Deep learning and energy regularization gradient descent deformation measurement method based on X-ray digital imaging

Abstract

The invention discloses a deep learning and energy regularization gradient descent deformation measurement method based on X-ray digital imaging, and relates to the field of digital image deformation measurement, and the method comprises the steps: obtaining an initial speckle image and a deformed speckle image of a measured material through X-ray imaging; performing displacement reverse mapping and gray reconstruction on the deformed speckle image based on a current displacement field, and constructing an image consistency residual error; performing feature extraction and correlation analysis on the initial speckle image and the deformed speckle image by adopting a deep learning optical flow network to serve as an initial state of displacement field optimization; and constructing a total loss function based on the image consistency residual error and the energy regularization item, and carrying out iterative updating on the displacement field by adopting a gradient descent optimization strategy to obtain full-field displacement distribution and corresponding strain information of the tested material under the X-ray imaging condition. According to the invention, stable and accurate measurement and inversion of the internal full-field deformation of the material can be realized under the conditions of complex textures and high noise.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of digital image deformation measurement, in particular to a deep learning and energy regularization gradient descent deformation measurement method based on X-ray digital imaging. BACKGROUND

[0002] As an ultra-high performance structural material composed of carbon fiber reinforced carbon matrix, carbon / silicon carbide composite material has become an irreplaceable key thermal structural material in supersonic and hypersonic aircraft because it can still maintain excellent mechanical properties and dimensional stability in extreme thermal environment. With the continuous development of aircraft to higher Mach number, the service environment of carbon / silicon carbide composite material is more severe, and internal multi-scale and multi-mechanism coupled damage evolution may occur, such as matrix micro-crack initiation and propagation, fiber / matrix interface debonding, delamination failure, pore growth, and even thermal-induced shear localization. Such damage often starts from the inside of the material, and its development process is highly concealed, nonlinear and irreversible. Therefore, it is of great significance to accurately, timely and quantitatively obtain the deformation field and damage propagation law inside the carbon / silicon carbide material for revealing its failure mechanism, improving material design and ensuring the safety of aircraft.

[0003] Due to the typical characteristics of carbon / silicon carbide composite material, such as complex internal structure, significant anisotropy, rough surface and uneven texture, traditional surface measurement methods often fail to effectively capture its true deformation behavior. Digital Image Correlation (DIC) technology relies on the correlation of speckle texture and calculates the surface displacement and strain field by comparing the visible light images before and after the deformation of the sample surface. With the advantages of non-contact, full-field and high precision, it is widely used in mechanical testing of general structural materials. However, the surface of C / SIC composite material is not uniform in reflection, making it difficult to form high-quality speckles. Under high-temperature environment, speckles are easily ablated, migrated or even disappeared, making it difficult for optical DIC to maintain stability. At the same time, optical imaging can only obtain surface information, and it is completely powerless for internal crack initiation, delamination expansion and pore evolution process which is particularly critical in actual service of aircraft, severely limiting its application in C / SIC composite material. In addition, under high-speed loading or large deformation, the correlation peak of traditional DIC often distorts, making its iterative process highly sensitive to initial value, and prone to false matching and non-physical oscillation when facing high gradient deformation field. Moreover, in practical application, C / SIC composite material will be subjected to thermal-mechanical-oxidative coupling, and in experimental simulation, there are problems such as severe thermal fog interference, blackbody radiation leading to image overexposure, and artificial speckle droplet falling off, which seriously limit the application of optical DIC.

[0004] To overcome the inherent limitations of optical discretization (DIC), which can only measure surfaces and is highly susceptible to environmental influences, X-ray digital imaging has been introduced into the study of internal damage in composite materials. X-rays possess strong penetrating power, reflecting changes in density, thickness, and structure within materials. They are naturally sensitive to internal cracks, pores, and delamination, and do not require speckle spraying, making them highly advantageous in high-temperature, confined, and inaccessible environments. However, the formation mechanism of X-ray images is complex. Their grayscale is not only related to surface deformation but also influenced by factors such as material thickness, density variations, fiber orientation, diffraction, and scattering. This renders the grayscale consistency assumption relied upon by traditional DIC largely invalid under X-ray imaging. Furthermore, X-ray images generally suffer from weak texture, low contrast, and high noise, making it difficult to obtain clear and stable peak values ​​for correlation matching. In addition, even slight mechanical drift in the imaging system during high-speed experiments can significantly alter the image grayscale distribution, causing grayscale-driven optimization processes to fail. The above factors together make it almost impossible for traditional DIC to obtain continuous, stable, and physically reliable displacement and strain fields in an X-ray environment. The results often show gradient oscillations and noise amplification, which severely limits its application in the internal deformation measurement of C / SIC composites. Summary of the Invention

[0005] The purpose of this application is to provide a deep learning and energy-regularized gradient descent deformation measurement method based on X-ray digital imaging, which can stably and accurately invert the full-field displacement and strain of materials in X-ray images.

[0006] To achieve the above objectives, this application provides a deep learning and energy-regularized gradient descent deformation measurement method based on X-ray digital imaging, comprising: The initial speckle image and the deformed speckle image of the material under test are acquired; both the initial speckle image and the deformed speckle image are obtained by X-ray imaging. The deformed speckle image is subjected to displacement inverse mapping and grayscale reconstruction to obtain a reconstructed speckle image. The image consistency residual between the reconstructed speckle image and the initial speckle image is calculated to characterize the matching error of image grayscale as displacement changes. A deep learning optical flow network is used to extract features and calculate correlations in the initial speckle image and the deformed speckle image to predict the initial displacement field describing the deformation characteristics of the material under test. The initial displacement field is parameterized to obtain a parameterized displacement field, which is then used as the initial state of the displacement field for subsequent optimization solutions based on physical constraints. Based on the parameterized displacement field, an energy regularization term is constructed to reflect the spatial continuity and physical rationality of the displacement field; the energy regularization term is used to constrain the smoothness and deformation consistency of the displacement field. The total loss function is constructed based on the image consistency residual and the energy regularization weighted combination, and the parameterized displacement field is iteratively updated using a gradient descent optimization strategy to obtain the full-field displacement distribution and corresponding deformation information of the material under test under X-ray imaging conditions, thereby realizing the measurement and monitoring of the internal deformation behavior of the material under test.

[0007] According to the specific embodiments provided in this application, this application has the following technical effects: by constructing an image consistency residual that can adapt to the physical mechanism of X-ray imaging and introducing a physical constraint mechanism based on energy regularization, stable and accurate inversion of full-field displacement and strain in X-ray images is achieved. Specifically, this application acquires initial and deformed speckle images of the material under test through X-ray imaging, combines displacement inverse mapping, grayscale reconstruction, and a deep learning optical flow network to achieve accurate extraction of the pixel-level initial displacement field, and uses this initial displacement field as the initial value for optimization. An energy regularization constraint is introduced to construct the total loss function, and iterative optimization is performed through a gradient descent strategy to finally output the full-field displacement field and strain data. By fully leveraging the penetration advantage of X-ray imaging and the feature extraction capability of the optical flow network, high-precision, full-domain monitoring of the deformation of the material under test under X-ray imaging conditions is achieved, effectively improving the accuracy and reliability of displacement field and strain calculations. At the same time, the iterative optimization mechanism ensures the stability of the measurement results, making it suitable for deformation monitoring needs of various materials in complex imaging scenarios. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of this application 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 this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a schematic diagram of X-ray imaging for a deep learning and energy-regularized gradient descent deformation measurement method based on X-ray digital imaging, according to an embodiment of this application.

[0010] Figure 2 This is a flowchart illustrating a deep learning and energy-regularized gradient descent deformation measurement method based on X-ray digital imaging, provided as an embodiment of this application.

[0011] Figure 3 This is a diagram of the hybrid optimized network architecture of GD-DIC in one embodiment of this application.

[0012] Figure 4 This is a carbon / silicon carbide natural texture image acquired based on X-ray digital imaging in one embodiment of this application.

[0013] Figure 5 This is a schematic diagram illustrating the process of pixel meshing and establishing finite element mesh mapping in one embodiment of this application.

[0014] Figure 6 This is a schematic diagram of the simulated speckle displacement field and gradient calculation results in one embodiment of this application. Detailed Implementation

[0015] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0016] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] Against the backdrop of fundamental bottlenecks in traditional Discrete Inversion (DIC), the Gradient Descent DIC (GD-DIC) method offers a new direction for X-ray deformation inversion. This type of method abandons the correlation matching approach that relies on local speckle features, instead treating the displacement field of the entire image as the variable to be solved. It constructs a global loss function that includes image grayscale reconstruction error and energy regularization terms, and iteratively solves this loss function using an automatic differentiation framework and gradient descent optimization algorithm. Because GD-DIC is independent of speckle, it is naturally robust to X-ray images with weak textures. Simultaneously, the displacement gradient constraint effectively suppresses non-physical oscillations caused by noise, ensuring the mechanical continuity of the deformation field. It also maintains high inversion accuracy in high-gradient regions such as crack tips and multi-material interfaces. Furthermore, the GD-DIC method can be combined with deep learning networks such as optical flow networks, using the coarse displacement field output by optical flow as initial values ​​to effectively overcome the convergence difficulties of traditional iterative methods under large displacements.

[0018] Based on the aforementioned technical approach, this application presents an X-ray digital imaging deformation measurement method that integrates deep learning, energy regularization, and gradient descent optimization. This method fully leverages the penetrating and sensitive advantages of X-ray imaging to the internal structure of materials, combines the capabilities of data-driven models in representing complex textures, and ensures the physical reliability of the inversion results through energy constraints. This method is particularly suitable for monitoring the internal deformation and damage evolution of carbon / silicon carbide composite materials under extreme conditions such as high temperature, high noise, and speckle loss, providing reliable technical support for the safety assessment and life prediction of key thermal structures in hypersonic vehicles.

[0019] like Figure 1As shown, X-rays 102 are first emitted from X-ray source 101 to the material under test 103. After passing through the imaging area 104 of the material under test 103, the X-rays 102 are captured by detector 105 and then sent to image data processing device 106 for processing.

[0020] In one exemplary embodiment, such as Figure 2 and Figure 3 As shown, an X-ray digital imaging deformation measurement method based on gradient descent, finite element analysis and deformation energy is provided, including the following steps 201 to 206.

[0021] Step 201: Obtain the initial speckle image and the deformed speckle image of the material under test. Both the initial speckle image and the deformed speckle image are obtained using X-ray imaging.

[0022] This application applies to composite materials under conditions of no surface speckle, weak texture, and high noise, including carbon / carbon composites, carbon / silicon carbide composites, and other ceramic matrix composites.

[0023] In a specific application example, multiple X-ray transmission images of the tested material before and after loading are acquired. After grayscale normalization and noise suppression processing, high-noise X-ray digital images with natural texture features are formed. This example uses an X-ray transmission imaging system to acquire images of the internal structure of carbon / silicon carbide composite materials before and after loading, such as... Figure 4 As shown, carbon / silicon carbide composite materials possess multi-scale fiber bundles and porous structures, and their transmission images exhibit fine and continuous textures. These textures are naturally formed by the internal microstructure of the material under X-ray imaging and can be used as natural speckle fields in digital image deformation measurements.

[0024] X-rays reach the detector after passing through the internal fiber bundles and porous structure of the material. X-rays obey Lambert-Beer's law as they pass through the material. The X-ray image is generated based on a transmission attenuation model, and its grayscale values ​​satisfy the following: ;in, The intensity of the incident X-rays, This is the local linear attenuation coefficient of the material. For the local thickness of the material, The pixel grayscale values ​​recorded by the detector indicate that there is an inherent physical relationship between the grayscale changes in the X-ray image and the internal structure and deformation state of the material. Based on the natural texture distribution of the image, image correlation tracking can be achieved without the need for artificial speckle spraying.

[0025] When a material deforms, its internal density distribution and path thickness change, thus forming the image before deformation (i.e., the initial speckle image). Compared with the deformed image .

[0026] Step 202: Perform displacement inverse mapping and grayscale reconstruction on the deformed speckle image to obtain a reconstructed speckle image, and construct the image consistency residual between the reconstructed speckle image and the initial speckle image to characterize the matching error of image grayscale as displacement changes.

[0027] In a specific application example, based on the idea of ​​optical flow consistency in deep learning, the deformed speckle image is first re-mapped to the coordinate system of the initial speckle image according to the current displacement field, to obtain the corresponding reconstructed speckle image: .in, To reconstruct the speckle image, for The displacement component of the pixel at that location in the x-direction. for The displacement component of the pixel at the location in the y direction is obtained by subsequent deep learning prediction and gradient descent optimization.

[0028] Since X-ray grayscale is affected by noise, scattering, and material thickness, traditional squared difference loss is severely impacted by abnormal grayscale. Therefore, this application introduces a robust Charbonnier-type loss function as the image consistency residual term. Specifically, based on the mapped speckle image and the initial speckle image, the formula is used... Calculate the image consistency residual; where, For image consistency residuals, For a set of pixels, For numerically stable terms, The initial speckle image, The coordinates of the pixel. A constant greater than 0 and less than 1, used to reduce the impact of abnormal pixels on the overall optimization. This application takes... =0.7.

[0029] Image consistency residuals can measure the interpretability of the displacement field to the deformation correspondence and serve as the main data item driving the gradient descent optimization process. In this application, the execution order of steps 202 and steps 203-205 is not limited; that is, steps 202 can be executed first, followed by steps 203-205, or steps 203-205 can be executed first, followed by steps 202, or steps 202 and 203-205 can be executed simultaneously.

[0030] Step 203: Use a deep learning optical flow network to extract features and calculate correlations in the initial speckle image and the deformed speckle image to predict the initial displacement field that describes the deformation characteristics of the material under test.

[0031] In a specific application example, the initial speckle image and the deformed speckle image are input into a deep learning optical flow network. Multi-scale features are extracted, and the correspondence between the images is calculated to obtain pixel-level displacement field prediction results as the initial state for gradient descent optimization. The deep learning optical flow network adopts a GMFlowNet structure incorporating a Swin-Transformer attention mechanism. Through multi-scale feature extraction and correlation modeling, it performs matching analysis on the initial speckle image and the deformed speckle image, constructs a global correlation cost body, and predicts the initial displacement field describing the deformation characteristics of the tested material. ;in, for The initial displacement component of the pixel at position in the x direction. for The initial displacement component of the pixel at the given location in the y-direction.

[0032] The Swin-Transformer encoder utilizes a local window attention mechanism to capture long-range correlations within an image, enhancing feature representation in weakly textured, low-contrast X-ray images. It then extracts depth features from the image, calculates correlations based on these depth features, and generates a high-dimensional matching cost volume between the initial and deformed speckle images, serving as the global correlation cost volume. Finally, optical flow decoding is performed to obtain the pixel-level initial displacement field.

[0033] The pixel-level initial displacement field is not used as the final measurement result, but as the initial displacement estimate for the subsequent gradient descent optimization process based on energy regularization. It is used to guide the global optimization direction, thereby effectively avoiding the problem of the gradient descent process getting stuck in local extrema or ineffective convergence under large displacement or complex deformation conditions.

[0034] Step 204: The initial displacement field is parameterized to obtain a parameterized displacement field, and the parameterized displacement field is used as the initial state of the displacement field for subsequent optimization solutions based on physical constraints.

[0035] In a specific application example, the pixel-level initial displacement field is spatially downsampled and mapped to a regular finite element mesh to obtain initial nodal displacement values ​​consistent with the finite element degrees of freedom. This finite element mesh is used to parameterize the displacement field and serves as the computational basis for the energy regularization term. The downsampling mapping process includes: interpolating and resampling the initial displacement field according to the resolution of the finite element mesh to obtain a smooth and continuous initial displacement field; converting the interpolated and resampled initial displacement field into a set of displacement parameters to obtain a parameterized displacement field, which is then used as the initial state for the gradient descent optimization process. The parameterized displacement field includes initial nodal displacement values ​​consistent with the finite element degrees of freedom, ensuring the spatial continuity of the nodal displacements and the consistency with the topology of the finite element elements.

[0036] Specifically, to ensure that the initial displacement values ​​are consistent with the degrees of freedom of the finite element mesh, this example performs spatial scale downsampling, resolution matching, and interpolation transformation on the pixel-level initial displacements. This maps the continuous pixel displacement field output by the deep learning network into initial node displacement values ​​in the form of finite-dimensional parameter vectors, thereby obtaining the initial node displacement values. This allows the prediction results of the deep network to naturally transition to the gradient descent optimization domain based on energy regularization. The initial values ​​of the node displacements can be expressed as: ; in, The initial displacement value for the first node is... This represents the total number of nodes.

[0037] Step 205: Based on the parameterized displacement field, construct an energy regularization term that reflects the spatial continuity and physical rationality of the displacement field. The energy regularization term is used to constrain the smoothness and deformation consistency of the displacement field.

[0038] In a specific application example, the finite element mesh is a four-node isoparametric element. Specifically, to perform finite-dimensional parameterization of the displacement field and construct an energy regularization term, the image domain is discretized into a pixel mesh, and the entire image region is discretized into a four-node isoparametric element mesh. Each node has two degrees of freedom, and each four-node isoparametric element contains one or more integration points for image sampling and energy regularization term calculation, such as... Figure 5 As shown.

[0039] Step 205 includes steps 51 to 56.

[0040] Step 51: For any four-node isoparametric element, construct the node displacement vector of the four-node isoparametric element based on the initial value of the node displacement corresponding to the four-node isoparametric element.

[0041] No. e The nodal displacement vectors of the four-node isoparametric elements are: ;in, For the first e The nodal displacement vectors of a four-node isoparametric element. This represents the initial displacement of the first node corresponding to a four-node isoparametric element. Let be the initial value of the displacement component in the x-direction for the first node corresponding to the four-node isoparametric element. This represents the initial value of the displacement component in the y-direction of the first node corresponding to the four-node isoparametric element.

[0042] Step 52: Select an integration point inside the four-node isoparametric element, and use a bilinear shape function to interpolate the displacement inside the four-node isoparametric element to obtain the continuous displacement field of the four-node isoparametric element at the integration point.

[0043] To ensure the spatial continuity of the displacement field, bilinear shape functions are used to interpolate arbitrary points within each four-node isoparametric element: ;in, For the first i The shape function values ​​of each node. , The natural coordinates of any point inside a four-node isoparametric element vary with the position of the integration point; , For the first i The fixed positions of each node in the natural coordinate system (with values ​​of ±1). Therefore ( ()( The structure ensures that the shape function takes the value 1 at this node and the value 0 at the other nodes, thus realizing the bilinear interpolation property.

[0044] The formula for the displacement of the integration point is: Where P is the integration point, For the displacement of the integration point, For the first i The shape function values ​​of each node. For the first i The displacement of each node.

[0045] Step 53: Determine the strain-displacement relationship of the four-node isoparametric element based on the continuous displacement field.

[0046] No. e The strain-displacement matrix of a four-node isoparametric element is: ;in, For the first e The strain-displacement matrix of a four-node isoparametric element. , Let represent the partial derivatives of the shape function at the i-th node with respect to the x and y coordinates, respectively.

[0047] Step 54: Calculate the small deformation strain of the four-node isoparametric element based on the strain-displacement relationship.

[0048] No. e The small deformation strain of a four-node isoparametric element is: Its continuous form is: .in, , These are the normal strain components along the x and y directions within a four-node isoparametric element, representing the relative elongation or compression of the material in the x and y directions. The shear strain components within a four-node isoparametric element represent the degree of shear deformation occurring in the material within the x–y plane. , These describe the displacement gradients of the material in the x and y directions, respectively.

[0049] Step 55: Calculate the strain energy of the four-node isoparametric element based on the small deformation strain.

[0050] Given the weak texture and high noise of X-ray images, if the displacement field is driven solely by the image consistency residual, non-physical phenomena such as displacement jumps and strain oscillations are highly likely to occur. Therefore, this application introduces strain energy as an energy regularization term to constrain the spatial continuity and physical rationality of the displacement field.

[0051] Specifically, the following formula is used to calculate the first... e Strain energy of a four-node isoparametric element: ; ; in, For the first e Strain energy of a four-node isoparametric element For the first e Integration region of four-node isoparametric elements Indicates the integration region. This represents a micro-element within the corresponding region. For the first e Small deformation strain of a four-node isoparametric element For the first e The strain-displacement matrix of a four-node isoparametric element. For the first e The nodal displacement vectors of four-node isoparametric elements, where D is the material's equivalent elastic matrix. The strain energy is not used to solve for the actual material stress, but rather participates in the construction of the total loss function as a regularization term.

[0052] Step 56: Accumulate the strain energies of all four-node isoparametric elements to obtain the global energy regularization term used to constrain the smoothness and physical rationality of the displacement field: .in, The total number of four-node isoparametric elements. The global deformation energy is used as an energy regularization term to constrain the spatial continuity and physical rationality of the global displacement distribution.

[0053] Step 206: Based on the image consistency residual and the energy regularization term, a total loss function is constructed by weighted combination, and the parameterized displacement field is iteratively updated using a gradient descent optimization strategy to obtain the full-field displacement distribution and corresponding deformation information of the material under test under X-ray imaging conditions, thereby realizing the measurement and monitoring of the internal deformation behavior of the material under test.

[0054] In a specific application example, the total loss function is: .in, This is the total loss function value. For image consistency residuals, For global deformation energy, The weights of the image consistency residuals, This is the weighting coefficient for the energy regularization term, used to balance the relationship between data consistency and the physical constraints of the displacement field.

[0055] To avoid getting trapped in local optima in the early stages of optimization, this application employs an adaptive weighting mechanism. It changes dynamically with iteration, and its expression is: ; in, k For adjustment coefficients, To prevent numerically stable parameters with a denominator of 0, in the early stages of iteration, when the image consistency residual is large, Taking a smaller value allows the optimization process to be dominated by the image consistency term, thereby enhancing the global registration capability; as the iteration progresses, as the image residual gradually decreases, By gradually increasing the energy regularization term, the continuity and smoothness of the displacement field are constrained. An adaptive weight adjustment mechanism is used to prioritize image matching in the early stages of optimization and physical constraints in the later stages, thus balancing global convergence with local physical plausibility.

[0056] This application employs a gradient descent optimization strategy or the AdamW optimizer to iteratively update the node displacements until the convergence condition is met. This optimization process is implemented based on an automatic differentiation framework, which can efficiently calculate the gradient of the total loss function with respect to the displacement parameters. In the early stages of iteration, image consistency residuals dominate, improving global registration capabilities; in the later stages, global deformation energy dominates, ensuring a continuous, smooth, and physically reliable displacement field.

[0057] Specifically, the gradient of each pixel displacement is first calculated using an automatic differentiation framework: Where L is the total loss function value, The displacement of the first node is given, and then the node displacement is updated iteratively using gradient descent or the AdamW optimizer: ; until the error converges. Wherein, For the firstj The displacement at the next iteration j The iteration count is denoted as . The iteration stops when any of the following conditions are met: the rate of change of the image consistency residual is less than a preset threshold, the change in global deformation energy tends to stabilize, or the maximum number of iterations is reached. This yields the final global displacement field, strain field, and gradient field, such as... Figure 6 As shown. This optimization process can be executed in parallel on a GPU platform to significantly improve the computational efficiency of large X-ray images.

[0058] After optimization, damage indicator variables such as displacement field, strain field, displacement gradient field, and energy field distribution inside the material can be obtained. Among them, the displacement field is the continuous interpolation result of nodal displacements, which can be further calculated to obtain the two-dimensional strain field inside the material, and is used for quantitative identification and evolution monitoring of crack initiation, interface debonding, and strain concentration regions inside carbon / silicon carbide composite materials.

[0059] This application addresses the urgent need for monitoring the internal damage evolution of carbon / silicon carbide composites under extreme thermal environments, overcoming the limitations of traditional optical DIC surface measurement and the technical challenges of incompatibility between X-ray image grayscale characteristics and traditional DIC methods based on local correlation matching.

[0060] Specifically, this application constructs a parameterized representation model of a continuous displacement field based on the physical mechanism of X-ray imaging. By parameterizing the image domain onto a regular computational grid and combining it with linear shape function interpolation, the spatial continuity and differentiability of the displacement field are guaranteed. This computational grid, serving as the carrier for displacement parameterization and energy regularization, is not limited to the finite element solution model in traditional structural mechanics analysis. Based on this, a global optimization objective function is established, including image consistency residuals and energy regularization terms. The image consistency residuals employ a robust Charbonnier loss function to enhance the algorithm's adaptability to noise, scattering, and weak texture features in X-ray images. The energy regularization term, by constraining the displacement gradient or equivalent energy variation, suppresses non-physical oscillations and ensures the spatial continuity and physical rationality of the inverted displacement field.

[0061] Furthermore, this application introduces a deep learning optical flow network to extract features and model the correlation between the initial and deformed speckle images, obtaining a pixel-level initial displacement field as the initial state for global optimization, significantly improving convergence stability under large deformation and complex texture conditions. Based on this, an innovative adaptive weight adjustment mechanism is introduced, allowing the energy regularization term to be dynamically adjusted during optimization: in the early stages of optimization, the focus is on image consistency residuals to obtain the global deformation trend, while in the later stages, the physical constraints are gradually strengthened, thereby obtaining a smooth, continuous, and physically reliable deformation field. Finally, an automatic differentiation framework and gradient descent optimization algorithm are used to iteratively update the displacement parameters, and GPU parallel computing is combined to achieve efficient solution.

[0062] This method significantly improves the deformation measurement accuracy and robustness of high-noise, weak-texture natural speckle feature images under X-ray digital imaging conditions. It is particularly suitable for real-time monitoring of the internal deformation field and damage evolution of woven carbon / carbon and carbon / silicon carbide composite materials under extreme conditions such as high temperature and high heat flux, providing a reliable technical means for safety assessment and life prediction of key thermal structures of hypersonic vehicles.

[0063] In summary, this application, within a unified framework integrating deep learning initial displacement prediction, energy regularization constraints, and gradient descent optimization mechanisms, achieves accurate matching of X-ray natural texture features by constructing a continuous mapping between the pixel domain and the parameterized displacement domain. Furthermore, it can adaptively adjust the regularization weights and optimization strategies based on local texture intensity, noise level, and deformation amplitude, thereby obtaining more accurate and physically consistent internal deformation field inversion results and enabling real-time stable monitoring of carbon / silicon carbide composite materials under ultra-high temperature conditions.

[0064] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0065] Those skilled in the art will understand that implementing all or part of the processes in the above embodiments, including deep learning feature extraction, energy regularization term construction, and gradient descent optimization, can all be accomplished by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The processors involved in the embodiments provided in this application can be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, etc., but are not limited thereto.

[0066] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0067] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, 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 this application.

Claims

1. A deep learning and energy-regularized gradient descent deformation measurement method based on X-ray digital imaging, characterized in that, The method includes: The initial speckle image and the deformed speckle image of the material under test are acquired; both the initial speckle image and the deformed speckle image are obtained by X-ray imaging. The deformed speckle image is subjected to displacement inverse mapping and grayscale reconstruction to obtain a reconstructed speckle image. The image consistency residual between the reconstructed speckle image and the initial speckle image is constructed to characterize the matching error of image grayscale as displacement changes. A deep learning optical flow network is used to extract features and calculate correlations in the initial speckle image and the deformed speckle image to predict the initial displacement field describing the deformation characteristics of the material under test. The initial displacement field is parameterized to obtain a parameterized displacement field, which is then used as the initial state of the displacement field for subsequent optimization solutions based on physical constraints. Based on the parameterized displacement field, an energy regularization term is constructed to reflect the spatial continuity and physical rationality of the displacement field; the energy regularization term is used to constrain the smoothness and deformation consistency of the displacement field. The total loss function is constructed by weighting the image consistency residual and the energy regularization term, and the parameterized displacement field is iteratively updated by using a gradient descent optimization strategy to obtain the full-field displacement distribution and corresponding deformation information of the material under test under X-ray imaging conditions, thereby realizing the measurement and monitoring of the internal deformation behavior of the material under test.

2. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 1, characterized in that, The material being tested is a composite material with a natural or artificially formed texture structure inside, including carbon / carbon composite materials and carbon / silicon carbide composite materials.

3. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 1, characterized in that, The process of performing displacement inverse mapping and grayscale reconstruction on the deformed speckle image to obtain a reconstructed speckle image, and constructing the image consistency residual between the reconstructed speckle image and the initial speckle image includes: Based on the current displacement field, the deformed speckle image is re-mapped to the coordinate system of the initial speckle image to obtain the corresponding reconstructed speckle image. The reconstructed speckle image is compared with the initial speckle image point by point in terms of gray level, and the gray level difference between the two is calculated to construct the image consistency residual.

4. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 3, characterized in that, The formula for calculating the image consistency residual is: ;in, For image consistency residuals, For a set of pixels, For numerically stable terms, To reconstruct the speckle image, The initial speckle image, The coordinates of the pixel. It is a constant greater than 0 and less than 1.

5. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 1, characterized in that, The deep learning optical flow network adopts the GMFlowNet structure containing the Swin-Transformer attention mechanism. Through multi-scale feature extraction and correlation modeling, it performs matching analysis on the initial speckle image and the deformed speckle image to predict the initial displacement field describing the deformation characteristics of the tested material.

6. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 1, characterized in that, The initial displacement field is parameterized to obtain a parameterized displacement field, and this parameterized displacement field is used as the initial state of the displacement field, including: The initial displacement field is interpolated and resampled according to a preset spatial resolution to obtain a smooth and continuous initial displacement field. The initial displacement field after interpolation and resampling is converted into a set of displacement parameters to obtain a parameterized displacement field, which is then used as the initial state for the gradient descent optimization process.

7. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 1, characterized in that, The energy regularization term is constructed using the finite element strain energy form, and the discrete element used for displacement field parameterization is a four-node isoparametric element. The process of constructing the energy regularization term includes: For any four-node isoparametric element, construct the node displacement vector of the four-node isoparametric element based on the initial values ​​of the node displacements corresponding to the four-node isoparametric element. An integration point is selected inside the four-node isoparametric element, and a bilinear shape function is used to interpolate the displacement inside the four-node isoparametric element to obtain the continuous displacement field of the four-node isoparametric element at the integration point. The strain-displacement relationship of the four-node isoparametric element is determined based on the continuous displacement field. Calculate the small deformation strain of the four-node isoparametric element based on the strain-displacement relationship; Calculate the strain energy of the four-node isoparametric element based on the small deformation strain; The strain energies of all four-node isoparametric elements are accumulated to obtain a global energy regularization term used to constrain the smoothness and physical rationality of the displacement field.

8. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 7, characterized in that, The strain energy of the four-node isoparametric element is calculated using the following formula: ； ； in, For the first e Strain energy of a four-node isoparametric element For the first e Integration region of four-node isoparametric elements For the integration region, For the corresponding infinitesimal elements within the region, For the first e Small deformation strain of a four-node isoparametric element For the first e The strain-displacement matrix of a four-node isoparametric element. For the first e The nodal displacement vectors of a four-node isoparametric element. This is the material's equivalent elastic matrix.

9. The method for measuring deformation based on X-ray digital imaging using deep learning and energy-regularized gradient descent according to claim 1, characterized in that, The expression for the total loss function is: ； in, This is the total loss function value. For image consistency residuals, For global deformation energy, The weights of the image consistency residuals, Let be the weighting coefficient of the energy regularization term, and The adaptive update method is used, and its calculation formula is as follows: ； k For adjustment coefficients, To prevent numerically stable parameters with a denominator of 0.

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