DIC physical field compression storage and super-resolution reconstruction method

Abstract

The invention discloses a DIC physical field compression storage and super-resolution reconstruction method, which solves the problems of low temporal-spatial resolution and data missing caused by the influence of speckle shedding in a measurement result of a digital image correlation method, and also has challenges of data processing and storage. The invention provides a new PINN framework, namely NeRF-PINN, based on NeRF inspiration. The new PINN framework is used for compression modeling and space-time super-resolution reconstruction of DIC data. According to the method, discrete DIC measurement points are coded and a multivariable output neural network is trained, so that the whole deformation process is implicitly expressed as a continuous and differentiable function, and the compression ratio of 1000: 1 is realized. Finally, the network not only learns a deformation rule in a data-driven manner, but also enables a reconstruction result to better conform to a physical law by embedding physical constraints such as a strain coordination equation.

Description

TECHNICAL FIELD

[0001] The present application relates to a DIC physical field compression storage and super-resolution reconstruction method, belonging to the technical field of DIC data compression modeling and space-time super-resolution reconstruction. BACKGROUND

[0002] Digital image correlation (DIC) is a non-contact optical technique that can achieve full-field displacement and strain measurement by tracking the random speckle pattern on the surface of an object. Since its inception in the 1980s, it has been widely used in deformation monitoring of fiber-reinforced composites, concrete fracture, rock dynamic rupture, micro materials, high-temperature scenarios, and other fields. After several stages of development and evolution, DIC has become a widely used high-precision measurement tool in material mechanics and structural testing, and is one of the preferred optical measurement methods in experimental mechanics.

[0003] The core principle of DIC is to track the movement of the speckle pattern on the surface of an object. It uses the image taken before the object is deformed as the reference image and the image taken after the object is deformed as the deformed image. Then, the reference image and the deformed image are divided into subsets, and the similarity between the subsets is calculated using a correlation function to find the subset with the highest matching degree before and after deformation. The difference between the position vectors of these two subsets is the displacement vector. By tracking all subsets in the measurement area, a full-field displacement field can be obtained, and by differentiation, a strain field can be further obtained. Although DIC technology has achieved great success, it still faces several inherent limitations in practical applications.

[0004] (1) Low resolution and storage problem. The spatial resolution of DIC is determined by the size of the subset and the step size. In theory, smaller subsets and step sizes can resolve finer deformation details. However, as the basic unit of correlation matching, the subset must contain enough unique and rich speckle feature information to ensure the uniqueness and accuracy of the matching result. If the subset size is too small, the internal gray-scale information tends to be single, and it is easy to be disturbed by image noise during the matching process, leading to matching errors and significantly reducing the measurement accuracy. Therefore, to ensure the robustness of the matching, the subset size cannot be infinitely reduced, which fundamentally limits the highest effective spatial resolution that DIC can achieve. Excessive reduction of step size (i.e., high-density calculation) will cause the calculation cost to grow exponentially and generate a large amount of data, causing great pressure on data storage and post-processing. The same is true in the time dimension, as high-frequency recording not only increases the calculation load but also increases the pressure on data storage.

[0005] (2) Data missing problem. During the material testing process, there are various factors that can cause the correlation matching algorithm to fail, resulting in data "holes" in the final physical field. For example, during the large deformation or fracture process of the material, the speckle pattern of the local region can change dramatically due to stretching, peeling, or being covered by a crack, causing the deformed sub-region to lose correlation with the reference sub-region. In addition, sub-regions located at the free edge or geometric discontinuity of the specimen may have their partial regions move out of the camera's field of view or be blocked after deformation, resulting in the inability to find a complete matching region, which also causes data loss at this location. These missing data points not only destroy the integrity of the physical field, but also bring difficulties to subsequent analysis, such as stress concentration or damage evolution analysis.

[0006] (3) Lack of physical law compliance. The displacement calculation of DIC is essentially a pure mathematical optimization process based on the gray-scale information of local image blocks. The matching calculation of each sub-region is carried out independently, and the algorithm itself does not contain any prior knowledge about material behavior or continuum mechanics. This results in the final full-field displacement map being a collection of discrete data points, and the inherent continuity and smoothness cannot be guaranteed. More seriously, the strain field obtained by numerically differentiating these discrete displacement fields may locally violate the basic physical laws, such as the strain compatibility equation, resulting in physically unreasonable deformation patterns.

[0007] To address the shortcomings of traditional DIC methods in spatial resolution, data missing, and physical consistency, existing research has made a large number of improvement studies from the two main directions of pre-processing and post-processing. In recent years, Physics-informed neural networks (PINN) marks a major advance in scientific machine learning, which embeds the physical laws described by the basic differential equations into the neural network, and has great potential in solving complex equations in a series of disciplines such as fluid mechanics, solid mechanics, and inverse problems of mechanics. It is hailed as a new paradigm for unstructured data in deep learning.

[0008] Inspired by this, a series of methods combining PINN ideas to improve DIC have emerged. Some studies use neural networks to enforce the continuity and compatibility of displacement fields by introducing continuity assumptions for displacement fields, thereby correcting and enhancing DIC solutions to make them more consistent with physical intuition. For example, Wang et al. used a mesh of 8-node quadrilateral shell elements that satisfy spatial continuity to determine the out-of-plane displacement of all nodes, and then obtained the entire out-of-plane displacement field based on the optimized displacement of these nodes. Wang et al. proposed MCNN-DIC, which uses neural networks combined with displacement compatibility equations to constrain the measured deformation field using a semi-supervised learning method, making it more physically meaningful. Li et al. proposed PINN-DIC, which applies the assumption of photometric consistency as a physical constraint and uses the gray difference between the predicted and actual deformation images to construct a loss function to iteratively optimize the displacement field. Cheng et al. further proposed DIC-PCNN based on the structure of U-Net, which introduces the strain-displacement relationship from elasticity theory to establish a physical link between the displacement field and the strain field, and proves that only one network can consider the errors of displacement and strain simultaneously. Yang et al. proposed two independent networks, DisplacementNet and StrainNet, based on CNN combined with DIC method to obtain displacement field and strain field respectively.

[0009] The above studies show that incorporating physical constraints into deep learning frameworks is an effective way to improve DIC measurement quality. However, most current methods still focus on spatial domain optimization of single-frame static physical fields. In fact, DIC experiments usually produce a sequence of tens to thousands of images, which contain rich temporal dynamic information. The temporal evolution characteristics of material and structure deformation fields during the entire loading process have not been fully explored and utilized. SUMMARY

[0010] The technical problem to be solved by the present application is to provide a DIC physical field compression storage and super-resolution reconstruction method, which models the discrete and multi-frame DIC measurement results from the perspective of space-time through the NeRF-PINN model. Not only does it learn the deformation law in a data-driven manner, but it also embeds physical constraints such as strain compatibility equations to make the reconstruction results more consistent with physical laws.

[0011] The present application adopts the following technical solutions to solve the above technical problems: A DIC physical field compression storage and super-resolution reconstruction method, comprising the following steps: Step 1, calculate the low-resolution displacement field of the monitoring plane at each time step using the digital image correlation method, and establish a DIC physical field super-resolution reconstruction data set, including the low-resolution displacement field calculated by the digital image correlation method and the super-resolution displacement field corresponding to the low-resolution displacement field; the DIC physical field super-resolution reconstruction data set is divided into a training set and a test set; Step 2, construct a DIC physical field super-resolution reconstruction model, which takes the low-resolution displacement field calculated by the digital image correlation method as input and the reconstructed super-resolution displacement field as output; the model includes an input layer, a high-frequency coding layer, a full connection network with a residual structure, and an output layer; Step 3, introduce a compound loss function, train the DIC physical field super-resolution reconstruction model constructed in step 2 using the training set, and minimize the compound loss function using the Adam optimizer through the back propagation algorithm, thereby obtaining the trained DIC physical field super-resolution reconstruction model; Step 4, input the low-resolution displacement field in the test set into the trained DIC physical field super-resolution reconstruction model to obtain the DIC super-resolution reconstruction result.

[0012] Compared with the prior art, the above technical scheme has the following technical effects: 1. The present application proposes a new PINN model framework inspired by Neural Radiance Fields (NeRF), NeRF-PINN, which can reconstruct the original DIC field with low resolution and missing data into a continuous, complete and smooth high-resolution field, and the maximum principal strain result obtained is more similar to the true crack morphology.

[0013] 2. The present application introduces a physical constraint term into the total loss function, which can effectively guide the learning behavior of the model, so that the reconstruction result of the model is more consistent with the physical law.

[0014] 3. The present application uses position encoding technology in the NeRF-PINN model, so that the model can better learn high-frequency information and ultimately obtain better reconstruction results.

[0015] 4. The method of the present application can encode a dynamic deformation process in a lightweight neural network model. The original time series data with a volume of more than 300MB is compressed into a model of only 298KB, achieving a compression ratio of more than 1000:1, greatly facilitating the efficient storage and transmission of data. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a flowchart of a DIC physical field compression storage and super-resolution reconstruction method of the present application; Figure 2 is the network structure diagram of the DIC physical field super-resolution reconstruction model NeRF-PINN proposed in the application; Figure 3 is the data set acquisition process diagram; Figure 4 is the data set acquisition process diagram; Figure 5 is the data set acquisition process diagram; Figure 6 is the reconstruction result of the displacement field of example 1 under the conditions of no high-frequency encoding, Fourier encoding and position encoding; Figure 7 is Figure 6 the corresponding strain field of the displacement field; Figure 8 is the comparison between the real crack of example 1 and the maximum principal strain under three conditions; Figure 9 is the total loss curve of example 1 under three conditions; Figure 10 is the determination coefficient and structural similarity of the reconstructed displacement field of example 1 under three conditions, wherein (a) is the determination coefficient, and (b) is the structural similarity; Figure 11 is the reconstruction result of the displacement field of example 2 under the conditions of no high-frequency encoding, Fourier encoding and position encoding; Figure 12 is Figure 11 the corresponding strain field of the displacement field; Figure 13 is the comparison between the real crack of example 2 and the maximum principal strain under three conditions; Figure 14 is the total loss curve of example 2 under three conditions; Figure 15 is the determination coefficient and structural similarity of the reconstructed displacement field of example 2 under three conditions, wherein (a) is the determination coefficient, and (b) is the structural similarity; Figure 16 is the time smoothing term loss value curve, wherein (a) is example 1, and (b) is example 2. DETAILED DESCRIPTION

[0017] The embodiments of the application are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the application, and cannot be explained as a limitation of the application.

[0018] As Figure 1 shown in the figure, the present application proposes a DIC physical field compression storage and super-resolution reconstruction method. First, the displacement field in three directions of the monitored plane is obtained by the DIC method. These data are usually low resolution and have missing data. Then, the displacement field in three directions is approximated by NeRF-PINN, and the basic physical laws of mechanics are taken as soft constraints and integrated into the network training process, ensuring that the reconstructed physical field not only fits the data, but is also physically reasonable and self-consistent. Finally, efficient compression storage of the entire spatiotemporal physical field is realized by using a single neural network model, which can output physical quantities at any spatiotemporal coordinate point and achieve super-resolution reconstruction.

[0019] PINN neural network has "spectral bias" when learning high-frequency functions. The network tends to preferentially learn low-frequency information and is difficult to capture high-frequency details in the data. For complex displacement fields, this may cause the reconstructed results to be too smooth and lose important local changes. The present application introduces a high-frequency encoding layer before inputting the original coordinates into the network, which maps low-dimensional coordinates to high-dimensional feature space, thereby overcoming this problem. Among them, position encoding and Fourier feature mapping can be used as effective encoding strategies.

[0020] Position encoding is derived from the classic method of NeRF, which expands the input coordinates through a set of preset trigonometric function bases. For the input coordinate vector , its encoding function is defined as: , where is a hyperparameter that controls the encoding dimension. This encoding method makes it easier for the network to learn position-related high-frequency changes.

[0021] Fourier feature mapping is another effective high-frequency encoding method. It linearly projects the input coordinates through a random Gaussian matrix , and then applies sine and cosine functions. Its mapping function is defined as: , where is a fixed matrix sampled from the Gaussian distribution , is the variance of the Gaussian distribution, which is a hyperparameter that controls the range of frequency sampling and affects the frequency distribution of the mapped features. is the dimension of the mapped feature. This method can map the input coordinates to a feature space that can cover a wide frequency band, thereby improving the model's fitting ability to details.

[0022] The NeRF-PINN model architecture is shown in FIG. 1, which mainly consists of three parts: the input layer, the high-frequency encoding layer, the fully connected network with residual structure, and the multivariate output layer. The architecture design of using one network to predict three directional displacement fields at the same time makes it possible to provide subsequent physical condition constraints. Figure 2

[0023] The network takes the spatiotemporal coordinates as input, and uses tanh as the activation function because it has the characteristics of smoothness and second-order derivability, which is crucial for subsequent automatic differentiation of physical constraints (such as strain and stress). The fully connected network is stacked by 5 fully connected layers, and the first four fully connected layers are stacked by linear layers and activation layers. In order to promote the propagation of gradients in deep networks and alleviate the problem of network degradation, residual connections are introduced, which are applied when the input and output dimensions of the layer are the same. After adding the residual structure, the output of each fully connected layer is the sum of its activated output and input: , The last layer of the fully connected network is a linear layer without any activation function, which directly outputs the predicted displacement component , and its differential calculation obtains the strain component , and then adds the relevant physical constraints.

[0024] In order to train the network parameters , a composite loss function is designed, which is composed of multiple parts weighted together. It not only forces the model to fit the observed data, but also incorporates prior physical knowledge to guide the model to generate physically reasonable solutions. The total loss function is as follows: , where is the weight hyperparameter of each loss, used to balance the importance of data fitting and each physical constraint. The specific expression and role of each loss are analyzed as follows.

[0025] 1) Data fidelity term loss is used to ensure that the network's prediction result DIC is consistent with the observed data. The mean squared error (MSE) is used to quantify the difference between the predicted displacement and the true displacement. Given a training data set containing observation points, where is the spatiotemporal coordinates, ​​This corresponds to the DIC measured displacement, and the data fidelity term is defined as follows: .

[0026] 2) Boundary loss ) In many real-world mechanics problems, the displacements at certain boundaries of an object are known. For example, when the displacement at the fixed end is zero, the framework of this invention can optionally introduce boundary condition constraints. This loss term, similar to the data fidelity term, is also calculated using MSE, but it applies to a known set of boundary points. This enhances the physical state defined at the boundary: , When a certain boundary of a structure is a fixed constraint, then the displacement of that boundary... It is 0.

[0027] The physical information regularization term encodes physical laws as constraints on the network output. These constraints are independent of the label data and are evaluated at randomly sampled placement points across the entire solution domain. Using PyTorch's automatic differentiation capabilities, the network output (displacement vector) is precisely computed. ) relative to its input (coordinates) The physical residuals are constructed by taking the partial derivatives of each order of ).

[0028] 3) Time evolution smoothing constraint ( ) To ensure that the reconstructed physical field changes smoothly over time and avoids abrupt changes and oscillations in predictions due to noise or data sparsity, a time smoothness constraint is introduced. This constraint penalizes the second derivative of the displacement field with respect to time, encouraging a gradual acceleration in displacement over time, which aligns with the physical laws of most quasi-static or low-speed dynamic loading processes. Its loss is defined as: , Calculated by differentiating the displacement with respect to time twice. And the mean of the sum of their squares is used as the loss term.

[0029] For the placement points (also the concept of coordinates) randomly sampled within the solution domain The number of points is not specified, but these points lack corresponding actual displacement measurements and can only be used to calculate the physical regularization loss. . Indicates all Sum the losses at each configuration point and finally divide by . Take the average to obtain the average value of the loss item. Indicates the three spatial directions ( displacement components Summation is performed, meaning that the constraint applies to displacements in all directions simultaneously. Indicates a specific spatiotemporal configuration point At that point, the second partial derivative of displacement with respect to time, i.e., the displacement acceleration in that direction, Indicates in Displacement components in the direction.

[0030] Squaring the second-order time derivative serves two purposes: first, to ensure the loss is positive, regardless of whether the derivative's sign is positive or negative (acceleration or deceleration); second, to impose a stronger penalty on larger acceleration values, as the squared term amplifies the effect of large values. The essence of this term is to encourage a quasi-static process, which is slow and quasi-static in most materials mechanics tests. This means that inertial effects are negligible, and the object's acceleration should theoretically be close to zero.

[0031] 4) Strain compatibility equations ( ) In continuum mechanics, a geometrically compatible deformation must satisfy the strain compatibility equations to ensure that the strain field can be integrated to obtain a single-valued, continuous displacement field. This condition is described by the Saint-Venant compatibility equations, which, for a two-dimensional plane problem, take the form: , Among them, strain components Derived from the displacement components through geometric equations: , , , The mean square value of the residuals of the coordination equation is used as the loss term. All partial derivatives are obtained through automatic differentiation. This constraint enables the model to generate physically possible deformation fields that satisfy the continuity assumption, even in regions where DIC data is unavailable.

[0032] 5) Incompressibility ) For certain materials, such as rubber, it can be assumed that the material is incompressible. Mathematically, this property is expressed as zero volumetric strain. For two-dimensional plane strain problems, this means: , When dealing with the deformation of approximately incompressible materials, the mean square value of the residuals under this condition can be used as the loss term. This will improve the rationality of the reconstruction results.

[0033] Through these physical regularization terms, the NeRF-PINN model, while relying on data-driven principles, is constrained by universal physical laws, thereby achieving high-quality super-resolution reconstruction and appropriate imputation of missing data. The entire training process uses the Adam optimizer to minimize the total loss function via backpropagation. .

[0034] The dataset used in this invention originates from a 3D-DIC experiment simulating the compressive failure process of a retaining wall, such as... Figure 3 As shown. The experimental specimen measures 0.9m × 0.8m × 0.6m. The left, right, and rear sides of this cube are reinforced concrete walls, the front side is a brick wall, and the interior is soil. During the experiment, a three-dimensional digital image correlation system was used to monitor the deformation of the front side of the specimen under compression in real time. During loading, a stereo vision system consisting of two synchronous cameras continuously captured a sequence of speckle images of the surface at a preset frequency. Subsequently, commercial DIC software was used to process the image sequence and calculate the three-dimensional full-field displacement of the observed surface at each time step. .

[0035] This invention uses two loading embodiments. Figure 4 (a) and (b) show the evolution of the number of missing data points per frame over time in two embodiments. In Embodiment 1, data loss persists throughout the experiment, and the number of missing points exhibits highly dynamic and unpredictable fluctuations. A significant peak in data loss occurs, particularly around Frame ID 600, corresponding to a critical damage event. This embodiment represents a persistent, gradual damage process accompanied by sudden events. Embodiment 2 exhibits a "two-stage" behavior. In the early stages of the experiment (approximately the first 800 frames), the material surface remains relatively intact with few missing data points; however, the number of missing data points increases rapidly in the later stages. This embodiment simulates a sudden instability and failure process after a material has been stable for a long period.

[0036] The non-uniformity of time sampling in the two embodiments is as follows: Figure 5 As shown in (a) and (b), the time sampling has a base frequency of approximately 5 seconds, but due to equipment or environmental factors during the experiment, the acquisition was interrupted, resulting in data loss at some time points. In comparison, the time loss situation in Example 2 is more severe. This sparse long time interval poses a more serious challenge to any algorithm that relies on the assumption of temporal continuity, as it requires the model to perform long-distance, physically plausible interpolation between extremely sparse time anchors.

[0037] Example 1 The training and test sets are divided into an 800:200 ratio. The reconstruction result of the frame with the most severe speckle drop in the test set is used as the demonstration example (Stage 651 at this time). Figure 6 and Figure 7 As shown, the displacement fields obtained by various methods ( ) and the corresponding strain field ( The reconstruction results.

[0038] The first row shows the measurement results directly obtained from Subset-DIC. Because it relies on discrete subset matching, the displacement field exhibits a noticeable pixelated block structure, a typical low-resolution characteristic. More importantly, during loading, due to speckle drop or object edge effects, matching fails in some areas, resulting in missing data in the physical field. The second row shows the results without high-frequency encoding. The model successfully learned the overall distribution of the displacement field and smoothly filled in the missing regions, making the entire field continuous and yielding a complete super-resolution result. However, compared to the encoded models in the third and fourth rows, the result image without high-frequency encoding is generally very smooth. The boundaries of high-gradient regions in the field appear somewhat "blurred" and "diffuse." This indicates that a typical MLP (without encoding) tends to learn low-frequency functions. While it can capture overall trends, it has limited ability to represent rapidly changing details, whereas a model using high-frequency encoding can overcome this limitation.

[0039] In summary, all three encoding strategies enable the models to reconstruct a continuous, smooth, high-resolution field from a discrete, incomplete input field. The core reason is that the model has learned the entire physical process as a continuous implicit function. Therefore, the model can not only perform smooth interpolation between original data points, but also perform physical interpolation in "hole" regions where there is no data at all. Based on the "anchor points" provided by the surrounding data points and the embedded physical laws (such as strain compatibility equations) as constraints, the model infers the most likely physical state of the missing region, thereby generating a complete and missing physical field, thus solving the problem of local data missingness in traditional DIC.

[0040] Embedded physical constraints, such as strain compatibility equations, guide the model to find a solution that satisfies both sparse data and physical laws. This ensures that the reconstructed high-strain concentration zone is physically real, according to the following equation, through... , , The maximum principal strain field obtained through further calculation : , The results are as follows Figure 8As shown, compared to the results of Subset-DIC, the high-strain region reconstructed using NeRF-PINN is no longer a blurry patch, but rather exhibits a clear, sharp, and geometrically precise crack path. Its tortuous and bifurcated shape more closely matches the actual physical crack. Furthermore, the reconstructed results show larger values ​​in the high-strain region, which is more consistent with the theory in fracture mechanics that there is extremely high strain concentration at the crack tip.

[0041] To understand the effectiveness of different encoding strategies from the perspective of model optimization, the total loss decrease curves of three models during training were recorded, such as... Figure 9 As shown, when the model has no encoding, its loss decreases rapidly in the early stages of training, then plateaus and eventually converges to... This indicates that the model has encountered an optimization bottleneck. This is a direct manifestation of "spectral bias": because the model itself has difficulty representing high-frequency functions, even after long-term training, it is difficult to find a set of network weights that can simultaneously and accurately fit the details in the data and satisfy physical constraints (especially terms involving higher-order derivatives), so its total loss cannot be further reduced.

[0042] With the introduction of high-frequency coding, the loss curve descends with a steeper slope and eventually converges to a lower loss level (approximately). This demonstrates that high-frequency encoding transforms the original, difficult-to-learn function fitting problem into a new problem that is easier to optimize in a new high-dimensional feature space. The network can find a high-quality solution that simultaneously satisfies data and physical constraints more quickly, thus achieving lower residuals.

[0043] In addition, from Figure 6 and Figure 7 The displacement and strain field reconstruction results clearly show that the uncoded model (second row) suffers from "spectral bias," making it difficult to learn the high-frequency components in the displacement field. This results in an overly smooth strain field, losing crucial details of strain concentration. In contrast, the models using Fourier and positional coding (third and fourth rows) reconstruct clear and sharp high-strain regions, more closely resembling the true crack shape, qualitatively demonstrating the effectiveness of high-frequency coding.

[0044] To quantitatively verify this observation, this invention calculated the displacement fields reconstructed by different models on 200 samples in the test set. The coefficient of determination () ) and structural similarity (SSIM). The model measures the goodness of fit between the predicted values ​​and the true values, with a value closer to 1 indicating a better fit. SSIM, on the other hand, evaluates the similarity between the reconstructed field and the true field in terms of brightness, contrast, and structure, with a greater emphasis on perceptual structural fidelity.

[0045] The calculation results are as follows Figure 10 As shown in (a) and (b), the model without coding performs slightly worse than the two coded models on the three displacement components. Specifically, this is manifested in: (1) lower accuracy: its The median of the SSIM score (the horizontal line in the box) is significantly lower, and the distribution range (the height of the box and the whiskers) is wider. This indicates that the uncoded model not only has poor average performance, but also has less stable reconstruction quality. (2) Worse structural fidelity: The uncoded model scores lower on the SSIM index, which means that the displacement field it generates deviates significantly from the real physical field in terms of overall structure and local details. This performance gap quantitatively demonstrates the "spectral bias" bottleneck faced by standard MLPs when learning complex physical fields. Without high-frequency encoding, the model cannot capture subtle fluctuations in the displacement field, which will be amplified into serious information loss when calculating strain by differentiation.

[0046] In the comparison of the two high-frequency coding strategies, both performed well, but positional coding had better performance and stability in this embodiment, specifically: (1) Higher precision: Both Fourier coding and positional coding achieved extremely high precision. The median of the SSIM scores is generally above 0.995, proving that they can effectively map coordinates to a high-dimensional space that is conducive to network learning, thereby achieving high-precision field reconstruction. (2) Higher stability: Observing the box plot, it can be found that the positional encoding score distribution is more compact, the boxes are narrower, the whiskers are shorter, and there are fewer outliers. Especially in and In the SSIM evaluation of the field, the Fourier coding evaluation result has a longer bin and contains more low-scoring outliers. This indicates that although Fourier coding has excellent average performance, its stability is slightly lower than that of positional coding. In some cases, it may produce reconstruction results that differ slightly from the ground truth structure. This instability may originate from the random matrix in the Fourier eigenmap. Initialization is straightforward, while the deterministic function basis of position encoding provides more consistent performance. Therefore, both qualitative visual comparisons and quantitative metric evaluations demonstrate that high-frequency input encoding is a crucial component for achieving high-fidelity DIC physics field reconstruction using the NeRF-PINN framework. It effectively overcomes the spectral bias problem of neural networks, enabling the model to more accurately capture full-scale details from displacement fields to strain fields.

[0047] It should be noted that all quantitative metrics were evaluated on a reserved test set, demonstrating the model's strong temporal generalization ability. Therefore, the trained NeRF-PINN can not only perform spatial interpolation but also predict the displacement field at unseen time steps, thus achieving super-resolution in the temporal dimension.

[0048] Example 2 The main challenge of Example 2 lies in the "abrupt" nature of its damage evolution—that is, in the later stages of loading, the material undergoes macroscopic and concentrated damage, leading to large-scale and sudden data loss. Consistent with Example 1, the ratio of the training set to the test set is 800:200. The reconstruction result of the frame with the most severe speckle drop in the test set is used as the demonstration example; in this case, Stage 851 is used. Figure 11 and Figure 12 As shown, the first row of images represents the DIC image before reconstruction, exhibiting low resolution and localized missing data. The second row shows the result without high-frequency coding; the model smoothly fills in the missing regions, making the entire field continuous and significantly improving resolution. However, similar to Example 1, the result without high-frequency coding is generally very smooth. The boundaries of high-gradient regions in the field appear somewhat "blurred" and "diffuse," limiting their ability to represent rapidly changing details. Adding positional encoding effectively solves this problem.

[0049] pass , , The maximum principal strain field of Example 2 was calculated. ,result Figure 13 As shown, the reconstructed high-strain region is no longer a blurry color block, but a clearer and more precisely shaped crack path, which better matches the actual physical crack. Consistent with the results of Example 1, the reconstructed result shows a larger value in the high-strain region, which is more in line with the theory in fracture mechanics that there is extremely high strain concentration at the crack tip, further demonstrating the effectiveness of NeRF-PINN.

[0050] The training loss curves for the three encoding methods in Example 2 are as follows: Figure 14 As shown. Before the introduction of high-frequency coding, the Loss value converges to After introducing high-frequency coding, the loss curve decreases faster and converges to a lower level. Among them, Fourier coding can decrease rapidly in the early stage, but eventually converges. The positional encoding has a lower loss and converges to .

[0051] The accuracy evaluation results of Example 2 on the test set are as follows: Figure 15 As shown in (a) and (b), although there is more missing data in the later stages, the accuracy of the three encoding methods can still maintain a high level, with the median... All values ​​exceeded 0.9, indicating high robustness of the model. Specifically, the positional encoding showed slightly higher accuracy, the box-shaped position was higher, and the box size was narrower. , and average The value reached 0.99592, and the average SSIM value reached 0.98471. Similar to Example 1, these quantitative indicators were evaluated on a reserved test set, demonstrating that the trained NeRF-PINN can not only perform spatial interpolation but also predict the displacement field at unseen time steps. This means that the model can acquire the physical field at any time point, achieving super-resolution in the time dimension.

[0052] It's worth noting that although the Fourier encoding error value (Loss) is significantly lower, the final evaluation results on the test set are very similar to, or even worse than, the accuracy results of the unencoded model. This indicates that, from the perspective of purely minimizing the loss function, while the Fourier encoding model finds an efficient solution, this solution is physically incorrect. This is because the high-dimensional random feature space of Fourier encoding may lead to problems such as excessive model capacity or insufficient regularization. The model may overfit to some non-physical combination of the data. It minimizes the mean squared error of the PDE residuals by generating high-frequency noise, rather than learning the underlying smooth physical laws.

[0053] In the NeRF-PINN framework proposed in this invention, various physical constraints are embedded in the form of weighted loss terms. These weight hyperparameters... The value of directly affects the balance between the model's two objectives: "fitting observed data" and "following physical laws." This invention, through comparative experiments, uses time evolution smoothness constraints... As the observation object, multiple training experiments were conducted to verify the effectiveness of the physical constraints. In both implementations, the weights were adjusted. The values ​​were calculated, and for each value, five independent repetitions were performed, for a total of 50 training trials, to obtain different results. Values Evolutionary curves, such as Figure 16 As shown in (a) and (b).

[0054] when At this time, it is equivalent to not adding physical constraints during training. As the size increases, the model, in order to perfectly fit noisy data, tends to learn a physically unreasonable "jitter" solution. When At that time, it can effectively constrain The evolutionary trend. Furthermore, The larger the value, the better. The stronger the inhibitory effect, the better. Therefore, in this method, the inhibition effect can be adjusted by adjusting the weights. It is possible to actively and controllably enhance or weaken the constraint of specific physical laws on the model solution.

[0055] However, it must be pointed out that the deformation and failure of materials under real loads is an extremely complex process, influenced by a combination of factors including microstructure, nonlinear effects, and damage evolution. Therefore, any partial differential equations embedded in the model (such as strain compatibility equations or time smoothness assumptions) are essentially only idealized approximations of this complex reality. This framework remains a data-driven training framework supplemented by physical constraints; overly strong constraints ( Excessively large constraints may suppress the true characteristics of the data, leading to underfitting; while excessively weak constraints ( If the value is too small, it will not be sufficient to correct the "overfitting" caused by data noise. Therefore, The choice is a process of weighing options and needs to be adjusted based on the true intention.

[0056] Traditional DIC analysis generates a separate, discrete data file for each time step. A typical time-series experiment may contain thousands of frames of data, posing challenges to data storage and transmission. After NeF-PINN post-processing, the entire dynamic process is completely and continuously distilled into a single neural network weight.

[0057] In the two embodiments, the total size of the original data was 305MB and 301MB, respectively. After training, the entire dynamic process was completely encapsulated in a NeRF-PINN model of only 298KB, achieving a data compression ratio of over 1000:1. This compressed model is not a static archive file, but a lightweight, executable physics generator. It can accept queries for arbitrary spatiotemporal coordinates and return the corresponding displacement vectors instantly. On a consumer-grade GPU (NVIDIA RTX 4060), the model can predict the entire field of data at a rate of 127.44 frames per second, which greatly facilitates data storage and transmission.

[0058] Based on the same inventive concept, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the aforementioned DIC physics field compression storage and super-resolution reconstruction method.

[0059] Based on the same inventive concept, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the aforementioned DIC physics field compression storage and super-resolution reconstruction method.

[0060] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0061] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0062] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0063] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0064] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A method for compressed storage and super-resolution reconstruction of DIC physical fields, characterized in that, Includes the following steps: Step 1: Calculate the low-resolution displacement field of the monitoring plane at each time step using the digital image correlation method, and establish the DIC physical field super-resolution reconstruction dataset, including the low-resolution displacement field calculated using the digital image correlation method and the super-resolution displacement field corresponding to the low-resolution displacement field; divide the DIC physical field super-resolution reconstruction dataset into a training set and a test set. Step 2: Construct a DIC physics field super-resolution reconstruction model. The model takes the low-resolution displacement field calculated by the digital image correlation method as input and the reconstructed super-resolution displacement field as output. The model includes an input layer, a high-frequency coding layer, a fully connected network with residual structure, and an output layer. Step 3: Introduce a composite loss function, train the DIC physics super-resolution reconstruction model constructed in Step 2 using the training set, and use the Adam optimizer to minimize the composite loss function through the backpropagation algorithm to obtain the trained DIC physics super-resolution reconstruction model. Step 4: Input the low-resolution displacement field from the test set into the trained DIC physics super-resolution reconstruction model to obtain the DIC super-resolution reconstruction result.

2. The DIC physics field compression storage and super-resolution reconstruction method according to claim 1, characterized in that, In step 2, the high-frequency coding layer is used to map the low-resolution displacement field input from the input layer to a high-dimensional feature space. The coding method used by the high-frequency coding layer is position coding or Fourier feature mapping. Position-coded encoding function Defined as: in, This represents the input of the input layer. , Represents the coordinates on the monitoring plane exist Displacement field at time t, Hyperparameters for controlling the encoding dimension; Mapping function of Fourier feature map Defined as: in, From Gaussian distribution A fixed matrix for sampling in the middle. Represents the real number field. Let V be the variance of the Gaussian distribution. This represents the feature dimension after mapping.

3. The DIC physics field compression storage and super-resolution reconstruction method according to claim 1, characterized in that, In step 2, the fully connected network with residual structure includes a first to a fifth fully connected layer connected sequentially. The first to fourth fully connected layers have the same structure, each including a linear layer and an activation layer. The activation function used in the activation layer is the hyperbolic tangent function tanh. The fifth fully connected layer includes a linear layer. The second to fifth fully connected layers are all residually connected to the previous fully connected layer. The output of each fully connected layer is defined as: in, The first The output of a fully connected layer and The first The weights and biases of each fully connected layer Indicates whether or not it is related to the first Residual connections are performed on each fully connected layer.

4. The DIC physics field compression storage and super-resolution reconstruction method according to claim 1, characterized in that, In step 3, the composite loss function Defined as: in, For data integrity loss, For boundary loss, To smooth the time evolution constraint loss, In order to coordinate and manage losses, For incompressible loss, The weighting hyperparameters for each loss; 1) To ensure that the model's predictions are consistent with the DIC measurement data, mean squared error is used to quantify the difference between the predicted and actual displacements. in, To monitor the number of observation points on the plane, For model parameters, This represents the DIC physics super-resolution reconstruction model. Indicates the first Coordinates of each observation point exist Displacement field at time t, For the first The DIC measured displacement corresponding to each observation point; 2) When the displacement on part of the boundary of the monitoring plane is known, introduce... Applying mean square error to a known set of boundary points : in, This represents the total number of boundary points selected. Indicates the first The spatiotemporal coordinates of the boundary points For the first The DIC measured displacement corresponding to each boundary point; 3) Introduction To ensure that the reconstructed physical field changes smoothly over time and avoids abrupt changes and oscillations in predictions caused by noise or data sparsity, calculation is performed by differentiating the displacement over time twice. The mean of the sum of squares is used as the loss term, defined as: in, To determine the number of randomly sampled placement points within the solution domain, Indicates time; Indicates a specific spatiotemporal configuration point At that point, the second partial derivative of displacement with respect to time, i.e. Displacement acceleration in the direction; Indicates in Displacement components in the direction; 4) Introduce the Saint-Venant coordination equation to describe This allows the model to generate physically possible deformation fields that satisfy the continuity assumption, even in regions where DIC data is unavailable. in, Indicates the predicted displacement components The strain components obtained by differential calculation; 5) When the Poisson's ratio of the material on the monitoring plane is 0, introduce... : 。 5. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the DIC physics field compression storage and super-resolution reconstruction method as described in any one of claims 1 to 4.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the DIC physics field compression storage and super-resolution reconstruction method as described in any one of claims 1 to 4.

Images