Extensible flexible GMR eddy current detection method and system for complex curved surface component

Abstract

The invention provides a deployable flexible GMR eddy current testing method and system for a complex curved surface component, and relates to the technical field of nondestructive testing. The method comprises the following steps: establishing a curved surface coordinate system and an expansion domain coordinate system, constructing a geometric mapping relation of a flexible sensing array, and performing clearance compensation, attitude correction and temperature drift correction on multi-frequency response data in an expansion domain to form a unified response data set; defect response distribution is generated through robust reconstruction and reprojected to the curved surface coordinate system, and space positioning and size and orientation recognition of defects are achieved; and adaptively updating the attitude, the path and the excitation scheme in combination with the fitting state parameters until the detection coverage and the confidence meet the requirements. According to the method, high-precision detection and process traceability of the defects of the complex curved surface component are realized.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing technology, and in particular to a developable flexible GMR eddy current testing method and system for complex curved surface components. Background Technology

[0002] Eddy current nondestructive testing (EDT) is widely used in defect identification, corrosion assessment, and service condition monitoring of conductive materials. Traditional testing methods often employ rigid coils or rigid magnetoresistive or Hall-type probes, utilizing a single frequency or a few excitation frequencies and employing a fixed geometric arrangement to identify surface and near-surface defects. In regular planes or areas with large radii of curvature, existing systems typically rely on standardized detection gap control and reference block calibration to achieve high repeatability. In recent years, to further improve detection sensitivity and anti-interference capabilities, the industry has gradually introduced improved technologies such as multi-channel synchronous acquisition, amplitude and phase comprehensive judgment, and temperature drift compensation. Simultaneously, the rapid development of flexible electronics and stretchable substrate materials has enabled the initial validation of flexible sensing arrays in the bonding detection of complex curved surfaces, providing new avenues for expanding the application boundaries of eddy current testing.

[0003] In fields such as aerospace composite skins, energy and chemical pressure vessels, transportation equipment crankshafts, and irregularly shaped thin-walled components, the demand for conductive structure detection is developing towards lightweight, fitability, high coverage, and real-time capabilities. Flexible giant magnetoresistive (GMR) sensor arrays, due to their advantages of small size, high bandwidth, low noise, and adjustable array density, are gradually becoming an important technical route for near-field detection of complex curved surfaces. Supporting signal processing and modeling technologies are also showing trends towards multi-frequency excitation, multi-phase response, array-based collaborative imaging, dual attitude and temperature compensation, and coordinate unification based on digital geometric models. For the detection of complex curved surfaces, research focus is gradually shifting to how to accurately handle the impact of factors such as fit deformation, geometric curvature, attitude drift, and environmental temperature changes on the stability of detection sensitivity under limited hardware complexity, thereby achieving quantitative evaluation results similar to those under planar detection conditions.

[0004] Existing flexible array bonding eddy current detection methods typically perform gap compensation and signal imaging directly within a physical surface coordinate system. This approach relies on local curvature and attitude estimation, which can easily lead to position-dependent deviations in sensitivity and spatial resolution in regions with significant curvature variations or freeform surfaces. The inevitable deformation of the array during bonding alters the element spacing and normal distribution. Without a unified spatial mapping and time synchronization mechanism, it is difficult to transfer calibration parameters between different regions, resulting in poor consistency and reproducibility of detection results. Furthermore, when performing inversion calculations directly within the surface coordinate system, the mesh is often uneven, and the kernel function distortion is significant, easily causing instability in the inversion equations and amplifying noise effects, making it difficult to unify the detection coverage and sensitivity threshold. Current technology has not yet developed a flexible GMR eddy current detection method that can simultaneously achieve geometric mapping, response calibration, and stable imaging under complex surface conditions, thus presenting significant limitations in engineering applications and standardization. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the purpose of this invention is to provide a developable flexible GMR eddy current detection method and system for complex curved surface components. Through the development domain reconstruction and adaptive update mechanism, high-precision identification and traceable detection of defects on complex curved surfaces are achieved.

[0006] To achieve the above objectives, the present invention provides the following solution: A developable flexible GMR eddy current detection method for complex curved surface components includes: A flexible GMR sensor array is attached to the complex curved outer surface of the target component, and a curved surface coordinate system and an unfolded domain coordinate system are established. The spatial position, normal direction and relative spacing of each sensing channel are determined according to the attachment state parameters, forming a mapping relationship between the curved surface and the unfolded domain. The flexible GMR sensor array is driven to perform multi-frequency excitation and synchronous acquisition under a unified time reference to obtain the raw response data of each sensing channel. Reference response data is also synchronously acquired in the reference area where the component is defect-free or has been calibrated on site, and the bonding pressure, temperature and attitude information are recorded to form the raw detection dataset. Within the expanded domain coordinate system, using the reference response data as a reference, gap compensation, attitude correction, and temperature drift correction are performed on the original detection dataset. The calibration parameters are propagated and updated through the mapping relationship to obtain a calibrated unified response dataset. Imaging reconstruction is performed using the unified response dataset within the expanded domain coordinate system to identify the defect response distribution. The reconstruction results are then projected back onto the surface coordinate system through the mapping relationship to determine the spatial location, size, and orientation information of the defect on the surface. Based on the feedback results and the bonding state parameters, adjust the bonding posture, scanning path and excitation parameters of the flexible GMR sensor array, and re-execute the acquisition and calibration steps until the detection coverage and result confidence meet the set requirements. The defect identification results and detection evaluation data are output in the surface coordinate system, and the mapping relationship, calibration parameters and detection trajectory are stored together.

[0007] Preferably, a flexible GMR sensor array is attached to the complex curved outer surface of the target component, establishing a surface coordinate system and an unfolded domain coordinate system. The spatial position, normal direction, and relative spacing of each sensing channel are determined based on the attachment state, forming a mapping relationship between the curved surface and the unfolded domain, including: An imageable positioning mark array is preset on the substrate of the flexible GMR sensor array. After being attached to the complex curved outer surface of the target component, the coordinate point set of the positioning mark in space is extracted by the imaging unit. The correspondence between each sensing channel and the coordinate point set is indexed according to the array design to obtain the initial curved surface discrete point cloud in the attached state. Using the positioning marks as constraints, and combining the bonding pressure and attitude measurement, the in-plane tension and shear parameters of the flexible substrate are estimated, and the initial estimate of the sensor channel spacing correction coefficient and channel normal is calculated to form the bonding state parameters. Based on the discrete point cloud of the surface and the set of fitting state parameters, a surface coordinate system is established. Local tangent plane fitting and normal consistency constraints are used to determine the spatial position and normal direction of each sensing channel in the surface coordinate system, and the relative spacing between the channels is updated accordingly. The surface coordinate system is parameterized under expandable deformation constraints to obtain the coordinates of each positioning mark and each sensing channel in the expanded domain coordinate system. The local area is limited to prevent flipping and the boundary is continuous, thus constructing a positive mapping relationship from the surface coordinate system to the expanded domain coordinate system. Based on the correspondence between the positioning markers and the sensing channels, the inverse mapping relationship from the expanded domain coordinates to the surface coordinates is calculated. The forward mapping relationship and the inverse mapping relationship are jointly checked using the positioning residual as the criterion. When the residual exceeds the preset threshold, the fitting state parameters are updated and the mapping relationship is iterated until the accuracy requirements are met.

[0008] Preferably, using the positioning mark as a constraint, and combining the bonding pressure and attitude measurement, the in-plane tensile and shear parameters of the flexible substrate are estimated, and the initial estimate of the sensor channel spacing correction coefficient and channel normal is calculated to form bonding state parameters, including: Based on the attitude measurement, the rotation matrix is ​​obtained. The three-dimensional observation coordinates of the positioning marker after bonding are extracted and projected onto the local tangent plane. The correspondence between the reference coordinates and the observation coordinates is established, as shown in the formula: ;in, For the first The two-dimensional coordinates of a positioning marker on a local tangent plane; The rotation matrix is ​​obtained from attitude measurement; For the first The three-dimensional observation coordinates of each positioning marker after fitting; For projection operators to the local tangent plane; For unit array; This is an initial estimate of the local normal. Within the expanded domain coordinate system, using the positioning marks as constraints, and combining the bonding pressure to estimate the in-plane deformation gradient, the in-plane tensile and shear parameters are obtained, as follows: ;in, This is the optimal solution for the in-plane deformation gradient; For the first The reference two-dimensional coordinates of each positioning marker; Number of available location markers; For determinant operators; Scalar measurement for fitting pressure; This represents the weighting coefficient for the volume consistency term; The coupling coefficient between pressure and area change; The right stretching tensor is obtained from the deformation gradient decomposition, and the spacing correction coefficient of each sensing channel is calculated based on the right stretching tensor, using the following formula: ;in, The right-side tensor; For the first The spacing correction factor for each sensing channel; For the first The unit direction vector of each sensing channel in the reference design; By combining attitude measurement and the effect of bonding pressure on stress-induced shear, an initial estimate of the channel normal is obtained, as shown in the formula: ;in, This is the initial estimated vector for the channel normal; Let be the unit normal basis vector of the device coordinate system; The coupling coefficient for pressure-normal correction tr is a symmetric partial operator constructed from the deformation gradient; The trace of the matrix; The estimation results are checked using the positioning residual as a criterion. When the residual exceeds the threshold, the fitting state parameters are updated and the solution is iterated until the accuracy requirement is met. The formula is as follows: ;in, To locate the residual; This is a preset threshold.

[0009] Preferably, the surface coordinate system is parameterized under expandable deformation constraints to obtain the coordinates of each positioning mark and each sensing channel in the unfolded domain coordinate system, ensuring that the local area does not flip and the boundary is continuous, and constructing a positive mapping relationship from the surface coordinate system to the unfolded domain coordinate system, including: Based on the discrete point set of positioning markers and sensing channels in the surface coordinate system, a triangular mesh that satisfies the boundary order and normal consistency is generated, and the boundary vertex sequence and boundary arc length sequence are extracted as parameterized boundary constraints. Initialize the two-dimensional coordinates of each mesh vertex in the expanded domain coordinate system. The initialization can be obtained based on the equidistant spreading of the boundary arc length or the minimum strain criterion, and is used as the starting point for subsequent optimization. Solve for the two-dimensional coordinates of each vertex in the expanded domain coordinate system to satisfy the expandable deformation constraint and the no-flip constraint, thus obtaining the optimized vertex set and forming the expanded domain coordinates, as shown in the formula: ;in, To expand the optimal set of vertices within the domain coordinate system; The set of vertices to be optimized; For the first The Jacobian matrix corresponding to each triangle in the expanded domain coordinate system; For unit array; It is the Frobenius norm; For the boundary sequence The two-dimensional coordinates of each vertex in the expanded domain coordinate system; This represents the arc length of the corresponding boundary edge in the surface coordinate system. The weighting coefficient for the consistency of boundary arc length; The weighting coefficients represent the non-reversal potential energy. Based on the optimized vertex set, a piecewise affine forward mapping is constructed from the surface coordinate system to the expanded domain coordinate system. For any vertex located at the _th ... For points within the triangle, the coordinates of the expanded domain are calculated using the centroid coefficient within the curved triangle, as follows: ;in, Let the coordinates of the point be the two-dimensional coordinates in the expanded domain coordinate system; For the first The two-dimensional coordinates of the three vertices of a triangle in the expanded domain coordinate system; The centroid coefficient of the point within the corresponding surface triangle; The forward mapping is evaluated based on the criteria of no local area flipping and boundary continuity. If the threshold condition is not met, optimization continues under the same initialization conditions until the requirements are met. The formula is: ;in, The threshold for determining whether the area is not flipped. This is the threshold for determining boundary continuity.

[0010] Preferably, the flexible GMR sensor array is driven under a unified time reference to perform multi-frequency excitation and synchronous acquisition, obtaining the raw response data of each sensing channel. Reference response data is also synchronously acquired in a defect-free or field-calibrated reference area, and the bonding pressure, temperature, and attitude information are recorded to form a raw detection dataset, including: Set the synchronization control signal and determine the multi-frequency drive scheme. ,in For driving frequency, For phase; Under the action of the synchronization control signal, the flexible GMR sensor array is sequentially subjected to... Each pair in The original responses of each sensor channel are read synchronously and recorded as original response data in the form of channel identifier-frequency index; In the reference area, the synchronous control signal and multi-frequency drive scheme are repeatedly collected to obtain reference response data, and the bonding pressure, temperature and attitude information are recorded at the same time. The bonding pressure, temperature and attitude information are bound to the channel identifier-frequency index. The original response data, the reference response data, the bonding pressure, the temperature, and the attitude information are aligned and merged according to the channel identifier-frequency index to generate the original detection dataset.

[0011] Preferably, within the expanded domain coordinate system, using the reference response data as a reference, gap compensation, attitude correction, and temperature drift correction are performed on the original detection dataset. The calibration parameters are propagated and updated through the mapping relationship to obtain a calibrated unified response dataset, including: The original detection dataset is paired with the reference response data in the form of channel identifier-frequency index to obtain the response to be calibrated; The detection gap is estimated based on the bonding state parameters, and a gap compensation factor is generated and applied to the response to be calibrated. The rotation matrix is ​​obtained from the attitude information, and attitude correction is applied to the channel orientation-related quantities. Establish a temperature drift baseline based on temperature information to eliminate amplitude and phase shifts caused by temperature. On the triangular mesh of the expanded domain, with the consistency of adjacent cells as a constraint, the calibration parameters are propagated and updated through the mapping relationship; The convergence check is performed using the residual threshold as the criterion. If the threshold is not met, the iteration continues until the requirement is met.

[0012] Preferably, imaging reconstruction is performed using the unified response dataset within the expanded domain coordinate system to identify the defect response distribution. The reconstructed result is then projected back onto the surface coordinate system through the mapping relationship to determine the spatial location, size, and orientation information of the defect on the surface, including: A unified response field is constructed within the expanded domain coordinate system; A robust reconstruction criterion is used to generate a defect response distribution map and extract candidate regions. The equivalent peak value, equivalent half-width at half-maximum and main direction of the candidate region are calculated to obtain the size and orientation parameters. Based on the mapping relationship, the distribution map is projected back onto the surface coordinate system using piecewise affine mapping and centroid coefficient method, and the spatial location, size and orientation information of the defects in the surface coordinate system are output.

[0013] Preferably, based on the feedback results and the bonding state parameters, the bonding posture, scanning path, and excitation parameters of the flexible GMR sensor array are adjusted, and the acquisition and calibration steps are re-executed until the detection coverage and result confidence meet the set requirements, including: The detection coverage and result confidence were assessed based on the resubmission results; When the coverage or confidence is insufficient, the attitude adjustment amount and the scan path update amount are generated based on the bonding state parameters, and the multi-frequency drive scheme is adjusted to a limited extent. After verifying the continuity of the mapping relationship, adjustments are made, and the unified collection and expansion domain calibration are repeated until the coverage and confidence reach the set threshold.

[0014] A developable flexible GMR eddy current testing system for complex curved surface components includes: The surface bonding modeling module is used to bond the flexible GMR sensor array to the complex curved outer surface of the target component, establish the surface coordinate system and the unfolded domain coordinate system, determine the spatial position, normal direction and relative spacing of each sensing channel according to the bonding state parameters, and form a mapping relationship between the surface and the unfolded domain. The multi-frequency synchronous acquisition module is used to drive the flexible GMR sensor array to perform multi-frequency excitation and synchronous acquisition under a unified time reference, obtain the raw response data of each sensing channel, and synchronously acquire reference response data in the reference area where the component is defect-free or has been calibrated on site, and record the bonding pressure, temperature and attitude information to form the raw detection dataset. The expanded domain calibration module is used to perform gap compensation, attitude correction and temperature drift correction on the original detection dataset within the expanded domain coordinate system, with the reference response data as a reference, and to propagate and update the calibration parameters through the mapping relationship to obtain a calibrated unified response dataset. The unfolded domain imaging and projection module is used to perform imaging reconstruction using the unified response dataset in the unfolded domain coordinate system, identify the defect response distribution, and project the reconstruction result back to the surface coordinate system through the mapping relationship to determine the spatial location, size and orientation information of the defect on the surface. The adaptive detection update module is used to adjust the bonding posture, scanning path and excitation parameters of the flexible GMR sensor array according to the re-projection results and the bonding state parameters, and re-execute the acquisition and calibration steps until the detection coverage and result confidence meet the set requirements. The result output and traceability module is used to output defect identification results and detection evaluation data in the surface coordinate system, and store the mapping relationship, calibration parameters and detection trajectory together.

[0015] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: (1) This invention establishes a surface coordinate system and an unfolded domain coordinate system and constructs a surface-unfolded domain mapping relationship, thereby realizing the deployable bonding and unified spatial parameter characterization of flexible GMR sensor arrays on complex curved surfaces. Compared with existing bonding methods that rely solely on local curvature estimation, this invention can maintain the consistency of the spatial position and normal direction of the sensing channel under conditions such as curvature abrupt changes and non-uniform bonding, significantly improving the geometric matching accuracy and data comparability of the detection area, and providing a foundation for high-fidelity detection of complex free-form surface components.

[0016] (2) This invention performs gap compensation, attitude correction, and temperature drift correction based on the reference response within the expanded domain coordinate system. Through mapping relationships, it achieves global propagation and updating of calibration parameters, forming a unified response dataset independent of local curvature. This method effectively eliminates the coupling effects of surface curvature, attitude drift, and environmental changes on the response data, ensuring that detection sensitivity and spatial resolution remain consistent across the entire domain, thereby significantly improving the stability and repeatability of the detection results.

[0017] (3) This invention combines unfolded domain imaging with surface retrieval to achieve equivalent planar reconstruction and precise localization of defects on complex curved surfaces. Furthermore, by incorporating an adaptive detection and update mechanism, it dynamically optimizes the fitting posture, scanning path, and excitation parameters, enabling the detection process to automatically converge to optimal coverage and confidence. This solution not only shortens the on-site inspection cycle but also achieves high-resolution defect identification and traceable evidence storage without altering the component's geometry, providing technical support for the intelligent inspection and digital recording of complex curved surface components. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart of the method provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the system structure provided in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The purpose of this invention is to provide a developable flexible GMR eddy current detection method and system for complex curved surface components, which realizes developable mapping and self-consistent calibration of flexible GMR arrays under complex curved surface conditions, and ensures that the detection sensitivity is uniform and reliable across the entire range.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] Figure 1 The method flowchart provided in the embodiments of the present invention is as follows: Figure 1 As shown, this invention provides a developable flexible GMR eddy current detection method for complex curved surface components, comprising: Step 100: Attach the flexible GMR sensor array to the complex curved outer surface of the target component, establish the curved surface coordinate system and the unfolded domain coordinate system, determine the spatial position, normal direction and relative spacing of each sensing channel according to the attachment state parameters, and form a mapping relationship between the curved surface and the unfolded domain. Step 200: Drive the flexible GMR sensor array to perform multi-frequency excitation and synchronous acquisition under a unified time reference to obtain the raw response data of each sensing channel, and synchronously acquire reference response data in the reference area where the component is defect-free or has been calibrated on site, and record the bonding pressure, temperature and attitude information to form the raw detection dataset. Step 300: In the expanded domain coordinate system, using the reference response data as a benchmark, perform gap compensation, attitude correction and temperature drift correction on the original detection dataset, and propagate and update the calibration parameters through the mapping relationship to obtain the calibrated unified response dataset. Step 400: Perform imaging reconstruction using the unified response dataset within the expanded domain coordinate system, identify the defect response distribution, and project the reconstruction results back onto the surface coordinate system through mapping relationships to determine the spatial location, size, and orientation information of the defect on the surface; Step 500: Adjust the bonding posture, scanning path and excitation parameters of the flexible GMR sensor array according to the feedback results and bonding status parameters, and re-execute the acquisition and calibration steps until the detection coverage and result confidence meet the set requirements; Step 600: Output the defect identification results and detection evaluation data in the surface coordinate system, and store the mapping relationship, calibration parameters and detection trajectory together.

[0024] Specifically, step 100 in this embodiment includes: In this embodiment, an imageable positioning marker array is uniformly set on the substrate surface of the flexible GMR sensor array. The positioning markers are arranged in a regular array, with a marker spacing preferably between 5 mm and 10 mm, and are used to calibrate the spatial position of the sensing channels after bonding. After the flexible array is bonded to the complex curved outer surface of the target component, the marker images are acquired using an integrated imaging unit with an imaging resolution of no less than 4 million pixels. The three-dimensional spatial coordinates of each positioning marker are recovered by using geometrically calibrated camera intrinsic and extrinsic parameters to form a marker point set. According to the channel-marker index table pre-stored in the array design file, the correspondence between sensing channels and marker points is established, thereby generating an initial curved surface discrete point cloud covering the entire detection area. To ensure the quality of the point cloud, this embodiment adopts a multi-angle shooting method during the imaging stage. When the single recognition rate is lower than 95%, a reshoot is automatically triggered to ensure the spatial integrity of the positioning markers.

[0025] This embodiment uses the spatial displacement of the positioning marks as the main constraint, combined with bonding pressure and attitude measurement data, to calculate the in-plane tensile and shear amounts of the flexible substrate, and thus form "bonding state parameters". The bonding pressure range is 0 to 30 kPa, with a typical working range of 3 to 12 kPa. The attitude measurement module outputs three-axis attitude angles, with a preferred resolution of 0.1 degrees. The system first calculates the displacement vector of each mark and establishes a mark spacing change rate model based on the pressure distribution in the bonding area. This model yields a channel spacing correction coefficient, ensuring that the spacing variation of each channel does not exceed ±8% of the reference value. Subsequently, the local normal direction is determined based on the attitude angle data, and the initial estimate of the channel normal is calculated based on its relationship with the channel direction vector. During the calculation process, the area change rate of each bonding unit is controlled within ±1.0% to ensure uniform deformation. Through solving this series of parameters, a set of bonding state parameters is obtained, describing the actual geometric shape of the array on the curved surface after bonding.

[0026] After acquiring the discrete point cloud and fitting state parameters of the curved surface, this embodiment establishes a curved surface mesh using triangulation, dividing each square decimeter into no less than 120 triangular elements to ensure unfolding accuracy. By introducing developable deformation constraints, the metric changes of local surface elements are kept constant, thus avoiding area flipping. When the local area of ​​any element is less than or equal to zero, the deformation parameters are automatically readjusted, with a maximum allowable ratio of 0%. When solving the coordinates of the unfolded domain, the length of the curved surface boundary is used as a constraint to ensure the continuity of the unfolded boundary, with a boundary length deviation not exceeding 1.0%. After optimization, the two-dimensional coordinates of all positioning marks and sensing channels are obtained in the unfolded domain coordinate system, realizing the forward mapping from the curved surface to the unfolded domain. A mapping function from any curved surface point to the unfolded domain point is established using the centroid coefficient of the triangular elements, and the inverse mapping from the unfolded domain to the curved surface is obtained by combining the correspondence of positioning marks. Finally, the positioning deviation of the forward and inverse mappings is judged. When the deviation is less than 0.15 mm, the mapping accuracy is considered to meet the requirements, forming a mapping basis that can be used for subsequent calibration and imaging.

[0027] Furthermore, this embodiment first determines the correspondence between the spatial orientation and the surface normal of the flexible GMR sensor array after bonding, based on the attitude information output by the attitude measurement module. Then, the three-dimensional coordinates of the positioning markers in the bonding state are projected onto a local tangent plane through geometric transformation to obtain a planarized projection coordinate set. Based on the channel-marker index table in the array design file, the correspondence between the reference coordinates and the observed coordinates is established. To ensure the accuracy of spatial positioning, the imaging unit acquires image data at a resolution of no less than 4 million pixels and automatically performs re-shooting when the recognition rate is below 95%. After camera calibration, the projection positioning error remains within 0.20 mm, thereby ensuring the stability and consistency of subsequent deformation calculation results.

[0028] Within the unfolded domain coordinate system, this embodiment uses the reference-observation correspondence as a constraint and combines bonding pressure information to calculate the in-plane deformation of the flexible substrate. The bonding pressure is controlled within the range of 3 to 12 kPa. In-plane tensile parameters are calculated through statistical analysis of the distance changes of marker points, and shear parameters are estimated using the rate of change of angle. To prevent excessive local deformation from causing geometric distortion, this embodiment limits the rate of change of local area to within ±1.0%. When the number of available positioning markers in a certain area is less than 64, the system automatically expands the participation range of the surrounding area to ensure stable convergence of the calculation results. The processed in-plane tensile and shear parameter set is used to describe the overall geometric changes of the array after bonding, providing basic data for channel position correction.

[0029] After obtaining the in-plane deformation results, this embodiment calculates the length change along the reference direction of each sensing channel to obtain the channel spacing correction coefficient, and updates the actual spacing of each channel based on this coefficient. To maintain the geometric consistency of the array structure, the correction range is limited to ±8% of the reference spacing. After the calculation is completed, the corrected channel spacing parameters are written into the fitting state parameter set and saved synchronously with the attitude and pressure information. To support the accuracy of subsequent mapping relationships, this embodiment ensures that there are at least 120 triangular elements per square decimeter when dividing the curved surface mesh, ensuring the stability and directional consistency of local scale transfer.

[0030] In this embodiment, based on the orientation information obtained from attitude measurement and combined with the coupling effect of in-plane shear and bonding pressure, the initial estimate of the normal direction of each sensing channel is determined. This estimation process controls the local tilt angle to within a range of no more than 2 degrees to maintain the relative consistency between the channel normal direction and the surface normal direction. Subsequently, the positioning residual is calculated, which is the deviation between the observed projected coordinates and the theoretical projected coordinates calculated by the deformation model. When the residual exceeds 0.15 mm, the tensile and shear parameters of the corresponding area are slightly corrected and re-solved, with no more than 5 iterations. Finally, when the positioning residual is below a preset threshold, the initial estimate of the channel normal and the channel spacing correction coefficient are jointly determined as the bonding state parameters, used for the unfolded domain calibration and subsequent imaging reconstruction stages, achieving stable maintenance of geometric parameters and consistency of measurement accuracy.

[0031] Furthermore, this embodiment first constructs a surface triangular mesh based on the discrete point set of positioning markers and sensing channels in the surface coordinate system using a progressively denser approach. "Ordered boundary" refers to the boundary vertices arranged in a fixed clockwise or counterclockwise order along the outer edge of the surface, without allowing jumps or reversals; "Normal consistency" means that the normal orientation of adjacent elements remains consistent, avoiding situations where adjacent elements have opposite orientations. During mesh generation, priority is given to ensuring the balance between element shape quality and local geometry: at least 120 triangular elements are divided per square decimeter, the minimum included angle of the elements is not less than 25 degrees, and the side lengths remain relatively balanced within allowable limits, avoiding long, thin strip elements. The outer edge sequence of boundary vertices is extracted, and the boundary arc length sequence is calculated as the boundary constraint input for subsequent parameterization. To improve the stability of subsequent unfolding, if a sudden change in local normal is detected, the mesh is fine-tuned in that region until the normal difference between adjacent elements is within an acceptable range.

[0032] In this embodiment, the aforementioned triangular mesh is initialized in two dimensions within the expanded domain coordinate system. Two initialization strategies can be chosen: one is to spread the boundary curves at equal intervals according to their original lengths on a plane, and then determine the internal vertex positions through area equalization interpolation of the interior points; the other is to optimize the vertex positions initially, focusing on maintaining the local shape, with the minimum strain criterion as the objective. Regardless of the strategy used, the boundary order must remain unchanged and the length deviation must be controlled, with the total length error of the boundaries not exceeding 1.0%. To control the scale, this embodiment matches the average side length of the initial layout with the average side length of the curved mesh, with the deviation controlled within 5%. After initialization, it checks for overlapping or intersecting units; if any are found, vertex positions are redistributed locally until all units are in a non-intersecting state.

[0033] After initialization, this embodiment iteratively solves for the two-dimensional position of each vertex within the unfolded domain coordinate system. The solution objective is to simultaneously satisfy two types of constraints: first, "developable deformable constraint," which aims to maintain the stability of the local metrics of the unfolded surface mesh as much as possible, ensuring that each triangular element closely approximates its surface shape in length and angle; second, "no-flip constraint," which ensures that the local area of ​​all elements remains positive, and no zero or negative area is allowed. To avoid excessive reliance on manual parameter tuning, this embodiment sets only a few fixed coefficients: the weight of the boundary consistency constraint is 1.0, the weight of the anti-flip potential energy is 0.1, and the iteration step size is adaptively adjusted. The iteration termination conditions are two: first, the global average vertex displacement change is less than 0.02 mm; second, the constraint residual is less than a set threshold; the maximum number of iterations does not exceed 50. During the iteration process, once an element area is detected to be close to zero, local thickening and directional adjustment are applied to the element and its neighborhood to ensure that the local area remains positive; simultaneously, length springback is applied to the boundary vertices to ensure that the boundary length error remains less than 1.0%.

[0034] After the iteration converges, this embodiment constructs a piecewise affine forward mapping from the surface coordinate system to the unfolded domain coordinate system based on the optimized 2D vertex set. Specifically, for any surface point, the triangular element containing it is first determined. Then, the coordinates of that point in the unfolded domain are calculated using the weighted combination of the three vertices of that element, ensuring a one-to-one correspondence between points at the vertices and points on the boundary within the unfolded domain. This weighted combination satisfies the conditions of non-negativity and summing to one, ensuring that the point always falls within the corresponding 2D element. Subsequently, combining the correspondence between the positioning markers and the channel coordinates, an inverse mapping from the unfolded domain to the surface is established, and the forward and inverse mappings are jointly verified: all elements are checked to have positive local areas, continuous boundaries, and length deviations less than 1.0%, with the repositioning deviation of the positioning markers used as an accuracy indicator, requiring this deviation to be no greater than 0.15 mm. If any indicator fails to meet the requirements, iterative optimization is re-executed under the original initialization conditions until all indicators meet the set thresholds. After verification, the forward and inverse mappings are solidified as the geometric basis for subsequent unfolded domain calibration and imaging reconstruction.

[0035] Specifically, step 200 in this embodiment includes: This embodiment first establishes a "synchronization control signal," which is a sequence of control pulses used for unified startup, switching, and alignment throughout the entire acquisition process, ensuring that each sensing channel and drive unit operates on the same beat. Then, a "multi-frequency drive scheme" is determined, which is a set of sequentially executed frequency and phase combinations used to excite the measured component to produce a distinguishable electromagnetic response. This embodiment selects no fewer than 5 frequency points in a single acquisition, covering an effective bandwidth of 0.5–50 kHz, with adjacent frequency points spaced at least 0.5 kHz to reduce spectral leakage; the phase resolution is no worse than 1 degree to improve the phase-type indicator's ability to distinguish defect orientation. To ensure the stability of the synchronization control signal, the trigger jitter of the control pulse is no greater than 100 microseconds; the excitation dwell time at each frequency point is no less than 100 milliseconds, and a stable transition time of no less than 10 milliseconds is maintained between switches; the excitation amplitude is set within a range that will not cause the sensor to enter the saturation region, and a safety margin of no less than 20% is confirmed through a rapid pre-scan.

[0036] Under the unified rhythm of the synchronous control signal, this embodiment sequentially applies each combination of the multi-frequency drive scheme and synchronously reads all channels of the flexible GMR sensor array. The sampling process adopts a quantization accuracy of no less than 16 bits and a sampling rate of no less than 20,000 samples per second. The front end is set with an anti-aliasing filter with a cutoff frequency of 45% of the sampling rate to ensure the stability of amplitude and phase reconstruction. To ensure data organization, this embodiment adds a double key of "channel identifier - frequency index" to each sampling record as a unique marker for subsequent alignment and merging. To reduce the impact of fluctuations caused by environmental disturbances, no less than 3 independent repetition segments are retained for each frequency point, and the amplitude and phase statistics of the repetition segments are robustly aggregated; when a repetition segment experiences a sudden jump in amplitude or a phase jump (amplitude change exceeding 20% ​​of the previous segment, or phase change exceeding 10 degrees), the segment is marked as invalid and automatically re-sampled. The above synchronous acquisition simultaneously records the bonding pressure, temperature, and attitude information, and binds them one by one with the "channel identifier - frequency index" to achieve frame-level correlation between measurement data and environmental quantities.

[0037] To establish a baseline, this embodiment repeats the aforementioned process in a reference area where the component is defect-free or has been calibrated on-site. The effective area of ​​the reference area is not less than 25 square centimeters, and it maintains the same driving and acquisition parameters as the target detection area. Acquisition of both the reference and target areas is performed for at least three complete cycles, with the frequency points and sequence remaining consistent within each cycle. During the dwell time at each frequency point, the variation in bonding pressure is limited to within 2 kPa, the relative displacement of the array is limited to within 0.5 mm, and the temperature fluctuation does not exceed 1 degree Celsius. After completing the acquisition of both types of areas, this embodiment aligns and merges the data according to the "channel identifier—frequency index" double key, generating raw response data and reference response data. These are then uniformly packaged with the bonding pressure, temperature, and attitude information from the same time window into a raw detection dataset. Simultaneously, quality indicators are written, including a signal-to-noise ratio of not less than 20 dB per frequency point, a trigger jitter of the synchronization control signal not exceeding 100 microseconds, and a repeat segment consistency passing the threshold of amplitude-phase dispersion not exceeding 10%. If any quality indicator fails to meet the standard, targeted supplementary sampling will be performed on the corresponding frequency points while maintaining the same parameters until the above threshold is met, and then the original test dataset of this batch will be solidified.

[0038] Preferably, step 300 in this embodiment includes: First, within the expanded domain coordinate system, the original detection data and reference responses are paired one by one according to the "channel identifier-frequency index" method to form "responses to be calibrated". "Responses to be calibrated" refer to the response pairs of the same channel and frequency in the target and reference regions, used to eliminate the common influence of the drive and link. Based on this, a "gap compensation factor" is generated according to the bonding gap and local curvature information in the bonding state parameters. The "gap compensation factor" is used to correct the amplitude error and phase hysteresis caused by the small distance change between the array and the surface. In this embodiment, it is calculated and applied separately for each channel and each frequency to avoid over-averaging of anisotropic regions. To ensure stability, the amplitude adjustment amount of a single compensation is limited to no more than 30% of the original amplitude, and the absolute amount of phase correction does not exceed 5 degrees; the effective range of the bonding gap involved in the solution is 0.2–1.5 mm, and the gap resolution is preferably 0.05 mm.

[0039] This embodiment performs "attitude correction" on the direction-related response based on attitude information. "Attitude correction" refers to transforming the channel's measurement direction from the actual direction under the conforming attitude to a reference direction consistent with the unfolded domain coordinate system, thereby eliminating directional response differences caused by attitude changes. After correction, the temperature correction stage begins: using the reference response as a baseline, a "temperature drift baseline" is established. The "temperature drift baseline" is a calibration curve grouped by frequency showing amplitude and phase changes with temperature, used to subtract the slow drift caused by ambient temperature fluctuations. In this embodiment, the time windows for acquiring temperature information and response data are aligned, and correction is performed under the same "channel identifier—frequency index". To ensure feasibility, the temperature operating range is set to 10–45 degrees Celsius, and the residual temperature drift after correction is controlled to have an amplitude not exceeding 0.5 dB and a phase not exceeding 2 degrees; the angle change for attitude correction is typically no more than 10 degrees, and channels exceeding this threshold will trigger a one-time incremental remeasurement.

[0040] In this embodiment, parameters that have undergone gap compensation, attitude correction, and temperature correction are propagated and updated on the triangular mesh of the expanded domain. "Neighboring cell consistency" serves as a propagation constraint, meaning that calibration parameters within adjacent mesh cells change smoothly in space without abrupt jumps. Boundary cells employ constraint strength consistent with the inner domain to prevent distortion introduced by edge effects. The propagation process uses mapping relationships as channels to extend the calibration results of discrete channel points to the coverage area: first, parameters are fixed at the channel landing points, then propagated to adjacent cells according to distance and mesh shape weights until a continuous calibration parameter field is formed. After each round of propagation, the "convergence residual" is calculated, which is a comprehensive measure of the difference statistics and spatial smoothness index between the response to be calibrated and the reference response under the same "channel identifier-frequency index." Iteration terminates when the convergence residual is less than a set threshold. The thresholds are set as follows: amplitude mean square error no greater than 0.5 dB, phase mean square error no greater than 2 degrees, and parameter difference between adjacent cells no greater than 10% of the local mean; the maximum number of iterations does not exceed 10. Once the threshold is met, a "unified response dataset" is output, which includes calibrated amplitude and phase data, gap compensation records, attitude correction records, and temperature drift baseline numbers. It also corresponds one-to-one with the "channel identifier - frequency index" for direct use in subsequent imaging reconstruction and re-projection positioning.

[0041] Specifically, step 400 in this embodiment includes: In this embodiment, within the expanded domain coordinate system, the calibrated unified response dataset is plotted onto grid nodes using a double-bond "channel identifier-frequency index" structure to form a unified response field. The "unified response field" refers to a two-dimensional scalar-direction composite field that aggregates amplitude and phase information using the expanded domain grid as a carrier, serving as the input for defect imaging. This embodiment sets the grid resolution to a sampling density of no less than 40×40 per square centimeter and employs weighted interpolation with a neighborhood radius of 3 to 5 grid cells to fuse data at the channel landing points, suppressing isolated noise. Subsequently, a robust reconstruction criterion is used to generate a defect response distribution map: first, amplitude and phase consistency are screened for each frequency channel, eliminating samples with amplitudes below 15 dB SNR or phase outliers exceeding 12 degrees; then, multi-frequency aggregation is performed on the remaining samples, with samples de-weighted significantly from the reference region during aggregation, with a lower weight limit of no less than 0.2; finally, edge-preserving smoothing is applied to the reconstruction results, with the smoothing intensity controlled within 1 to 2 grid cells, suppressing particle noise while preserving gradient information at defect boundaries.

[0042] After obtaining the defect response distribution map, this embodiment extracts candidate regions through threshold segmentation and connected component analysis. An adaptive thresholding strategy is adopted: using the statistical distribution of the reference region as a baseline, pixels within the expanded domain that are 3 to 5 times higher than the background mean are selected as initial seeds, and a morphological closing operation of 1 to 2 grid cells is performed to connect the responses of the fine crack pattern. For each candidate region, this embodiment calculates the equivalent peak value, equivalent half-width at half-maximum (HWHM), and principal direction parameters: the equivalent peak value is the robust median neighborhood statistics of the local maximum response, with a neighborhood side length not exceeding 5 grid cells; the equivalent HWHM is obtained by measuring the half-width along the principal and secondary axes and taking the geometric mean; the principal direction is determined by the directional index of the second-order matrix of the region, with an preferred directional angle accuracy better than 5 degrees. To eliminate artifacts, this embodiment sets a minimum effective area of ​​not less than 4 grid cells and requires the compactness index of the candidate region to be between 0.2 and 0.9. Regions exceeding this range are marked as low confidence and are downweighted during the re-projection stage.

[0043] After parameter calculation, this embodiment projects the defect response distribution map back onto the surface coordinate system based on the mapping relationship. The "mapping relationship" refers to the combination of the aforementioned forward mapping from the surface to the expanded domain and its inverse mapping. During the projection, a piecewise affine mapping and centroid coefficient calculation method is used: for pixels in the expanded domain located within the same triangular unit, the pixel position and response quantity are mapped onto the surface using the weights of the three vertices of that unit, and pixels at the boundary are continuously stitched together according to the weights of adjacent units to avoid cracks. This embodiment performs a surface neighborhood consistency check after projection, requiring that the rate of change of defect parameters at adjacent sampling points not exceed 15% of the local mean; for low-confidence regions, parameters are weighted and synthesized with a reduction of 0.5 to 0.8 before entering the final result. Finally, the spatial location (in millimeters), dimensions (half-width and half-height of the principal and secondary axes, in millimeters), and orientation (in degrees) of each defect are output in the surface coordinate system, along with a confidence score for the candidate region. When the positional uncertainty of any region is greater than 0.8 millimeters or the orientation uncertainty is greater than 8 degrees, it is automatically marked as "suggested to be retested" to trigger subsequent adaptive detection updates.

[0044] Optionally, step 500 in this embodiment includes: In this embodiment, after completing the unfolded domain imaging and projecting it back onto the curved surface coordinate system, a "coverage map" and a "confidence map" are generated. The "coverage map" refers to the area that has been effectively measured, marked in units of curved surface grids. The criteria for coverage include a signal-to-noise ratio of not less than 20 dB, amplitude-phase dispersion of not more than 10%, and mapping positioning deviation of not more than 0.15 mm. Grids meeting all three conditions are marked as covered. The "confidence map" is a score obtained by combining multi-frequency consistency, post-projection neighborhood consistency, and candidate region stability for each grid, with a score range of 0 to 1. This embodiment specifies an overall coverage target of not less than 95%, and a local coverage of not less than 90% for any key area (such as curvature abrupt change zone or weld heat-affected zone). A confidence threshold of 0.80 is also specified. If the confidence of a certain area is lower than this threshold, or if a continuous uncovered strip exceeds 5 mm in width or a single uncovered area exceeds 400 square millimeters, the current detection effect is deemed insufficient, and the adaptive update process begins.

[0045] When the coverage or confidence level is insufficient, this embodiment generates three types of incremental adjustments based on the saved bonding state parameters: (1) "Attitude adjustment amount", used to fine-tune the spatial attitude of the array relative to the curved surface. The single amplitude of the three-axis small angle correction is no more than 3 degrees, and the relative displacement of the array is no more than 1.0 mm; (2) "Scan path update amount", used to refine the trajectory and step size in the insufficient area. The typical approach is to reduce the step size in the insufficient area by 20% to 30%, add a cross scan in the strip gap direction, and add an edge scan in the boundary transition area; (3) "Small adjustment of multi-frequency drive scheme", used to improve the response resolution of the target area. The typical approach is to add 1 to 2 adjacent frequency points on the basis of the original frequency points, the frequency fine-tuning amplitude is no more than ±5%, the phase offset is no more than 10 degrees, the dwell time of each frequency point is increased by 50 milliseconds, and the sensor safety margin is kept at no less than 20% to avoid saturation. The above three types of adjustments are only effective locally with the insufficient area as the center, avoiding unnecessary repeated acquisition of the already qualified area.

[0046] Before implementing adjustments, this embodiment performs a "continuity check" on the mapping relationship. The "continuity check" refers to checking the smoothness of geometry and parameters under the bidirectional mapping of the surface and the unfolded domain: requiring all triangular elements to have positive local areas, boundary length deviations not exceeding 1.0%, and calibration parameter jumps between adjacent elements not exceeding 10% of the local mean. After passing the check, an incremental acquisition and unfolded domain calibration are performed, and the coverage map and confidence map are updated. If the overall coverage reaches 95% or more, the key area coverage reaches 90% or more, and the overall confidence is not less than 0.80 (and the confidence of the insufficient area increases by not less than 0.10), then this round of updates ends and the parameters are fixed. If the standards are not met, the next round of small-scale adjustments is performed in the same insufficient area. To control on-site time and energy consumption, the maximum number of iterations is set to 3. If the threshold is not met after 3 iterations, the area is marked as "suggested supplementary measurement," and the main cause of the deficiency (e.g., excessive curvature abrupt change or excessive ambient temperature fluctuation) is recorded to guide subsequent targeted supplementary measurements or operating condition stabilization processing.

[0047] Further, step 600 of this embodiment includes: This embodiment outputs a "defect result set" and "inspection evaluation data" in a surface coordinate system. The "defect result set" includes the defect's ID, spatial location in the surface coordinate system (in millimeters), dimensional parameters (equivalent half-width and height of the principal and secondary axes, in millimeters), orientation angle (in degrees), amplitude index, and signal-to-noise ratio index, along with a confidence score consistent with the unified response field. The "inspection evaluation data" includes a coverage map, confidence map, signal-to-noise ratio distribution, threshold settings, and version identifier, and records the parameter window and grid resolution used to generate these evaluation quantities. This embodiment sets explicit output precision for key values: position coordinate precision no less than 0.10 mm, dimensional precision no less than 0.10 mm, and orientation angle precision no less than 1 degree; when the position uncertainty is greater than 0.80 mm or the orientation uncertainty is greater than 8 degrees, the defect is automatically marked as "recommended for retesting" in the results. To facilitate subsequent calls, this embodiment also outputs the association between each defect and the corresponding candidate region, as well as its original index in the expanded domain, to ensure that the surface coordinates, the expanded domain index, and the confidence score correspond one-to-one.

[0048] This embodiment stores "mapping relationship," "calibration parameters," and "detection trajectory" in batches. "Mapping relationship" refers to the bidirectional mapping data between the surface and the unfolded domain, along with its boundary length constraints, area positivity markers, and mesh version information. "Calibration parameters" refer to gap compensation records, attitude correction records, temperature drift baseline numbers, and the parameter field formed by the consistency constraints of adjacent elements. "Detection trajectory" refers to the actual motion path, step size, and attitude sequence of the array on the surface, as well as the multi-frequency drive scheme index bound to each path segment. This embodiment writes the batch number, acquisition round number, and reference area marker when storing each batch, ensuring bidirectional tracking of defect results and process data within the same batch. For ease of engineering application, the process data is organized in a time-sequential frame format, with each frame containing a channel index, frequency index, and environmental quantity binding key. The data size of a single batch is controlled to no more than 1.0 gigabyte for easy on-site transmission. Records after storage are set to read-only to prevent subsequent modifications. The spatial sampling interval for mapping and trajectory is consistent with the surface mesh, typically no greater than 1.0 mm, and can be refined to 0.5 mm in critical areas.

[0049] This embodiment performs a "result-process consistency check" before solidifying the results. The "consistency check" involves verifying the completeness of references between the defect result set and mapping relationships, calibration parameters, and detection trajectories. It requires a 100% binding rate between defect numbers and process frames, a boundary length deviation of no more than 1.0%, a mapping positioning deviation of no more than 0.15 mm, and a parameter difference between adjacent units of no more than 10% of the local mean. After passing the check, a batch summary is generated, including key indicators such as the number of defects, effective coverage, and overall confidence level, along with parameter versions and generation time. "Archiving" refers to writing the batch summary, defect result set, and process data to a long-term storage area, with a recommended retention period of at least 5 years. To facilitate access by the upstream quality system, this embodiment provides a standardized export interface, supporting the generation of structured files and image reports. A single export latency should not exceed 60 seconds, and the exported file size should not exceed 500 megabytes. When consistency indicators fail to meet the aforementioned thresholds, this embodiment does not solidify the current batch but instead records a list of unmet items and prompts for targeted supplementary testing or parameter adjustments before outputting again.

[0050] Corresponding to the above methods, such as Figure 2 As shown, this embodiment also provides a developable flexible GMR eddy current testing system for complex curved surface components, including: The surface bonding modeling module is used to bond the flexible GMR sensor array to the complex curved outer surface of the target component, establish the surface coordinate system and the unfolded domain coordinate system, determine the spatial position, normal direction and relative spacing of each sensing channel according to the bonding state parameters, and form a mapping relationship between the surface and the unfolded domain. The multi-frequency synchronous acquisition module is used to drive the flexible GMR sensor array to perform multi-frequency excitation and synchronous acquisition under a unified time reference, obtain the raw response data of each sensing channel, and synchronously acquire reference response data in the reference area where the component is defect-free or has been calibrated on site, and record the bonding pressure, temperature and attitude information to form the raw detection dataset. The expanded domain calibration module is used to perform gap compensation, attitude correction and temperature drift correction on the original detection dataset within the expanded domain coordinate system, with the reference response data as a reference, and to propagate and update the calibration parameters through the mapping relationship to obtain a calibrated unified response dataset. The unfolded domain imaging and projection module is used to perform imaging reconstruction using the unified response dataset in the unfolded domain coordinate system, identify the defect response distribution, and project the reconstruction result back to the surface coordinate system through the mapping relationship to determine the spatial location, size and orientation information of the defect on the surface. The adaptive detection update module is used to adjust the bonding posture, scanning path and excitation parameters of the flexible GMR sensor array according to the re-projection results and the bonding state parameters, and re-execute the acquisition and calibration steps until the detection coverage and result confidence meet the set requirements. The result output and traceability module is used to output defect identification results and detection evaluation data in the surface coordinate system, and store the mapping relationship, calibration parameters and detection trajectory together.

[0051] The beneficial effects of this invention are as follows: (1) By establishing a surface coordinate system and an unfolded domain coordinate system and constructing a bidirectional mapping, this invention unifies the bonding, positioning, and geometric parameters of the flexible GMR array into the same reference frame, significantly reducing the impact of curvature, bonding deformation, and attitude changes on the measurement results. Compared with the approach of directly compensating on the physical surface, this invention completes parameter solving and propagation within the unfolded domain coordinate system, which can maintain the stability of the spatial relationship and response quantity between channels under conditions of high curvature gradient, free-form surface, and local non-uniform bonding, thereby improving the consistency of detection sensitivity and threshold.

[0052] (2) This invention uses the reference response as a benchmark to decompose and correct the three main error sources: gap, attitude, and temperature. It also relies on surface-expanded domain mapping to achieve parameter propagation and updating on the mesh to ensure "consistency between adjacent cells," forming a global calibration closed loop. This mechanism can control the cumulative error of amplitude and phase shift, reduce system drift caused by local curvature or environmental fluctuations, and make the unified response dataset comparable across different regions and frequencies, providing a stable input for subsequent quantitative evaluation.

[0053] (3) This invention performs imaging reconstruction in the unfolded domain coordinate system, uses multi-frequency robust aggregation and edge preservation processing to obtain the defect response distribution, and then uses piecewise affine transformation and centroid weighting to back-project to the surface coordinate system, outputting the spatial location, size and orientation of the defect. The process of "unfolded domain imaging - surface back-projection" in this invention reduces the mesh distortion and ill-posed kernel function problems caused by direct inversion on the surface, improves the stability of boundary resolution and size measurement, and is suitable for the identification and quantification of cracks, corrosion and multi-orientation composite defects.

[0054] (4) Based on the re-projection results and bonding status parameters, this invention performs local, limited-amplitude adaptive updates to the bonding posture, scanning path, and multi-frequency drive until the coverage and confidence levels meet the set thresholds. Simultaneously, the mapping relationship, calibration parameters, and detection trajectory are batch-stored and a consistency check is performed, enabling the entire process from acquisition to imaging to output to be queryable and traceable. This mechanism improves the stability and usability of the results while ensuring detection efficiency, facilitating engineering promotion and standardized application.

[0055] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0056] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A developable flexible GMR eddy current detection method for complex curved surface components, characterized in that, include: A flexible GMR sensor array is attached to the complex curved outer surface of the target component, and a curved surface coordinate system and an unfolded domain coordinate system are established. The spatial position, normal direction and relative spacing of each sensing channel are determined according to the attachment state parameters, forming a mapping relationship between the curved surface and the unfolded domain. The flexible GMR sensor array is driven to perform multi-frequency excitation and synchronous acquisition under a unified time reference to obtain the raw response data of each sensing channel. Reference response data is also synchronously acquired in the reference area where the component is defect-free or has been calibrated on site, and the bonding pressure, temperature and attitude information are recorded to form the raw detection dataset. Within the expanded domain coordinate system, using the reference response data as a reference, gap compensation, attitude correction, and temperature drift correction are performed on the original detection dataset. The calibration parameters are propagated and updated through the mapping relationship to obtain a calibrated unified response dataset. Imaging reconstruction is performed using the unified response dataset within the expanded domain coordinate system to identify the defect response distribution. The reconstruction results are then projected back onto the surface coordinate system through the mapping relationship to determine the spatial location, size, and orientation information of the defect on the surface. Based on the feedback results and the bonding state parameters, adjust the bonding posture, scanning path and excitation parameters of the flexible GMR sensor array, and re-execute the acquisition and calibration steps until the detection coverage and result confidence meet the set requirements. The defect identification results and detection evaluation data are output in the surface coordinate system, and the mapping relationship, calibration parameters and detection trajectory are stored together.

2. The method for developing flexible GMR eddy current detection of complex curved surface components according to claim 1, characterized in that, A flexible GMR sensor array is attached to the complex curved outer surface of the target component. A surface coordinate system and an unfolded domain coordinate system are established. Based on the attachment state, the spatial position, normal direction, and relative spacing of each sensing channel are determined, forming a mapping relationship between the curved surface and the unfolded domain, including: An imageable positioning mark array is preset on the substrate of the flexible GMR sensor array. After being attached to the complex curved outer surface of the target component, the coordinate point set of the positioning mark in space is extracted by the imaging unit. The correspondence between each sensing channel and the coordinate point set is indexed according to the array design to obtain the initial curved surface discrete point cloud in the attached state. Using the positioning marks as constraints, and combining the bonding pressure and attitude measurement, the in-plane tension and shear parameters of the flexible substrate are estimated, and the initial estimate of the sensor channel spacing correction coefficient and channel normal is calculated to form the bonding state parameters. Based on the discrete point cloud of the surface and the set of fitting state parameters, a surface coordinate system is established. Local tangent plane fitting and normal consistency constraints are used to determine the spatial position and normal direction of each sensing channel in the surface coordinate system, and the relative spacing between the channels is updated accordingly. The surface coordinate system is parameterized under expandable deformation constraints to obtain the coordinates of each positioning mark and each sensing channel in the expanded domain coordinate system. The local area is limited to prevent flipping and the boundary is continuous, thus constructing a positive mapping relationship from the surface coordinate system to the expanded domain coordinate system. Based on the correspondence between the positioning markers and the sensing channels, the inverse mapping relationship from the expanded domain coordinates to the surface coordinates is calculated. The forward mapping relationship and the inverse mapping relationship are jointly checked using the positioning residual as the criterion. When the residual exceeds the preset threshold, the fitting state parameters are updated and the mapping relationship is iterated until the accuracy requirements are met.

3. The method for developing flexible GMR eddy current detection of complex curved surface components according to claim 2, characterized in that, Using the positioning marks as constraints, and combining bonding pressure and attitude measurements, the in-plane tensile and shear parameters of the flexible substrate are estimated. The initial estimates of the sensor channel spacing correction coefficient and channel normal are calculated to form bonding state parameters, including: Based on the attitude measurement, the rotation matrix is ​​obtained. The three-dimensional observation coordinates of the positioning marker after bonding are extracted and projected onto the local tangent plane. The correspondence between the reference coordinates and the observation coordinates is established, as shown in the formula: ;in, For the first The two-dimensional coordinates of a positioning marker on a local tangent plane; The rotation matrix is ​​obtained from attitude measurement; For the first The three-dimensional observation coordinates of each positioning marker after fitting; For projection operators to the local tangent plane; For unit array; This is an initial estimate of the local normal. Within the expanded domain coordinate system, using the positioning marks as constraints, and combining the bonding pressure to estimate the in-plane deformation gradient, the in-plane tensile and shear parameters are obtained, as follows: ;in, This is the optimal solution for the in-plane deformation gradient; For the first The reference two-dimensional coordinates of each positioning marker; Number of available location markers; For determinant operators; Scalar measurement for fitting pressure; This represents the weighting coefficient for the volume consistency term; The coupling coefficient between pressure and area change; The right stretching tensor is obtained from the deformation gradient decomposition, and the spacing correction coefficient of each sensing channel is calculated based on the right stretching tensor, using the following formula: ;in, The right-side tensor; For the first The spacing correction factor for each sensing channel; For the first The unit direction vector of each sensing channel in the reference design; By combining attitude measurement and the effect of bonding pressure on stress-induced shear, an initial estimate of the channel normal is obtained, as shown in the formula: ;in, This is the initial estimated vector for the channel normal; Let be the unit normal basis vector of the device coordinate system; The coupling coefficient for pressure-normal correction tr is a symmetric partial operator constructed from the deformation gradient; The trace of the matrix; The estimation results are checked using the positioning residual as a criterion. When the residual exceeds the threshold, the fitting state parameters are updated and the solution is iterated until the accuracy requirement is met. The formula is as follows: ;in, To locate the residual; This is a preset threshold.

4. The developable flexible GMR eddy current detection method for complex curved surface components according to claim 2, characterized in that, The surface coordinate system is parameterized under expandable deformation constraints to obtain the coordinates of each positioning mark and each sensing channel in the unfolded domain coordinate system. This ensures that the local area does not flip and the boundaries are continuous, constructing a positive mapping relationship from the surface coordinate system to the unfolded domain coordinate system, including: Based on the discrete point set of positioning markers and sensing channels in the surface coordinate system, a triangular mesh that satisfies the boundary order and normal consistency is generated, and the boundary vertex sequence and boundary arc length sequence are extracted as parameterized boundary constraints. Initialize the two-dimensional coordinates of each mesh vertex in the expanded domain coordinate system. The initialization can be obtained based on the equidistant spreading of the boundary arc length or the minimum strain criterion, and is used as the starting point for subsequent optimization. Solve for the two-dimensional coordinates of each vertex in the expanded domain coordinate system to satisfy the expandable deformation constraint and the no-flip constraint, thus obtaining the optimized vertex set and forming the expanded domain coordinates, as shown in the formula: ;in, To expand the optimal set of vertices within the domain coordinate system; The set of vertices to be optimized; For the first The Jacobian matrix corresponding to each triangle in the expanded domain coordinate system; For unit array; It is the Frobenius norm; For the boundary sequence The two-dimensional coordinates of each vertex in the expanded domain coordinate system; This represents the arc length of the corresponding boundary edge in the surface coordinate system. The weighting coefficient for the consistency of boundary arc length; The weighting coefficients represent the non-reversal potential energy. Based on the optimized vertex set, a piecewise affine forward mapping is constructed from the surface coordinate system to the expanded domain coordinate system. For any vertex located at the _th ... For points within the triangle, the coordinates of the expanded domain are calculated using the centroid coefficient within the curved triangle, as follows: ;in, Let the coordinates of the point be the two-dimensional coordinates in the expanded domain coordinate system; For the first The two-dimensional coordinates of the three vertices of a triangle in the expanded domain coordinate system; The centroid coefficient of the point within the corresponding surface triangle; The forward mapping is evaluated based on the criteria of no local area flipping and boundary continuity. If the threshold condition is not met, optimization continues under the same initialization conditions until the requirements are met. The formula is: ;in, The threshold for determining whether the area is not flipped. This is the threshold for determining boundary continuity.

5. The method for developing flexible GMR eddy current detection of complex curved surface components according to claim 1, characterized in that, The flexible GMR sensor array is driven to perform multi-frequency excitation and synchronous acquisition under a unified time reference to obtain the raw response data of each sensing channel. Reference response data is also synchronously acquired in a reference area where the component is defect-free or has been calibrated in the field. Adhesion pressure, temperature, and attitude information are recorded to form a raw detection dataset, including: Set the synchronization control signal and determine the multi-frequency drive scheme. ,in For driving frequency, For phase; Under the action of the synchronization control signal, the flexible GMR sensor array is sequentially subjected to... Each pair in The original responses of each sensor channel are read synchronously and recorded as original response data in the form of channel identifier-frequency index; In the reference area, the synchronous control signal and multi-frequency drive scheme are repeatedly collected to obtain reference response data, and the bonding pressure, temperature and attitude information are recorded at the same time. The bonding pressure, temperature and attitude information are bound to the channel identifier-frequency index. The original response data, the reference response data, the bonding pressure, the temperature, and the attitude information are aligned and merged according to the channel identifier-frequency index to generate the original detection dataset.

6. The method for developing flexible GMR eddy current detection of complex curved surface components according to claim 1, characterized in that, Within the expanded domain coordinate system, using the reference response data as a reference, gap compensation, attitude correction, and temperature drift correction are performed on the original detection dataset. The calibration parameters are propagated and updated through the mapping relationship to obtain a calibrated unified response dataset, including: The original detection dataset is paired with the reference response data in the form of channel identifier-frequency index to obtain the response to be calibrated; The detection gap is estimated based on the bonding state parameters, and a gap compensation factor is generated and applied to the response to be calibrated. The rotation matrix is ​​obtained from the attitude information, and attitude correction is applied to the channel orientation-related quantities. Establish a temperature drift baseline based on temperature information to eliminate amplitude and phase shifts caused by temperature. On the triangular mesh of the expanded domain, with the consistency of adjacent cells as a constraint, the calibration parameters are propagated and updated through the mapping relationship; The convergence check is performed using the residual threshold as the criterion. If the threshold is not met, the iteration continues until the requirement is met.

7. The method for developing flexible GMR eddy current detection of complex curved surface components according to claim 1, characterized in that, Imaging reconstruction is performed using the unified response dataset within the expanded domain coordinate system to identify the defect response distribution. The reconstructed results are then projected back onto the surface coordinate system through the mapping relationship to determine the spatial location, size, and orientation information of the defect on the surface, including: A unified response field is constructed within the expanded domain coordinate system; A robust reconstruction criterion is used to generate a defect response distribution map and extract candidate regions. The equivalent peak value, equivalent half-width at half-maximum and main direction of the candidate region are calculated to obtain the size and orientation parameters. Based on the mapping relationship, the distribution map is projected back onto the surface coordinate system using piecewise affine mapping and centroid coefficient method, and the spatial location, size and orientation information of the defects in the surface coordinate system are output.

8. The method for developing flexible GMR eddy current detection of complex curved surface components according to claim 1, characterized in that, Based on the feedback results and the bonding state parameters, adjust the bonding posture, scanning path, and excitation parameters of the flexible GMR sensor array, and re-execute the acquisition and calibration steps until the detection coverage and result confidence meet the set requirements, including: The detection coverage and result confidence were assessed based on the resubmission results; When the coverage or confidence is insufficient, the attitude adjustment amount and the scan path update amount are generated based on the bonding state parameters, and the multi-frequency drive scheme is adjusted to a limited extent. After verifying the continuity of the mapping relationship, adjustments are made, and the unified collection and expansion domain calibration are repeated until the coverage and confidence reach the set threshold.

9. A developable flexible GMR eddy current testing system for complex curved surface components, characterized in that, include: The surface bonding modeling module is used to bond the flexible GMR sensor array to the complex curved outer surface of the target component, establish the surface coordinate system and the unfolded domain coordinate system, determine the spatial position, normal direction and relative spacing of each sensing channel according to the bonding state parameters, and form a mapping relationship between the surface and the unfolded domain. The multi-frequency synchronous acquisition module is used to drive the flexible GMR sensor array to perform multi-frequency excitation and synchronous acquisition under a unified time reference, obtain the raw response data of each sensing channel, and synchronously acquire reference response data in the reference area where the component is defect-free or has been calibrated on site, and record the bonding pressure, temperature and attitude information to form the raw detection dataset. The expanded domain calibration module is used to perform gap compensation, attitude correction and temperature drift correction on the original detection dataset within the expanded domain coordinate system, with the reference response data as a reference, and to propagate and update the calibration parameters through the mapping relationship to obtain a calibrated unified response dataset. The unfolded domain imaging and projection module is used to perform imaging reconstruction using the unified response dataset in the unfolded domain coordinate system, identify the defect response distribution, and project the reconstruction result back to the surface coordinate system through the mapping relationship to determine the spatial location, size and orientation information of the defect on the surface. The adaptive detection update module is used to adjust the bonding posture, scanning path and excitation parameters of the flexible GMR sensor array according to the re-projection results and the bonding state parameters, and re-execute the acquisition and calibration steps until the detection coverage and result confidence meet the set requirements. The result output and traceability module is used to output defect identification results and detection evaluation data in the surface coordinate system, and store the mapping relationship, calibration parameters and detection trajectory together.

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