A large deformation full-field deformation measurement method based on incremental artificial intelligence digital volume correlation

Abstract

The application discloses a large deformation full-field deformation measurement method based on an incremental artificial intelligence digital volume correlation, and comprises the following steps: performing format conversion and gray scale normalization processing on acquired multiple frames of continuous three-dimensional images, synchronously constructing a three-dimensional voxel coordinate grid, acquiring each voxel coordinate, and performing normalization processing to obtain three-dimensional normalized coordinates. The normalized physical coordinates are input into a physical information neural network, iterative optimization is performed to make a composite loss function converge, and a three-dimensional displacement field and a six-component strain field are output. Finally, the cumulative displacement and cumulative strain of each step are summarized and visually displayed, equivalent strain is calculated, and the overall deformation degree of the object to be measured in the three-dimensional space is evaluated. The application adopts an incremental three-dimensional analysis framework, decomposes a continuous large deformation process into several small incremental steps for step-by-step solving, and takes the updated current three-dimensional configuration as a reference at each step, so that the three-dimensional volume image mismatching problem caused by large deformation when taking the initial configuration as a reference is fundamentally overcome.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of experimental mechanics and computed tomography image processing, specifically a method for measuring large deformations across the entire field based on incremental artificial intelligence digital volume correlation. Background Technology

[0002] Digital volume correlation (DLC) is a non-contact optical measurement technique that extends the principles of digital image correlation from a two-dimensional plane to a three-dimensional volume space. It compares the grayscale distribution changes of three-dimensional speckle volume images before and after deformation of an object, solving for the three-dimensional displacement field through sub-volume correlation matching or global optimization, and then calculating the three-dimensional strain field through numerical differentiation. This technique relies on imaging methods such as X-ray computed tomography (CT), synchrotron radiation tomography (SCT), and neutron tomography (NCT) to obtain images of the internal three-dimensional structure of objects. It has been widely applied to the three-dimensional full-field mechanical property characterization of porous metallic materials, rock-like geological materials, composite laminate structures, and biological tissues such as bone and cartilage, possessing significant research value and engineering application significance in materials science, geomechanics, and biomechanics. However, traditional DLC methods have several inherent limitations when facing large deformation measurement scenarios:

[0003] First, traditional subvolume correlation methods use the initial configuration as a reference for 3D matching. When the cumulative 3D deformation is large, the difference in grayscale distribution between the corresponding subvolumes before and after deformation increases significantly, leading to a decrease in correlation coefficient or even matching failure. The measurement accuracy deteriorates significantly with the increase in the degree of deformation, making it difficult to adapt to extreme mechanical scenarios such as material fracture and large compression.

[0004] Secondly, traditional methods typically separate displacement field measurement and strain field calculation into two independent steps. First, discrete displacement data is obtained through three-dimensional volume image matching, and then three-dimensional strain is estimated using numerical differentiation. The numerical differentiation process itself introduces an error amplification effect, which is particularly prominent in local areas with large strain gradients, resulting in a serious decrease in the accuracy of the local strain field.

[0005] Third, traditional digital volume correlation methods, when processing multi-frame continuous volume sequences, usually analyze the displacement between adjacent frames independently and lack continuous tracking of the three-dimensional motion history of material points. This makes it difficult to accurately describe the three-dimensional motion trajectory of material points during large deformation processes, which is not conducive to in-depth research on the three-dimensional constitutive behavior of materials.

[0006] Fourth, in recent years, physical information neural networks (PINs) have emerged as a novel computational framework that embeds mechanical constraints into the neural network training process, offering new insights into solving inverse mechanical problems. However, most existing PIN digital volume correlation methods still rely on the initial configuration for overall analysis, failing to establish an effective incremental large deformation 3D analysis mechanism. Furthermore, they haven't fundamentally addressed the critical issue of dynamic imbalance in the gradient magnitudes of the two types of constraints. The gradient magnitudes of image grayscale consistency constraints and physical compatibility constraints often differ significantly. If fixed weighting coefficients are applied to both types of constraints, the optimization process is prone to bias towards the constraint with the larger gradient, rendering the other constraint ineffective. This severely impacts measurement accuracy and physical reliability, hindering its practical application in large deformation engineering 3D measurement scenarios. Summary of the Invention

[0007] The purpose of this invention is to provide a method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation, comprising the following steps:

[0008] S1. Acquire multiple consecutive three-dimensional images of the object under test during its deformation process;

[0009] The format of the 3D image is converted to obtain a floating-point format image array, and then the floating-point format image array is normalized to grayscale.

[0010] S2. Based on the spatial dimension of the floating-point format image array, construct a three-dimensional voxel coordinate grid, obtain the coordinates of each voxel, and perform normalization processing to obtain three-dimensional normalized coordinates.

[0011] S3. Set the training iteration rounds, network structure parameters, and optimization strategies;

[0012] S4. Set the total number of increment steps. and initialize the increment step number. ,make =0;

[0013] Setting the first The frame image volume is the reference volume for step 0; the volume is a three-dimensional array composed of the gray values ​​of each voxel in the image; the frame image volume is set to... The three-dimensional normalized coordinates of the frame image are the coordinates of the material point at step 0; The initial value is 1;

[0014] S5, the first The coordinates of the material points are input into the physical information neural network to obtain the first... +1 step prediction of incremental three-dimensional displacement field and the first +1 step prediction of incremental strain field; The initial value is 0;

[0015] S6, based on the first +1 step predicts incremental displacement field, updates the 1st step. +1 step material point coordinates;

[0016] Based on the trilinear interpolation method, for the th The reference volume is remapped step by step to obtain the first step. +1 step reference volume;

[0017] S7, Order = +1, judgment Is it equal to If so, output the first... Step the reference volume as the reconstructed volume, and simultaneously output the predicted cumulative displacement field and the predicted cumulative strain field, then proceed to step S8; otherwise, return to step S5.

[0018] S8, the first The volume of the +1 frame image is used as the target volume. The composite loss value is calculated. It is determined whether the composite loss value is less than the threshold. If it is, proceed to step S9. Otherwise, the network parameters are updated based on the selected optimization strategy, and the process returns to step S5.

[0019] S9, Order = +1, judgment Is it equal to the number of image frames acquired? If yes, proceed to step S10; otherwise, return to step S4.

[0020] S10. Summarize and visualize the cumulative displacement and cumulative strain of each step, calculate the equivalent strain, and evaluate the overall deformation of the object under test in three-dimensional space.

[0021] Furthermore, in step S1, the object to be tested includes porous metallic materials, rock-like geological materials, biological hard tissues such as bones, biological soft tissues, and composite laminate structures.

[0022] Further, in step S1, the format conversion includes: batch converting multiple consecutive 3D image files into a four-bit array of shape (T, D, H, W), where T is the number of captured frames, D is the image depth, H is the pixel height of a single slice, and W is the pixel width of a single slice. Then, the four-bit array is converted into a floating-point number format.

[0023] Furthermore, in step S2, the spatial dimension of the floating-point format image array includes image depth. Pixel height of a single slice and the pixel width of a single slice .

[0024] In the three-dimensional voxel coordinate grid, the origin is located at the corner of the first voxel (0, 0, 0) of the volume image. The X-axis extends along the width direction with a coordinate range of [0, W-1], the Y-axis extends along the height direction with a coordinate range of [0, H-1], and the Z-axis extends along the depth direction with a coordinate range of [0, D-1]. The side length of each voxel is 1.

[0025] Three-dimensional normalized coordinates ( The formula for calculating ) is:

[0026] (1)

[0027] (2)

[0028] (3)

[0029] In the formula: ( () represents voxel coordinates.

[0030] The range of the three-dimensional normalized coordinates is [0, 1].

[0031] Furthermore, in step S5, the first +1 step prediction of incremental three-dimensional displacement field is ( , , ),in , , The first +1 step prediction of incremental displacements along the X, Y, and Z directions.

[0032] No. +1 step prediction of incremental strain field is ( , , , , , ),in , , The first +1 step prediction of incremental normal strain along the X, Y, and Z directions. , , The first +1 step prediction of incremental tangential shear strain along the XY, XZ, and YZ planes.

[0033] Furthermore, in step S6, the first +1 step material point coordinates ( The update formula for ) is:

[0034] = + (4)

[0035] = + (5)

[0036] = + (6)

[0037] In the formula: ( ) is the first The coordinates of the material point at the end of the step.

[0038] The process of reconstructing the reference image volume based on trilinear interpolation is as follows:

[0039] For any voxel coordinate within the volume domain ( Apply a predicted incremental three-dimensional displacement field ( , , ), to obtain the sampling coordinates ( ),in = - , = - , = - .

[0040] Let the sampling coordinates be ( The 8-neighbor voxel coordinates of ) are respectively ( ), ( ), ( ), ( ), ( ), ( ), ( ), ( The subscript numbers 0 and 1 of the coordinates represent the low-index and high-index neighborhood voxels in the corresponding directions, respectively, and the coordinates of the neighborhood voxels satisfy: =floor( ), =floor( ), =floor( ), = +1, = +1, = +1.

[0041] Performing a fourth linear interpolation along the X direction on the 8-neighbor voxels yields:

[0042] (16)

[0043] (17)

[0044] (18)

[0045] (19)

[0046] In the formula: , , , These are the four intermediate gray values ​​obtained after the first linear interpolation along the X direction; , , , , , , , These are the gray values ​​corresponding to the coordinates of the 8 neighboring voxels; The fractional part of the sampled coordinates along the X direction. = - .

[0047] Performing a second linear interpolation along the Y direction yields:

[0048] (20)

[0049] (twenty one)

[0050] In the formula: , These are two intermediate gray values ​​obtained after the second linear interpolation along the Y direction; To sample the decimal part of the coordinates along the Y direction, = - .

[0051] Perform a linear interpolation along the Z direction to obtain the reconstructed voxel gray value at the sampling coordinates. :

[0052] (twenty two)

[0053] In the formula: The fractional part of the sampled coordinates along the Z direction. = - .

[0054] Furthermore, in step S7, the cumulative displacement field is predicted ( , , The formula for calculating ) is:

[0055] (7)

[0056] (8)

[0057] (9)

[0058] In the formula: ( ) represents the initial voxel coordinates of the k-th frame image; () represents the coordinates of the material point at the end of step n.

[0059] Predicting cumulative strain field ( The formula for calculating ) is:

[0060] (10)

[0061] (11)

[0062] (12)

[0063] (13)

[0064] (14)

[0065] (15)

[0066] In the formula: The depth index corresponding to the Z direction. The corresponding height index in the Y direction, Width index corresponding to the X direction.

[0067] Furthermore, in step S8, the composite loss value The function expression is:

[0068] (twenty three)

[0069] (twenty four)

[0070] (25)

[0071] In the formula: These are the weighting coefficients; Image consistency constraints; Physical compatibility constraints; It is the set of all voxels within the domain. ; The total number of voxels; To reconstruct the volume, For the target volume; ( () is for predicting the cumulative strain field; , , These are the central difference approximate partial derivatives of the cumulative displacement R along the X direction with respect to the initial voxel coordinates of the X, Y, and Z directions in the nth frame image, respectively. , , These are the approximate partial derivatives of the central difference of the cumulative displacement along the Y direction with respect to the initial voxel coordinates of the X, Y, and Z directions in the nth frame image, respectively. , , Let be the central difference approximate partial derivatives of the cumulative displacement along the Z direction with respect to the X, Y, and Z directions in the initial voxel coordinates of the nth frame image.

[0072] Furthermore, in step S8, the selected optimization strategy includes the Adam optimization strategy, the L-BFGS optimization strategy, or the Adam and L-BFGS two-stage cascade optimization strategy.

[0073] Furthermore, during training, when the selected optimization strategy is the Adam optimization strategy or the Adam and L-BFGS two-stage cascade optimization strategy, the weight coefficients in the composite loss function need to be adjusted. The update is performed based on the following criteria: If the current training iteration has reached the weight update iteration, calculate the image loss gradient and the physical loss weighted gradient, and update the weight coefficients based on the exponential moving average; otherwise, continue calculating the composite loss value using the current weight coefficients. .

[0074] The formula for calculating the image loss gradient is:

[0075] (26)

[0076] In the formula: This represents the maximum absolute value of the gradient of the image consistency loss with respect to all trainable weight parameters of the network.

[0077] The formula for calculating the weighted gradient of physical loss is:

[0078] (27)

[0079] In the formula: This represents the current weighting coefficient; The mean of the absolute values ​​of the gradients of the physical compatibility loss, weighted by the current weight coefficients, with respect to all trainable parameters of the network.

[0080] The formula for updating the weight coefficients is:

[0081] (28)

[0082] In the formula: These are the weight coefficients updated in the current round; It is a numerically stable term; This is the momentum coefficient.

[0083] Furthermore, the measurement system employed includes a volume sequence loading and preprocessing unit, a material point coordinate tracking unit, a physical information neural network training unit, an adaptive weighted annealing calculation unit, and a full-field result output unit.

[0084] The volume sequence loading and preprocessing unit includes a volume reading module, a format conversion module, a normalization processing module, and a voxel coordinate grid construction module.

[0085] The volume reading module is used to batch convert multiple consecutive three-dimensional volume image files into four-bit arrays of shape (N, D, H, W), wherein the four-bit arrays are in NumPy or MATLAB format.

[0086] The format conversion module is used to convert a four-digit array into a floating-point number format.

[0087] The normalization module is used to standardize the gray value of each material point.

[0088] The voxel coordinate mesh construction module is used to construct a three-dimensional voxel coordinate mesh.

[0089] The material point coordinate tracking unit updates the three-dimensional coordinates of the material point step by step based on the prediction increment step, and after each step of coordinate update is completed, it updates the reference volume of the current step using the trilinear interpolation remapping method.

[0090] The physical information neural network training unit incorporates a physical information neural network. This network takes the three-dimensional coordinates of the current material point as input and outputs an incremental three-dimensional displacement field and a six-component strain field, iteratively optimizing and converging the composite loss function. During the iterative optimization process, the composite loss function is updated via an adaptive weighted annealing calculation unit.

[0091] The full-field result output unit includes a cumulative displacement field visualization module, a cumulative strain field visualization module, a three-dimensional rendering module, an equivalent strain calculation module, an automatic parameter recommendation module, and a data export module.

[0092] The cumulative displacement field visualization module is used to display the predicted cumulative displacement field. , , It generates a pseudo-color cloud map and can display slices in the three orthogonal cross-sectional directions of XY, XZ, and YZ, as well as at any percentage position.

[0093] The cumulative strain field visualization module is used to display the six-component strain field calculated from the central difference of the cumulative displacement field. , , , , , Orthogonal cross-section pseudo-color slice cloud map.

[0094] The 3D rendering module includes Delaunay triangulation convex hull shading mode, triorthogonal section mode, and scatter cloud mode.

[0095] The equivalent strain calculation module is used to calculate the three-dimensional equivalent strain. And based on three-dimensional equivalent strain Evaluate the overall degree of deformation of the object under test in three-dimensional space.

[0096] Three-dimensional equivalent strain The calculation formula is:

[0097] (29)

[0098] The automatic parameter recommendation module integrates an image volume size-level parameter lookup table. Using the total number of elements in the image volume S=D×H×W as the image volume size, the module determines the position of the image volume size in the image volume size-level parameter lookup table and obtains the recommended parameter configuration.

[0099] The data export module supports four export formats: NumPy compressed array format, MATLAB matrix file format, VTK legacy format, and CSV statistical table format.

[0100] Furthermore, the physical information neural network adopts a fully connected neural network structure, including an input layer, an output layer, and several hidden layers.

[0101] The input layer receives three-dimensional normalized coordinates ( ).

[0102] Each hidden layer consists of a fully connected linear transformation and a hyperbolic tangent activation function, which restricts the neuron output to the (-1, 1) interval.

[0103] The output layer is a linear layer without an activation function, with an output dimension of 9, corresponding to incremental displacements in the X direction. incremental displacement in the Y direction Incremental displacement in the Z direction and six strain components , , , , , .

[0104] The weight matrices of the hidden layer and the output layer are initialized using a uniform Xavier distribution, and the biases are initialized to zero.

[0105] The technical effects of this invention are undeniable, and its beneficial effects are as follows:

[0106] 1. This invention adopts an incremental three-dimensional analysis framework based on the current configuration, which decomposes the continuous large deformation process into several small incremental steps for step-by-step solution. Each step takes the updated current three-dimensional configuration as a reference, which fundamentally overcomes the problem of three-dimensional volume image mismatch caused by large deformation when the initial configuration is used as a reference, and significantly improves the accuracy and robustness of large deformation three-dimensional measurement.

[0107] 2. This invention introduces an adaptive weighted annealing mechanism, which dynamically evaluates the gradient magnitudes of image consistency loss and physical compatibility loss and adjusts the weight coefficients in real time using an exponential moving average method. This fundamentally solves the problem of optimization bias caused by the imbalance of the gradient magnitudes of the two types of constraints in the fixed weight scheme, and improves the actual effectiveness of physical constraints in the training process.

[0108] 3. This invention integrates the prediction of the three-dimensional displacement field and the six-component strain field into a single network synchronous output. The self-consistency of the two is ensured by physical compatibility constraints, avoiding the error amplification caused by the traditional digital volume correlation method when numerically differentiating discrete three-dimensional displacement data, and improving the overall measurement accuracy of the three-dimensional strain field.

[0109] 4. This invention introduces a continuous three-dimensional coordinate tracking mechanism for material points. By gradually accumulating incremental displacements in three directions, the three-dimensional motion trajectory of each material point throughout the entire deformation history can be accurately reconstructed, providing a reliable data foundation for the study of material three-dimensional constitutive behavior and deformation evolution analysis.

[0110] 5. This invention provides three optimization strategies: Adam, L-BFGS, and two-stage cascade. In the two-stage strategy, the L-BFGS stage directly inherits the network parameters and convergence weight coefficients of the Adam stage, achieving a seamless connection between coarse convergence and fine solution, and comprehensively considering both convergence speed and solution accuracy.

[0111] 6. The full-field result output unit of this invention provides three 3D rendering modes: Delaunay convex hull, triorthogonal section, and scattered point cloud, as well as data export in multiple formats such as NumPy, MATLAB, VTK, and CSV, which has high engineering practicality and scalability. Attached Figure Description

[0112] Figure 1 A schematic diagram of the overall architecture of an incremental artificial intelligence digital volume-related large deformation full-field deformation measurement system;

[0113] Figure 2 A schematic diagram illustrating the principle of incremental three-dimensional material point coordinate tracking and current configuration reference volume update;

[0114] Figure 3 This is a schematic diagram of a physical information neural network structure;

[0115] Figure 4 A schematic diagram of the adaptive weighted annealing mechanism;

[0116] Figure 5 This is a schematic diagram illustrating the principle of three-dimensional trilinear interpolation volume reconstruction.

[0117] Figure 6 This is a schematic diagram illustrating the calculation principle of the composite loss function;

[0118] Figure 7 This is a schematic diagram of the three-dimensional full-field measurement results for large deformation. Detailed Implementation

[0119] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0120] Example 1:

[0121] A method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation includes the following steps:

[0122] S1. Acquire multiple consecutive three-dimensional images of the object under test during its deformation process;

[0123] The format of the 3D image is converted to obtain a floating-point format image array, and then the floating-point format image array is normalized to grayscale.

[0124] S2. Based on the spatial dimension of the floating-point format image array, construct a three-dimensional voxel coordinate grid, obtain the coordinates of each voxel, and perform normalization processing to obtain three-dimensional normalized coordinates.

[0125] S3. Set the training iteration rounds, network structure parameters, and optimization strategies;

[0126] S4. Set the total number of increment steps. and initialize the increment step number. ,make =0;

[0127] Setting the first The frame image volume is the reference volume for step 0; the volume is a three-dimensional array composed of the gray values ​​of each voxel in the image; the frame image volume is set to... The three-dimensional normalized coordinates of the frame image are the coordinates of the material point at step 0; The initial value is 1;

[0128] S5, the first The coordinates of the material points are input into the physical information neural network to obtain the first... +1 step prediction of incremental three-dimensional displacement field and the first +1 step prediction of incremental strain field; The initial value is 0;

[0129] S6, based on the first +1 step predicts incremental displacement field, updates the 1st step. +1 step material point coordinates;

[0130] Based on the trilinear interpolation method, for the th The reference volume is remapped step by step to obtain the first step. +1 step reference volume;

[0131] S7, Order = +1, judgment Is it equal to If so, output the first... Step the reference volume as the reconstructed volume, and simultaneously output the predicted cumulative displacement field and the predicted cumulative strain field, then proceed to step S8; otherwise, return to step S5.

[0132] S8, the first The volume of the +1 frame image is used as the target volume. The composite loss value is calculated. It is determined whether the composite loss value is less than the threshold. If it is, proceed to step S9. Otherwise, the network parameters are updated based on the selected optimization strategy, and the process returns to step S5.

[0133] S9, Order = +1, judgment Is it equal to the number of image frames acquired? If yes, proceed to step S10; otherwise, return to step S4.

[0134] S10. Summarize and visualize the cumulative displacement and cumulative strain of each step, calculate the equivalent strain, and evaluate the overall deformation of the object under test in three-dimensional space.

[0135] Example 2:

[0136] The main structure of this embodiment is the same as that of Embodiment 1. Furthermore, in step S1, the object to be tested includes porous metal materials, rock-like geological materials, biological hard tissues such as bones, biological soft tissues, and composite material laminated structures.

[0137] Example 3:

[0138] The main structure of this embodiment is the same as any one of embodiments 1 to 2. Further, in step S1, the format conversion includes: batch converting multiple consecutive three-dimensional image files into a four-bit array of shape (T, D, H, W), where T is the number of acquisition frames, D is the image depth, H is the pixel height of a single slice, and W is the pixel width of a single slice; then, converting the four-bit array into a floating-point number format.

[0139] Example 4:

[0140] The main structure of this embodiment is the same as any one of embodiments 1 to 3. Further, in step S1, the grayscale is normalized using the minimum-maximum normalization method to obtain the global minimum grayscale value of the volumetric image sequence. With the maximum gray value Based on this, the gray values ​​of each voxel are... The linear mapping to the [0,1] interval is specifically handled by the following formula: , The gray values ​​of each voxel after normalization are in the range [0,1].

[0141] Example 5:

[0142] The main structure of this embodiment is the same as any one of embodiments 1 to 4. Further, in step S2, the spatial dimension of the floating-point format image array includes image depth. Pixel height of a single slice and the pixel width of a single slice .

[0143] In the three-dimensional voxel coordinate grid, the origin is located at the corner of the first voxel (0, 0, 0) of the volume image. The X-axis extends along the width direction with a coordinate range of [0, W-1], the Y-axis extends along the height direction with a coordinate range of [0, H-1], and the Z-axis extends along the depth direction with a coordinate range of [0, D-1]. The side length of each voxel is 1.

[0144] Three-dimensional normalized coordinates ( The formula for calculating ) is:

[0145] (1)

[0146] (2)

[0147] (3)

[0148] In the formula: ( () represents voxel coordinates.

[0149] The range of the three-dimensional normalized coordinates is [0, 1].

[0150] Under the premise that the voxel side length is 1 and the origin of the material point coordinate system is aligned with the origin of the three-dimensional voxel coordinate grid, the value of the voxel coordinate is equal to the value of the material point coordinate.

[0151] Example 6:

[0152] The main structure of this embodiment is the same as any one of embodiments 1 to 5. Further, in step S3, the network is a physical information neural network, including an input layer, several hidden layers, and an output layer. The network structure parameters include the number of hidden layer nodes (i.e., network width), the number of hidden layers, and the learning rate.

[0153] Example 7:

[0154] The main structure of this embodiment is the same as any one of embodiments 1 to 6. Furthermore, the reference volume mentioned in steps S4, S6, and S7 and the target volume mentioned in step S8 are both three-dimensional arrays composed of the gray values ​​of each voxel in the image, and are not physical volumes in a geometric sense.

[0155] The reconstructed volume is based on the predicted incremental displacement field, for the first... The grayscale value is obtained after trilinear interpolation remapping of the reference volume. The target volume is the first... The grayscale value is obtained after format conversion and grayscale normalization of the frame 3D image. In step S8, both the reconstructed volume and the target volume are compared using the grayscale value at the voxel position.

[0156] Example 8:

[0157] The main structure of this embodiment is the same as any one of embodiments 1 to 7. Further, in step S5, the... +1 step prediction of incremental three-dimensional displacement field is ( , , ),in , , The first +1 step prediction of incremental displacements along the X, Y, and Z directions. +1 step prediction of incremental strain field is ( , , , , , ),in, , , The first +1 step prediction of incremental normal strain along the X, Y, and Z directions. , , The first +1 step prediction of incremental tangential shear strain along the XY, XZ, and YZ planes.

[0158] Example 9:

[0159] The main structure of this embodiment is the same as any one of embodiments 1 to 8. Further, in step S6, the... +1 step material point coordinates ( The update formula for ) is:

[0160] = + (4)

[0161] = + (5)

[0162] = + (6)

[0163] In the formula: ( ) is the first The coordinates of the material point at the end of the step; , , The first +1 step prediction of incremental displacement along the X, Y, Z directions.

[0164] Example 10:

[0165] The main structure of this embodiment is the same as any one of embodiments 1 to 9. Further, in step S6, the process of reconstructing the reference image volume based on the trilinear interpolation method is as follows:

[0166] For any voxel coordinate within the volume domain ( Apply a predicted incremental three-dimensional displacement field ( , , ), to obtain the sampling coordinates ( ),in = - , = - , = - .

[0167] Let the sampling coordinates be ( The 8-neighbor voxel coordinates of ) are respectively ( ), ( ), ( ), ( ), ( ), ( ), ( ), ( The subscript numbers 0 and 1 of the coordinates represent the low-index and high-index neighborhood voxels in the corresponding directions, respectively, and the coordinates of the neighborhood voxels satisfy: =floor( ), =floor( ), =floor( ), = +1, = +1, = +1.

[0168] Performing a fourth linear interpolation along the X direction on the 8-neighbor voxels yields:

[0169] (16)

[0170] (17)

[0171] (18)

[0172] (19)

[0173] In the formula: , , , These are the four intermediate gray values ​​obtained after the first linear interpolation along the X direction. Specifically... This represents the X-direction interpolation results at the Z-low index and Y-low index positions. This represents the X-direction interpolation result at the Z-low index and Y-high index positions. This represents the X-direction interpolation result at the Z-high index and Y-low index positions. This represents the X-direction interpolation results at the Z-high index and Y-high index positions; , , , , , , , These are the gray values ​​corresponding to the coordinates of the 8 neighboring voxels; The fractional part of the sampled coordinates along the X direction. = - .

[0174] Performing a second linear interpolation along the Y direction yields:

[0175] (20)

[0176] (twenty one)

[0177] In the formula: , These are the two intermediate gray values ​​obtained after the second linear interpolation along the Y direction. Specifically... The Y-direction interpolation result at the Z-low index position is obtained from... and Interpolation value is obtained. The Y-direction interpolation result at the Z-high index position is obtained from... and Interpolation is obtained; To sample the decimal part of the coordinates along the Y direction, = - ;

[0178] Perform a linear interpolation along the Z direction to obtain the reconstructed voxel gray value at the sampling coordinates. :

[0179] (twenty two)

[0180] In the formula: The fractional part of the sampled coordinates along the Z direction. = - .

[0181] Example 11:

[0182] The main structure of this embodiment is the same as any one of embodiments 1 to 10. Further, in step S7, the cumulative displacement field is predicted ( , , The formula for calculating ) is:

[0183] (7)

[0184] (8)

[0185] (9)

[0186] In the formula: ( , , )for The cumulative displacement along the X, Y, and Z directions after each increment step; ) represents the initial voxel coordinates of the k-th frame image; () represents the coordinates of the material point at the end of step n.

[0187] Predicting cumulative strain field ( The formula for calculating ) is:

[0188] (10)

[0189] (11)

[0190] (12)

[0191] (13)

[0192] (14)

[0193] (15)

[0194] In the formula: ( ) are respectively The cumulative normal strain along the X, Y, and Z directions after each increment step, ( ) are respectively After each increment step, the accumulated tangential shear strain is carried out along the XY plane, XZ plane, and YZ plane; The depth index corresponding to the Z direction. The corresponding height index in the Y direction, The width index corresponding to the X direction, for example voxel point The cumulative displacement along the X direction.

[0195] Example 12:

[0196] The main structure of this embodiment is the same as any one of embodiments 1 to 11. Further, in step S8, the composite loss value... The function expression is:

[0197] (twenty three)

[0198] (twenty four)

[0199] (25)

[0200] In the formula: These are the weighting coefficients; Image consistency constraints; Physical compatibility constraints; It is the set of all voxels within the domain. ; The total number of voxels; To reconstruct the volume, For the target volume; ( () is for predicting the cumulative strain field; , , These are the central difference approximate partial derivatives of the cumulative displacement R along the X direction with respect to the initial voxel coordinates of the X, Y, and Z directions in the nth frame image, respectively. , , These are the approximate partial derivatives of the central difference of the cumulative displacement along the Y direction with respect to the initial voxel coordinates of the X, Y, and Z directions in the nth frame image, respectively. , , These are the cumulative displacements along the Z direction. Regarding the first The central difference approximate partial derivatives of the X, Y, and Z directions in the initial voxel coordinates of the frame image.

[0201] The initial voxel coordinates are the three-dimensional voxel coordinate grid coordinates constructed in step S2. The voxel side length is 1, the X coordinate (corresponding to the width direction, denoted as k) ranges from [0, W-1], the Y coordinate (corresponding to the height direction, denoted as j) ranges from [0, H-1], and the Z coordinate (corresponding to the depth direction, denoted as i) ranges from [0, D-1]. The above-mentioned central difference partial derivatives are approximately calculated by dividing the displacement difference between adjacent integer voxel positions by 2. The calculation method is the same as the calculation method of the central difference of the cumulative strain field defined in equations (10) to (15), for example... The same applies to the remaining components.

[0202] In step S8, the threshold is a user-configurable parameter and has no fixed, unique value. Its reasonable range depends on the grayscale level and voxel count of the specific volumetric image. In practical applications, the threshold is set to the mean square error level corresponding to the image grayscale normalization to the [0,1] interval, with a typical value range of [missing value]. ~ Users can also flexibly adjust the settings based on the convergence pattern of the loss curve during training.

[0203] Example 13:

[0204] The main structure of this embodiment is the same as any one of embodiments 1 to 12. Furthermore, in step S8, the selected optimization strategy includes the Adam optimization strategy, the L-BFGS optimization strategy, or the Adam and L-BFGS two-stage cascade optimization strategy.

[0205] When the Adam optimization strategy is selected, perform the following steps:

[0206] S8.1.1 Calculate the current network structure parameters gradient of the composite loss function ;

[0207] Composite loss function gradient The calculation formula is:

[0208]

[0209] In the formula: For the first The composite loss value of each training iteration; For the first The gradient vector of the training iteration has dimensions of... same;

[0210] S8.1.2, Based on the gradient of the composite loss function Update the first-order moment and the second-order moment;

[0211]

[0212]

[0213] In the formula: , The first The training iteration and the The first-order moment of the training iteration, =0; , The first The training iteration and the The second moment of training iteration, =0; This is the first-order moment decay rate, used to control the exponential decay rate of the first-order moment estimation of the gradient; The second-order moment decay rate is used to control the exponential decay rate of the second-order moment estimation based on the squared gradient. In this embodiment, the first-order moment decay rate... The preferred value is 0.9, the second moment decay rate. The preferred value is 0.999.

[0214] S8.1.3 Since the initial values ​​of the first and second moments are usually set to 0, there is an estimation bias in the early stage of training. Therefore, the bias correction formula is used to correct the first and second moments to obtain the corrected first moment. and modified second moment ;

[0215] The deviation correction formula is:

[0216]

[0217]

[0218] In the formula: , They are respectively , of Power;

[0219] As the number of training iterations increases, the correction coefficient... , As the value approaches 1, the correction effect gradually becomes negligible;

[0220] S8.1.4. Update network structure parameters based on the corrected first-order moment and the corrected second-order moment. ;

[0221] Network structure parameters The update formula is:

[0222]

[0223] In the formula: , The first The training iteration, the... Network structure parameters for each training iteration; The learning rate is used to control the step size for each parameter update. This is a stabilizing term used to avoid a denominator of zero and improve numerical stability. In this embodiment, the learning rate... Preferred selection Stable terms Preferred selection .

[0224] When the L-BFGS optimization strategy is selected, the following steps are performed:

[0225] S8.2.1 Initialize queues S and Y, which are used to store the most recently... The parameter difference vector of the next iteration and gradient difference vector Let the upper limit of the queue be A. When the queue length exceeds A, the earliest stored vector will be automatically removed. In this embodiment, the upper limit A is preferably 10.

[0226] S8.2.2 Calculate the current network structure parameters gradient of the composite loss function ; The initial value is 0;

[0227] S8.2.3, Using the L-BFGS double recursive method, based on Given queues S and Y, calculate the search direction. ;

[0228] S8.2.4. Based on the strong Wolfe condition, perform a line search to determine the optimal step size along the search direction. In this embodiment, the Wolfe conditional parameter coefficients and the Armijo conditional coefficients are used. Preferred selection curvature condition coefficient The preferred value is 0.9;

[0229] S8.2.5, Based on step size Update network structure parameters ;

[0230]

[0231] S8.2.6 Calculate network structure parameters gradient at Then, the parameter difference vector and gradient difference vector generated in this iteration are stored in queues S and Y, respectively.

[0232] The formulas for calculating the parameter difference vector and the gradient difference vector are:

[0233]

[0234]

[0235] S8.2.6, Judgment Is it equal to the maximum number of iterations? Or, whether the L2 norm of the composite loss function gradient at the updated network structure parameters is less than the preset gradient convergence accuracy threshold. If yes, output the network structure parameters; otherwise, let... = +1, return to step S8.2.2.

[0236] In this embodiment, the maximum number of iterations The preferred value is 500, which is the gradient convergence accuracy threshold. Preferred selection .

[0237] When the two-stage cascaded optimization strategy of Adam and L-BFGS is selected, the first-stage Adam optimizer quickly completes the coarse convergence of parameters and simultaneously performs adaptive weight annealing, so that the network structure parameters enter the neighborhood of the better solution and λ reaches dynamic equilibrium.

[0238] Then, the algorithm switches to the L-BFGS optimizer, which directly uses the network structure parameters at the end of the first stage as the initial point. At the same time, it uses the λ value of the Adam stage annealing convergence and utilizes the approximate solution formed in the first stage to achieve a high-precision solution.

[0239] After each incremental step is completed, the system automatically saves the network parameters to the user-specified checkpoint file for recovery in case of unexpected training interruption.

[0240] Example 14:

[0241] The main structure of this embodiment is the same as any one of embodiments 1 to 13. Furthermore, during the training process, when the selected optimization strategy is the Adam optimization strategy or the Adam and L-BFGS two-stage cascade optimization strategy, the weight coefficients in the composite loss function need to be adjusted. Update the weighting coefficients. The initial value can be set to 1.0, that is, to constrain image consistency in the early stages of training. Physical compatibility constraints They have the same initial weights. During subsequent training, the weights are dynamically updated based on the magnitude of the gradients between the two weights with respect to the trainable parameters of the network. The specific update is based on the following criteria: If the current training iteration has reached the weight update iteration, calculate the image loss gradient and the physical loss weighted gradient, and update the weight coefficients based on the exponential moving average; otherwise, continue calculating the composite loss value using the current weight coefficients. In this embodiment, the weight coefficients are updated every 10 training iterations. Alternatively, depending on the loss convergence, the update frequency can be set to every 10 to 100 training iterations. Preferably, the weight coefficients are updated every 10 training iterations.

[0242] Furthermore, the formula for calculating the image loss gradient is:

[0243] (26)

[0244] In the formula: The maximum absolute value of the gradient of the image consistency loss with respect to all trainable weight parameters of the network is given. All trainable parameters of the network include the connection weight matrix and bias vector from the input layer to the first hidden layer, the connection weight matrix and bias vector between adjacent hidden layers, and the connection weight matrix and bias vector from the last hidden layer to the output layer. These parameters are updated by the optimizer during training.

[0245] The formula for calculating the weighted gradient of physical loss is:

[0246] (27)

[0247] In the formula: This represents the current weighting coefficient; The mean of the absolute values ​​of the gradients of the physical compatibility loss, weighted by the current weight coefficients, with respect to all trainable parameters of the network;

[0248] The formula for updating the weight coefficients is:

[0249] (28)

[0250] In the formula: These are the weight coefficients updated in the current round;

[0251] This is a numerically stable term used to avoid... When the value is too small or zero, the denominator becomes zero or the weighting coefficients change abruptly. In this embodiment, Preferred selection This value is much smaller than the mean gradient during normal training and is only used for numerical stability, without substantially affecting the calculation of weight ratios. The momentum coefficient is used to smooth out the weighting coefficients. To prevent drastic weight oscillations between adjacent training iterations, this embodiment updates the weights. The optimal value is 0.9, which improves training stability while maintaining the ability to adaptively adjust weights.

[0252] In practical applications, Available ~ Select from the range, It can be selected within the range of 0.8 to 0.99.

[0253] Example 15:

[0254] The main structure of this embodiment is the same as any one of embodiments 1 to 14. Furthermore, the measurement system used includes a volume sequence loading and preprocessing unit, a material point coordinate tracking unit, a physical information neural network training unit, an adaptive weighted annealing calculation unit, and a full-field result output unit.

[0255] The volume sequence loading and preprocessing unit includes a volume reading module, a format conversion module, a normalization processing module, and a voxel coordinate grid construction module.

[0256] The volume reading module is used to batch convert multiple consecutive three-dimensional volume image files into four-bit arrays of shape (N, D, H, W), wherein the four-bit arrays are in NumPy or MATLAB format.

[0257] The format conversion module is used to convert a four-digit array into a floating-point number format.

[0258] The normalization module is used to standardize the gray value of each material point.

[0259] The voxel coordinate mesh construction module is used to construct a three-dimensional voxel coordinate mesh.

[0260] The material point coordinate tracking unit updates the three-dimensional coordinates of the material point step by step based on the prediction increment step, and after each step of coordinate update is completed, it updates the reference volume of the current step using the trilinear interpolation remapping method.

[0261] The physical information neural network training unit incorporates a physical information neural network. This network takes the three-dimensional coordinates of the current material point as input and outputs an incremental three-dimensional displacement field and a six-component strain field, iteratively optimizing and converging the composite loss function. During the iterative optimization process, the composite loss function is updated via an adaptive weighted annealing calculation unit.

[0262] The full-field result output unit includes a cumulative displacement field visualization module, a cumulative strain field visualization module, a three-dimensional rendering module, an equivalent strain calculation module, an automatic parameter recommendation module, and a data export module.

[0263] The cumulative displacement field visualization module is used to display the predicted cumulative displacement field. , , It generates a pseudo-color cloud map and can display slices in the three orthogonal cross-sectional directions of XY, XZ, and YZ, as well as at any percentage position.

[0264] The cumulative strain field visualization module is used to display the six-component strain field calculated from the central difference of the cumulative displacement field. , , , , , Orthogonal cross-section pseudo-color slice cloud map.

[0265] The 3D rendering module includes Delaunay triangulation convex hull shading mode, triorthogonal section mode, and scatter cloud mode.

[0266] The equivalent strain calculation module is used to calculate the three-dimensional equivalent strain. And based on three-dimensional equivalent strain Evaluate the overall degree of deformation of the object under test in three-dimensional space.

[0267] Three-dimensional equivalent strain The calculation formula is:

[0268] (29)

[0269] The three-dimensional equivalent strain As a dimensionless scalar, it is used to comprehensively characterize the three-dimensional six-component strain field as a single equivalent variable. The larger its value, the greater the overall deformation at that location. Since the deformation capacity varies under different materials, loading methods, and testing scales, there is no unique fixed threshold between the three-dimensional equivalent strain and the "large, medium, and small" deformation levels. Therefore, in this application, it is used as a configurable evaluation standard.

[0270] For ease of engineering application, this embodiment can adopt the following preferred classification:

[0271] when When this occurs, it is determined to be a small deformation area;

[0272] when At that time, it was determined to be a medium deformation area;

[0273] when When the condition is met, it is identified as a large deformation region. Users can also adjust the above thresholds according to the type of material being tested, the loading conditions, and the experimental calibration results.

[0274] The automatic parameter recommendation module integrates an image volume size-level parameter lookup table. In this embodiment, the total number of elements in the image volume S = D × H × W is used as the image volume size. The recommended parameter configuration is obtained by determining the position of the image volume size in the image volume size-level parameter lookup table. The recommended parameters include the number of hidden layers, the number of hidden layer nodes, and the number of training iterations.

[0275] Furthermore, the process of establishing the image volume scale-level parameter reference table is as follows: the image volume scale is segmented according to the scale threshold, and each segment is divided into several levels according to the image volume scale from small to large. Each level corresponds to a set of recommended parameter configurations.

[0276] When the volume size S input to the automatic parameter recommendation module falls into a certain level, the module automatically outputs recommended parameters such as the number of hidden layer nodes, the number of network layers, and the number of training iterations corresponding to that level. The higher the volume size level, the larger the recommended number of hidden layer nodes and network layers, and the more training iterations.

[0277] In this embodiment, the total number of pixels in the image volume S = D × H × W is used as the image volume size index. The volume size is divided into several levels from small to large according to a size threshold. Each level corresponds to a set of recommended parameter configurations. The higher the volume size level, the larger the recommended number of hidden layer nodes and network layers, and the more training iterations. The size threshold and the number of levels can be flexibly adjusted according to actual hardware conditions, image size distribution, and accuracy requirements. The default recommended parameter configurations are as follows: For small volumes, the recommended number of hidden layer nodes is 32, the number of network layers is 3, the Adam optimization rounds are 1000, and the L-BFGS optimization rounds are 50; for small to medium volumes, the recommended number of hidden layer nodes is 40, the number of network layers is 4, the Adam optimization rounds are 1500, and the L-BFGS optimization rounds are 100; for medium to large volumes, the recommended number of hidden layer nodes is 64, the number of network layers is 5, the Adam optimization rounds are 2000, and the L-BFGS optimization rounds are 150; for large volumes, the recommended number of hidden layer nodes is 80, the number of network layers is 6, the Adam optimization rounds are 2500, and the L-BFGS optimization rounds are 200. The above default recommended parameter configurations and size thresholds can be adjusted according to actual hardware conditions and accuracy requirements.

[0278] The data export module supports four export formats: NumPy compressed array format, MATLAB matrix file format, VTK legacy format, and CSV statistical table format.

[0279] Example 16:

[0280] The main structure of this embodiment is the same as that of embodiment 15. Furthermore, the physical information neural network adopts a fully connected neural network structure, including an input layer, an output layer and several hidden layers.

[0281] The input layer receives three-dimensional normalized coordinates ( );

[0282] Each hidden layer consists of a fully connected linear transformation and a hyperbolic tangent activation function, which restricts the neuron output to the (-1, 1) interval.

[0283] The output layer is a linear layer without an activation function, with an output dimension of 9, corresponding to incremental displacements in the X direction. incremental displacement in the Y direction Incremental displacement in the Z direction and six strain components , , , , , .

[0284] The weight matrices of the hidden layer and the output layer are initialized using a uniform Xavier distribution, and the biases are initialized to zero.

[0285] Example 17:

[0286] The main structure of this embodiment is the same as any one of embodiments 1 to 16. Further, the measurement system includes a volume sequence loading and preprocessing unit, a material point coordinate tracking unit, a physical information neural network training unit, an adaptive weighted annealing calculation unit, a composite loss function calculation unit, and a full-field result output unit.

[0287] The volume sequence loading and preprocessing unit reads a multi-frame continuous three-dimensional volume image sequence of the internal structure of the object under test, converts the volume data into a standardized floating-point format and performs grayscale normalization processing, and establishes a regularized voxel coordinate grid corresponding to the three-dimensional size of the volume to provide an initial coordinate reference for subsequent material point tracking.

[0288] The volume sequence loading and preprocessing unit includes a volume reading module, a format conversion module, a normalization processing module, and a voxel coordinate grid construction module;

[0289] The volume reading module supports reading NumPy 3D array format files and MATLAB matrix format files. For MATLAB format files, the system automatically identifies the main data variables in the file and transposes them into a row-major 3D array according to the depth, height, and width order to ensure the consistency of the coordinate axis directions.

[0290] The format conversion module converts the read three-dimensional array into a floating-point format to meet the numerical precision requirements of subsequent neural network calculations.

[0291] The normalization module standardizes the volume grayscale values ​​to ensure that the numerical distribution meets the input requirements of the neural network.

[0292] The voxel coordinate mesh construction module uses volume depth D, height H, and width W as parameters to generate a three-dimensional regular coordinate mesh through a three-dimensional meshing operation. The X coordinate range of the mesh nodes is [0, W-1], the Y coordinate range is [0, H-1], and the Z coordinate range is [0, D-1], serving as the initial three-dimensional spatial coordinate reference for all material points. After loading all volumes, the system automatically performs a consistency check on the three-dimensional dimensions of each frame's volume. If any frame's depth, height, or width is found to be inconsistent with the first frame, loading is immediately terminated and the user is prompted.

[0293] The material point coordinate tracking unit maintains and gradually updates the three-dimensional spatial coordinates of each material point under the current configuration. By continuously superimposing the three-dimensional displacement components predicted in each incremental step onto the material point coordinates, it realizes an incremental three-dimensional deformation description based on the current configuration, and updates the current reference volume synchronously with trilinear interpolation remapping after each step.

[0294] The material point coordinate tracking unit adopts an incremental update strategy. After each incremental step of training, the predicted incremental displacements in the X, Y, and Z directions of the current step are superimposed onto the current three-dimensional coordinates of the material point, that is:

[0295] = + (4)

[0296] = + (5)

[0297] = + (6)

[0298] in, , and For the first The current three-dimensional spatial coordinates of the material point at the end of the step. , and For the first The three incremental displacement components predicted step by step; , , For the first The current three-dimensional spatial coordinates of the material point at the end of the step;

[0299] The cumulative displacement is calculated from the difference between the current coordinates and the initial coordinates of the material point:

[0300] (7)

[0301] (8)

[0302] (9)

[0303] in, , and These are the initial coordinates of the voxel coordinate grid.

[0304] After each incremental step of training is completed, the material point coordinate tracking unit applies trilinear interpolation voxel remapping to the reference volume of the previous step with the incremental three-dimensional displacement field predicted in the current step, and uses the remapping result as the reference volume for the next incremental step, thereby achieving a strict update of the current configuration reference.

[0305] The physical information neural network training unit takes the normalized three-dimensional coordinates of the material point under the current configuration as input and the incremental three-dimensional displacement field and six-component strain field as output, and makes the composite loss function converge through iterative optimization.

[0306] The physical information neural network training unit is a standard fully connected feedforward neural network structure. The input layer receives three-dimensional normalized voxel coordinates, which are calculated from the original voxel coordinates using the following formula:

[0307] (1)

[0308] (2)

[0309] (3)

[0310] The normalized coordinates all take values ​​in the range [0,1].

[0311] The output layer simultaneously outputs incremental displacement in the X direction. incremental displacement in the Y direction Incremental displacement in the Z direction and six strain components , , , , , There are nine physical quantities in total. No activation function is used in the output layer. The hidden layers use the hyperbolic tangent activation function. The weight matrices of all linear layers are initialized with a uniform Xavier distribution, and the biases are initialized to zero.

[0312] The composite loss function calculation unit integrates the three-dimensional volume image grayscale consistency constraint and the three-dimensional displacement strain physical compatibility constraint, and constructs a unified optimization objective function by weighted summation with adaptive weight coefficients.

[0313] The composite loss function calculation unit constructs the following composite loss function:

[0314] (twenty three)

[0315] Where λ is the weighting coefficient.

[0316] The image consistency constraint By applying a predicted incremental displacement field to the current reference volume and performing trilinear interpolation reconstruction, the reconstructed volume is compared with the target deformed volume voxel by voxel, and the mean square of the gray-level difference over the entire domain is calculated.

[0317] (twenty four)

[0318] in, It is the set of all voxels within the domain. The total number of voxels. To reconstruct the volume, For the target volume;

[0319] The physical compatibility constraints This is achieved by comparing the differences between the six strain components directly predicted by the neural network and the strain estimates calculated by the central difference of the displacement field:

[0320] (25)

[0321] The physical information neural network training unit supports three optimization strategies:

[0322] The first is the Adam optimization strategy, which, combined with an adaptive learning rate scheduling mechanism, automatically reduces the learning rate when the loss function does not decrease within a set number of rounds.

[0323] The second approach is the L-BFGS optimization strategy, which employs a strong Wolfe conditional line search method and utilizes historical gradient information to construct a curvature approximation. This approach has a faster convergence speed in regions where the loss function is close to a quadratic form.

[0324] The third approach is a two-stage cascaded optimization strategy using Adam and L-BFGS. In the first stage, the Adam optimizer completes the coarse convergence of parameters and simultaneously performs adaptive weight annealing. In the second stage, the L-BFGS optimizer is switched to perform a fine-grained solution. The second stage directly uses the network parameters at the end of the first stage as the initial point, without the need for re-initialization, and uses the λ value converged by the annealing in the first stage as a fixed weight, thus achieving a seamless connection between coarse convergence and fine-grained solution.

[0325] The adaptive weighted annealing calculation unit dynamically evaluates the gradient magnitudes of image consistency loss and physical compatibility loss during training, and adjusts the weight coefficients of the two types of constraints in real time through an exponential moving average mechanism to ensure that the gradient contributions of the two types of losses are in a dynamic balance during the optimization process.

[0326] The adaptive weight annealing calculation unit performs a weight update operation every fixed training epoch during the Adam optimization phase. First, it calculates the maximum absolute value of the gradient of the image consistency loss with respect to all trainable weight parameters of the network. And the mean absolute value of the gradient of the current λ-weighted physical compatibility loss with respect to all trainable weight parameters of the network. The weighting coefficients are then updated according to the exponential moving average formula:

[0327] (28)

[0328] in, The momentum coefficient, It is a numerically stable term;

[0329] The update mechanism maintains a dynamic balance between image loss and physical loss in terms of gradient magnitude, fundamentally avoiding the problem of network training being biased towards a single constraint due to the significant difference in gradient magnitude between the two types of losses.

[0330] In the two-stage optimization strategy, the λ value at the end of the Adam training stage is passed to the L-BFGS stage as a fixed value, serving as a constant weight coefficient for the refinement solution stage.

[0331] The full-field result output unit provides multi-mode three-dimensional visualization of the cumulative three-dimensional displacement field, the cumulative six-component strain field, and the equivalent strain, and supports exporting the analysis results in multiple formats.

[0332] The full-field result output unit includes a cumulative displacement field visualization module, a cumulative strain field visualization module, a three-dimensional rendering module, an equivalent strain calculation module, an automatic parameter recommendation module, and a data export module.

[0333] The 3D rendering module provides three rendering modes:

[0334] The first method is the Delaunay triangulation convex hull coloring mode, which extracts convex hull patches after performing Delaunay triangulation on sparsely sampled grid points, and maps the distribution of physical quantity values ​​with the patch colors.

[0335] The second type is the three orthogonal section mode, which simultaneously displays a pseudo-color cloud map of three orthogonal sections XY, XZ and YZ passing through the center of the volume in three-dimensional space.

[0336] The third type is the scattered cloud mode, which uses the color of sparse sampling points to map physical quantity values ​​and enhances the three-dimensional effect through depth shading.

[0337] The equivalent strain calculation module calculates the three-dimensional equivalent strain index according to the following formula:

[0338] (29)

[0339] The automatic parameter recommendation module automatically provides recommended parameter configurations for the network hidden layer width, the number of network layers, and the number of training epochs based on the overall number of elements in the three-dimensional volume and segmented according to thresholds.

[0340] The data export module supports exporting the cumulative displacement field and strain field at each step in four formats: NumPy compressed array format, MATLAB matrix file format, VTK legacy format, and CSV statistical table.

[0341] The method for using the system to measure large deformation across the entire field includes the following steps:

[0342] Step 1: Load the three-dimensional volume image sequence of the deformation process of the object under test, perform format conversion and grayscale normalization, and construct the initial three-dimensional voxel coordinate grid;

[0343] Step 2: Set network structure parameters, training epochs, learning rate and optimization strategy, or automatically obtain recommended parameter configurations based on the three-dimensional volume size through the automatic parameter recommendation module;

[0344] Step 3: Using the volume of the first frame in the sequence as the initial reference volume, initialize the three-dimensional coordinates of the material points to a voxel coordinate grid;

[0345] Step 4: For each incremental step, input the normalized three-dimensional coordinates of the current material point into the physical information neural network to predict the incremental three-dimensional displacement field and the six-component strain field;

[0346] Step 5: Dynamically update the weight coefficients λ using the adaptive weight annealing mechanism, calculate the composite loss function, and iteratively update the network parameters using the selected optimization strategy until the loss function reaches the convergence criterion.

[0347] Step 6: Update the three-dimensional coordinates of the material point with the incremental three-dimensional displacement predicted in the current step, and update the current reference volume to the deformed volume after trilinear interpolation and remapping;

[0348] Step 7: Repeat steps 4 to 6 until all incremental steps in the sequence have been processed;

[0349] Step 8: Summarize the accumulated three-dimensional displacement field and accumulated six-component strain field from each step, calculate the three-dimensional equivalent strain, display the full-field measurement results through the three-dimensional visualization module, and export the analysis data in the selected format.

[0350] In this embodiment, the object to be tested includes, but is not limited to, porous metallic materials, rock-like geological materials, biological hard tissues such as bones, biological soft tissues such as cartilage and soft tissues, and composite material laminated structures. It is suitable for large deformation full-field deformation analysis of three-dimensional volume image sequences obtained by means of X-ray computed tomography, synchrotron radiation tomography, and neutron tomography.

[0351] The trilinear interpolation volume reconstruction process in step 5 is as follows: For any voxel coordinate within the volume domain ( Apply a predicted incremental three-dimensional displacement field ( , , ), to obtain the sampling coordinates ( ),in = - , = - , = - ;set up =floor( ), =floor( ), =floor( ), = +1, = +1, = +1, the decimal part of the coordinates is = - , = - , = - Trilinear interpolation is then performed in three steps:

[0352] The first step is to perform 4-order linear interpolation on the 8-neighbor voxels along the X direction:

[0353] (16)

[0354] (17)

[0355] (18)

[0356] (19)

[0357] The second step is to perform two linear interpolations along the Y direction:

[0358] (20)

[0359] (twenty one)

[0360] The third step is to perform a linear interpolation along the Z direction to obtain the final voxel grayscale value of the reconstructed volume:

[0361] (twenty two)

[0362] in, to The gray values ​​are represented by 8 neighboring voxels, with the numbers 0 and 1 in the subscripts corresponding to the low-index and high-index neighboring voxels in the corresponding direction, respectively; the gradient computability is maintained throughout the interpolation process, supporting backpropagation training.

[0363] The reference volume update strategy in step 6 follows the current configuration principle. After each incremental step of training is completed, the incremental three-dimensional displacement field predicted by the neural network in the current step is used to perform three-dimensional voxel remapping on the reference volume of the previous step. The remapped volume is used as the reference volume for the next incremental step, so that the network always uses the current deformation state as the basis for incremental analysis in each step.

[0364] By employing the above strategy, the deformation amount in each incremental step is controlled within a small range, satisfying the assumption of local small deformation. This transforms the large deformation measurement problem into a stepwise solution problem over several small incremental steps, ensuring the accuracy and robustness of the three-dimensional full-field analysis results under large deformation conditions.

[0365] Example 18:

[0366] The main structure of this embodiment is the same as any one of embodiments 1 to 17. Furthermore, the purpose of this invention is to provide a large deformation full-field deformation measurement method based on incremental artificial intelligence digital volume correlation, so as to overcome the defects of existing technology such as insufficient measurement accuracy in large deformation three-dimensional scenes, imbalance of two types of constraint gradients, separation of displacement and strain calculations, and inability to effectively track the three-dimensional motion history of material points.

[0367] The apparatus used in this method includes a volume sequence loading and preprocessing unit, a material point coordinate tracking unit, a physical information neural network training unit, an adaptive weighted annealing calculation unit, a composite loss function calculation unit, and a full-field result output unit.

[0368] The volume sequence loading and preprocessing unit is responsible for reading a series of continuous three-dimensional volume images of the internal structure of the object under test, converting the volume data into a floating-point format and performing grayscale normalization, and establishing a regularized voxel coordinate grid corresponding to the three-dimensional dimensions of the volume to provide an initial coordinate reference for subsequent material point tracking. The system supports reading two types of data files: NumPy three-dimensional array format and MATLAB matrix format, and automatically verifies the consistency of three-dimensional dimensions for all loaded volumes.

[0369] After each incremental step of training, the material point coordinate tracking unit superimposes the predicted three-dimensional incremental displacement onto the current three-dimensional coordinates of the material point, so that the material point coordinates are continuously updated with the deformation process, always reflecting the true three-dimensional spatial position of the material point under the current configuration. After each step, the reference volume is remapped by trilinear interpolation using the predicted incremental displacement field to achieve synchronous update of the reference volume of the current configuration.

[0370] The physical information neural network training unit takes the normalized three-dimensional coordinates of the material point under the current configuration as input and simultaneously outputs nine physical quantities, including three incremental displacement components and six strain components. It supports three optimization strategies: Adam, L-BFGS, and two-stage cascade.

[0371] The adaptive weighted annealing calculation unit monitors the gradient magnitudes of image consistency loss and physical compatibility loss in real time during the Adam optimization phase. It dynamically adjusts the physical loss weight coefficient λ using the exponential moving average formula to ensure that the two types of constraints maintain a dynamic balance in the gradient space, thus avoiding the optimization process from being biased towards a single type of constraint.

[0372] The composite loss function calculation unit integrates the three-dimensional volume image grayscale consistency constraint and the three-dimensional displacement strain physical compatibility constraint into a single objective function, and then sums them using adaptive weight coefficients.

[0373] The full-field result output unit provides multiple forms of visualization of the accumulated three-dimensional displacement field, accumulated six-component strain field and equivalent strain. It offers three three-dimensional rendering modes: Delaunay triangulation convex hull coloring, three orthogonal sections and scattered point clouds. It also supports exporting analysis results in multiple formats such as NumPy compressed arrays, MATLAB matrices, VTK and CSV.

[0374] Furthermore, the volume sequence loading and preprocessing unit has an automatic volume sequence integrity check function. After loading is completed, the system automatically compares whether the depth, height and width of each frame volume are completely consistent with the first frame. If a size mismatch is found, loading is immediately terminated and the user is prompted to prevent calculation errors caused by subsequent misalignment of the three-dimensional coordinate system.

[0375] Furthermore, the reference volume update mechanism of the material point coordinate tracking unit performs three-dimensional voxel remapping on the reference volume of the previous step after each incremental step, using the incremental three-dimensional displacement field predicted in the current step. The remapping result is used as the reference volume for the next step, thereby achieving a strict update of the current configuration reference and ensuring the effectiveness of three-dimensional volume image matching under large deformation conditions.

[0376] Furthermore, the trilinear interpolation module in the physical information neural network training unit performs three-step weighted interpolation on the 8-neighbor voxels of the sampling coordinates, performing linear interpolation sequentially along the X, Y, and Z directions. The interpolation weights are determined by the fractional part of the sampling coordinates. The interpolation process maintains gradient computability throughout and supports backpropagation training.

[0377] Furthermore, when calculating physical compatibility constraints, the composite loss function calculation unit uses the central difference method to approximate the spatial partial derivatives of the three-dimensional displacement field, and only calculates the voxels inside the volume, excluding the voxels around the boundary, in order to ensure the accuracy of the difference and avoid boundary effects from contaminating the results.

[0378] Furthermore, the automatic parameter recommendation module in the full-field result output unit provides recommended configurations for network width, number of layers, and training epochs in segments according to the total number of elements in the input volume and scale thresholds, so that users can obtain reasonable initial parameter settings without professional parameter tuning experience.

[0379] Example 19:

[0380] The main structure of this embodiment is the same as any one of embodiments 1 to 18. Further, see [link to embodiment 1]. Figures 1 to 7 A method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation is proposed. The device used includes a volume sequence loading and preprocessing unit, a material point coordinate tracking unit, a physical information neural network training unit, an adaptive weighted annealing calculation unit, a composite loss function calculation unit, and a full-field result output unit.

[0381] like Figure 1 As shown, the above units are connected sequentially according to the data flow direction, together forming a complete three-dimensional full-field deformation measurement process for large deformation.

[0382] After the volume sequence is processed by the loading and preprocessing unit, the image data and voxel coordinate grid information are input into the physical information neural network training unit.

[0383] The prediction results output by the physical information neural network training unit are simultaneously fed into the composite loss function calculation unit and the material point coordinate tracking unit.

[0384] The adaptive weighted annealing calculation unit continuously provides dynamically updated weight coefficients λ to the composite loss function calculation unit.

[0385] The loss function guides the iterative update of network parameters, while the coordinate tracking unit maintains the current 3D position of the material points and updates the reference volume synchronously. The full-field results output unit summarizes the results from each step and completes 3D visualization and multi-format data export.

[0386] The volume sequence loading and preprocessing unit includes a volume reading module, a format conversion module, a normalization processing module, and a voxel coordinate grid construction module.

[0387] The volume reading module supports reading two types of 3D volume data: NumPy format files and MATLAB format files. For MATLAB format files, the system automatically identifies the main data variables in the file and transposes them into a row-major 3D array according to the depth, height, and width order, ensuring that the coordinate axis directions are consistent with those of the NumPy format data.

[0388] The format conversion module converts the read three-dimensional array into a floating-point format to ensure the numerical accuracy of subsequent calculations.

[0389] The normalization module standardizes the volume grayscale values ​​to ensure that the numerical distribution meets the input requirements of the neural network.

[0390] The voxel coordinate mesh construction module uses volume depth D, height H, and width W as parameters to generate a three-dimensional regular coordinate mesh through a three-dimensional meshing operation. The X coordinate range of the mesh node is [0, W-1], the Y coordinate range is [0, H-1], and the Z coordinate range is [0, D-1], which serves as the initial three-dimensional spatial coordinate reference for all material points.

[0391] After the system loads the entire volume, it automatically checks the consistency of the three-dimensional dimensions of each frame. If the depth, height, or width of any frame does not match the first frame, the loading is immediately terminated and the user is notified to prevent calculation errors caused by misalignment of the subsequent three-dimensional coordinate system.

[0392] The working principle of the material point coordinate tracking unit is as follows: Figure 2 As shown. Before the analysis begins, the system initializes the coordinate matrices of the material points in the X, Y, and Z directions to the corresponding coordinate components of the voxel coordinate grid.

[0393] In the After each incremental step of training is completed, the incremental displacement field predicted by the neural network is extracted. , , Update the current coordinates of the material point in the X, Y, and Z directions according to equations (4), (5), and (6), respectively.

[0394] The cumulative displacement field is calculated by the difference between the current material point coordinates and the initial coordinates according to equations (7), (8), and (9), reflecting the entire displacement history of the material point from the initial state to the current state.

[0395] At the same time, a three-dimensional voxel remapping is applied to the reference volume of the previous step using the incremental three-dimensional displacement field predicted in the current step, and the remapping result is used as the first... The system uses a reference volume for each step, thus enabling gradual updates to the reference configuration and ensuring that the neural network operates within the assumption of local small deformations at each step. Through this mechanism, the system decomposes the macroscopic large deformation problem into several small deformation subproblems that hold true under the current local configuration, achieving an accurate description of the entire large deformation process while ensuring physical plausibility.

[0396] The network structure of the physical information neural network training unit is as follows: Figure 3 As shown, this is a standard fully connected feedforward neural network.

[0397] The input layer receives three-dimensional normalized coordinates ( The normalization operation maps the original voxel coordinates to the [0,1] interval according to equations (1), (2), and (3), thus eliminating the influence of volume size on the network input magnitude.

[0398] The network consists of several hidden layers connected in series. Each hidden layer is composed of a fully connected linear transformation and a hyperbolic tangent activation function. The hyperbolic tangent function restricts the neuron output to the (-1,1) interval, has good gradient propagation characteristics, and is suitable for expressing smooth displacement and strain field distributions.

[0399] The output layer is a linear layer without an activation function, with an output dimension of 9, corresponding to an increment x shift. Incremental Y-displacement Incremental Z-displacement positive strain positive strain positive strain Shear strain Shear strain and shear strain .

[0400] The weight matrices of all linear layers are initialized using a uniform Xavier distribution, and the biases are initialized to zero. Xavier initialization automatically determines the weight initialization range based on the number of input and output nodes in the layer, effectively avoiding the gradient vanishing and gradient exploding problems in deep networks.

[0401] The displacement component output by the network is used for trilinear interpolation volume reconstruction to calculate the image consistency loss, while the strain component is compared with the strain estimate obtained from the center difference of the displacement field to calculate the physical compatibility loss. The joint output of displacement and strain enables synchronous self-supervised training of the two physical quantities.

[0402] The workflow of the adaptive weighted annealing calculation unit is as follows: Figure 4 As shown.

[0403] During the Adam optimization phase, a weight update operation is performed every fixed number of training rounds.

[0404] Specifically, the system first addresses the image consistency loss. Backpropagation is performed on all trainable weight parameters of the network, traversing the gradients of each layer's weights, and extracting the maximum value among the absolute values ​​of all weight gradients. This metric reflects the magnitude of the gradient in the direction where the image loss has the strongest impact on the network parameters.

[0405] Then regarding the current situation Weighted physical compatibility loss Perform backpropagation to extract the global mean of the absolute values ​​of the weight gradients of each layer. This metric reflects the average gradient contribution of physical loss to network parameters.

[0406] The weight coefficients are updated using an exponential moving average method according to equation (28). The momentum coefficient β controls the smoothness between historical values ​​and current estimates, while the numerical stability term ε prevents numerical anomalies where the denominator is zero.

[0407] The physical meaning of the above mechanism is that when the maximum gradient of the image loss is much greater than the weighted average gradient of the physical loss, it indicates that the effective influence of the physical constraints is relatively insufficient. In this case, increasing the weighted average gradient of the physical loss is necessary. To enhance the influence of physical constraints. Conversely, to reduce them. To avoid physical constraints excessively dominating the optimization direction, a dynamic balance between the two types of constraints in the gradient space is maintained at all times. During the L-BFGS refinement solution stage, The convergence value at the end of the Adam phase is fixed, and annealing updates are no longer performed to ensure that the optimization direction in the refinement phase remains stable and consistent.

[0408] The workflow of the composite loss function calculation unit is as follows: Figure 6 As shown, the calculation is divided into two branches: three-dimensional image consistency constraint and three-dimensional physical compatibility constraint. Finally, the total loss is obtained by weighted summation using the adaptive weight coefficient λ, and calculated according to equation (23).

[0409] The calculation process for the image consistency constraint branch is as follows:

[0410] First, the incremental 3D displacement components of the network output are extracted and reconstructed into a 3D displacement tensor corresponding to the volume size. Then, this displacement field is applied to the coordinates of each voxel in the current reference volume to obtain sampled coordinates, which are then processed by trilinear interpolation (see...). Figure 5 Calculate the grayscale values ​​of each voxel in the reconstructed volume to obtain the reconstructed deformed volume. .

[0411] Reconstruct volume With the target deformation volume The image consistency loss is obtained by subtracting voxels one by one and squaring the results, and then averaging the results over the entire domain. Calculate according to formula (24).

[0412] Image consistency loss-driven network learning can accurately describe the displacement mapping relationship of volume grayscale field changes, and is the core data driving force of the entire self-supervised training process.

[0413] The calculation process for the physical compatibility constraint branch is as follows:

[0414] The incremental three-dimensional displacement field output by the network is extracted, and central differences are applied to the X displacement u, Y displacement v, and Z displacement w in the X, Y, and Z directions, respectively, resulting in a total of 9 partial derivative components: , , , , , , , , .

[0415] Based on the geometric equations under the small deformation assumption, and using the aforementioned partial derivatives, a six-component strain estimate based on the displacement gradient is constructed, where the normal strain estimate is... , , The shear strain is estimated to be 0.5 ( + ), 0.5 + ), 0.5 + The above strain estimates are compared with the six strain components directly output by the network. , , , , , Subtracting element by element and squaring the results, then averaging the results over the effective internal volume domain and summing them up, yields the physical compatibility loss. Calculate according to formula (25).

[0416] Physical compatibility constraints ensure that the strain components directly output by the network and the gradient of the displacement field satisfy the requirements of the geometric equations of continuum mechanics, thus achieving physical self-consistency between the displacement field and strain field predictions.

[0417] like Figure 5 As shown, the trilinear interpolation module performs three-step weighted interpolation on the 8-neighbor voxels of the sampled coordinates according to equations (16) to (22):

[0418] The first step is to perform four linear interpolations along the X direction, and then weight and merge the gray values ​​of the eight voxels into four intermediate values.

[0419] The second step involves performing two linear interpolations along the Y direction, further weighting the four intermediate values ​​pairwise and merging them into two intermediate values.

[0420] The third step involves performing a linear interpolation along the Z-axis to obtain the final reconstructed volume voxel grayscale values. Gradient computability is maintained throughout the process to support backpropagation.

[0421] The physical information neural network training unit supports three optimization strategies. The Adam optimization strategy, combined with an adaptive learning rate scheduler, automatically reduces the current learning rate by a certain proportion when the loss function does not decrease within several consecutive training epochs. This allows the training process to automatically reduce the step size during the loss plateau period in order to find a better extreme value. At the same time, it dynamically adjusts λ in conjunction with an adaptive weight annealing mechanism throughout the Adam phase.

[0422] The L-BFGS optimization strategy employs a strong Wolfe conditional line search and utilizes historical gradient information to construct a low-rank approximation of the Hessian matrix. It exhibits a fast superlinear convergence speed in regions where the loss function is close to a quadratic form, making it suitable for refined solutions when good initial values ​​are available.

[0423] The two-stage cascaded optimization strategy comprehensively balances convergence speed and solution accuracy:

[0424] In the first stage, the Adam optimizer quickly completes coarse parameter convergence and simultaneously performs adaptive weight annealing, which allows the network parameters to enter the neighborhood of the better solution and makes λ reach dynamic equilibrium.

[0425] The system then seamlessly switches to the L-BFGS optimizer, using the network parameters at the end of the first stage as the initial point. It also maintains a fixed λ value for convergence during the Adam stage annealing, fully utilizing the approximate solution formed in the first stage to achieve a refined and high-precision solution. After each incremental step, the system automatically saves the network parameters to a user-specified checkpoint file for recovery in case of unexpected training interruptions.

[0426] The full-field result output unit includes a cumulative displacement field visualization module, a cumulative strain field visualization module, a 3D rendering module, an equivalent strain calculation module, an automatic parameter recommendation module, and a data export module. The measurement results are illustrated below. Figure 7 As shown. Among them, Figure 7 Each column corresponds to the full-field measurement results of the 1st, n / 2nd, and nth increment steps, respectively. The contour plot uses the JET pseudo-color scheme, with blue representing low values ​​and red representing high values. The color range of each row is based on the value range of the nth step. A complete three-dimensional displacement field is output. , , and six-component strain field ( (The image is omitted) , , , The distribution pattern of the four components is similar. The three-dimensional equivalent strain is calculated according to formula (29).

[0427] The cumulative displacement field visualization module displays pseudo-color cloud maps of the cumulative X displacement U, cumulative Y displacement V, and cumulative Z displacement W for each incremental step. It can display slices in the three orthogonal cross-sectional directions of XY, XZ, and YZ and at any percentage position. The color scale range is adaptively adjusted according to the data range of the current step, reflecting the evolution law of deformation as the incremental step progresses.

[0428] The cumulative strain field visualization module displays the six-component strain field calculated from the central difference of the cumulative displacement field. The formulas for the orthogonal cross-section pseudo-color slice cloud map are as follows:

[0429] (10)

[0430] (11)

[0431] (12)

[0432] (13)

[0433] (14)

[0434] (15)

[0435] Where i corresponds to the depth index in the Z direction, j corresponds to the height index in the Y direction, and k corresponds to the width index in the X direction.

[0436] The 3D rendering module offers three rendering modes.

[0437] The Delaunay triangulation convex hull coloring mode extracts convex hull patches after Delaunay triangulation of the sampled mesh points. The patch colors are used to map the distribution of physical quantity values, which can intuitively present the distribution of physical quantities on the outer surface of the three-dimensional volume.

[0438] The triorthogonal section mode simultaneously displays pseudo-color cloud maps of three orthogonal sections (XY, XZ, and YZ) passing through the center of the volume in three-dimensional space, and can simultaneously present the internal distribution characteristics of the three-dimensional field in three principal directions.

[0439] The scatter cloud mode maps physical quantity values ​​to the colors of sparse sampling points and enhances the three-dimensional effect through depth shading, making it suitable for quickly previewing the overall distribution trend of a three-dimensional field. All three modes support free adjustment of the viewing angle (elevation and azimuth) as well as flexible configuration of sampling step size, transparency, and color scheme.

[0440] The equivalent strain calculation module calculates the three-dimensional equivalent strain according to formula (29). This index comprehensively reflects the overall deformation degree of the material in three-dimensional space and is an important indicator for evaluating the deformation degree of the material.

[0441] The automatic parameter recommendation module provides recommended configurations based on the total number of elements in the volume and segmented by scale threshold, covering typical application scenarios from small to large size, so that users can obtain reasonable initial parameter settings without professional parameter tuning experience.

[0442] The data export module supports four export formats:

[0443] NumPy's compressed array format is suitable for subsequent data analysis in a Python environment.

[0444] The MATLAB matrix file format facilitates further processing within the MATLAB environment.

[0445] The VTK legacy format is organized in the STRUCTURED_POINTS format, with voxel spacing set to unit spacing, and can be directly imported into professional visualization software such as ParaView for 3D post-processing analysis.

[0446] The CSV statistical table exports the mean, standard deviation, maximum and minimum values ​​of physical quantities at each step, which facilitates rapid assessment of deformation evolution patterns and horizontal comparison of deformation states at different increment steps.

[0447] Example 20:

[0448] The main structure of this embodiment is the same as any one of embodiments 15 to 19. Furthermore, the volume sequence loading and preprocessing unit also includes a multi-frame sequence interactive preview function: after the volume loading is completed, the system automatically activates the sequence preview slider, and the user can drag the slider to browse the loaded volume sequence frame by frame.

[0449] The preview interface displays the three-dimensional grayscale distribution of the current frame simultaneously in the form of two-dimensional slice pseudo-color cloud maps of three orthogonal sections: XY, XZ, and YZ. It supports free adjustment of slice direction and slice position percentage, and the color scheme can be selected by the user from a variety of preset schemes.

[0450] During the preview process, the system synchronously displays the current frame number, volume 3D dimensions, and grayscale range on the interface, which facilitates intuitive verification of data quality, imaging uniformity, and sequence integrity before analysis, effectively avoiding training failures caused by poor data quality.

[0451] Example 21:

[0452] The main structure of this embodiment is the same as any one of embodiments 15-20. Furthermore, during each incremental step training process, the physical information neural network training unit outputs the current loss value to the log panel once every set number of training rounds.

[0453] The output includes the values ​​of image consistency loss, physical compatibility loss, and total loss, as well as the real-time value of the current adaptive weight coefficient λ.

[0454] The system synchronously and in real time plots the total loss evolution curve, image consistency loss curve, physical compatibility loss curve, and λ evolution curve. Users can judge whether the training is proceeding normally by observing the convergence shape of the loss curve.

[0455] If the loss curve exhibits abnormal oscillations or fails to converge for an extended period, the user can click the stop button at any time to interrupt the training of the current incremental step. The system will save all results of the completed steps to avoid wasting computational resources.

[0456] The system also supports training pause and resume operations. During the pause, the current state of network parameters, material point coordinates and current reference volume is fully maintained to ensure strict continuity of the training process before and after the pause.

[0457] Example 22:

[0458] The main structure of this embodiment is the same as any one of embodiments 15-21. Furthermore, the batch cloud map export function of the full-field result output unit supports batch export of two-dimensional slice cloud maps of all incremental steps and all physical quantities. Users can freely select the cutting direction (XY, XZ or YZ), slice position percentage, exported physical quantum set, image format (PNG, PDF, SVG or TIFF), output resolution and color scheme in the export configuration interface. The system uses a combination of step number and physical quantity name as the file naming prefix and saves all result images to the user-specified directory. During the export process, the current completion progress is displayed in real time with a progress dialog box. All result files are stored in order of step number, which facilitates subsequent step-by-step retrieval and batch processing, and completely records the field quantity evolution information of the entire large deformation process.

[0459] Example 23:

[0460] The main structure of this embodiment is the same as any one of embodiments 15 to 22. Furthermore, the physical information neural network training unit also includes a checkpoint saving function: after each incremental step training is completed, the system automatically saves the network parameter status, step number and current λ value of the current step to the user-specified directory in the form of a checkpoint file.

[0461] When training is interrupted unexpectedly, users can resume from the network parameter state of a specified step by loading checkpoints. The system reads the checkpoint file, restores the network parameters, and displays the step number and λ value corresponding to the restored checkpoint to the user. This avoids the significant time wastage caused by recalculating from scratch and has important practical value when dealing with long-term training tasks involving large-volume sequences.

[0462] Example 24:

[0463] The main structure of this embodiment is the same as any one of embodiments 1 to 23. Furthermore, the object to be tested includes, but is not limited to, porous metal materials such as aluminum foam and titanium alloy porous structures, rock geological materials such as sandstone and granite, carbon fiber reinforced resin matrix composite laminated structures, and biological hard tissues such as bones and biological soft tissues such as cartilage and tendons.

[0464] This system is suitable for processing three-dimensional volumetric image sequences obtained by X-ray computed tomography, synchrotron radiation tomography, and neutron tomography. It is particularly suitable for processing large deformation, ultra-large deformation, and material damage evolution scenarios where the deformation exceeds the applicable range of traditional digital volume correlation methods.

[0465] By using an incremental analysis framework and a current configuration reference update mechanism, this system transforms the large deformation problem into a small deformation problem that is solved step by step over several small incremental steps. Combined with an adaptive weighted annealing mechanism, the effectiveness of physical constraints is ensured throughout the training process. While ensuring physical rationality, this system achieves an accurate description of the three-dimensional displacement field and the six-component strain field throughout the large deformation process.

[0466] Example 25:

[0467] The main structure of this embodiment is the same as any one of embodiments 1 to 24. Furthermore, a method for measuring the large deformation full-field deformation of the system described herein includes the following steps:

[0468] Step 1: Start the system, click the volume sequence loading button, select multiple consecutive three-dimensional volume image files (no less than 2 frames) during the deformation process of the object to be tested. The system will automatically complete the format conversion, grayscale normalization processing and initial three-dimensional voxel coordinate grid construction, and automatically check the three-dimensional size consistency of all volume frames. After loading, the system will automatically activate the sequence preview function, and users can check the data quality and sequence integrity through the preview interface.

[0469] Step 2: In the training parameter panel, set the number of hidden layer nodes, number of network layers, training epochs and learning rate, or click the automatic parameter recommendation button, and the system will automatically provide recommended parameter configurations based on the three-dimensional size of the input volume;

[0470] In the optimizer selection drop-down menu, select Adam, L-BFGS, or Adam plus L-BFGS two-stage strategy, and configure the training rounds for each stage according to the selected strategy.

[0471] If you select the option to enable the checkpoint saving function and specify the save directory, the system will automatically save the network parameter checkpoint file after each incremental step, so that it can be restored in case of training interruption.

[0472] Step 3: Click the Start Training button. The system uses the volume of the first frame as the initial reference volume, initializes the three-dimensional coordinates of the material points to a voxel coordinate grid, and then executes the physical information neural network training step by step in increments.

[0473] During training, the system refreshes the total loss curve, component loss curves, adaptive weight λ evolution curve, and the current step's displacement and strain field preview slice cloud map in real time, allowing users to monitor training progress and convergence status in real time.

[0474] After each incremental step is completed, the system automatically updates the three-dimensional coordinates of the material point and the current reference volume, and saves the results of this step to the checkpoint file (if enabled).

[0475] Step 4: After all incremental steps are completed, browse the cumulative three-dimensional displacement field, cumulative six-component strain field and orthogonal cross-sectional pseudo-color cloud map of equivalent strain for each step in the result slice viewing tab using the step switching control and slice parameter control, and observe the deformation evolution process step by step.

[0476] Switch to the 3D field visualization tab, select the rendering mode (Delaunay convex hull, triorthogonal section or scattered cloud), target physical quantity and viewpoint parameters, click the render button to view the 3D full field distribution stereo effect, and observe from multiple angles by dragging the mouse to rotate the viewpoint.

[0477] The complete loss evolution curves and λ evolution history for each step can be reviewed in the training monitoring tab.

[0478] Step 5: Click the "Export Results" button, select the export format (NumPy compressed array, MATLAB matrix, VTK, or CSV), and specify the output directory. The system will automatically classify and save the cumulative displacement field, cumulative strain field, and equivalent strain data of all steps. If you need to export two-dimensional slice contour maps in batches, you can select the cutting direction, slice position, physical quantum set, image format, and output resolution through the batch export configuration interface. The system will automatically complete the batch export of contour maps of all steps and all physical quantities, completing the complete analysis process of large deformation three-dimensional full-field deformation measurement.

[0479] Example 26:

[0480] The main structure of this embodiment is the same as that of embodiment 25. Furthermore, in step 3, if the user finds that the loss curve oscillates abnormally or fails to converge for a long time during the training process, the user can click the pause button at any time to pause the training of the current increment step. The system will completely maintain the current state of the network parameters, the three-dimensional coordinates of the material points and the current reference volume.

[0481] After users adjust parameters such as learning rate, training rounds, or optimization strategies, they can click the continue button to resume training. The system will seamlessly resume training from the paused position, ensuring strict continuity of the training state before and after the pause.

[0482] You can also click the stop button to terminate all training. The system will save all the results of the completed steps completely. Users can view the results of the completed steps in a visual format and export them in a formatted way to avoid the loss of the completed calculation results.

Claims

1. A method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation, characterized in that, Includes the following steps: S1. Acquire multiple consecutive three-dimensional images of the object under test during its deformation process; The format of the 3D image is converted to obtain a floating-point format image array, and then the floating-point format image array is normalized to grayscale. S2. Based on the spatial dimension of the floating-point format image array, construct a three-dimensional voxel coordinate grid, obtain the coordinates of each voxel, and perform normalization processing to obtain three-dimensional normalized coordinates. S3. Set the training iteration rounds, network structure parameters, and optimization strategies; S4. Set the total number of increment steps. and initialize the increment step number. ,make =0; Setting the first The frame image volume is the reference volume for step 0; the volume is a three-dimensional array composed of the gray values ​​of each voxel in the image; the frame image volume is set to... The three-dimensional normalized coordinates of the frame image are the coordinates of the material point at step 0; The initial value is 1; S5, the first The coordinates of the material points are input into the physical information neural network to obtain the first... +1 step prediction of incremental three-dimensional displacement field and the first +1 step prediction of incremental strain field; The initial value is 0; No. +1 step prediction of incremental three-dimensional displacement field is ( , , ),in , , The first +1 step prediction of incremental displacements along the X, Y, and Z directions; the first step +1 step prediction of incremental strain field is ( , , , , , ),in , , The first +1 step prediction of incremental normal strain along the X, Y, and Z directions. , , The first +1 step prediction of incremental tangential shear strain along the XY plane, XZ plane, and YZ plane; The physical information neural network adopts a fully connected neural network structure, including an input layer, an output layer, and several hidden layers. The input layer receives three-dimensional normalized coordinates. Each hidden layer consists of a fully connected linear transformation and a hyperbolic tangent activation function, which restricts the neuron output to the (-1, 1) interval. The output layer is a linear layer without an activation function, with an output dimension of 9, corresponding to incremental displacement in the X direction. incremental displacement in the Y direction Incremental displacement in the Z direction and six strain components , , , , , The weight matrices of the hidden layer and the output layer are initialized using a uniform Xavier distribution, and the biases are initialized to zero. S6, based on the first +1 step predicts incremental displacement field, updates the 1st step +1 step material point coordinates; Based on the trilinear interpolation method, for the th The reference volume is remapped step by step to obtain the first step. +1 step reference volume; S7, Order = +1, judgment Is it equal to If so, output the first... Step the reference volume as the reconstructed volume, and simultaneously output the predicted cumulative displacement field and the predicted cumulative strain field, then proceed to step S8; otherwise, return to step S5. S8, the first The volume of the +1 frame image is used as the target volume. The composite loss value is calculated. It is determined whether the composite loss value is less than the threshold. If it is, proceed to step S9. Otherwise, the network parameters are updated based on the selected optimization strategy, and the process returns to step S5. S9, Order = +1, judgment Is it equal to the number of image frames acquired? If yes, proceed to step S10; otherwise, return to step S4. S10. Summarize and visualize the cumulative displacement and cumulative strain of each step, calculate the equivalent strain, and evaluate the overall deformation of the object under test in three-dimensional space.

2. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation as described in claim 1, characterized in that: In step S1, the object to be tested includes porous metallic materials, rock-like geological materials, skeletal hard tissue, biological soft tissue, and composite laminated structures.

3. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation as described in claim 1, characterized in that: In step S1, the format conversion includes: batch converting multiple consecutive 3D image files into a four-bit array of shape (T, D, H, W), where T is the number of captured frames, D is the image depth, H is the pixel height of a single slice, and W is the pixel width of a single slice; then, converting the four-bit array into a floating-point number format.

4. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation as described in claim 1, characterized in that: In step S2, The spatial dimension of the floating-point format image array includes image depth. Pixel height of a single slice and the pixel width of a single slice ; In the three-dimensional voxel coordinate grid, the origin is located at the corner of the first voxel (0, 0, 0) of the volume image. The X-axis extends along the width direction with a coordinate range of [0, W-1], the Y-axis extends along the height direction with a coordinate range of [0, H-1], and the Z-axis extends along the depth direction with a coordinate range of [0, D-1]. The side length of each voxel is 1. Three-dimensional normalized coordinates ( The formula for calculating ) is: （1） （2） （3） In the formula: ( () represents voxel coordinates; The range of the three-dimensional normalized coordinates is [0, 1].

5. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation according to claim 1, characterized in that: In step S6, the first +1 step material point coordinates ( The update formula for ) is: = + （4） = + （5） = + （6） In the formula: ( ) is the first The coordinates of the material point at the end of the step; In step S7, the cumulative displacement field is predicted ( , , The formula for calculating ) is: （7） （8） （9） In the formula: ( ) represents the initial voxel coordinates of the k-th frame image; () represents the coordinates of the substance point at the end of step n; Predicting cumulative strain field ( The formula for calculating ) is: （10） （11） （12） （13） （14） （15） In the formula: The depth index corresponding to the Z direction. The corresponding height index in the Y direction, Width index corresponding to the X direction.

6. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation according to claim 1, characterized in that, In step S6, the process of reconstructing the reference image volume based on trilinear interpolation is as follows: For any voxel coordinate within the volume domain ( Apply a predicted incremental three-dimensional displacement field ( , , ), to obtain the sampling coordinates ( ),in = - , = - , = - ; Let the sampling coordinates be ( The 8-neighbor voxel coordinates of ) are respectively ( ), ( ), ( ), ( ), ( ), ( ), ( ), ( The subscript numbers 0 and 1 of the coordinates represent the low-index and high-index neighborhood voxels in the corresponding directions, respectively, and the coordinates of the neighborhood voxels satisfy: =floor( ), =floor( ), =floor( ), = +1, = +1, = +1; Performing a fourth linear interpolation along the X direction on the 8-neighbor voxels yields: （16） （17） （18） （19） In the formula: , , , These are the four intermediate gray values ​​obtained after the first linear interpolation along the X direction; , , , , , , , These are the gray values ​​corresponding to the coordinates of the 8 neighboring voxels; The fractional part of the sampled coordinates along the X direction. = - ; Performing a second linear interpolation along the Y direction yields: （20） （21） In the formula: , These are two intermediate gray values ​​obtained after the second linear interpolation along the Y direction; To sample the decimal part of the coordinates along the Y direction, = - ; Perform a linear interpolation along the Z direction to obtain the reconstructed voxel gray value at the sampling coordinates. : （22） In the formula: The fractional part of the sampled coordinates along the Z direction. = - .

7. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation according to claim 1, characterized in that, In step S8, the composite loss value The function expression is: （23） （24） （25） In the formula: These are the weighting coefficients; Image consistency constraints; Physical compatibility constraints; It is the set of all voxels within the volume domain. ; The total number of voxels; To reconstruct the volume, For the target volume; ( () is used to predict the cumulative strain field; , , These are the central difference approximate partial derivatives of the cumulative displacement R along the X direction with respect to the initial voxel coordinates of the X, Y, and Z directions in the nth frame image, respectively. , , These are the approximate partial derivatives of the central difference of the cumulative displacement along the Y direction with respect to the initial voxel coordinates of the X, Y, and Z directions in the nth frame image, respectively. , , Let be the central difference approximate partial derivatives of the cumulative displacement along the Z direction with respect to the X, Y, and Z directions in the initial voxel coordinates of the nth frame image.

8. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation according to claim 1, characterized in that: In step S8, the selected optimization strategy includes the Adam optimization strategy, the L-BFGS optimization strategy, or the Adam and L-BFGS two-stage cascade optimization strategy. During training, when the selected optimization strategy is the Adam optimization strategy or the Adam and L-BFGS two-stage cascade optimization strategy, the weight coefficients in the composite loss function need to be adjusted. The update is performed based on the following criteria: If the current training iteration has reached the weight update iteration, calculate the image loss gradient and the physical loss weighted gradient, and update the weight coefficients based on the exponential moving average; otherwise, continue calculating the composite loss value using the current weight coefficients. ; The formula for calculating the image loss gradient is: （26） In the formula: The maximum absolute value of the gradient of the image consistency loss with respect to all trainable weight parameters of the network; The formula for calculating the weighted gradient of physical loss is: （27） In the formula: This represents the current weighting coefficient; The mean of the absolute values ​​of the gradients of the physical compatibility loss, weighted by the current weight coefficients, with respect to all trainable parameters of the network; The formula for updating the weight coefficients is: （28） In the formula: These are the weight coefficients updated in the current round; It is a numerically stable term; This is the momentum coefficient.

9. The method for measuring large deformation across the entire field based on incremental artificial intelligence digital volume correlation according to claim 1, characterized in that: The measurement system used includes a volume sequence loading and preprocessing unit, a material point coordinate tracking unit, a physical information neural network training unit, an adaptive weighted annealing calculation unit, and a full-field result output unit. The volume sequence loading and preprocessing unit includes a volume reading module, a format conversion module, a normalization processing module, and a voxel coordinate grid construction module; The volume reading module is used to batch convert multiple consecutive three-dimensional volume image files into four-bit arrays of shape (N, D, H, W), wherein the four-bit arrays are in NumPy or MATLAB format. The format conversion module is used to convert a four-digit array into a floating-point number format. The normalization processing module is used to standardize the gray value of each material point; The voxel coordinate mesh construction module is used to construct a three-dimensional voxel coordinate mesh; The material point coordinate tracking unit updates the three-dimensional coordinates of the material point step by step based on the prediction increment step, and after each step of coordinate update is completed, it updates the reference volume of the current step using the trilinear interpolation remapping method. The physical information neural network training unit has a built-in physical information neural network; the physical information neural network takes the three-dimensional coordinates of the current material point as input and the incremental three-dimensional displacement field and six-component strain field as output, and converges the composite loss function through iterative optimization; and updates the composite loss function through the adaptive weighted annealing calculation unit during the iterative optimization process. The full-field result output unit includes a cumulative displacement field visualization module, a cumulative strain field visualization module, a three-dimensional rendering module, an equivalent strain calculation module, an automatic parameter recommendation module, and a data export module. The cumulative displacement field visualization module is used to display the predicted cumulative displacement field. , , The pseudo-color cloud map can be displayed in slices at any percentage position in the three orthogonal cross-sectional directions of XY, XZ, and YZ. The cumulative strain field visualization module is used to display the six-component strain field calculated from the central difference of the cumulative displacement field. , , , , , Orthogonal cross-sectional pseudo-color slice cloud map; The 3D rendering module includes Delaunay triangulation convex hull shading mode, triorthogonal section mode, and scatter cloud mode; The equivalent strain calculation module is used to calculate the three-dimensional equivalent strain. And based on three-dimensional equivalent strain To assess the overall degree of deformation of the object under test in three-dimensional space; Three-dimensional equivalent strain The calculation formula is: （29） The automatic parameter recommendation module integrates an image volume size-level parameter lookup table. The total number of elements in the image volume S=D×H×W is used as the image volume size. The module determines the position of the image volume size in the image volume size-level parameter lookup table and obtains the recommended parameter configuration. The data export module supports four export formats: NumPy compressed array format, MATLAB matrix file format, VTK legacy format, and CSV statistical table format.

Images