RVE modeling method for additive manufacturing alloy complex grain morphology
By combining generative machine learning and image processing techniques with a lightweight U-Net network to train a grain morphology generation framework, the generation efficiency and accuracy issues of additive manufacturing alloy RVE models are solved, achieving high-fidelity and rapid microstructure modeling and supporting fatigue performance prediction and optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF MECHANICS CHINESE ACAD OF SCI
- Filing Date
- 2026-03-26
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies struggle to efficiently generate representative volume element (RVE) models that reflect the complex microstructure of additively manufactured alloys, leading to inaccurate fatigue performance predictions.
By combining generative machine learning and image processing techniques, a grain morphology generation framework is trained using a lightweight U-Net network to learn the grain morphology features in real EBSD images, and a post-processing algorithm is designed to generate digital microstructure files containing crystallographic orientation information.
It achieves efficient and accurate construction of RVE models for additive manufacturing alloys, improving the reliability and efficiency of fatigue performance prediction, and is applicable to the microstructure analysis of polycrystalline materials.
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Figure CN122242250A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of materials science and computational mechanics, specifically to an RVE modeling method for complex grain morphology of additive manufacturing alloys. Background Technology
[0002] Additive manufacturing technologies, such as laser powder bed melting (LPBF), have revolutionized the ability to fabricate components with complex geometries. However, their inherently rapid melting and solidification processes lead to significant microstructural inhomogeneities within the material, such as non-uniform grain size distribution, columnar grain growth, and localized orientation gradients. These microstructural inhomogeneities, along with defects introduced during manufacturing, are key factors contributing to the dispersion and anisotropy of fatigue properties in additively manufactured alloys, severely impacting the reliable prediction of their fatigue life.
[0003] Currently, establishing a quantitative relationship between microstructure and fatigue performance is a core challenge in the field. The crystal plasticity finite element method (CPFEM) combined with fatigue indicator parameters (FIPs) is a powerful tool for studying this problem, but the reliability of the results is highly dependent on whether the input representative volume element (RVE) model can truly reflect the microstructural characteristics of the material.
[0004] Traditional Reactive Velocity (RVE) modeling methods, such as Voronoi diagram segmentation, while computationally efficient, typically generate equiaxed and isotropic grains, failing to accurately capture the complex and non-uniform grain morphologies in additively manufactured alloys, such as grain boundary features and grain shape diversity. Physics-based cellular automata methods can simulate grain growth more realistically, but are computationally expensive. Despite improved algorithms such as anisotropic Voronoi diagrams, the gap between the synthesized model and the actual microstructure remains significant, leading to discrepancies between simulation results and experimental observations. Electron backscatter diffraction (EBSD) technology can provide high-precision microstructure data, but its sample preparation is difficult and its characterization area is limited, making it difficult to obtain sufficient RVE models for large-scale statistical analysis.
[0005] Therefore, there is an urgent need for a new RVE modeling method that can efficiently generate high-fidelity images that accurately reflect the complex microstructure (especially grain morphology) of additively manufactured alloys, in order to support high-confidence fatigue mechanism research and life prediction. Summary of the Invention
[0006] To address the technical problems existing in the background art, this invention proposes an RVE modeling method for complex grain morphology of additive manufacturing alloys. It cleverly combines generative machine learning and image processing technology. By training a lightweight grain boundary-denoised diffusion probability model, it learns the grain morphology features in real EBSD images and designs a post-processing algorithm to automatically convert the generated grain boundary images into digital microstructure files containing crystallographic orientation information, which can be directly used for CPFEM calculation.
[0007] To address the aforementioned technical problems, this invention provides an RVE modeling method for complex grain morphology in additive manufacturing alloys, comprising the following steps:
[0008] (1) Extract high-angle grain boundary images from electron backscatter diffraction data of additive manufacturing alloys and perform data augmentation operations to construct a training dataset;
[0009] (2) Construct a grain morphology generation framework based on a denoising diffusion probability model. The grain morphology generation framework uses a lightweight U-Net network as the backbone network. The lightweight U-Net network is used to train the grain morphology generation framework. The lightweight U-Net network is used to predict the noise component in the diffusion process of the grain morphology generation framework and learn the reverse diffusion process from the noise image to the real grain boundary image.
[0010] (3) Using the trained grain morphology generation framework, iteratively denoise from random noise to generate a high-fidelity grain boundary image;
[0011] (4) Post-process the generated grain boundary image, including removing noise and redundant lines, and identifying the closed connected domains enclosed by the grain boundary as grains; then, through the orientation propagation algorithm based on four-neighbor search, automatically assign crystallographic orientation to each pixel in the entire grain region, thereby converting the two-dimensional image into a digital microstructure file containing complete microstructure information.
[0012] (5) Import the digital microstructure file into Abaqus finite element preprocessing software, mesh it, and construct a representative volume element model.
[0013] As a preferred embodiment of the present invention, the data augmentation operation in step (1) is to perform cropping and horizontal flipping operations. The specific process is as follows: randomly crop 100 512-pixel-512-pixel sub-images from the 2320-pixel-2320-pixel image, and horizontally flip them to obtain 200 images. Each training image is a single-channel image with a size of 512×512×1, forming a dataset of 200 512×512×1 training images.
[0014] As a preferred embodiment of the present invention, the construction process of the grain morphology generation framework based on the denoising diffusion probability model in step (2) includes a forward diffusion process and a reverse diffusion process.
[0015] The forward diffusion process involves gradually adding Gaussian noise to the real grain boundary image, transforming it from the original image into an approximately pure noise image. The forward diffusion process is expressed as follows:
[0016] (1);
[0017] In the above formula (1), This indicates the forward diffusion process. This is represented as the noisy image after diffusion at step t. For the image at step t-1, Indicates a Gaussian distribution. The covariance matrix representing the Gaussian distribution is a diagonal matrix;
[0018] The backdiffusion process utilizes a U-Net network to predict noise components in the image at the current moment, and gradually performs denoising based on the prediction results, thereby recovering the grain boundary image; the backdiffusion process is expressed as follows:
[0019] (2);
[0020] In the above formula (2), Indicates the reverse diffusion process. Let be the noise variance at time t. The mean predicted by the U-Net parameters, The variance predicted by the U-Net parameters, This represents the parameters of the lightweight U-Net network.
[0021] As a preferred embodiment of the present invention, the specific process of step (2) using a lightweight U-Net network to train the grain morphology generation framework is as follows:
[0022] The noisy image and its corresponding time step are input into a lightweight U-Net network, which outputs a predicted image noise value. The network parameters are optimized by minimizing the mean squared error loss function between the predicted noise and the actual noise.
[0023] (3);
[0024] In equation (3) above, t is the diffusion time step. To reduce the noise in U-Net predictions, This is real noise.
[0025] As a preferred embodiment of the present invention, the specific process of iterative denoising starting from random noise in step (3) is as follows: taking a random Gaussian noise image as the initial input, iteratively denoising is performed step by step from step T along the reverse diffusion path; in each step, the trained lightweight U-Net network is used to predict the noise component in the current image and update the image at the previous moment; after 200 iterations, a large number of high-fidelity grain boundary images similar to the statistical characteristics of the real microstructure are generated.
[0026] As a preferred embodiment of the present invention, the process of automatically assigning crystallographic orientation to each pixel within the entire grain region using an orientation propagation algorithm based on four-neighbor search in step (4) is as follows:
[0027] For any identified connected region of a grain, let the set of pixels within that region be denoted as . :
[0028] (4);
[0029] in, Denotes the connected domain of the i-th grain. This represents the k-th pixel within the connected component.
[0030] First of all Seed pixels selected from within And assign initial Euler angles:
[0031] (5);
[0032] In the above formula, For pixel grain orientation, the initial Euler angles ;
[0033] Then, a queue to be traversed is created, and seed pixels are pushed into the queue; each time, an assigned pixel is retrieved from the queue. Search for its four adjacent pixels above, below, left, and right:
[0034] (6);
[0035] In the above formula, N4(P) represents the four adjacent pixels above, below, left, and right of pixel p;
[0036] If adjacent pixels belong to the same connected region of the same grain and have not yet been assigned a value:
[0037] (7);
[0038] Then the pixels The Euler angle is assigned to the adjacent pixel:
[0039] (8);
[0040] Then add adjacent pixels to the queue; repeat the above process until all pixels in the queue have been assigned Euler angles, thus completing the orientation assignment of all pixels in the connected domain of the grain.
[0041] As a preferred embodiment of the present invention: in step (5), the mesh is divided according to the grain boundary, and different grains are assigned grain parameters to construct a polycrystalline representative volume element RVE model.
[0042] By adopting the above technical solution, the present invention has the following beneficial effects:
[0043] The RVE modeling method for complex grain morphology of additive manufacturing alloys presented in this invention is rationally conceived and is a representative volume element (RVE) modeling method for additive manufacturing alloy materials (such as laser powder bed fusion LPBF). This modeling method is particularly suitable for constructing high-fidelity, high-efficiency microstructure models of additive manufacturing alloys with complex microstructures (such as diverse grain morphologies and uneven crystal orientation distribution), providing a foundation for subsequent crystal plasticity finite element simulation, fatigue performance prediction, and material microstructure optimization.
[0044] This invention cleverly combines generative machine learning and image processing techniques. It trains a lightweight grain morphology generation framework (GB-DDPM) to learn the grain morphology features in real EBSD images and designs a post-processing algorithm to automatically convert the generated grain boundary images into digital microstructure files containing crystallographic orientation information, which can be directly used for CPFEM calculations.
[0045] Compared with the prior art, the present invention has the following features and advantages:
[0046] (1) Based on real EBSD data, this invention uses GB-DDPM to learn the grain boundary morphology distribution characteristics, which can generate grain morphology that is closer to the real additive manufacturing alloy microstructure, and has higher morphology authenticity than the traditional Voronoi method.
[0047] (2) This invention uses a lightweight U-Net network and sets the total number of diffusion steps to 200, which reduces the computational cost of training and inference while ensuring the quality of generation and improves the efficiency of RVE modeling;
[0048] (3) The present invention can generate digital microstructure samples with statistical representativeness in batches, which provides a basis for uncertainty analysis of microstructure of additive manufacturing alloys, finite element simulation of crystal plasticity and fatigue life prediction.
[0049] (4) This invention is not only applicable to GH4169 alloy formed by LPBF, but can also be extended to microstructure modeling of other additive manufacturing alloys and polycrystalline materials. Attached Figure Description
[0050] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0051] Figure 1 This is an initial microstructure diagram of the LPBF GH4169 alloy involved in the embodiments of the present invention;
[0052] Figure 2 A schematic diagram of the process for creating a dataset from high-angle grain boundary images of EBSD data involved in this invention;
[0053] Figure 3 This is a schematic diagram illustrating the forward noise addition and reverse noise reduction process of the denoising diffusion probability model involved in this invention.
[0054] Figure 4 This is a schematic diagram of the U-Net network structure involved in the present invention;
[0055] Figure 5 This is a flowchart illustrating the process of imparting an initial orientation to the grain-forming region as per the present invention.
[0056] Figure 6 This is a schematic diagram of the orientation propagation algorithm based on four neighborhoods involved in the present invention;
[0057] Figure 7 This is a comparison chart of the RVE model generated based on this invention and the model generated based on the traditional Voronoi method;
[0058] Figure 8 This is a cloud map of the simulation results involved in the present invention. Detailed Implementation
[0059] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0060] The present invention will be further explained below with reference to specific embodiments.
[0061] This embodiment provides a lightweight and efficient RVE modeling method for complex grain morphology in additive alloys, which includes the following steps:
[0062] S100, Data Preparation
[0063] High-angle grain boundary images were extracted from the electron backscatter diffraction (EBSD) data of the additively manufactured alloys obtained from experiments, and data augmentation operations, namely cropping and horizontal flipping operations, were performed (e.g., Figure 2 As shown in the figure, a training dataset is constructed. The data augmentation process is as follows: 100 512-pixel-512-pixel sub-images are randomly cropped from the 2320-pixel-2320-pixel image and horizontally flipped to obtain 200 images. Each training image is a single-channel image with a size of 512×512×1, forming a training image dataset of 200 images of 512×512×1.
[0064] S200, Model Building and Training
[0065] A grain morphology generation framework based on the denoising diffusion probability model (DDPM) (GB-DDPM for short) is constructed. This GB-DDPM uses a lightweight U-Net network ( Figure 4 As the backbone network, a lightweight U-Net network is used to train the grain morphology generation framework to predict the noise component in the diffusion process of the grain morphology generation framework and learn the reverse diffusion process from the noise image to the real grain boundary image.
[0066] The construction process of the above-mentioned grain morphology generation framework based on the denoised diffusion probability model (DDPM) (GB-DDPM for short) is as follows:
[0067] The forward diffusion process involves gradually adding Gaussian noise to the real grain boundary image, transforming it from the original image into an approximately pure noise image. In the reverse diffusion process of GB-DDPM, the U-Net network is used to predict the noise components in the image at the current moment, and the noise is gradually removed based on the prediction results, thereby restoring the grain boundary image.
[0068] The aforementioned forward diffusion process can be represented as:
[0069] (1);
[0070] in, This indicates the forward diffusion process. This is represented as the noisy image after diffusion at step t. The image is at step t-1, where "|" is the condition symbol, indicating "under the condition of...". Indicates a Gaussian distribution. The covariance matrix representing the Gaussian distribution is a diagonal matrix;
[0071] The reverse diffusion process uses a U-Net network to predict the noise components in the image at the current moment, and gradually performs denoising based on the prediction results, thereby restoring the grain boundary image;
[0072] The above-described reverse diffusion (reverse denoising) process can be represented as:
[0073] (2);
[0074] in, Indicates the reverse diffusion process. Let be the noise variance at time t. The mean predicted by the U-Net parameters, The variance predicted by the U-Net parameters, This represents the parameters of the lightweight U-Net network.
[0075] To reduce training and inference costs, the GB-DDPM mentioned above adopts a cosine noise scheduling strategy and sets the total number of diffusion steps to 200. Cosine noise scheduling refers to setting the noise intensity at different diffusion times according to the variation law of the cosine function, so as to distribute noise more smoothly in the early and late stages of diffusion and improve generation stability.
[0076] The specific process of training the grain morphology generation framework using the lightweight U-Net network is as follows: The noisy image and its corresponding time step are input into the lightweight U-Net network, the image noise prediction value is output, and the network parameters are optimized by minimizing the mean square error loss function between the predicted noise and the actual noise.
[0077] (3);
[0078] In equation (3) above, t is the diffusion time step. To reduce the noise in U-Net predictions, This is real noise.
[0079] In this embodiment, the training parameters are set as follows: epoch is 400, batch size is 8, and learning rate is 5×10⁻⁶. -5 The optimizer was AdamW, and the training hardware was a GeForce RTX 4090 GPU.
[0080] S300, grain morphology formation
[0081] Using the GB-DDPM trained in step S200 above, such as Figure 3As shown, iterative denoising starting from random noise generates high-fidelity grain boundary images. The specific process of iterative denoising starting from random noise is as follows: using a random Gaussian noise image as the initial input, iterative denoising is performed step-by-step following a back-diffusion path starting from step T; in each step, the trained lightweight U-Net network is used to predict the noise components in the current image and update the image from the previous time step; after 200 iterations, a large number of high-fidelity grain boundary images similar to the statistical characteristics of the real microstructure are generated.
[0082] S400, Image Post-processing and Orientation Assignment
[0083] The grain boundary image generated in step S300 is post-processed, including noise and redundant lines removal, and grain orientation assignment. The specific process is as follows: Figure 5-6 The algorithm identifies closed connected domains enclosed by grain boundaries as grains. Then, using an orientation propagation algorithm based on four-neighbor search, it automatically assigns crystallographic orientations (such as Euler angles) to each pixel within the entire grain region, thereby converting the two-dimensional image into a digital microstructure file (such as CTF format) containing complete microstructure information (grain morphology + crystal orientation).
[0084] The process described above, which uses an orientation propagation algorithm based on four-neighbor search to automatically assign crystallographic orientation to every pixel within the entire grain region, is as follows:
[0085] For any identified connected region of a grain, let the set of pixels within that region be denoted as . :
[0086] (4);
[0087] in, Denotes the connected domain of the i-th grain. This represents the k-th pixel within the connected component.
[0088] First of all Seed pixels selected from within And assign initial Euler angles:
[0089] (5);
[0090] In the above formula, For pixel grain orientation, the initial Euler angles ;
[0091] Then, a queue to be traversed is created, and seed pixels are pushed into the queue; each time, an assigned pixel is retrieved from the queue. Search for its four adjacent pixels above, below, left, and right:
[0092] (6);
[0093] In the above formula, N4(P) represents the four adjacent pixels above, below, left, and right of pixel p;
[0094] If adjacent pixels belong to the same connected region of the same grain and have not yet been assigned a value:
[0095] (7);
[0096] Then the pixels The Euler angles are assigned to the above adjacent pixels:
[0097] (8);
[0098] Then add adjacent pixels to the queue; repeat the above process until all pixels in the queue have been assigned the corresponding Euler angle, thereby completing the orientation assignment of all pixels in the connected domain of the grain.
[0099] The orientation propagation algorithm based on four-neighbor search can ensure that pixels within the same grain region have consistent crystallographic orientation, and at the same time realize the conversion from two-dimensional grain boundary image to digital microstructure file; the digital microstructure file contains complete microstructure information (grain morphology + crystal orientation).
[0100] S500. Import the digital microstructure file generated in step S400 into the Abaqus finite element simulation software. In this embodiment, each grain is a finite element entity with independent orientation properties. Mesh division is completed according to the grain boundary. Different grains are assigned grain parameters, and a polycrystalline representative volume element RVE model can be constructed.
[0101] The following section uses GH4169 nickel-based superalloy formed by LPBF forming as an example to illustrate the implementation process of the method of the present invention in detail.
[0102] Step 1: Data Preparation and Augmentation
[0103] First, the GH4169 alloy specimen formed by LPBF was characterized by EBSD to obtain its microstructure images, such as... Figure 1As shown, high-angle grain boundary (HAGBs, >15°) images were extracted from EBSD data using the MTEX toolkit in MATLAB. The specific process included: filtering out grain boundary lines with orientation differences less than 15°; removing extremely small grains with an area less than 20 pixels; and outputting a 2320×2320 pixel grain boundary image. Then, 100 512×512 pixel sub-images were uniformly cropped from this image and data augmentation was performed by horizontal flipping, resulting in 200 training images. All images were single-channel with a size of (512, 512, 1). These images primarily represent the high-angle grain boundary morphology of additive alloys.
[0104] Step 2: Building and training the GB-DDPM model
[0105] A grain morphology generation framework based on the denoised diffusion probability model (DDPM), abbreviated as GB-DDPM, is constructed. This framework uses U-Net as the backbone network and introduces a spatial self-attention mechanism, as shown in the following structure: Figure 4 As shown. Cosine scheduling is used for noise scheduling during the diffusion process, and the total number of diffusion steps T is set to 200 to reduce computational burden and achieve lightweighting. During training, the noisy image and time steps are input into U-Net, and the predicted noise is output. The network parameters are optimized by minimizing the mean square error between the predicted noise and the true noise. The training hyperparameters are set as follows: epoch=400, batch size=8, learning rate=5e-5, using the AdamW optimizer. Training is performed on a GeForce RTX 4090 GPU.
[0106] Step 3: Generate grain morphology images
[0107] After training, from purely noisy images Initially, following the learned reverse diffusion process, denoising was iterated for 200 steps to gradually generate clear grain boundary images. The generated images are highly similar in morphology to real EBSD images, but are pure black and white line drawings and have not yet been given physical meaning.
[0108] Step 4: Image post-processing and orientation assignment
[0109] The generated images require further processing before they can be used in CPFEM simulations. Write a Python script to implement the following functionality:
[0110] (1) Image cleaning: Remove isolated noise and redundant lines from the image to ensure that the grain boundary lines form a closed region.
[0111] (2) Grain identification: Through connected component analysis, the white areas surrounded by black grain boundaries in the image are identified as independent grains and numbered sequentially.
[0112] (3) Orientation assignment and propagation: such as Figure 5 and Figure 6 As shown, each connected component is first randomly assigned a set of initial Euler angles that conform to the experimental statistical distribution. Then, using a four-neighborhood-based propagation algorithm, orientation values are iteratively assigned to adjacent grain boundary pixels (black pixels) starting from the already assigned region. This process is repeated multiple times until all pixels have been assigned orientation values. Finally, the coordinates of each pixel and its corresponding Euler angles are written into a standard CTF format file, completing the conversion from the generated image to a digital microstructure file.
[0113] Step 5: Build and validate the RVE model
[0114] Compared to models generated by traditional Voronoi methods, such as Figure 7 As shown. This invention can more faithfully establish grain information similar to the real additive alloy microstructure, thereby achieving more accurate simulation results. The generated CTF file is imported into finite element software such as Abaqus, and a polycrystalline RVE model containing grain geometry and orientation is generated through a plugin, and then meshed. Corresponding crystal plastic constitutive parameters are assigned to each grain. This process can also be performed in Abaqus by adding defects of different morphologies and sizes, such as incomplete fusion defects or inclusions. Cyclic loading is then applied for CPFEM simulation. Force response, fatigue indicator factors, etc., are extracted from the simulation results. Figure 8 As shown, the simulation results agree well with the experimental data, demonstrating the accuracy and reliability of the RVE model established in this invention.
[0115] This invention can rapidly generate high-fidelity microstructure models, providing a powerful tool for performance prediction and microstructure optimization of additive manufacturing alloys.
[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method of RVE modeling of complex grain morphology of additively manufactured alloys, characterized in that, Includes the following steps: (1) Extract high-angle grain boundary images from electron backscatter diffraction data of additive manufacturing alloys and perform data augmentation operations to construct a training dataset; (2) Construct a grain morphology generation framework based on a denoising diffusion probability model. The grain morphology generation framework uses a lightweight U-Net network as the backbone network. The lightweight U-Net network is used to train the grain morphology generation framework. The lightweight U-Net network is used to predict the noise component in the diffusion process of the grain morphology generation framework and learn the reverse diffusion process from the noise image to the real grain boundary image. (3) Using the trained grain morphology generation framework, iteratively denoise from random noise to generate a high-fidelity grain boundary image; (4) Post-process the generated grain boundary image, including removing noise and redundant lines, and identifying the closed connected domains enclosed by the grain boundary as grains; then, through the orientation propagation algorithm based on four-neighbor search, automatically assign crystallographic orientation to each pixel in the entire grain region, thereby converting the two-dimensional image into a digital microstructure file containing complete microstructure information. (5) Import the digital microstructure file into Abaqus finite element preprocessing software, mesh it, and construct a representative volume element model.
2. The RVE modeling method of additive manufacturing alloy complex grain morphology of claim 1, wherein, The data augmentation operation in step (1) is to perform cropping and horizontal flipping operations. The specific process is as follows: randomly crop 100 512-pixel-512-pixel sub-images from the 2320-pixel-2320-pixel image and horizontally flip them to obtain 200 images. Each training image is a single-channel image with a size of 512×512×1, forming a dataset of 200 512×512×1 training images.
3. The RVE modeling method of additive manufacturing alloy complex grain morphology of claim 1, wherein, The construction process of the grain morphology generation framework based on the denoised diffusion probability model in step (2) includes a forward diffusion process and a reverse diffusion process. The forward diffusion process involves gradually adding Gaussian noise to the real grain boundary image, transforming it from the original image into an approximately pure noise image. The forward diffusion process is expressed as follows: (1)； In the above formula (1), denotes a forward diffusion process, denotes a noisy image after diffusion at the t-th step, is the image at the t-1-th step, denotes a Gaussian distribution, the covariance matrix of the Gaussian distribution is a diagonal matrix; The backdiffusion process utilizes a U-Net network to predict noise components in the image at the current moment, and gradually performs denoising based on the prediction results, thereby recovering the grain boundary image; the backdiffusion process is expressed as follows: (2)； In the above equation (2), denotes the reverse diffusion process, is the noise variance at time t, is the mean predicted by the U-Net parameters, is the variance predicted by the U-Net parameters, denotes the parameters of the light-weight U-Net network.
4. The RVE modeling method for complex grain morphology of additive manufacturing alloys as described in claim 1, characterized in that, The specific process of training the grain morphology generation framework using a lightweight U-Net network in step (2) is as follows: The noisy image and its corresponding time step are input into a lightweight U-Net network, which outputs a predicted image noise value. The network parameters are optimized by minimizing the mean squared error loss function between the predicted noise and the actual noise. (3)； In equation (3) above, t is the diffusion time step. To reduce the noise in U-Net predictions, This is real noise.
5. The RVE modeling method for complex grain morphology of additive manufacturing alloys as described in claim 1, characterized in that, The specific process of iterative denoising starting from random noise in step (3) is as follows: using a random Gaussian noise image as the initial input, iteratively denoising is performed step by step from step T along the reverse diffusion path; in each step, the trained lightweight U-Net network is used to predict the noise component in the current image and update the image at the previous moment; after 200 iterations, a large number of high-fidelity grain boundary images similar to the statistical characteristics of the real microstructure are generated.
6. The RVE modeling method for complex grain morphology of additive manufacturing alloys as described in claim 1, characterized in that, In step (4), the process of automatically assigning crystallographic orientation to each pixel within the entire grain region using an orientation propagation algorithm based on four-neighbor search is as follows: For any identified connected region of a grain, let the set of pixels within that region be denoted as . : (4)； in, Denotes the connected domain of the i-th grain. This represents the k-th pixel within the connected component. First of all Seed pixels selected from within And assign initial Euler angles: (5)； In the above formula, For pixel grain orientation, the initial Euler angles ; Then, a queue to be traversed is created, and seed pixels are pushed into the queue; each time, an assigned pixel is retrieved from the queue. Search for its four adjacent pixels above, below, left, and right: (6)； In the above formula, N4(P) represents the four adjacent pixels above, below, left, and right of pixel p; If adjacent pixels belong to the same connected region of the same grain and have not yet been assigned a value: (7)； Then the pixels The Euler angle is assigned to the adjacent pixel: (8)； Then add adjacent pixels to the queue; repeat the above process until all pixels in the queue have been assigned Euler angles, thus completing the orientation assignment of all pixels in the connected domain of the grain.
7. The RVE modeling method for complex grain morphology of additive manufacturing alloys as described in claim 1, characterized in that: In step (5), the mesh is divided according to the grain boundaries, and different grains are assigned grain parameters to construct the polycrystalline representative volume element RVE model.