equivalent slow field to obtain the calibrated propagation time of each sensor path.

[0009] Furthermore, the iterative inversion of the flight time of the direct wave using algebraic reconstruction techniques to obtain the equivalent slowness field at the path scale includes: The aircraft curved skin is unfolded along the curvature direction, and a calibration grid is established in the unfolded plane; The reciprocal of the equivalent group velocity obtained from dispersion analysis is used as the initial slowness value for each calibration grid cell; the slowness value of each calibration grid cell is iteratively updated according to the Kaczmarz form. After each iteration, neighborhood smoothing is applied to the slow-speed field; When the normalized sound residual converges or reaches the preset number of iterations, the iteration stops, and the equivalent slow field is obtained.

[0010] Furthermore, the construction of the time-of-flight constrained probability map based on the calibrated propagation time includes: Based on the propagation time of each calibrated sensing path, the direct wave time window and the scattered wave time window are adaptively determined. The scattering time-of-flight characteristics of each sensing path are extracted within the scattering wave time window, and the scattering time-of-flight characteristics are mapped into a time-of-flight constrained probability map using the equivalent slowness field.

[0011] Furthermore, based on the multiple sets of healthy baseline guided wave signals and the current guided wave signal, sensitivity classification compensation and coverage density equalization are performed on the sensing path, including: Based on the correlation coefficient between the health baseline guided wave signal and the current guided wave signal of each sensing path, the normalized signal differential coefficient is obtained; The reliability weight of the sensing path is obtained based on the correlation coefficients between pairs of multiple sets of healthy baseline guided wave signals. Based on the normalized signal differential coefficients and the reliability weights, the paths are divided into highly sensitive paths, weakly sensitive paths, and low-reliability paths; the highly sensitive paths are assigned a weight consistent with the sensitivity of the weighted paths, the weakly sensitive paths are compensated and enhanced, and the low-reliability paths are suppressed. The spatial probability kernels of each sensing path are weighted and superimposed according to the weights after classification compensation to obtain the cumulative probability result; and the path coverage density is obtained based on the spatial probability kernel of each path.

[0012] Further, the generation of the compensated signal differential coefficient probability map includes: Based on the probability accumulation result and the path coverage density, the probability map of the differential coefficients of the compensation signal is obtained. , is represented as: in, This is the coverage density equalization coefficient; This represents the cumulative probability result; Indicates path coverage density; Represents the regularization constant; This represents the global normalization operator.

[0013] Furthermore, based on the consistency between the auxiliary evidence and the main evidence, a reliability discount is applied to the auxiliary evidence, including: Calculate the spatial distance between the peak position of the auxiliary evidence and the peak position of the main evidence, and determine a first discount factor based on the spatial distance; Calculate the Hellinger distance between the auxiliary evidence and the main evidence on the full graph distribution, and determine the second discount factor based on the Hellinger distance; Calculate the spatial overlap between the auxiliary evidence and the main evidence, and determine a third discount factor based on the spatial overlap; The product of the initial reliability of the auxiliary evidence and the first discount factor, the second discount factor, and the third discount factor is used as the discounted reliability of the auxiliary evidence.

[0014] Furthermore, the calculation process for the fused damage mass distribution is as follows: For each pixel, the quality of the non-damage hypothesis in the basic probability allocation of the main evidence is assigned to the uncertainty set, and the quality of the non-damage hypothesis in the basic probability allocation of the auxiliary evidence is assigned to the uncertainty set, thus obtaining the basic probability allocation of the two types of evidence. The Dempster combination rule is used to fuse the basic probability assignments of the two types of evidence to obtain the fused damage quality of the pixel.

[0015] Furthermore, the final probabilistic imaging map of surface skin damage is generated as follows: in, This represents the final probabilistic imaging map of surface skin damage. Indicates the quality of damage after fusion; This represents the compensated SDC probability diagram; This represents a controlled TOF auxiliary plot; The consistency enhancement coefficient, The coefficient for primary evidence is retained. This represents the normalization operator.

[0016] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: To address the problem of incomplete single-damage feature information and insufficient localization accuracy due to the difficulty in fully leveraging the complementary advantages of linear superposition, this invention uses a compensated SDC probability map as the primary evidence and a TOF constrained probability map as the secondary evidence in the fusion process. This is achieved by implementing an adaptive reliability discount on the TOF secondary evidence to weaken conflict responses, and by utilizing the spatial distribution characteristics of the primary evidence to construct a spatial support gating system. This constrains the TOF secondary map to the neighborhood of the SDC main peak, ensuring that the TOF evidence only plays an auxiliary enhancement role and does not dominate imaging independently. This fusion strategy effectively avoids the interference of conflict evidence caused by traditional fixed-weight fusion or simple superposition, fundamentally eliminating artifacts generated in densely intersecting areas of the sensor network paths, and maintaining the reliability of global damage screening. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0018] Figure 1 This specification provides a schematic flowchart of a guided wave damage imaging method for aircraft curved skin. Figure 2 This is a schematic diagram of the circumferential Lamb wave dispersion curve provided in this specification, where (a) is the phase velocity and (b) is the group velocity; Figure 3 This is a schematic diagram of the longitudinal mode (L-mode) dispersion curve provided in this specification, where (a) is the phase velocity and (b) is the group velocity; Figure 4 This is a schematic diagram illustrating the equivalent mapping of curved skin cylindrical surface development and geodesics provided in this specification. Figure 5 This is a schematic diagram of the curved panel 6×6 transceiver sensor network and the path coverage of the monitoring area provided in this manual, where T1-T6 are the transmitting ends and R1-R6 are the receiving ends; Figure 6 This is a schematic diagram of the time-domain waveform and spectrum of the excitation signal provided in this specification, where (a) is the time domain and (b) is the spectrum; Figure 7 This is a schematic diagram comparing the path received signals provided in this specification, where (a) is the time-domain waveform of healthy and damaged signals, and (b) is the difference signal S_n(t). Figure 8 This is a comparative diagram of numerical simulation damage localization imaging provided in this specification, wherein (a) is the distribution of damage index (CDI) for each channel; (b) is the traditional RAPID; and (c) is the method of this invention. Figure 9The following are TOF feature and ART-calibrated TOF constraint damage probability maps for different defect locations provided in this specification: (a)-(c) are TOF feature damage probability maps; (d)-(f) are ART-calibrated TOF constraint damage probability maps. Figure 10 This is a schematic diagram comparing the received signals of a typical path in the through-hole working condition provided in this manual, where (a) is the time-domain waveform of healthy alignment and damaged state; and (b) is the damage scattering / reflection differential signal. Figure 11 The normalized SDC index for the 36 paths under the through-hole condition provided in this manual. Distribution diagram; Figure 12 This is a comparative diagram of damage imaging results at different defect locations provided in this specification; where (a)-(c) represent traditional RAPID; (d)-(f) represent classification compensation SDC; and (g)-(i) represent the complete method of this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0020] To address the aforementioned issues, this invention proposes a guided wave damage imaging method for aircraft curved skin based on adaptive calibration of the equivalent slow-degree field and multi-feature fusion. This method first utilizes the direct-arrival time of a healthy baseline to calibrate the equivalent slow-degree field at the path scale using ART (Automatic Traverse Time) to compensate for propagation parameter mismatches caused by surface geometry and system errors. Then, based on the calibrated path propagation time, it adaptively determines the direct-arrival time window and the scattered-wave time window to constrain SDC (Sound Speed ​​Conversion) feature extraction, scattering TOF (Time-of-Flight) identification, and probability kernel construction, thereby reducing the interference of boundary echoes and multipath reflections on feature calculations. Subsequently, path reliability is evaluated based on healthy repeated acquisition signals, and path classification compensation is performed using reliability-weighted sensitivity. Furthermore, false probability accumulation in densely intersecting path regions is suppressed through coverage density equalization. Finally, the compensated SDC map and TOF constraint map are transformed into pixel-level evidence, and a DS (Dual Path Evidence) fusion mechanism with uncertain quality and conflict discount is introduced to achieve complementarity between correlation features and spatial constraint features. Compared to traditional RAPID (Rapid Acquisition Processing), this method is more suitable for engineering scenarios where propagation speed and surface configuration mismatch, sparse path coverage, and weak scattering features coexist.

[0021] For a thin-walled curved panel with large curvature, its local propagation can be approximated as a guided wave problem in a cylindrical shell, and the dispersion relationship between phase velocity and group velocity in different modes can be obtained through numerical solution. Figure 2 and Figure 3 The dispersion results for the circumferential Lamb wave and the longitudinal L-mode are presented separately. It can be seen that in the range of 150–200 kHz, the group velocities of the circumferential Lamb wave and the longitudinal L-mode are quite similar, which can be used as the basis for subsequent equivalent group velocities. The selection of parameters provides a reference. It should be noted that the simulations and experiments in this invention mainly focus on the low-frequency guided wave branch with dominant out-of-plane response at the sensing node, and do not strictly equate different surface modes; the above dispersion analysis is only used to determine the operating frequency and the initial slowness of the ART. The out-of-plane vibration dominant branch corresponding to this frequency band is more sensitive to small surface defects and through cracks, and is beneficial for separating damage scattering and boundary reflection in the time domain.

[0022] To explicitly consider the surface geometry in subsequent acoustic time-inversion, the skin is approximated as a cylindrical surface of radius R in the curvature direction, and the geodesic path of the surface is approximated using Euclidean distance on the unfolded plane. Let two points on the surface be... and Where z is the axial coordinate of the cylinder and Rθ is the arc length coordinate after the surface is unfolded, the geodesic length can be written as:

[0023] (1) Figure 4 A schematic diagram illustrating the equivalent mapping between the cylindrical surface development and geodesics is given. This approximation is applicable at large diameter-to-thickness ratios (...). This invention is valid when the curvature changes slowly and the sensor is approximately attached to the same cylindrical surface. Therefore, surface propagation can be approximated as a two-dimensional path calculation in the unfolded plane, thus providing a geometric basis for subsequent ART slow inversion and imaging localization.

[0024] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0025] Figure 1 This is a schematic diagram of a guided wave damage imaging method for curved aircraft skin as described in this specification, which specifically includes the following steps: S101: ART-based adaptive calibration of equivalent slow field.

[0026] The acoustic time of guided waves in curved skin is affected by factors such as surface geometry, sensor coupling, and system delay. If a globally fixed wave velocity is used, path acoustic time errors will be transmitted to the elliptic probability kernel and Time-of-Flight (TOF) constraints, leading to image peak shift or probability map defocusing. To address this, this invention utilizes the time-of-flight of the direct wave from a healthy baseline and calibrates the path-scale equivalent slowness field using algebraic reconstruction (ART) technique. It should be noted that this slowness field does not represent the true local wave velocity of the material, but rather is used to compensate for apparent acoustic time deviations caused by path propagation and the testing system.

[0027] After unfolding the curved skin along the curvature direction, a coarse-scale calibration mesh is established within the unfolded plane. Because the 6×6 transceiver array of this invention only provides... For an effective path, directly inverting the slowness field on a 1 mm × 1 mm imaging grid would result in severe underdetermination. Therefore, ART is performed only on the macroscopic calibration grid, and the resulting equivalent slowness is then interpolated and mapped back to the imaging grid. Let the intercept length of the i-th path within the j-th calibration cell be... The equivalent slowness of the j-th unit is In a healthy state, the direct wave flight time of the i-th path is Then we have:

[0028] (2) Or written in matrix form: (3) Where W is the path-grid intercept matrix, and s is the equivalent slowness vector to be estimated. This represents measurement noise and model approximation error.

[0029] Equivalent group velocity obtained from dispersion analysis Let be the initial value, let In the k-th iteration, the slowness vector is updated in Kaczmarz form:

[0030] (4) in, As a relaxation factor, To prevent small constants with zero denominators, {·} represents the physical range of slowness. The projection operator on, and , To suppress local oscillations caused by abnormal paths, a weak neighborhood smoothing is applied to the macroscopic slow-speed field after each iteration:

[0031] (5) in, This is the neighborhood smoothing coefficient, which controls the smoothness of the slow-speed field. This represents the set of neighboring grid cells of the j-th calibration grid cell.

[0032] Iterative convergence is evaluated using normalized acoustic residuals: (6) when Or the number of iterations reaches Stop when the path matrix W is insufficient in rank or too large in condition number. The ART result will only be interpreted as path-scale equivalent acoustic time calibration, without a fine two-dimensional wave velocity distribution interpretation. In actual calculations, the calibration grid should be significantly coarser than the imaging grid. , It can be determined by the apparent velocity quantile of the health pathway or the velocity range predicted by dispersion; , , and The residual convergence curve was selected from the repeated health data collection.

[0033] After calibration, the propagation time between any two points a and b is obtained by integrating the slow field along the geodesic path of the unfolded surface: (7) Based on the propagation time, the direct wave time window and the scattered wave time window are adaptively determined, and the scattering flight time features of each sensing path are extracted within the scattering wave time window. The scattering flight time features are then mapped into a flight time constrained probability map using the equivalent slowness field.

[0034] Since ART calibration only uses direct wave information from the healthy baseline, it does not introduce the damage scattering response into the propagation parameter estimation, thus avoiding feature confusion between propagation calibration and damage identification.

[0035] S102: Compensated SDC imaging method based on reliability classification and coverage density equalization.

[0036] Traditional RAPID directly superimposes the damage probabilities of each path, which is easily affected by channel stability and uneven path coverage. To address this, this invention evaluates path reliability based on healthy repetition signals, performs path classification compensation by combining reliability-weighted sensitivity, and suppresses the accumulation of probability repetitions in densely populated areas of the path through coverage density equalization.

[0037] Let the correlation coefficient between the health signal of the k-th path and the current guided wave signal be... Its normalized SDC is: (8) in, These represent the original signal differential coefficients for the k-th path. Denotes the normalized signal difference coefficients of the k-th path. is the regularization constant.

[0038] Based on the pairwise correlation coefficients of the M group of healthy repetitive signals Define path reliability: (9) Further define reliability-weighted path sensitivity: (10) according to and The paths are divided into three categories: (11) in, , and These represent highly sensitive, weakly sensitive, and low-trust paths, respectively. , and These are the reliability threshold, high sensitivity threshold, and low sensitivity threshold, respectively.

[0039] The classification compensation weight is defined as follows: (12) in, For weakly sensitive paths, This represents the low-confidence path suppression coefficient.

[0040] For pixel x, the spatial probability kernel of the k-th path is: (13) in: (14) The cumulative probability result and path coverage density after classification compensation are as follows: (15) Finally, the compensated SDC probability map after coverage density equalization is as follows: (16) in, The coverage density balance coefficient, The scale parameter of the spatial probability kernel controls the decay rate of the elliptic probability distribution in the direction deviating from the path. This method enhances reliable weak responses and suppresses unstable paths through reliability classification, while reducing the accumulation of false probabilities in densely intersecting path regions.

[0041] S103: DS Evidence Fusion Based on Adaptive Reliability Discount

[0042] To improve the stability of damage imaging, this invention uses a compensated SDC probability map with overlay density equalization. With ART calibration of TOF probability plot Pixel-level DS evidence fusion is performed. Since the main peak location of the compensated SDC image is relatively stable, while the TOF image is easily affected by false detections of scattering peaks, boundary reflections, and late-arriving packets, this invention adopts an adaptive reliability discount strategy with compensated SDC as the main evidence and TOF as the auxiliary evidence.

[0043] First, and Normalized to [0,1]. The consistency between TOF evidence and compensated SDC evidence is evaluated based on the peak distance, Hellinger distribution differences, and spatial overlap. When the TOF peak is far from the SDC main peak, the overall distribution conflict is strong, or the overlap is low, the TOF reliability is automatically reduced. Its reliability can be uniformly expressed as:

[0044] (17) in, For the initial reliability of TOF, , and Let represent the peak distance, Hellinger conflict, and distribution overlap discount factor, respectively. The reliability of the compensated SDC as the primary evidence is denoted as r. SDC .

[0045] To avoid the formation of spurious peaks in the low SDC support region of the TOF elliptical loop, this invention further utilizes a compensated SDC diagram to construct spatial support gating, constraining the TOF diagram to obtain a controlled TOF auxiliary diagram. This processing ensures that TOF evidence primarily plays a supporting role in enhancing the SDC main peak neighborhood, rather than dominating the final imaging on its own.

[0046] Let the recognition framework be Where D represents the damage hypothesis and H represents the non-damage hypothesis. Considering that a low-response region does not necessarily represent definitive health, this invention primarily assigns it to the uncertain set. The basic probability distribution of the two types of evidence is as follows:

[0047] (18) (19) According to Dempster's combinatorial principle, the damage mass after fusion is: (20) Finally, to preserve the stable main peak already formed by the compensation SDC and to enhance the region jointly supported by both types of evidence, the final damage probability map is defined as follows: (twenty one) in, The consistency enhancement coefficient, The coefficient for primary evidence is retained. This represents the normalization operator. This fusion strategy can enhance spatially consistent regions using reliable TOF evidence while maintaining the dominant localization role of the compensated SDC, thereby improving imaging focus and suppressing artifacts caused by false detection scattering peaks.

[0048] Example 1: Numerical Simulation Finite element model analysis To reveal the propagation mechanism of ultrasonic guided waves in curved surfaces with large radii of curvature and their transient interaction with minute defects, a three-dimensional curved shell model was constructed using Abaqus finite element software. Material parameters and panel dimensions are shown in Table 1.

[0049] Table 1 Aluminum Alloy Material Parameters and Curved Panel Dimensions In the finite element modeling process, to comprehensively compare and analyze the impact of damage on wave field evolution, a structurally complete healthy state model and a damage state model incorporating local geometric discontinuities were established. In the damage model, a cylindrical blind hole with a diameter of 5 mm was introduced at the center of the monitoring area by removing local mesh nodes to represent an equivalent local corrosion pit. Simultaneously, a through-type interface with a length of 5 mm was constructed to simulate early fatigue cracks. It should be noted that the damage size in the numerical simulation is mainly used to amplify the scattering mechanism and verify the algorithm link; its purpose is not to correspond one-to-one with the damage size in subsequent experiments. The excitation and pickup mechanism of the ultrasonic signal is achieved through a symmetrically distributed set of nodes on the model surface, approximating the electromechanical coupling effect of a real piezoelectric ceramic sensor (PZT) on the structural surface. The arrangement of the transceiver nodes on the plate is the same as the experimental platform: N=6 nodes are set on each side of the monitoring area, with a column spacing L=300 mm, forming a total of 6×6=36 transceiver paths, as shown below. Figure 5 As shown.

[0050] To induce a low-frequency guided wave response dominated by out-of-plane displacement in the structure, the excitation load is set as a transient concentrated force applied radially along the skin. The load is applied to the surface node set corresponding to the PZT location, and the radial displacement response of the same node set is extracted from the received signal. The excitation signal is as follows: Figure 6 As shown, the center frequency is used. The time-domain analytical expression of a five-cycle Hanning window modulated sinusoidal beam of kHz is:

[0051] (twenty two) In the formula, For the excitation amplitude coefficient, The number of periods of the modulation packet (in this simulation) ).

[0052] To ensure the computational accuracy and numerical convergence of the high-frequency transient wavefield in the explicit dynamics solution process, physical constraints need to be imposed on the spatial discretization scale and the time integration step. The entire curved surface skin model is meshed using reduced integral eight-node linear hexahedral elements (C3D8R), with a global mesh size of 1 mm × 1 mm × 1 mm. This mesh size is less than one-tenth of the center wavelength of the dominant guided wavepath at the target frequency, which helps to reduce numerical dispersion. The analysis time step is set to... s, total simulation time is The outer boundary of the curved panel adopts a free boundary condition to preserve boundary reflections in the finite-size skin; subsequently, direct and scattered wave windows are used to reduce the impact of boundary echoes on feature extraction. No quality scaling is used in the simulation; the output variable is the radial displacement time series of surface nodes, used for health / damage signal differential analysis, TOF extraction, and probabilistic imaging.

[0053] Simulation Result Analysis By extracting and visualizing the spatiotemporal displacement field output by the Abaqus explicit solver, the propagation characteristics of guided waves in highly curved metal skins can be analyzed. In the initial stage of beam excitation, the wavefront energy approximately expands along the curved surface. As the propagation distance increases, the surface geometry and finite boundaries cause slight fluctuations in the wavefront phase and result in local energy redistribution. For paths passing through the damaged region, the incident wave undergoes diffraction and reflection at the aperture edge, causing energy attenuation and waveform broadening in the forward transmitted wave packet. For paths deviating from the damage center, the main characteristics are phase delay and weak scattering response caused by diffraction. This non-uniform wavefield distribution is consistent with the basic laws of defect scattering.

[0054] The surface displacement response time series of the array sensing nodes is further extracted and compared with the health baseline signal under the corresponding path. With damage signals ,like Figure 7 As shown in (a), the secondary scattering signal induced by the damaged boundary can be obtained by subtracting the time-domain waveforms of the two states. ,like Figure 7 As shown in (b), it is defined as:

[0055] (twenty three) Analysis of the simulated scattering data reveals an observable travel time offset (TOF difference) between the peak positions of healthy and damaged signals within the effective time window of the direct-arrival wave packet. Furthermore, the signal envelope energy ratio or Correlation Damage Index (CDI) indicates that paths traversing the damage exhibit more significant energy attenuation and waveform mismatch; paths deviating from the damage center show weaker scattering envelope peaks. These phenomena provide numerical evidence for path classification based on direct-arrival wave damage sensitivity and scattering TOF constraints.

[0056] The typical multipath time-domain response under simulated conditions with Tx1 excitation and Rx1-Rx6 reception is presented. The main wave packet of each path can be identified within the direct wave window, and the arrival time difference varies with the receiving position. Secondary echoes also appear in some paths within the scattering window, providing numerical basis for subsequent TOF constraint extraction and path classification.

[0057] However, numerical simulations also reveal limitations of using a single feature. While strong signal variation can be extracted near the center of the damage, in areas with sparse sensor network coverage, weak damage features are easily aliased with surface boundary echoes and secondary scattering. In such cases, relying solely on amplitude, energy, or cross-correlation thresholds may lead to positioning errors. Numerical results validate the feasibility of simultaneously extracting TOF and correlation features from curved skin structures, and also demonstrate the necessity of introducing ART equivalent slow-field calibration and DS multi-feature fusion. Figure 8 The imaging results of CDI for each path and the traditional RAPID method compared with the method of this invention under numerical simulation conditions are presented. The traditional RAPID image has a wide high-probability band in the path intersection region, while the main peak of the method of this invention is more concentrated in the preset damage neighborhood, indicating that multi-feature constraints help improve imaging focusing.

[0058] Example 2: Experimental Verification and Analysis To verify the effectiveness of the proposed method, a 2024-T3 aluminum alloy curved panel experimental platform was constructed to verify and quantitatively analyze the ART equivalent slow field calibration, classification compensation SDC, and DS multi-feature fusion methods.

[0059] Experimental Platform and Testing Scheme: The experimental object was a 2024-T3 aerospace aluminum alloy curved panel, measuring 600 mm × 600 mm, with a curvature radius R = 2000 mm and a thickness h = 3 mm. Its geometric dimensions and sensor arrangement were consistent with the numerical model. Three curved panel specimens of identical size, material, and curvature were used. An xz coordinate system was established with the midpoint of the lower edge of the curved panel as the origin. Through-holes with a radius of 5 mm were machined at positions a (0, 300) mm, b (-90, 300) mm, and c (100, 250) mm, respectively (simulating corrosion damage). Five sets of healthy baseline signals were collected for each specimen before the damage was processed. Keeping the sensor arrangement and testing system configuration unchanged, five sets of damage signals were collected after the through-holes were machined. Therefore, a total of 15 sets of healthy baseline data and 15 sets of damage test data were obtained at the three damage locations.

[0060] Sensor Network and Data Acquisition System: Six PZT-5A piezoelectric sensors are arranged on each side of the monitoring area, totaling 12 sensing nodes. The PZTs are 10 mm in diameter and 1 mm thick, and are bonded to the curved panel surface with epoxy resin. The transmitting columns T1-T6 are located at z=150 mm, and the receiving columns R1-R6 are located at z=450 mm, with an axial spacing of 300 mm between the two columns and a center-to-center spacing of 60 mm between adjacent sensors. The six transmitting sensors are sequentially excited, forming 36 transmit-receive paths; the path lengths are approximated using the aforementioned geodesic pattern. The excitation signal is a 5-cycle Hanning window modulated sine pulse with a center frequency of 180 kHz. The signal is generated by a signal generator, amplified by a high-voltage amplifier, and applied to the transmitting PZTs at a terminal voltage of 250 Vpp; the received signal is synchronously acquired by an oscilloscope at a sampling rate of 10 MHz and a resolution of 14 bits.

[0061] Signal preprocessing and baseline establishment: Each signal group is first subjected to DC removal and uniform bandpass filtering, and then time alignment is performed based on the excitation trigger point or direct wave cross-correlation. Path reliability. The correlation coefficients of five sets of healthy signals from the same specimen were calculated; the ART calibration used the average arrival time of the five sets of healthy direct waves; the damage status SDC was calculated using the mean of the aligned healthy signals as the baseline. All signal preprocessing parameters remained consistent across the three damage locations and four imaging methods.

[0062] Evaluation metrics: Damage localization accuracy and probability map focusing accuracy are evaluated using positioning error and image standard deviation, respectively. For the r-th repeated measurement of the j-th damage condition, the positioning error is defined as:

[0063] (twenty four) in, This represents the peak position of the damage probability map. This represents the actual damage center. The smaller the two indicators, the smaller the positioning error and the more concentrated the high-probability area, respectively.

[0064] ART equivalent slow-field calibration effect: ART calibration is performed before damage imaging, using only the direct-path acoustic wave from the healthy baseline. The initial equivalent group velocity is taken as... m / s, upper limit of iteration =15.

[0065] The convergence characteristics of the ART calibration process reveal the following trend in the normalized acoustic time residual with increasing iteration count: the residual decreases rapidly in the first 10 iterations, then stabilizes between iterations 10 and 15. During the ART iteration process, the normalized acoustic time residual decreases from approximately 0.0210 to 0.0167, a relative reduction of about 20.5%. In the calibrated macroscopic equivalent group velocity field distribution, the equivalent group velocity within the monitoring area transitions from approximately 3000 m / s at the edge to approximately 2700 m / s in the central region.

[0066] To evaluate the improvement effect of ART calibration on path time of sound, the absolute TOF errors of 36 paths were compared under both fixed wave velocity and ART calibration conditions. Under the fixed wave velocity assumption, the TOF errors of many paths were significantly larger, while after ART calibration, the overall errors of each path decreased to a lower level, indicating that equivalent slow field calibration can effectively suppress path-scale time of sound mismatch.

[0067] To further evaluate the impact of ART calibration on TOF feature imaging, original TOF probability maps and ART-calibrated TOF constrained probability maps were constructed for three typical defect locations. The results are shown in [Figure number missing]. Figure 9 . Figure 9 (a)-(c) are the TOF feature maps obtained using a uniform propagation speed. Figure 9 (d)-(f) show the results after calibration with an equivalent slow-degree field. Without calibration, the elliptical constraints corresponding to each path exhibit significant time-of-sound mismatch, resulting in a wide overlap of probability rings and the formation of spurious peaks deviating from the actual defects in some regions. After ART calibration, the high-probability regions shrink towards the neighborhood of the actual defects, and the main response regions at all three locations show better consistency with the actual damage locations. However, due to factors such as scattering peak identification errors and limited path coverage, a certain arc-shaped background still exists in the TOF images, and the imaging results need further improvement through feature fusion.

[0068] Reliability Classification and Compensation: SDC Imaging Validation - Path Reliability With weighted sensitivity The 36 paths were categorized into three classes: highly sensitive, weakly sensitive, and low-reliability.

[0069] The time-domain response of a typical path traversing the damaged area under the condition of penetrating a circular hole is shown below. Figure 10Within the direct wave window, the healthy alignment baseline and the waveform of the damaged state are basically consistent; within the scattering time window, the damaged signal shows identifiable amplitude changes and waveform distortion. Differentiation between the two allows for the extraction of scattering / reflection packets induced by the defect boundary, which are then used for subsequent SDC indices. The calculation and TOF feature extraction provide experimental basis.

[0070] SDC metrics normalized from 36 paths Distribution (see) Figure 11 As can be seen, the paths related to the location of the damage (such as channels 16, 21, etc.) The values ​​were significantly higher than those of other paths and exhibited a certain degree of symmetrical distribution. This was combined with data obtained from repeated health data collection. Further calculations are possible. And construct , and Classification criteria are used to suppress low-reliability channels and enhance the contribution of reliable weak response paths.

[0071] Multi-feature fusion damage imaging and quantitative assessment: Experimental imaging results of traditional RAPID, compensated SDC, and intact methods at different defect locations are as follows: Figure 12 As shown. Figure 12 (a)-(c) Figure 12 (d)-(f) and Figure 12 (g)-(i) correspond to the three methods mentioned above respectively; from left to right, they are the damage locations a (0, 300) mm, b (-90, 300) mm and c (100, 250) mm.

[0072] Depend on Figure 12 As can be seen in (a)-(c), traditional RAPID forms a relatively wide high-probability band in areas with dense path intersections, and there are still some peak shifts and background artifacts at the eccentric damage locations. After path reliability classification and coverage density equalization, Figure 12 The low-confidence path contributions in (d)-(f) are suppressed, the cumulative repetition probability in path intersection regions is significantly reduced, and the high-probability regions at the three damage locations all concentrate in the neighborhood of the true hole. Based on this, after introducing ART-calibrated TOF evidence, the complete method utilizes compensated SDC to provide stable main peak positions and leverages reliable TOF evidence to enhance regions consistent with both feature spaces. Figure 12 As can be seen from (g)-(i), the main peak of the complete method is further concentrated, while the background response and wide probability band are weakened.

[0073] To analyze the impact of different features and fusion steps on imaging performance, the traditional RAPID, ART-calibrated TOF, classification-compensated SDC, and complete methods were compared. All four methods used the same healthy baseline, guided wave damage signal, imaging region, and spatial grid. Based on defined indices, the localization error and spatial standard deviation of the high-probability region for 15 damage tests were calculated, and the average results are shown in Table 2.

[0074] Table 2 Quantitative Assessment of Damage Imaging Accuracy Imaging indicators Traditional RAPID ART calibration of TOF Classification Compensation SDC Complete method Positioning error / mm 15.6 8.9 7.8 5.4 Image standard deviation / mm 8.83 4.01 3.22 1.39 Table 2 shows that the average localization error of the complete method is 5.4 mm, and the spatial standard deviation of the high-probability region is 1.39 mm. Compared with the traditional RAPID method, the average localization error is reduced by 65.4%, and the image standard deviation is reduced by 84.3%. The results indicate that ART calibration can reduce path acoustic time mismatch, classification compensation SDC can reduce the influence of unstable paths and uneven coverage, and DS fusion can further improve the damage localization accuracy and imaging focus.

[0075] This invention addresses the problems of waveguide propagation parameter mismatch, uneven sensing path coverage, and insufficient stability of single damage features in curved thin-walled metal structures. It proposes a waveguide damage imaging method based on equivalent slow-field calibration and multi-feature fusion. ART calibration reduces path acoustic time mismatch caused by the fixed wave velocity assumption; reliability classification and coverage density equalization suppress the accumulation of false probabilities in unstable channels and densely populated areas; SDC and TOF feature fusion further improves imaging focusing and positioning stability. Abaqus numerical simulations preliminarily validate the algorithm's effectiveness in damage identification. Experimental results on a 5 mm radius through-hole defect on a 2024-T3 aluminum alloy curved panel with a curvature radius of 2000 mm and a thickness of 3 mm show that the average positioning error of the proposed complete method is 5.4 mm, which is approximately 65.4% and 39.3% lower than the 15.6 mm of the traditional RAPID method and the 8.9 mm of the ART-calibrated TOF method, respectively. This indicates that the method can effectively improve the positioning accuracy and imaging stability of hole-type damage in curved panels.

[0076] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. An aircraft curved skin guided wave damage imaging method, characterized by, include: Acquire multiple sets of healthy baseline guided wave signals of the aircraft curved skin and the current guided wave signal under the state to be detected, and extract the flight time of the healthy direct wave from the healthy baseline guided wave signals; The propagation time of each sensing path is calibrated based on the time-of-flight of the health direct wave, and a time-of-flight constrained probability map is constructed based on the calibrated propagation time. Based on the multiple sets of healthy baseline guided wave signals and the current guided wave signal, the sensing path is subjected to sensitivity classification compensation and coverage density equalization to generate a compensated signal differential coefficient probability map. Using the compensated SDC probability map as primary evidence and the TOF constrained probability map as secondary evidence, and based on the consistency between the secondary evidence and the primary evidence, the reliability of the secondary evidence is discounted to obtain the discounted TOF reliability. Spatial support gating is constructed using the spatial distribution characteristics of the primary evidence to constrain the secondary evidence, resulting in a controlled TOF auxiliary map. Finally, based on the primary evidence, the discounted TOF reliability, and the controlled TOF auxiliary map, the two types of evidence are fused at the pixel level using evidence theory to obtain the fused damage quality distribution. Based on the fused damage quality distribution, a final surface skin damage probability imaging map is generated.

2. The method for imaging guided wave damage on aircraft curved skin as described in claim 1, characterized in that, The calibration of the propagation time of each sensing path based on the time-of-flight of the healthy direct wave includes: The flight time of the healthy direct wave is iteratively inverted using algebraic reconstruction techniques to obtain the equivalent slowness field at the path scale. The propagation time of each sensor path is recalculated using the equivalent slow field to obtain the calibrated propagation time of each sensor path.

3. The guided wave damage imaging method for aircraft curved skin as described in claim 2, characterized in that, The iterative inversion of the flight time of the direct wave using algebraic reconstruction techniques to obtain the equivalent slowness field at the path scale includes: The aircraft curved skin is unfolded along the curvature direction, and a calibration grid is established in the unfolded plane; The reciprocal of the equivalent group velocity obtained from dispersion analysis is used as the initial slowness value for each calibration grid cell; the slowness value of each calibration grid cell is iteratively updated according to the Kaczmarz form. After each iteration, neighborhood smoothing is applied to the slow field; When the normalized sound residual converges or reaches the preset number of iterations, the iteration stops, and the equivalent slow field is obtained.

4. The method for imaging guided wave damage on aircraft curved skin as described in claim 1, characterized in that, The construction of the time-of-flight constrained probability map based on the calibrated propagation time includes: Based on the propagation time of each calibrated sensing path, the direct wave time window and the scattered wave time window are adaptively determined. The scattering time-of-flight characteristics of each sensing path are extracted within the scattering wave time window, and the scattering time-of-flight characteristics are mapped into a time-of-flight constrained probability map using the equivalent slowness field.

5. The guided wave damage imaging method for aircraft curved skin as described in claim 1, characterized in that, Based on the multiple sets of healthy baseline guided wave signals and the current guided wave signal, sensitivity classification compensation and coverage density equalization are performed on the sensing path, including: The normalized signal differential coefficients are obtained based on the correlation coefficient between the health baseline guided wave signal and the current guided wave signal for each sensing path. The reliability weight of the sensing path is obtained based on the correlation coefficients between pairs of multiple sets of healthy baseline guided wave signals. Based on the normalized signal differential coefficients and the reliability weights, the paths are divided into highly sensitive paths, weakly sensitive paths, and low-reliability paths; the highly sensitive paths are assigned a weight consistent with the sensitivity of the weighted paths, the weakly sensitive paths are compensated and enhanced, and the low-reliability paths are suppressed. The spatial probability kernels of each sensing path are weighted and superimposed according to the weights after classification compensation to obtain the cumulative probability result; and the path coverage density is obtained based on the spatial probability kernel of each path.

6. The guided wave damage imaging method for aircraft curved skin as described in claim 5, characterized in that, The generation of the compensated signal differential coefficient probability map includes: Based on the probability accumulation result and the path coverage density, the probability map of the differential coefficients of the compensation signal is obtained. , is represented as: Where, γ c ∈[0,1] is the coverage density equalization coefficient; This represents the cumulative probability result; Indicates path coverage density; Represents the regularization constant; {} represents the global normalization operator.

7. The method for imaging guided wave damage on aircraft curved skin as described in claim 1, characterized in that, Based on the consistency between the supporting evidence and the main evidence, the reliability of the supporting evidence is discounted, including: Calculate the spatial distance between the peak position of the auxiliary evidence and the peak position of the main evidence, and determine a first discount factor based on the spatial distance; Calculate the Hellinger distance between the auxiliary evidence and the main evidence on the full graph distribution, and determine the second discount factor based on the Hellinger distance; Calculate the spatial overlap between the auxiliary evidence and the main evidence, and determine a third discount factor based on the spatial overlap; The product of the initial reliability of the auxiliary evidence and the first discount factor, the second discount factor, and the third discount factor is used as the discounted reliability of the auxiliary evidence.

8. The method for imaging guided wave damage on aircraft curved skin as described in claim 1, characterized in that, The calculation process for the fused damage mass distribution is as follows: For each pixel, the quality of the non-damage hypothesis in the basic probability allocation of the main evidence is assigned to the uncertainty set, and the quality of the non-damage hypothesis in the basic probability allocation of the auxiliary evidence is assigned to the uncertainty set, thus obtaining the basic probability allocation of the two types of evidence. The Dempster combination rule is used to fuse the basic probability assignments of the two types of evidence to obtain the fused damage quality of the pixel. A method for imaging guided wave damage to curved aircraft skin as described in claim 1, characterized in that, The final probabilistic imaging map of surface skin damage is generated as follows: in, This represents the final probabilistic imaging map of surface skin damage. Indicates the quality of damage after fusion; This represents the SDC probability diagram after compensation. Represents a controlled TOF auxiliary plot; η c η is the consistency enhancement coefficient. s The coefficients are preserved for the main evidence, and N{·} denotes the normalization operator.

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