Method for generating three-phase microstructure of rigid insulating tile, performance prediction method and system

Abstract

The present application relates to a rigid insulation tile three-phase microstructure generation method, performance prediction method and system, belonging to the technical field of composite material structure analysis, solves the problem that the three-phase microstructure generated by the prior art has fuzzy boundaries, inter-phase confusion, lacks phase proportion constraints and inter-layer continuity constraints, and is difficult to apply to material performance prediction. The method comprises: obtaining a real slice sample set in different spatial directions; wherein the real slice sample set includes a plurality of three-phase labeled slices; training a generative adversarial network using the real slice sample set in all spatial directions and a multi-dimensional loss function to obtain a trained generative adversarial network; wherein the generative adversarial network includes a three-dimensional generator and a plurality of two-dimensional discriminators; and obtaining a final three-phase structure using the trained three-dimensional generator. The present application realizes three-phase microstructure generation that preserves the multi-phase characteristics and anisotropic characteristics of the material, and can be directly applied to material performance prediction.

Description

Technical Field

[0001] This invention relates to the field of composite material structure analysis technology, and in particular to a method for generating the three-phase microstructure of rigid thermal insulation tiles, a method for predicting their performance, and a system. Background Technology

[0002] Lightweight resin-based rigid thermal insulation tile composites possess characteristics such as lightweight, porousness, thermal insulation, and enhanced load-bearing capacity. Their heat transfer behavior is not solely determined by the intrinsic thermophysical properties of each component, but is closely related to various microstructural factors, including porosity, fiber volume fraction, pore morphology, connectivity, and spatial topology. For this type of composite thermal insulation material, characterized by multiphase, non-homogeneous, and anisotropic properties, relying solely on limited experimental results or empirical formulas is insufficient to systematically reveal the complex coupling relationship between microstructural parameters and effective thermal conductivity. Therefore, obtaining three-dimensional microstructural data that accurately reflects the internal microstructure of the material, and establishing a quantitative structure-performance correlation based on this data, is a crucial prerequisite for conducting thermal performance analysis and optimization design of this type of material.

[0003] The interior of lightweight resin-based rigid thermal insulation tile composites simultaneously contains porous phases, fiber phases, and matrix phases, exhibiting significant multiphase characteristics and directional differences. Due to limitations in the number of experimental samples, scanning costs, and sample size, relying directly on limited real samples for structural statistics and thermal conductivity prediction often results in insufficient data scale and limited sample representativeness, making it difficult to meet the requirements of subsequent data-driven modeling for sample quantity and statistical stability.

[0004] While the generation of 3D structures from 2D slices offers a possibility for creating 3D structural samples of thermal insulation tiles, existing slice-based generation methods still have the following shortcomings when applied to lightweight resin-based rigid thermal insulation tile composites: First, the input data for lightweight resin-based rigid thermal insulation tile composites consists of three-phase labeled slices containing pores, fibers, and the matrix, unlike the simpler data representation in single-phase or two-phase structures. If the original slice-based generation of adversarial networks is used directly, it is difficult to accurately characterize the category boundaries between the three phases, easily leading to interface ambiguity and phase confusion, thus affecting the authenticity of the subsequent 3D structure reconstruction results. Second, this type of thermal insulation tile exhibits significant anisotropy in three orthogonal directions. If only a uniform directional constraint method is used, it is difficult to fully preserve the differences in microstructure in different directions. Third, existing methods focus more on generating 3D structures, lacking specific constraints on the fidelity of multiphase boundaries, the rationality of the three-phase proportions, and the topological continuity between layers, which can easily affect the reliability of subsequent structural parameter statistics.

[0005] Therefore, there is an urgent need for a method and system for generating the three-phase microstructure of rigid thermal insulation tiles, predicting their performance, and using two-dimensional real slices as a basis. This method would preserve the multiphase and anisotropic characteristics of the material, achieve statistically consistent three-dimensional structure generation, and be applicable to material performance prediction. This would provide reliable methods and data support for the structural design and thermal performance optimization of lightweight resin-based rigid thermal insulation tile composites (referred to as rigid thermal insulation tiles in this application). Summary of the Invention

[0006] Based on the above analysis, the embodiments of the present invention aim to provide a method for generating a three-phase microstructure of rigid thermal insulation tiles, a method for predicting performance, and a system that solves the problems of blurred boundaries, phase confusion, lack of phase ratio constraints, and interlayer continuity constraints in the three-phase microstructure generated by the prior art, making it difficult to apply to material performance prediction.

[0007] On one hand, embodiments of the present invention provide a method for generating a three-phase microstructure of a rigid thermal insulation tile, comprising: Obtain a real slice sample set in different spatial directions; wherein, the real slice sample set includes several three-phase labeled slices; The generative adversarial network is trained using the real slice sample set in all spatial directions and a multidimensional loss function to obtain the trained generative adversarial network; wherein, the generative adversarial network includes a three-dimensional generator and multiple two-dimensional discriminators; The final three-phase structure is obtained using the trained 3D generator.

[0008] Furthermore, the generative adversarial network is trained using the real slice sample set in all spatial directions and a multidimensional loss function to obtain the trained generative adversarial network, including: The three-dimensional generator is used to generate a training three-phase probability volume, and several three-phase generated slices in different spatial directions are obtained. Each of the three-phase generated slices, each of the three-phase labeled slices, and the multidimensional loss function are used to train each of the two-dimensional discriminators; The three-dimensional generator is trained using the training three-phase probability body, each of the three-phase generation slices, each of the three-phase label slices, and the multidimensional loss function; Once the training stopping condition is met, the trained generative adversarial network is obtained.

[0009] Furthermore, the multidimensional loss function includes a first adversarial loss function; Training each of the two-dimensional discriminators using the three-phase generated slices, the three-phase labeled slices, and the multidimensional loss function includes: Each three-phase generated slice and each three-phase labeled slice in each spatial direction are input into the corresponding two-dimensional discriminator to obtain the corresponding discrimination result; wherein, each spatial direction corresponds to one two-dimensional discriminator; Based on the discrimination results, the corresponding first adversarial loss value is calculated using the first adversarial loss function; The corresponding two-dimensional discriminator is trained based on each of the first adversarial loss values.

[0010] Furthermore, the first adversarial loss function is expressed as: In the formula, Indicates the first The two-dimensional discriminator corresponding to each spatial direction The first adversarial loss value, Indicates the first The real slice sample set in each spatial direction, Indicates the first The three-phase generation slices in each spatial direction This refers to the two-dimensional discriminator. The three-phase generation slice The aforementioned discrimination result, express Includes each of the three-phase generated slices Corresponding discrimination results Expectations Indicates the first Each of the three-phase tag slices in each spatial direction The set, This refers to the two-dimensional discriminator. For the three-phase label slice The aforementioned discrimination result, express Includes each of the aforementioned three-phase tag slices The corresponding discrimination result Expectations This refers to the two-dimensional discriminator. Three-phase interpolation slices The aforementioned discrimination result, This represents the three-phase interpolation slice. The corresponding partial derivative gradient The 2-norm, Represents all the aforementioned three-phase interpolation slices corresponding Expectations This represents the gradient penalty coefficient.

[0011] Furthermore, the multidimensional loss function also includes a second adversarial loss function, a classification loss function, a Dice loss function, a three-phase constraint loss function, and an inter-layer constraint loss function; The 3D generator is trained using the training three-phase probability body, each of the three-phase generated slices, each of the three-phase label slices, and the multidimensional loss function, including: Based on each of the three-phase generated slices and each of the three-phase labeled slices in all spatial directions, the corresponding second adversarial loss value, classification loss value, and Dice loss value are calculated using the second adversarial loss function, the classification loss function, and the Dice loss function. Based on the training three-phase probability body and each of the three-phase label slices, the corresponding three-phase constraint loss value and inter-layer constraint loss value are calculated using the three-phase constraint loss function and the inter-layer constraint loss function. The generator's total loss value is calculated based on the second adversarial loss value, the classification loss value, the Dice loss value, the three-phase constraint loss value, and the inter-layer constraint loss value. The 3D generator is trained based on the total loss value of the generator.

[0012] Furthermore, the inter-layer constraint loss function is expressed as: In the formula, This represents the interlayer constraint loss value. Indicates the number of floors. Indicates the first Layer, First line, number The predicted probability array of the column. Indicates the first Layer, First line, number The predicted probability array of the column, express The 2-norm.

[0013] On the other hand, embodiments of the present invention provide a method for predicting the three-phase microstructural performance of rigid thermal insulation tiles, including: For each three-phase structure, parameter values ​​corresponding to multiple structural parameters are extracted, and the parameter values ​​corresponding to the performance parameters are calculated; wherein, the three-phase structure includes the final three-phase structure obtained by the method described in the first aspect; the performance parameters include thermal conductivity; Based on the correlation between the structural parameters and the performance parameters, key structural parameters are selected to construct an enhanced structure-performance dataset. The enhanced structure-performance dataset is used to train several performance prediction models under constraints, resulting in several trained performance prediction models. Based on the prediction results of several performance prediction models that have been trained, a performance analysis result is generated.

[0014] Furthermore, based on the correlation between each of the structural parameters and the performance parameters, key structural parameters are selected to construct an enhanced structure-performance dataset, including: Based on the parameter values ​​of the structural parameters and performance parameters corresponding to each of the three-phase structures, the correlation coefficient between each structural parameter and the performance parameter is calculated, and key structural parameters are selected according to the correlation coefficients. Based on the key structural parameters and the parameter values ​​corresponding to the performance parameters, a basic structure-performance dataset is constructed. Based on the infrastructure-performance dataset, a Gaussian mixture model is used to perform sample augmentation, generating multiple augmented samples, which are then added to the infrastructure-performance dataset to obtain the augmented infrastructure-performance dataset.

[0015] Furthermore, the performance prediction model includes a multilayer perceptron model; the training objective function corresponding to the training is expressed as: In the formula, , , The training objective loss, data fitting loss, and physical constraint loss corresponding to the multilayer perceptron model are represented in that order, respectively. Indicates the weight of physical constraints; in, , In the formula, This indicates the number of training samples corresponding to the constrained training. Indicates the first training samples The corresponding prediction performance value, Indicates the first The training samples The parameter values ​​corresponding to the performance parameters, No. The training samples The Porosity perturbation sample The corresponding predicted performance value, No. The training samples The fiber volume fraction perturbation sample The corresponding predicted performance value.

[0016] On the other hand, embodiments of the present invention provide a rigid thermal insulation tile three-phase microstructure generation system, comprising: The sample set management module is used to acquire real slice sample sets in different spatial directions; wherein, the real slice sample set includes several three-phase labeled slices; The network training module is used to train the generative adversarial network using the real slice sample set in all spatial directions and a multidimensional loss function to obtain the trained generative adversarial network; wherein, the generative adversarial network includes a three-dimensional generator and multiple two-dimensional discriminators; The structure generation module is used to obtain the final three-phase structure using the trained 3D generator.

[0017] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. To address the anisotropic microstructure differences of rigid thermal insulation tiles in different spatial directions, a set of real slice samples in multiple directions and multiple two-dimensional discriminators are constructed. A generative adversarial network (including a 3D generator and multiple two-dimensional discriminators) is trained using a multidimensional loss function. This enables the trained 3D generator to retain the microstructure differences of the material in different spatial directions during the generation of the final three-phase structure, avoiding the simplistic treatment of the microstructure of composite thermal insulation tiles with obvious directional characteristics as an isotropic structure. This improves the ability of the generated final three-phase structure to maintain the anisotropic characteristics of the material.

[0018] 2. By encoding the three-phase label slices, discrete data (i.e., binary label slices corresponding to different substances) is constructed, avoiding the discriminator from misinterpreting discrete phase categories as continuous grayscale information, thereby improving the clarity of multiphase interface representation and enhancing the adaptability of the generated three-dimensional training three-phase structure to the actual phase distribution of the material; corresponding two-dimensional discriminators are set for different spatial directions, and independent discrimination constraints are applied to each two-dimensional discriminator to improve the generative adversarial network's ability to maintain the differences in organization in different directions.

[0019] 3. A multi-dimensional loss function is constructed, including a first adversarial loss function, a second adversarial loss function, a classification loss function, a Dice loss function, a three-phase constraint loss function, and an inter-layer constraint loss function. This function can jointly constrain the accuracy of category discrimination, boundary fidelity, rationality of three-phase proportions, and inter-layer topological continuity during the generation of three-dimensional training three-phase structures. Compared with generation methods that rely solely on adversarial losses, this invention is more suitable for generating microstructures of resin-based fiber rigid ceramic thermal insulation tiles with complex multiphase boundaries, significant differences in pore scale, and high requirements for inter-layer continuity. This is beneficial for improving the physical rationality and structural integrity of the generated final three-dimensional three-phase structure.

[0020] 4. Based on the three-phase structure, a trained performance prediction model is obtained by enhancing the structure-performance dataset for predicting the performance of rigid thermal insulation tiles, forming an application from three-dimensional structure generation to structure-performance mapping. The three-dimensional microstructural information of the rigid thermal insulation tile is directly converted into structural parameter data (e.g., thermal conductivity) for performance prediction, realizing a quantitative correlation between the microstructure and performance parameters of the rigid thermal insulation tile, thereby improving the practicality of this invention in the structural characterization and thermal performance prediction of thermal insulation materials.

[0021] 5. Using thickness-direction thermal conductivity as the performance prediction target can better reflect the key heat transfer characteristics of rigid thermal insulation tiles under the influence of layup structure and interface debonding. Compared with averaging thermal conductivity in three directions, this embodiment is more consistent with the anisotropic heat transfer characteristics of this type of material, and also helps to highlight the important significance of thickness-direction heat transfer behavior for thermal insulation performance evaluation. Based on generative adversarial networks, the generation (i.e., three-phase structure) and application (performance parameter prediction) of the microstructure of rigid thermal insulation tiles can provide methodological support for the digital characterization of the microstructure, thermal performance analysis and subsequent optimization design of this type of composite thermal insulation material, and has good engineering application value.

[0022] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0023] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a schematic flowchart of a method for generating a three-phase microstructure of a rigid thermal insulation tile according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the model structure of a three-phase splitting model provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a training three-phase structure provided in an embodiment of the present invention; Figure 4 This is a flowchart illustrating a method for predicting the three-phase microstructure performance of rigid thermal insulation tiles according to an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the prediction effects of various performance prediction models provided in the embodiments of the present invention; Figure 6This is a schematic diagram of the performance analysis results of the XGBoost-LSTM fusion model provided in this embodiment of the invention; Figure 7 This is a schematic diagram of the main modules of a rigid thermal insulation tile three-phase microstructure generation system in an embodiment of the present invention. Detailed Implementation

[0024] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0025] A specific embodiment of the present invention discloses a method for generating a three-phase microstructure of a rigid thermal insulation tile, such as... Figure 1 As shown, it includes: Step S1: Obtain a real slice sample set in different spatial directions; wherein, the real slice sample set includes several three-phase labeled slices.

[0026] A set of real-world slice samples in different spatial orientations is obtained; wherein the set of real-world slice samples includes several three-phase labeled slices. In this embodiment, microscopic CT images of rigid thermal insulation tile samples in different spatial orientations are acquired, and three-phase annotations are performed manually to obtain several three-phase labeled slices in each spatial orientation. Each pixel position in the slice corresponds to a phase label. In this embodiment, the phase labels include porous phase, fibrous phase, and matrix phase, represented by 0, 1, and 2, respectively.

[0027] In this embodiment, considering the anisotropic characteristics of rigid thermal insulation tiles, three orthogonal directions are selected to construct real slice sample sets in three spatial directions respectively. , , Furthermore, based on the material characteristics of rigid heat-insulating tiles, the thickness direction is calibrated when acquiring micro-CT images, for example, the thickness direction is characterized by the Z direction.

[0028] Furthermore, to improve annotation efficiency, each micro-CT image is automatically annotated using a three-phase segmentation model to obtain corresponding three-phase label slices, specifically including step S11.

[0029] Step S11: Input the microscopic CT image into the three-phase segmentation model for segmentation processing to obtain the corresponding three-phase label slices; wherein, the three-phase segmentation model includes an encoder, channel attention branch, spatial attention branch, decoder and classifier connected in sequence.

[0030] In this embodiment, a three-phase segmentation model is used to segment microscopic CT images to obtain corresponding three-phase labeled slices. The three-phase segmentation model includes an encoder, channel attention branch, spatial attention branch, decoder, and classifier connected sequentially, such as... Figure 2 The three-phase segmentation model can segment a single microscopic CT image or perform batch processing, specifically including steps S111-S115.

[0031] Step S111: Input the microscopic CT image into the encoder for downsampling to generate multiple basic feature maps. Transmit one basic feature map to the decoder and transmit the other basic feature maps to the channel attention branch.

[0032] In this embodiment, the microscopic CT image is preprocessed. The preprocessed microscopic CT image is input into the encoder, and the encoder downsamples the microscopic CT image to generate multiple basic feature maps. One basic feature map is transmitted to the decoder, and the other basic feature maps are transmitted to the channel attention branch. The preprocessing includes noise reduction and pixel grayscale value stretching.

[0033] Specifically, the encoder includes multiple first convolutional layers and a bottleneck layer. The base feature maps generated by each first convolutional layer are transmitted to the channel attention branches, and the base feature maps generated by the bottleneck layer are transmitted to the decoder. The multi-layered first convolutional layers of the encoder use convolutional blocks of the VGG16 model. Each first convolutional layer performs convolution, activation, and max pooling processing on the received microscopic CT image or the base feature map transmitted from the previous first convolutional layer, completing downsampling, generating a new base feature map, and transmitting it to the next first convolutional layer, until it reaches the bottleneck layer. The bottleneck layer performs downsampling on the received base feature map transmitted from the previous first convolutional layer, generating a new base feature map, and transmitting it to the decoder. In this embodiment, the encoder includes four first convolutional layers with corresponding output channel numbers of 64, 128, 256, and 512, respectively. The base feature maps generated by the first convolutional layers are transmitted to the corresponding channel attention branches; the bottleneck layer has 1024 output channels. Step S112: The channel attention branch performs channel attention weighted fusion on the received basic feature map to generate the corresponding channel weighted feature map, and transmits it to the spatial attention branch.

[0034] The channel attention branch performs channel attention weighted fusion on the received basic feature map to generate a corresponding channel weighted feature map, which is then transmitted to the spatial attention branch. In this embodiment, the channel attention branch includes a first global average pooling layer, a first global max pooling layer, a first connection layer, a first activation layer, and a first fusion layer.

[0035] Specifically, the first global average pooling layer and the first global max pooling layer perform pooling processing on the received basic feature map to obtain the corresponding pooling results (including channel global information corresponding to the basic feature map). These two pooling results are then input into the first connection layer (in this embodiment, a fully connected network layer, including hidden layers). After processing by the ReLU activation function of the first activation layer, a channel attention weight map is output through the sigmoid function. The first fusion layer multiplies the channel attention weight map with the received basic feature map channel by channel to obtain the corresponding channel-weighted feature map, which is then transmitted to the spatial attention branch. The dimension of the channel-weighted feature map is the same as the dimension of the received basic feature map.

[0036] Step S113: The spatial attention branch performs spatial attention weighted fusion on the received channel weighted feature map to generate the corresponding spatial weighted feature map, and transmits it to the decoder.

[0037] The spatial attention branch performs spatial attention weighted fusion on the received channel weighted feature maps to generate corresponding spatial weighted feature maps, which are then transmitted to the decoder. In this embodiment, the spatial attention branch includes a second global average pooling layer, a second global max pooling layer, a second connection layer, a second activation layer, and a second fusion layer.

[0038] Specifically, the second global average pooling layer performs channel-dimensional global average pooling on the received channel-weighted feature map to obtain a first single-channel feature map. The second global max pooling layer performs channel-dimensional global max pooling on the received channel-weighted feature map to obtain a second single-channel feature map. The second connection layer concatenates the first and second single-channel feature maps along their channel dimensions to obtain a dual-channel feature map. The second activation layer performs convolution on the dual-channel feature map and outputs a spatial attention weight map using the sigmoid function. The second fusion layer multiplies the spatial attention weight map element-wise with the received channel-weighted feature map to obtain the corresponding spatial weighted feature map, which is then transmitted to the decoder. The dimension of the spatial weighted feature map is the same as the dimension of the received channel-weighted feature map.

[0039] Step S114: The decoder upsamples the received base feature map and each spatially weighted feature map to generate a high-dimensional feature map, which is then transmitted to the classifier.

[0040] The decoder upsamples the received base feature map and each spatially weighted feature map to generate a high-dimensional feature map, which is then transmitted to the classifier. In this embodiment, the decoder includes a second convolutional layer that upsamples the received base feature map and each spatially weighted feature map to generate a high-dimensional feature map, which is then transmitted to the classifier.

[0041] Furthermore, the decoder includes multiple second convolutional layers. Each second convolutional layer performs transposed convolution on the received base feature map or the high-dimensional feature map transmitted from the next second convolutional layer, reducing the channel dimension of the base feature map or the high-dimensional feature map and increasing the image size. This ensures that the base feature map or high-dimensional feature map after reducing the channel dimension maintains the same channel dimension as the received spatially weighted feature map, and the channel dimensions are concatenated. Then, the concatenated feature map is convolved to generate a new high-dimensional feature map, completing the upsampling operation. The generated high-dimensional feature map is then transmitted to the next second convolutional layer, and so on, until it reaches the top second convolutional layer, generating a new high-dimensional feature map, which is then transmitted to the classifier. In this embodiment, layer-by-layer upsampling through multiple second convolutional layers yields a high-dimensional feature map with high-resolution semantic features. The high-dimensional feature map generated by the top second convolutional layer is transmitted to the classifier, and the size of the high-dimensional feature map generated by the top second convolutional layer is the same as the size of the microscopic CT image. In this embodiment, the decoder includes four second convolutional layers with corresponding input channel numbers of 1024, 512, 256, and 128, respectively. Taking the bottom second convolutional layer as an example, it receives a 1024-dimensional basic feature map and a 512-dimensional spatial weighted feature map. First, the channel dimension of the basic feature map is reduced to 512 through transpose convolution, while the size of the basic feature map after reducing the channel dimension is doubled. The basic feature map (512-dimensional channel) after reducing the channel dimension is concatenated with the spatial weighted feature map (512-dimensional channel) to generate a 1024-channel concatenated feature map. The concatenated feature map is then subjected to convolutional dimensionality reduction to obtain a 512-dimensional high-dimensional feature map. The upsampling operation is completed, and the result is output to the next second convolutional layer.

[0042] Step S115: The classifier performs three-phase classification on the high-dimensional feature map and generates the corresponding three-phase segmentation results.

[0043] The classifier performs three-phase classification on the high-dimensional feature map and generates the corresponding three-phase segmentation result. In this embodiment, the classifier includes a convolutional classification layer and a third activation layer.

[0044] Specifically, the convolution classification layer performs convolution operations on the received high-dimensional feature map, mapping it into three output channels corresponding to fibers, matrix, and interlayer pores, respectively. The size of the mapped image is consistent with the size of the measured XCT stretched image. In this embodiment, the convolution classification layer uses a 1×1 convolution kernel for convolution operations. The third activation layer is activated by the Softmax function to obtain the probability of each pixel belonging to each phase. For each pixel, the phase corresponding to the output channel with the highest probability is selected as the single-phase category of that pixel. Based on the single-phase categories corresponding to all pixels, a three-phase segmentation result is constructed. For example, if the three output channels sequentially represent fibers, matrix, and interlayer pores, and for a certain pixel, the corresponding three probabilities are 0.80, 0.15, and 0.05 respectively, then the single-phase category of that pixel is determined to be fiber.

[0045] It should be noted that the three-phase segmentation model in this embodiment is constructed based on the traditional Unet model and obtained through training. Based on the microscopic CT images of rigid heat insulation tiles, manual annotation is used as training samples to train the three-phase segmentation model. Existing model training methods can be used, which will not be elaborated here.

[0046] Furthermore, to avoid the discriminator misinterpreting discrete phase categories as continuous grayscale information, thereby improving the clarity of multiphase interface representation and enhancing the adaptability of the generated three-dimensional training three-phase structure to the actual phase distribution of the material, step S1 also includes: Step S12: Encode each three-phase label slice to generate binary label slices corresponding to different objects.

[0047] Since the labels (0 / 1 / 2) in the three-phase label slices are essentially discrete phase labels rather than continuous grayscale intensities, this embodiment encodes each three-phase label slice in each spatial direction to generate corresponding binary label slices, which are then added to the corresponding real slice sample set.

[0048] In this embodiment, one-hot encoding is used to convert each three-phase label slice into a binary label slice, explicitly preserving the multi-phase interface information and preventing the discriminator from misinterpreting the category label as a grayscale pattern.

[0049] For example, a three-phase label slice is represented as ,in This represents the coordinates of each pixel in the three-phase label slice, with 0, 1, and 2 corresponding to the porous phase, fiber phase, and matrix phase, respectively. Three independent binary channel images are constructed using one-hot encoding. , , ,in Only retain the location information of the porous phase. Only retain the location information of the fiber phase. Only the location information of the matrix phase is retained, and all other locations are set to 0; the channel dimensions of the three binary channel plots are combined to obtain three-channel discrete input data (i.e., binary label slices). If the size of the three-phase label slice is... By encoding and combining dimensions, the size is obtained as follows: For a binary tag slice, if any pixel in a three-phase tag slice belongs to the porous phase, its encoding result is: If it belongs to the fibrous phase, then its coding result is: If it belongs to the matrix phase, then its encoding result is: .

[0050] Through encoding, the original two-dimensional three-phase label slices are explicitly converted into three-channel discrete input data (binary label slices) for the porous phase, fibrous phase and matrix phase, thereby avoiding the misinterpretation of phase labels as continuous grayscale information.

[0051] Step S2: Train the generative adversarial network using the real slice sample set in all spatial directions and a multidimensional loss function to obtain the trained generative adversarial network; wherein the generative adversarial network includes a three-dimensional generator and multiple two-dimensional discriminators.

[0052] The generative adversarial network is trained using a real slice sample set in all spatial directions and a multidimensional loss function to obtain a trained generative adversarial network; wherein the generative adversarial network includes a three-dimensional generator and multiple two-dimensional discriminators, specifically including steps S21-S24.

[0053] Step S21: Use the three-dimensional generator to generate a training three-phase probability volume and obtain several three-phase generated slices in different spatial directions.

[0054] The random latent variables are processed using a 3D generator to generate a training three-phase probability body, thereby obtaining several three-phase generated slices in different spatial directions, specifically including steps S211-S212.

[0055] Step S211: Use a 3D generator to process the random latent variables and generate a training three-phase probability body.

[0056] In this embodiment, the 3D generator is built based on SliceGAN and includes a Softmax module, which performs convolution and activation processing on random latent variables to obtain a training three-phase probability volume.

[0057] In this embodiment, the Softmax module includes an input layer, a convolutional hidden layer, and an output layer. The convolutional hidden layer employs a five-layer 3D transposed convolutional structure, with each hidden layer connected to Batch Normalization and ReLU activation functions to perform convolution processing on random latent variables, ultimately outputting a three-channel image. Each generated channel represents a phase, and each output image includes the activation values ​​corresponding to each voxel. The output layer uses the Softmax activation function to convert each activation value into a phase probability. Generate a training three-phase probability body that matches the size of the three-phase label slice, wherein, Indicates the first One generation channel, The activation value corresponding to the voxel at the coordinate position. Indicates the first One generation channel, The phase probability corresponding to the voxel at the coordinate.

[0058] For example, the three-phase label slice size is The size of the input random latent variable is set to (These represent the image channels, length, width, and height in that order, with each variable element being a random value). The kernel size, stride, and padding of the five-layer 3D transposed convolutional structure are set sequentially as follows: , , , , Layer by layer, the size is obtained as , , , , The image is converted into a 3D training three-phase probability volume using the Softmax activation function, with three channels and three directional slice sizes consistent with the three-phase label slice sizes. Each voxel position in this training three-phase probability volume contains the probabilities of the output of three generated channels (i.e., phase probabilities), representing the probabilities that the voxel belongs to the porous phase, fibrous phase, and matrix phase, respectively (e.g., ...). Figure 3 (As shown on the left).

[0059] Furthermore, the 3D generator also includes an argmax module, which performs argmax operation on the training three-phase probability volume to obtain the training three-phase structure.

[0060] Specifically, based on the training three-phase probability volume, the argmax operation is performed to determine the phase corresponding to each voxel according to the phase probabilities of the three generation channels at each voxel in the training three-phase probability volume, expressed as follows: In the formula, express The phase corresponding to the voxel at the coordinate position. This represents the set of generation channels. For example, the first generation channel represents the porous phase, the second generation channel represents the fibrous phase, and the third generation channel represents the matrix phase. Iterating through each voxel of the training three-phase probability volume, if the maximum value of the phase probability values ​​of the three generation channels for that voxel comes from the first generation channel, then the phase of that voxel is determined to be the porous phase; if the maximum value comes from the second generation channel, then the phase of that voxel is determined to be the fibrous phase; if the maximum value comes from the third generation channel, then the phase of that voxel is determined to be the matrix phase. Based on the phase of each voxel, a training three-phase structure is constructed (e.g., ...). Figure 3 (As shown on the right).

[0061] Step S212: Extract slices from the training three-phase probability volume according to different spatial directions to obtain several three-phase generation slices in different spatial directions.

[0062] In this embodiment, the training three-phase probability volume is sliced ​​according to the spatial directions corresponding to the three-phase label slices, resulting in several three-phase generated slices in different spatial directions. For example, the training three-phase probability volume is sliced ​​layer by layer along three orthogonal directions (e.g., X, Y, and Z directions) to obtain several three-phase generated slices in each spatial direction, forming a set of generated slices. , , .

[0063] Further, each three-phase generation slice is encoded according to step S12 to generate a corresponding binary generation slice, which is then added to the corresponding generation slice set.

[0064] Step S22: Train each of the two-dimensional discriminators using the three-phase generated slices, the three-phase labeled slices, and the multidimensional loss function.

[0065] In this embodiment, the multidimensional loss function includes a first adversarial loss function, and each two-dimensional discriminator is trained using each three-phase generated slice, each three-phase label slice and the multidimensional loss function, including steps S221-S223.

[0066] Step S221: Input the three-phase generated slices and the three-phase label slices of each spatial direction into the corresponding two-dimensional discriminator to obtain the corresponding discrimination result; wherein, each spatial direction corresponds to one two-dimensional discriminator.

[0067] Each spatial direction corresponds to a two-dimensional discriminator. The three-phase generated slices and three-phase label slices for each spatial direction are input into the corresponding two-dimensional discriminator to obtain the corresponding discrimination results. Each two-dimensional discriminator adopts the same hierarchical structure, but the discriminator parameters are independent of each other. In this embodiment, to avoid the two-dimensional discriminator misinterpreting the phase labels as continuous grayscale information, the binary label slices and the binary generated slices corresponding to each three-phase generated slice are input into the two-dimensional discriminator to obtain the corresponding discrimination results.

[0068] For example, three two-dimensional discriminators are established based on three orthogonal directions. , , Each discriminator employs a six-layer convolutional structure, with each hidden layer using the LeakyReLU activation function and a negative slope of 0.2. The dimensions of the binary label slices and the binary generated slices are... The kernel size, stride, and padding of the first five convolutional layers are set to... The kernel size, stride, and padding of the sixth convolutional layer are set as follows: Layer by layer, the size is obtained as , , , , , The processing result is a scalar-formatted discrimination result.

[0069] Step S222: Based on each of the discrimination results, calculate the corresponding first adversarial loss value using the first adversarial loss function.

[0070] Based on the discrimination results for each spatial direction, the corresponding first adversarial loss value is calculated using the first adversarial loss function. In this embodiment, the first adversarial loss function is expressed as: In the formula, Indicates the first Two-dimensional discriminant corresponding to each spatial direction The first adversarial loss value, Indicates the first A set of real slice samples in each spatial direction Indicates the first Three-phase generation slices in each spatial direction Represents a two-dimensional discriminator Three-phase generation slices The judgment result, express Includes each of the three-phase generated slices Corresponding discrimination results Expectations Indicates the first Three-phase tag slices in each spatial direction The set of slices (i.e., the set of slices generated). Represents a two-dimensional discriminator Three-phase label slices The judgment result, express Includes each of the three-phase tag slices Corresponding discrimination results Expectations Represents a two-dimensional discriminator Three-phase interpolation slices The judgment result, Represents a three-phase interpolation slice The corresponding partial derivative gradient The 2-norm, Represents all three-phase interpolation slices corresponding Expectations Represents the gradient penalty coefficient (e.g.) ).

[0071] In this embodiment, the two-dimensional discriminator Three-phase generation slices The discrimination result refers to the three-phase generation slice. The corresponding binary generated slice input to the two-dimensional discriminator The obtained discrimination results; two-dimensional discriminator Three-phase label slices The discrimination result refers to the three-phase label slices The corresponding binary label slice is input into the two-dimensional discriminator. The obtained discrimination results; two-dimensional discriminator Three-phase interpolation slices The discrimination result refers to the three-phase interpolation slice The corresponding binary interpolation slice is input to the two-dimensional discriminator. The obtained discrimination result; the three-phase interpolation slice refers to the linear interpolation slice between the three-phase label slice and the three-phase generated slice. Each three-phase interpolation slice is encoded according to step S12 to obtain the corresponding binary interpolation slice.

[0072] For example, the three-phase interpolation slice is In the formula, Represents the interpolation coefficients, with a range of values ​​of 1000. In this embodiment, the value is 0.5. For example, starting from the first... For each spatial direction, a three-phase labeled slice and a three-phase generated slice are extracted from the real slice sample set and the generated slice set, respectively, to generate the corresponding linear interpolation slice. Multiple linear interpolation slices are extracted and generated multiple times to form the corresponding interpolation slice set, which is used to calculate the first adversarial loss for that spatial direction.

[0073] To reduce computational cost, the same number (e.g., 10) of three-phase labeled slices and three-phase generated slices can be extracted from the real slice sample set and the generated slice set respectively to form real slice groups and generated slice groups. These can then be paired one-to-one to generate corresponding interpolated slice groups, which are used to calculate the corresponding first adversarial loss.

[0074] Step S223: Train the corresponding two-dimensional discriminator based on each of the first adversarial loss values.

[0075] Based on the first adversarial loss value corresponding to each spatial direction, the two-dimensional discriminator corresponding to that spatial direction is trained, and the discriminator parameters of each two-dimensional discriminator are updated.

[0076] In this embodiment, the Adam optimizer is used for training. For example, the learning rate of the two-dimensional discriminator is set to... Batch size is set to 8, training epochs are set to 300, and Adam parameters are set accordingly. , .

[0077] The binary labeled slices and the binary generated slices corresponding to each three-phase generated slice are input into the two-dimensional discriminator. The two-dimensional discriminator is trained adversarially using the real slice sample set and the generated slice set. The discriminator parameters are updated by the first adversarial loss value to improve the ability of the two-dimensional discriminator to distinguish between real slices (i.e., binary labeled slices) and generated slices (i.e., binary generated slices). The two-dimensional discriminators corresponding to different directions force the three-dimensional generator to generate a three-phase structure that is more in line with the anisotropic characteristics of rigid heat insulation tiles.

[0078] Step S23: Train the 3D generator using the training three-phase probability body, each of the three-phase generation slices, each of the three-phase label slices, and the multidimensional loss function.

[0079] The generator's total loss value is calculated using the training three-phase probability volume, each three-phase generation slice, each three-phase label slice, and a multidimensional loss function. The 3D generator is then trained based on this total loss value.

[0080] In this embodiment, the multidimensional loss function also includes a second adversarial loss function, a classification loss function, a Dice loss function, a three-phase constraint loss function, and an inter-layer constraint loss function. Step S23 includes steps S231-S234.

[0081] Step S231: Based on each of the three-phase generated slices and each of the three-phase label slices in all spatial directions, calculate the corresponding second adversarial loss value, classification loss value, and Dice loss value using the second adversarial loss function, the classification loss function, and the Dice loss function.

[0082] Based on each three-phase generated slice and each three-phase label slice in all spatial directions, the corresponding second adversarial loss value, classification loss value, and Dice loss value are calculated using the second adversarial loss function, classification loss function, and Dice loss function, including steps A-C.

[0083] Step A: Generate slices based on each of the three phases in all spatial directions, and calculate the corresponding second adversarial loss value using the second adversarial loss function.

[0084] In this embodiment, the second adversarial loss function is expressed as: In the formula, This represents the second adversarial loss value corresponding to the 3D generator. Indicates the first Direction coefficients in each spatial direction Represents the set of spatial directions. Indicates the first A set of real slice samples in each spatial direction Indicates the first Three-phase generation slices in each spatial direction Represents a two-dimensional discriminator Three-phase generation slices The judgment result, express Includes each of the three-phase generated slices Corresponding discrimination results The expected outcome. Among them, the two-dimensional discriminator. Three-phase generation slices The discrimination result refers to the three-phase generation slice. The corresponding binary generated slice input to the two-dimensional discriminator The obtained discrimination results.

[0085] Furthermore, based on the material characteristics of rigid thermal insulation tiles, and considering the more significant structural features such as interlayer porosity evolution, fiber layup undulation, and obstructed heat transfer paths along the material thickness direction, a higher directional coefficient is set for the thickness. For example, the thickness direction is represented by the Z direction, and the spatial direction set includes the X, Y, and Z directions, with the directional coefficients as follows: , , .

[0086] Step B: Generate slices and label slices for each of the three phases in all spatial directions, and calculate the corresponding classification loss value using the classification loss function.

[0087] First, based on each three-phase generated slice and each three-phase labeled slice in each spatial direction, the corresponding single-slice classification loss value is calculated using the classification loss function.

[0088] In this embodiment, the classification loss function is expressed as follows: In the formula, Indicates the first The spatial direction, the first Individual classification loss value; , These represent the height and width of the three-phase generated slice, respectively; Indicates the first The spatial direction, the first Three-phase label slice coordinates The corresponding number The label value of each phase is determined based on the corresponding binary channel plot; Indicates the first The spatial direction, the first Three-phase generation slice coordinates The corresponding number The probability of each phase can be determined by the slice location, based on... Determine, for example, if the first The spatial direction, the first Each three-phase generation slice is used as a training three-phase probability body. The slice obtained from the location, and , ,but ; To represent extremely small numbers and avoid zero values ​​in logarithmic calculations, for example... .

[0089] For example, for each spatial direction, a certain number of three-phase label slices are randomly sampled from the corresponding real slice sample set, and the same number of three-phase generated slices are randomly sampled from the generated slice set of that spatial direction. The randomly sampled three-phase label slices and three-phase generated slices are paired one by one, and the corresponding single-slice classification loss value is calculated respectively.

[0090] Secondly, based on the classification loss value of each individual piece in each spatial direction, the corresponding one-way classification loss value is calculated.

[0091] Based on the classification loss value of each individual piece in each spatial direction, the formula is used. Calculate the corresponding one-way classification loss value, where, Indicates the first The one-way classification loss value corresponding to each spatial direction. Indicates the first The number of three-phase label slices corresponding to each spatial direction.

[0092] Finally, the classification loss value is calculated based on the unidirectional classification loss values ​​in all spatial directions.

[0093] Based on the unidirectional classification loss values ​​in all spatial directions, using the formula... Calculate the classification loss value, where, Represents the classification loss value. It represents a set of spatial directions, such as the three directions X, Y, and Z.

[0094] The classification loss value is used to constrain the accuracy of local three-phase category discrimination of the three-phase generated slice. Unlike traditional segmentation tasks, this embodiment does not have voxel labels of real three-dimensional structures. Therefore, the classification loss function does not supervise the fixed-position voxel reconstruction at the three-dimensional structure level. Instead, after training the three-phase probability volume to slice along different spatial directions, the three-phase generated slice is compared with the real two-dimensional label slice (i.e., three-phase label slice) randomly sampled in the corresponding direction for category supervision.

[0095] It should be noted that although the classification loss value is calculated pixel-by-pixel based on the three-phase generated slices and the three-phase label slices, its role in this embodiment is not to force the generated structure (i.e., the training three-phase probability volume and the training three-phase structure) to be reconstructed into a certain real structure. Instead, it works in conjunction with the second adversarial loss value, the Dice loss value, the three-phase constraint loss value, and the inter-layer constraint loss value as an auxiliary loss term to provide local three-phase category correction for the randomly sampled three-phase generated slices. The overall statistical authenticity and diversity of the generated structure are guaranteed by the generator's total loss value.

[0096] Step C: Generate slices and label slices for each of the three phases in all spatial directions, and calculate the corresponding Dice loss value using the Dice loss function.

[0097] First, based on each three-phase generated slice and each three-phase labeled slice in each spatial direction, the corresponding single-phase Dice loss value is calculated using the Dice loss function.

[0098] In this embodiment, the Dice loss function is expressed as: In the formula, Indicates the first The spatial direction, the first Phase 1, Phase 2 Single-phase Dice loss value; , These represent the height and width of the three-phase generated slice, respectively; Indicates the first The spatial direction, the first Three-phase generation slice coordinates The corresponding number The probability of each phase can be determined by the slice location, based on... Sure; Indicates the first The spatial direction, the first Three-phase label slice coordinates The corresponding number The label value of each phase can be determined based on the corresponding binary channel plot; To represent extremely small numbers and avoid abnormal calculation results, for example... .

[0099] For example, for each spatial direction, a certain number of three-phase labeled slices are randomly sampled from the corresponding real slice sample set, and the same number of three-phase generated slices are randomly sampled from the generated slice set of that spatial direction. The randomly sampled three-phase labeled slices and three-phase generated slices are paired one by one, and the corresponding single-slice single-phase Dice loss value is calculated respectively.

[0100] Secondly, based on the single-phase Dice loss value of each three-phase label slice, the corresponding single-slice Dice loss value is calculated.

[0101] Based on the single-phase Dice loss value of each individual slice of the three-phase tag, the formula is used. Calculate the corresponding single-chip Dice loss value, where, Indicates the first The spatial direction, the first Individual Dice loss values.

[0102] Next, based on the individual Dice loss values ​​for each spatial direction, the corresponding unidirectional Dice loss value is calculated.

[0103] Based on the Dice loss value of each individual chip in each spatial direction, the formula is used. Calculate the corresponding one-way Dice loss value, where, Indicates the first The unidirectional Dice loss value corresponding to each spatial direction. Indicates the first The number of three-phase label slices corresponding to each spatial direction.

[0104] Finally, the Dice loss value is calculated based on the unidirectional Dice loss values ​​in all spatial directions.

[0105] Based on the unidirectional Dice loss values ​​in all spatial directions, using the formula... Calculate the Dice loss value, where, This represents the Dice loss value. It represents a set of spatial directions, such as the three directions X, Y, and Z.

[0106] Dice loss enhances the fidelity of interfacial debonding pores, elongated pores, and weak boundary regions by increasing the overlap between the three-phase generated slices and the three-phase label slices in the porous phase, fibrous phase, and matrix phase regions.

[0107] Step S232: Based on the training three-phase probability volume and each of the three-phase label slices, calculate the corresponding three-phase constraint loss value and inter-layer constraint loss value using the three-phase constraint loss function and the inter-layer constraint loss function.

[0108] Based on the training three-phase probability volume and each three-phase label slice, the corresponding three-phase constraint loss value and inter-layer constraint loss value are calculated using the three-phase constraint loss function and the inter-layer constraint loss function, including steps D-E.

[0109] Step D: Based on the training three-phase probability volume and each three-phase label slice, calculate the corresponding three-phase constraint loss value using the three-phase constraint loss function.

[0110] First, based on the training of three-phase probability volumes, the generated volume fraction corresponding to each object is statistically calculated.

[0111] In this embodiment, the formula is used based on the training three-phase probability body. Calculate the corresponding volume fraction of each product, where, , , Let the length, height, and width of the training three-phase probability body be represented respectively. This represents the total number of elements in the training three-phase probability body; Represents the coordinates of the training three-phase probability volume. The voxel corresponding to the first The probability of each phase.

[0112] In other embodiments, based on the training three-phase structure corresponding to the training three-phase probability body, the formula is used. Calculate the corresponding volume fraction of each product, where, Indicates the training of the three-phase structure. Phase, coordinates The phase label corresponding to the voxel at that location, through Determine, for example, the first A phase, if The phase corresponding to the voxel at the coordinate is the first. If there is a phase, the corresponding phase label is 1; otherwise, it is 0.

[0113] Secondly, based on the three-phase label slices in all spatial directions, the sample volume fraction corresponding to each object is calculated.

[0114] For each rigid insulation tile sample, for all three-phase label slices in each spatial direction, calculate the unidirectional sample volume fraction for each phase corresponding to that spatial direction. For example, In the formula, Indicates the first The first rigid heat insulation tile sample, the first The spatial direction, the first The sample volume fraction corresponding to each item; Indicates the first The first rigid heat insulation tile sample, the first The number of three-phase tag slices corresponding to each spatial direction , These represent the height and width of the three-phase label slice, respectively; Indicates the first The first rigid heat insulation tile sample, the first The spatial direction, the first Three-phase label slice coordinates The corresponding number The label value of each phase can be determined based on the corresponding binary channel plot.

[0115] For each rigid insulation tile sample, calculate the unidirectional sample volume fraction in all spatial directions, and then calculate the corresponding sample volume fraction for each object. For example, In the formula, Indicates the number of rigid thermal insulation tile samples; This indicates the number of spatial directions. For example, if the set of spatial directions includes three directions: X, Y, and Z, then... .

[0116] Finally, based on the generated volume fraction and sample volume fraction of each phase, the corresponding three-phase constraint loss value is calculated using the three-phase constraint loss function.

[0117] Based on the generated volume fraction and sample volume fraction of each phase, the three-phase constraint loss function is used. Calculate the corresponding three-phase constraint loss value .

[0118] The three-phase constraint loss value characterizes the consistency constraint loss of the three-phase volume fraction. It is used to constrain the overall proportion of the porous phase, fiber phase and matrix phase in the generated training three-phase structure to be consistent with the statistical results of the real material (three-phase label slice), so as to ensure the rationality of the three-phase proportion.

[0119] The three-phase constraint loss value is not calculated at the two-dimensional slice level, but is directly based on the three-dimensional three-phase probability volume output by the three-dimensional generator for global statistical constraint. This is used to prevent abnormal drift in the proportion of porous phase, fiber phase or matrix phase in the training three-phase probability volume and training three-phase structure, thereby ensuring that the three-phase ratio on which the structural parameter extraction and performance prediction (such as thickness direction thermal conductivity prediction) depend in subsequent applications has physical rationality.

[0120] Step E: Based on the training three-phase probability volume and each three-phase label slice, calculate the corresponding inter-layer constraint loss value using the inter-layer constraint loss function.

[0121] For the structural features of rigid thermal insulation tiles, such as more significant interlayer porosity evolution, fiber layup undulation, and obstructed heat transfer paths in the thickness direction, the corresponding interlayer constraint loss value is calculated in the thickness direction of the material.

[0122] In this embodiment, the inter-layer constraint loss function is expressed as: In the formula, This represents the interlayer constraint loss value. Indicates the number of floors. Indicates the first Layer, First line, number The predicted probability array of the column. Indicates the first Layer, First line, number The predicted probability array of the column. express The 2-norm.

[0123] in, Characterizing two adjacent layers (the first layer) Layer, First (layer) in the same phase and in the same spatial location (the first) line, number Differences in the column.

[0124] For example, regarding the 2-norm After demonstration, the inter-layer constraint loss function is expressed as: In the formula, , These represent the height and width of the three-phase generated slice, respectively; Indicates the first Three-phase generation slice coordinates of the layer The corresponding number The probability of each phase can be determined by the slice location, based on... Sure; Indicates the first Three-phase generation slice coordinates of the layer The corresponding number The probability of each phase can be determined by the slice location, based on... Sure.

[0125] Interlayer constraint loss values ​​are used to penalize excessive changes in phase distribution between adjacent layers, thereby improving interlayer topological continuity. These interlayer constraint loss values ​​suppress non-physical abrupt changes in the thickness direction of the generated 3D structures (training three-phase probabilistic volumes and training three-phase structural volumes). The purpose is not to force adjacent layers to become completely identical, but rather to serve as a lightweight regularization constraint in the generator's total loss value. This constraint is used to suppress unrealistic faults and random jumps, preventing faults, abrupt changes, or discontinuities between adjacent thickness layers in the generated structure. Simultaneously, it preserves the inherent structural differences in the thickness direction of rigid thermal insulation tiles caused by the layered structure and interfacial debonding.

[0126] Step S233: Calculate the generator's total loss value based on the second adversarial loss value, the classification loss value, the Dice loss value, the three-phase constraint loss value, and the inter-layer constraint loss value.

[0127] Based on the second adversarial loss value, classification loss value, Dice loss value, three-phase constraint loss value, and inter-layer constraint loss value, using the formula Calculate the total loss of the generator, where, , , , These represent the classification loss weight, Dice loss weight, three-phase constraint loss weight, and inter-layer constraint loss weight, respectively.

[0128] In this embodiment, the generator's total loss value is dominated by the second adversarial loss value. , , , All less than 1, for example , , , .

[0129] By using the second adversarial loss value as the main factor, combined with the classification loss value, Dice loss value, three-phase constraint loss value, and interlayer constraint loss value, the 3D generator can maintain the overall consistency of the generated structure (training three-phase probabilistic volume and training three-phase structure) while strengthening the learning of microstructural features in key directions. This improves the fidelity of fiber orientation, interface debonding pores, and directional pore connectivity features in the generated structure, while avoiding excessive suppression of the diversity of generated samples and material anisotropy features.

[0130] Step S234: Train the 3D generator based on the total loss value of the generator.

[0131] Based on the generator's total loss value, the 3D generator is trained and its generator parameters are updated, enabling the 3D generator to generate more realistic training three-phase probability bodies and training three-phase structures.

[0132] In this embodiment, the Adam optimizer is used for training. For example, the learning rate of the 3D generator is set to... Batch size is set to 8, training epochs are set to 300, and Adam parameters are set accordingly. , .

[0133] Step S24: After the training stopping condition is met, the trained generative adversarial network is obtained.

[0134] After the training stopping condition is met, a trained generative adversarial network (GAN) is obtained, i.e., a trained 3D generator. In this embodiment, the training stopping condition includes a preset number of training iterations. When the training iterations of the 3D generator reach the preset number of training iterations, training stops, and the trained GAN is obtained. In other embodiments, the training stopping condition may include a generator loss threshold. If the total loss value of the generator is lower than the generator loss threshold, training stops, and the trained GAN is obtained. Early stopping strategies and multiple training stopping conditions can be set based on existing technologies, and no limitations are imposed here.

[0135] In this embodiment, an alternating training method is used to train multiple two-dimensional discriminators and generators. For example, firstly, multiple two-dimensional discriminators are trained in parallel. If the first adversarial loss value corresponding to each two-dimensional discriminator is less than the first adversarial threshold, the discriminator parameters of multiple two-dimensional discriminators are frozen. Then, the three-dimensional generator is trained. If the total loss value of the generator is less than the generator loss threshold, the generator parameters are frozen, and multiple two-dimensional discriminators are retrained. This process is repeated until the training stop condition is met, and then the trained generative adversarial network is obtained, which is the trained three-dimensional generator.

[0136] In other embodiments, multiple two-dimensional discriminators and three-dimensional generators can be trained simultaneously. To enhance training stability, the number of updates for the multiple two-dimensional discriminators in each round can be set to 3, and the number of updates for the three-dimensional generator in each round can be set to 1.

[0137] To address the significant anisotropy issues caused by fiber layup orientation, interfacial debonding pores, and local non-uniform distribution of three-phase components in rigid thermal insulation tiles, this embodiment constructs an independent statistical constraint mechanism based on different spatial directions. Unlike methods that rely solely on a single two-dimensional slice to characterize directional statistical features, this invention constructs a set of real slices in different spatial directions. During training, a two-dimensional discriminator corresponding to each spatial direction distinguishes the three-phase labeled slices and three-phase generated slices in that spatial direction. This allows each two-dimensional discriminator to learn the statistical distribution differences of the fiber phase, matrix phase, and pore phase in different spatial directions, reducing the bias effect of local random structures in a single slice on the generation results.

[0138] Furthermore, considering the more significant structural features of interlayer pore evolution, fiber layup undulation, and heat transfer path obstruction in the thickness direction of rigid thermal insulation tiles, the adversarial loss corresponding to the 3D generator is assigned differential weights in different spatial directions to construct a weighted adversarial constraint term (i.e., the second adversarial loss value). This allows the 3D generator to enhance its learning of microstructural features in key directions while maintaining the overall consistency of the 3D structure. This improves the fidelity of fiber orientation, interface debonding pores, and directional pore connectivity features in the final three-phase structure, providing a more realistic 3D sample basis for subsequent anisotropic transfer performance calculations and thickness direction thermal conductivity prediction.

[0139] Step S3: Obtain the final three-phase structure using the trained 3D generator.

[0140] Based on random latent variables, the final three-phase structure is obtained using a trained 3D generator.

[0141] Specifically, random latent variables are input into the trained 3D generator, and the Softmax module generates the final three-phase probability volume. The Softmax module then sends the final three-phase probability volume to the argmax module, which generates the corresponding final three-phase structure. The principle is the same as step S211, and will not be repeated here.

[0142] By using a trained 3D generator, 3D structural samples (final three-phase structures) that are consistent with the statistical characteristics of real materials can be obtained, which can solve the problem of insufficient 3D three-phase structural samples and provide a data source for the extraction of rigid thermal insulation tile structural parameters and performance prediction to a certain extent.

[0143] This invention provides a method for predicting the three-phase microstructural properties of rigid thermal insulation tiles, such as... Figure 4 As shown, it includes: Step S4: For each three-phase structure, extract the parameter values ​​corresponding to multiple structural parameters and calculate the parameter values ​​corresponding to the performance parameters; wherein, the three-phase structure includes the final three-phase structure obtained in the aforementioned embodiments; the performance parameters include thermal conductivity.

[0144] For each three-phase structure, the parameter values ​​of multiple structural parameters of the three-phase structure are extracted, and the parameter values ​​of the performance parameters of the three-phase structure are calculated; wherein, the three-phase structure includes the final three-phase structure obtained in the aforementioned embodiments; the performance parameters include thermal conductivity. It is understood that multiple final three-phase structures can be generated using the trained 3D generator.

[0145] In this embodiment, the three-phase structure also includes a sample three-phase structure generated based on the microscopic CT image of the rigid heat insulation tile sample. For example, the rigid heat insulation tile sample is scanned with monomers at intervals to obtain multiple microscopic CT images, and corresponding three-phase label slices are generated. All three-phase label slices are spliced ​​together in the scanning order to obtain the sample three-phase structure corresponding to the rigid heat insulation tile sample.

[0146] In this embodiment, AVIZO software is used to extract the parameter values ​​of multiple structural parameters for each three-phase structure. For example, the structural parameters include average pore volume, sphericity, tortuosity, average pore area, equivalent average pore diameter, fiber volume fraction, number of pores, Euler number, and porosity. The value of each structural parameter is extracted, which is the corresponding parameter value.

[0147] In this embodiment, based on the anisotropy of rigid thermal insulation tiles and the fact that heat transfer in the thickness direction is more susceptible to the effects of ply structure and interface debonding, the thermal conductivity is adopted in the thickness direction. For each three-phase structure, the parameter value corresponding to the thermal conductivity in the thickness direction of the three-phase structure is calculated using the PuMA open-source package. The multiple structural parameters, thermal conductivity, and corresponding parameter values ​​of each three-phase structure are used as training samples to form the original structure-performance dataset.

[0148] In other embodiments, thermal conductivity in other directions can also be calculated, and multiple structural parameters, multiple thermal conductivity, and corresponding parameter values ​​corresponding to each three-phase structure can be used as training samples to construct an original structure-performance dataset; alternatively, based on existing technologies, parameter values ​​corresponding to other performance parameters can be calculated to construct the original structure-performance dataset.

[0149] Step S5: Based on the correlation between each of the structural parameters and the performance parameters, select key structural parameters and construct an enhanced structure-performance dataset.

[0150] Based on the correlation between various structural parameters and performance parameters, key structural parameters are selected, and an enhanced structure-performance dataset is constructed, including steps S51-S53.

[0151] Step S51: Based on the parameter values ​​of the structural parameters and performance parameters corresponding to each of the three-phase structures, calculate the correlation coefficient between each structural parameter and the performance parameter, and select key structural parameters according to the correlation coefficients.

[0152] In this embodiment, based on the parameter values ​​of each structural parameter and performance parameter corresponding to each three-phase structure, the Pearson correlation analysis method is used to calculate the correlation coefficient of each structural parameter and performance parameter. Structural parameters with correlation coefficients greater than the correlation threshold are selected as key structural parameters to reduce the redundancy of input features in the subsequent performance prediction model, improve the stability of the performance prediction model, and reduce the risk of model overfitting.

[0153] In other embodiments, structural parameters with higher correlation coefficients (e.g., the top three structural parameters with the highest correlation coefficients) can be selected as key structural parameters according to a preset number.

[0154] For example, the key structural parameters selected in this embodiment include eight structural parameters: average pore volume, sphericity, average pore area, equivalent average pore diameter, fiber volume fraction, number of pores, Euler number, and porosity.

[0155] Step S52: Construct a basic structure-performance dataset based on the key structural parameters and the parameter values ​​corresponding to the performance parameters.

[0156] Based on the key structural parameters, performance parameters, and their corresponding values, a basic structure-performance dataset is constructed. For example, each key structural parameter, its value, and its performance parameters and values ​​are used as a basic sample for each three-phase structure. Multiple basic samples formed by all three-phase structures constitute the basic structure-performance dataset.

[0157] Step S53: Based on the infrastructure-performance dataset, perform sample augmentation using a Gaussian mixture model to generate multiple augmented samples, add them to the infrastructure-performance dataset, and obtain the augmented infrastructure-performance dataset.

[0158] In this embodiment, considering the operating cost and time of the 3D generator, a Gaussian mixture model is used for sample augmentation to generate multiple augmented samples. These are then added to the basic structure-performance dataset to obtain an augmented structure-performance dataset, thereby further expanding the training samples for the performance prediction model. Specifically, this includes steps S531-S533.

[0159] Step S531: Determine the enhancement constraints based on the infrastructure-performance dataset.

[0160] In this embodiment, the enhanced constraints include single-parameter constraints and multi-parameter coupled constraints.

[0161] Based on the infrastructure-performance dataset, the value range of each key structural parameter is statistically analyzed, serving as the single-parameter constraint for each key structural parameter. In the formula, , The parameter values ​​representing porosity are respectively The minimum and maximum values; statistically analyze the correlation relationships corresponding to the correlation parameters, using them as multi-parameter coupling constraints for the correlation parameters, for example... In the formula, The parameter value representing the fiber volume fraction. , In this embodiment, the constraint range is indicated. , The correlation parameters can be determined based on statistical patterns or experience.

[0162] Step S532: Based on the infrastructure-performance dataset, generate multiple enhanced samples using a Gaussian mixture model.

[0163] Based on the infrastructure-performance dataset, a Gaussian mixture model is used to fit the data distribution corresponding to the infrastructure-performance dataset. Multiple Gaussian samplings are performed from the fitted distribution to obtain multiple enhanced samples.

[0164] For example, the Gaussian Mixture Model (GMM) parameters are set as follows: the number of Gaussian mixture components is set to 5, the covariance matrix type is full, the maximum number of iterations is 100, the random seed is 42, and the convergence threshold is 1e-3.

[0165] Gaussian mixture models (GMMs) are used to augment the infrastructure-performance dataset, ensuring that the augmented samples maintain a consistent statistical distribution with the base samples, thereby effectively improving the generalization ability and robustness of the performance prediction model.

[0166] Step S533: Based on the enhancement constraints, perform a physical consistency judgment on each enhancement sample, and add the enhancement samples that pass the judgment to the infrastructure-performance dataset to obtain the enhancement structure-performance dataset.

[0167] Based on the enhancement constraints, a physical consistency judgment is performed on each enhancement sample. Enhancement samples that pass the judgment are added to the infrastructure-performance dataset to obtain the enhancement infrastructure-performance dataset.

[0168] In this embodiment, the physical consistency judgment includes single-parameter constraint judgment and multi-parameter coupling constraint judgment.

[0169] First, for each augmented sample, the parameter values ​​of each key structural parameter of the augmented sample are judged by single-parameter constraint. If the parameter values ​​of each key parameter in the augmented sample are within the corresponding range, the single-parameter constraint is judged to be passed.

[0170] Then, for each enhanced sample that passes the single-parameter constraint, the parameter values ​​of the associated parameters of the enhanced sample are judged by multi-parameter coupling constraints. If the calculated parameter values ​​of the associated parameters in the enhanced sample are within the corresponding constraint range, the physical consistency judgment is passed.

[0171] This embodiment introduces a physical constraint mechanism on the basis of Gaussian mixture model (GMM) to constrain the physical relationship between structural parameters, so that the generated enhanced samples are more consistent with the material structure characteristics and heat transfer mechanism, thereby improving the reliability, stability and generalization ability of the subsequent performance prediction model.

[0172] Step S6: Use the enhanced structure-performance dataset to perform constrained training on several performance prediction models to obtain several trained performance prediction models.

[0173] Several performance prediction models were trained under constraints using an enhanced structure-performance dataset, resulting in several fully trained performance prediction models.

[0174] To avoid performance prediction models relying solely on data fitting and resulting in predictions that violate material performance mechanisms (such as heat transfer mechanisms), training constraints are determined based on the performance characteristics of rigid thermal insulation tiles. These constraints are then used to train each performance prediction model, resulting in trained models. Taking thermal conductivity as an example, the basic heat transfer characteristics of rigid thermal insulation tiles are established: as porosity increases, the continuous heat transfer path in the solid phase decreases, and the overall thermal conductivity should decrease; conversely, as the fiber volume fraction increases, the solid-phase heat conduction network strengthens, and the overall thermal conductivity should increase. Therefore, during the training of each performance prediction model, the negative correlation between porosity and thermal conductivity, and the positive correlation between fiber volume fraction and thermal conductivity, are used as training constraints, resulting in several trained performance prediction models.

[0175] In this embodiment, the performance prediction model includes one or more of the following: Multilayer Perceptron (MLP), Multiple Linear Regression (MLR), Decision Tree, Long Short-Term Memory (LSTM), and XGBoost-LSTM fusion model. In other embodiments, the performance prediction model also includes a Support Vector Machine (SVM) model. Step S6 includes at least one of steps S61, S62, S63, S64, and S65.

[0176] Step S61: Use the enhanced structure-performance dataset to perform constrained training on the multilayer perceptron model to obtain the trained multilayer perceptron model.

[0177] The multilayer perceptron model belongs to the gradient-optimized neural network model. During training, the update of model parameters depends on the backpropagation mechanism of the loss function. In this embodiment, the training objective function is improved based on training constraints, which constrain the corresponding directions of the model parameters with respect to the key structural parameters. The improved training objective function is expressed as follows: In the formula, , , These represent the training objective loss, data fitting loss, and physical constraint loss for the multilayer perceptron model, in that order. Represents the physical constraint weights; where, , In the formula, This indicates the number of training samples corresponding to the constrained training. Indicates the first training samples The corresponding prediction performance value, Indicates the first The training samples The parameter values ​​corresponding to the performance parameters, No. The training samples The Porosity perturbation sample The corresponding predicted performance value, No. The training samples The fiber volume fraction perturbation sample The corresponding predicted performance value.

[0178] The multilayer perceptron model is trained based on the improved training objective function to obtain the trained multilayer perceptron model, specifically including: 1) For each training sample, construct several perturbation samples based on the key structural parameters and their corresponding parameter values.

[0179] In this embodiment, the training sample refers to any base sample or enhancement sample in the enhanced structure-performance dataset; the perturbation samples include porosity perturbation samples and fiber volume perturbation samples, each perturbation sample including key structural parameters and corresponding perturbation parameter values. For example, the perturbation parameter value corresponding to the porosity of the porosity perturbation sample is greater than the parameter value corresponding to the porosity of the corresponding training sample, denoted as... The perturbation parameter values ​​corresponding to other key structural parameters are consistent with the parameter values ​​corresponding to the key structural parameters of the corresponding training samples; the perturbation parameter value corresponding to the fiber volume fraction of the fiber volume perturbation sample is greater than the parameter value corresponding to the fiber volume fraction of the corresponding training sample, which is expressed as follows. The perturbation parameter values ​​corresponding to other key structural parameters are consistent with the parameter values ​​corresponding to the key structural parameters of the corresponding training samples. Among them, , The numbers represent the order of the numbers. training samples The Porosity perturbation sample The perturbation parameter value corresponding to the porosity, the first fiber volume fraction perturbation sample The perturbation parameter value corresponding to the fiber volume fraction. , The numbers represent the order of the numbers. training samples The parameter values ​​corresponding to porosity and fiber volume fraction.

[0180] 2) Use the key structural parameters and corresponding parameter values ​​of each training sample, and the key structural parameters and corresponding perturbation parameter values ​​of each perturbed sample as inputs to the multilayer perceptron model to obtain the corresponding prediction performance values.

[0181] Based on training constraints, we have , .in, , The numbers represent the order of the numbers. training samples The Porosity perturbation sample , No. fiber volume fraction perturbation sample The corresponding prediction performance value, Indicates the first training samples The corresponding prediction performance value.

[0182] In this embodiment, the multilayer perceptron model is configured with a two-layer hidden layer structure (64 and 32 neurons), the activation function is ReLU, and the random seed is fixed at 42.

[0183] 3) Based on the parameter values ​​and prediction performance values ​​corresponding to the performance parameters of each training sample, calculate the corresponding target loss value using the improved training objective function, and train the multilayer perceptron model based on the target loss value to obtain the trained multilayer perceptron model.

[0184] In this embodiment, the multilayer perceptron model is set with an initial learning rate of 0.001, a maximum number of iterations of 500, an early stopping mechanism, and a physical constraint weight of 0.5.

[0185] Based on the improved training objective function, the multilayer perceptron model can learn the mapping relationship between key structural parameters and performance parameters while satisfying training constraints (in this embodiment, the negative correlation between porosity and thermal conductivity, and the positive correlation between fiber volume fraction and thermal conductivity) to avoid prediction results that violate the laws of material performance.

[0186] Step S62: Use the enhanced structure-performance dataset to perform constrained training on the multiple linear regression model to obtain the trained multiple linear regression model.

[0187] In this embodiment, the multiple linear regression model is expressed as follows: In the formula, This represents the predicted performance value (e.g., predicted thermal conductivity). This represents the regression fit remainder term. Indicates the first One regression coefficient, Indicates the first The parameter values ​​of the key structural parameters, This indicates the number of key structural parameters.

[0188] This embodiment uses the least squares method to fit the data of the base samples and enhanced samples in the enhanced structure-performance dataset, and uses training constraints to constrain the regression coefficients, including the regression coefficients corresponding to porosity. ) constraint is The regression coefficients corresponding to the fiber volume fraction ( ) constraint is To satisfy the inhibitory effect of porosity on thermal conductivity and the promoting effect of fiber volume fraction on thermal conductivity at the coefficient level, the model parameters of the multiple linear regression model are determined. , This ensures that the resulting multiple linear regression model satisfies the negative correlation between porosity and thermal conductivity, and the positive correlation between fiber volume fraction and thermal conductivity, thus making the multiple linear regression model conform to the performance characteristics of rigid thermal insulation tile materials.

[0189] Step S63: Use the augmented structure-performance dataset to perform constrained training on the decision tree model to obtain the trained decision tree model.

[0190] In this embodiment, the decision tree model adopts the Extreme Gradient Boosting Tree (XGBoost) model, represented as follows: In the formula, This represents the predicted performance value (e.g., predicted thermal conductivity). Indicates the first The output of each decision tree Indicates the number of decision trees. express The values ​​of key structural parameters. For example, the XGBoost model is set with 100 base learners, a maximum depth of 6, a learning rate of 0.1, a sample ratio of 0.8, a feature ratio of 0.8, and a fixed random seed of 42. Random forests or other types of decision tree models can also be used in other embodiments.

[0191] In this embodiment, based on training constraints, a monotonicity constraint is introduced during the XGBoost model training process, denoted as: , In the XGBoost model's feature constraint parameters, the feature constraint parameter corresponding to porosity is set to negative monotonicity, and the feature constraint parameter corresponding to fiber volume fraction is set to positive monotonicity. Other structural parameters are not forced to have a monotonic direction. When generating each decision tree, the model still calculates the gain of candidate split points according to the gradient boosting approach, but simultaneously judges whether the split satisfies the above monotonic relationship when selecting a split point. For nodes with porosity as the splitting feature, if the predicted thermal conductivity value corresponding to the region with higher porosity after splitting is higher than that of the region with lower porosity, then the candidate split is restricted or discarded. For nodes with fiber volume fraction as the splitting feature, if the predicted thermal conductivity value corresponding to the region with higher fiber volume fraction after splitting is lower than that of the region with lower fiber volume fraction, then the candidate split is restricted or discarded. Therefore, the model does not perform additional result correction after the objective function, but directly eliminates splitting paths that do not conform to the heat transfer law during the tree structure generation stage.

[0192] Step S64: Use the enhanced structure-performance dataset to perform constrained training on the long short-term memory network model to obtain the trained long short-term memory network model.

[0193] Long Short-Term Memory (LSTM) network models belong to gradient-optimized neural network models. During training, the update of model parameters relies on the backpropagation mechanism of the loss function. In this embodiment, the LSM network model is trained using a training objective function improved from the multilayer perceptron model; details are omitted here. For example, the key structural parameters are organized in a fixed order into an input sequence of length 8, with an input dimension of 1 at each time step. A two-layer LSTM structure is set up with 64 hidden units, the activation function is tanh, the Adam optimizer is used, the learning rate is 0.001, the training epochs are 100, and the batch size is 16.

[0194] Step S65: Use the augmented structure-performance dataset to perform constrained training on the XGBoost-LSTM fusion model to obtain the trained XGBoost-LSTM fusion model.

[0195] In this embodiment, the XGBoost-LSTM fusion model includes an XGBoost branch and an LSTM branch, which are built based on the XGBoost model and the Long Short-Term Memory (LSTM) network model, respectively. The XGBoost branch can leverage the XGBoost model's strong adaptability to features of different dimensions and types, directly adapting to various static structural parameters such as volume fraction, pore size and morphology, and topological connectivity corresponding to rigid thermal insulation tiles. It can efficiently mine nonlinear interaction relationships between features, possesses strong feature selection and noise resistance capabilities, good interpretability, and outstanding stability in modeling material structural features that combine discrete and continuous structures. The LSTM branch can utilize the LSTM network model to mine implicit sequential / spatial correlation information such as pore morphology, size gradient, topological connectivity paths, and component distribution, capturing complex long-range nonlinear dependencies between structural parameters. It can deeply learn the coupling effects between multiple structural parameters (such as the synergistic influence between pore size, connectivity, and volume fraction) to compensate for the shortcomings of tree models in modeling high-order correlations of complex structures.

[0196] The XGBoost-LSTM fusion model is represented as follows: ,in, This represents the prediction performance value output by the XGBoost-LSTM fusion model. This represents the prediction performance value of the XGBoost branch output. This represents the prediction performance value of the LSTM branch output. This represents the XGBoost branch weight, for example, 0.5.

[0197] This embodiment combines the nonlinear feature interaction modeling capability of the XGBoost model with the structural parameter correlation learning capability of the LSTM model by integrating the XGBoost branch and the LSTM branch. The two branches are weighted equally to avoid amplifying local errors or overfitting biases due to excessive weight bias towards one branch, thereby improving the stability of the predicted performance values ​​output by the XGBoost-LSTM fusion model. In this embodiment, the predictive ability of the XGBoost-LSTM fusion model for thermal conductivity is further enhanced, with a higher coefficient of determination. Mean absolute error Root mean square error .

[0198] Step S7: Based on the prediction results of several performance prediction models that have been trained, generate the result-performance analysis result.

[0199] To evaluate the predictive performance of each performance prediction model for the performance parameters, this embodiment uses the coefficient of determination. The mean absolute error (MAE) and root mean square error (RMSE) are used as evaluation metrics. Based on the prediction results (i.e., prediction performance values) of several trained performance prediction models, the evaluation metrics corresponding to each performance prediction model are calculated, such as... Figure 5 As shown, Figure 5 In the table, (a)-(g) represent the evaluation index results of the multiple linear regression model, support vector machine, random forest, long short-term memory network model, multilayer perceptron model, extreme gradient boosting tree model, and XGBoost-LSTM fusion model, respectively. The performance prediction model with the highest evaluation index is selected, and the SHAP interpretable analysis method is used to generate the results-performance analysis results. The contribution weight and influence direction of each microscopic key structural parameter on the performance parameter (such as thermal conductivity) are quantified, and the dominant role of porosity, fiber volume fraction, and Euler number parameters is determined, providing a quantitative basis for material structure control and thermal performance optimization.

[0200] For example, the XGBoost-LSTM fusion model is selected for SHAP analysis, such as... Figure 6 As shown, the various characteristics affecting the thermal conductivity of composite materials are quantitatively analyzed, and the contribution weight and mechanism of each parameter are systematically explored. The relevant analysis results are based on the SHAP feature importance map and dependency map obtained from experimental tests.

[0201] The SHAP feature importance analysis results show that the contributions of each key structural parameter to the thermal conductivity of the composite material are significantly different. Among them, fiber volume fraction, Euler number and porosity are the core features that regulate thermal conductivity, accounting for 29.4%, 17.6% and 23.3% of the feature importance, respectively, with a total contribution of over 70%. In contrast, the contribution weights of conventional pore geometric parameters such as sphericity, average pore volume, equivalent average pore diameter, pore number and average pore area are all less than 12%. This indicates that the thermal insulation performance of this type of composite material is mainly determined by pore topological connectivity, fiber distribution and overall pore content, while the influence of conventional pore geometric parameters is relatively weakened.

[0202] Fiber volume fraction, as the primary core parameter affecting the thermal conductivity of composite materials, exhibits a significant nonlinear relationship with thermal conductivity as shown in the SHAP dependency graph. Specifically, as the fiber volume fraction increases, its SHAP contribution to thermal conductivity gradually changes from negative to positive, showing a clear monotonic nonlinear trend. In the range of low fiber volume fraction, the fibers are dispersed in the matrix, resulting in a relatively sufficient interface between the fiber and matrix. This leads to significant interfacial debonding, with numerous elongated lamellar pores forming and overlapping along the fiber-matrix interface, creating a continuous, interconnected two-dimensional air insulation network. Due to the extremely thin thickness of these lamellar pores, the convective heat transfer effect of the internal air is completely suppressed, with only weak molecular heat conduction. Since the thermal conductivity of air is much lower than that of mullite fibers and the matrix, this continuous lamellar air network effectively blocks the heat conduction path of the solid skeleton, significantly weakening the overall heat conduction efficiency. In this case, the fiber volume fraction makes a negative contribution to thermal conductivity. As the fiber volume fraction continues to increase, the dispersed fibers gradually overlap and stack with each other to form a continuous fiber solid thermal conductivity network. At this point, the continuous fiber network becomes the dominant path for heat transfer. At the same time, the densely distributed fibers will divide the lamellar pores formed by interfacial debonding, breaking down the originally connected lamellar pores into isolated closed pores. The thermal insulation and blocking effect of the pores is significantly weakened, and the dominant role of solid thermal conductivity gradually becomes prominent. Therefore, the contribution of fiber volume fraction to thermal conductivity changes from negative to positive.

[0203] The Euler number, as a core topological parameter characterizing pore topological connectivity, exhibits a highly consistent trend in its SHAP dependence with fiber volume fraction, further confirming the coupled regulatory role of fiber distribution and pore topology. Based on the definition of the Euler number in Avizo software, it follows the Euler-Poincaré formula χ=β0. β1+β2, where β0 is the number of connected domains, β1 is the number of through pores, and β2 is the number of closed isolated cavities. Therefore, the value of the 3D Euler number directly reflects the connectivity and distribution characteristics of the pores. The smaller the Euler number, the more through pores there are in the system, and the stronger the pore connectivity. The larger the Euler number, the fewer through pores there are, the more isolated closed pores there are, and the weaker the pore connectivity. Specifically, in the range of lower 3D Euler numbers, the lamellar pores generated by the debonding of the fiber matrix interface are interconnected, forming continuous air insulation channels that can effectively block the heat conduction of the solid skeleton. Therefore, in this range, the 3D Euler number makes a negative SHAP contribution to thermal conductivity. As the 3D Euler number increases, the number of interconnected lamellar pores gradually decreases, the β1 value decreases while the β2 value increases. The originally interconnected lamellar pores are divided into isolated closed pores, and the continuity of the solid skeleton is significantly improved. Heat transfer mainly relies on the continuous solid skeleton. Therefore, the contribution of the 3D Euler number to thermal conductivity gradually changes from negative to positive, and the SHAP value changes from negative to positive as the Euler number increases. It is noteworthy that this trend differs significantly from that of conventional porous materials. In conventional porous materials, interconnected pores promote convective heat transfer of air within the pores, thereby improving overall thermal conductivity, while closed pores suppress gas convection, achieving better thermal insulation. However, the micropores in this system are elongated two-dimensional lamellar pores formed by debonding at the fiber matrix interface, with extremely low thickness. The air convection effect is completely suppressed, and the heat conduction mechanism changes from "gas convection-dominated" in conventional porous materials to "solid skeleton continuity-dominated," thus exhibiting a unique positive correlation between 3D Euler number and thermal conductivity. The characteristic importance of 3D Euler number fully demonstrates that pore topological connectivity is the decisive factor in regulating the thermal insulation performance of this composite material. Porosity alone cannot fully explain the variation in thermal conductivity, further highlighting the core role of pore topology in regulating the thermal performance of composite materials.

[0204] Porosity, as the third core parameter affecting the thermal conductivity of composite materials, exhibits a significant piecewise nonlinear characteristic in its SHAP dependence. With a porosity of 42.8% as the critical dividing point, when the porosity is below this value, the SHAP value is generally positive, showing a slight promoting effect on thermal conductivity; when the porosity exceeds this critical value, the SHAP value rapidly turns negative, and its inhibitory effect on thermal conductivity significantly increases. Within the low porosity range, the pores in the system are mainly small, isolated closed pores. These pores are few in number and dispersed, having little impact on the continuity of the solid skeleton. Heat transfer is still mainly conducted by the solid skeleton. Therefore, the increase in porosity has a weak effect on thermal conductivity, and may even slightly weaken the thermal conductivity of the solid due to the presence of a small number of pores, showing a small positive contribution. As the porosity increases above the critical value, the debonding behavior of the fiber matrix interface intensifies, a large number of lamellar pores are generated and interconnected, forming a continuous air insulation network. The solid thermal conduction path is significantly blocked, and the thermal conduction efficiency is greatly reduced. Therefore, porosity shows a significant negative contribution to thermal conductivity.

[0205] Compared to the three core parameters mentioned above, conventional pore geometry parameters such as sphericity, average pore volume, equivalent average pore diameter, number of pores, and average pore area have a relatively weaker impact on thermal conductivity, with their characteristic importance all below 12%. Among them, the correlation between sphericity and thermal conductivity shows that as sphericity increases, the SHAP value changes from negative to positive, indicating that the more spherical the pore morphology, the better the continuity of the solid skeleton, the smoother the heat transfer, and the higher the thermal conductivity. However, the SHAP contribution values ​​of parameters such as equivalent average pore diameter and average pore volume are more dispersed and do not show a strict monotonic change law.

[0206] This invention provides a system for generating the three-phase microstructure of rigid thermal insulation tiles, such as... Figure 7 As shown, it includes: The sample set management module is used to acquire real slice sample sets in different spatial directions; wherein, the real slice sample set includes several three-phase labeled slices; The network training module is used to train the generative adversarial network using the real slice sample set in all spatial directions and a multidimensional loss function to obtain the trained generative adversarial network; wherein, the generative adversarial network includes a three-dimensional generator and multiple two-dimensional discriminators; The structure generation module is used to obtain the final three-phase structure using the trained 3D generator.

[0207] The above-described method and system embodiments are based on the same principles, and their related aspects can be referenced from each other to achieve the same technical effects. For specific implementation processes, please refer to the foregoing embodiments, which will not be repeated here.

[0208] In summary, the method for generating the three-phase microstructure of rigid thermal insulation tiles, the method for predicting performance, and the system according to embodiments of the present invention have at least one of the following beneficial effects: 1. To address the anisotropic microstructure differences of rigid thermal insulation tiles in different spatial directions, a set of real slice samples in multiple directions and multiple two-dimensional discriminators are constructed. A generative adversarial network (including a 3D generator and multiple two-dimensional discriminators) is trained using a multidimensional loss function. This enables the trained 3D generator to retain the microstructure differences of the material in different spatial directions during the generation of the final three-phase structure, avoiding the simplistic treatment of the microstructure of composite thermal insulation tiles with obvious directional characteristics as an isotropic structure. This improves the ability of the generated final three-phase structure to maintain the anisotropic characteristics of the material.

[0209] 2. By encoding the three-phase label slices, discrete data (i.e., binary label slices corresponding to different substances) is constructed, avoiding the discriminator from misinterpreting discrete phase categories as continuous grayscale information, thereby improving the clarity of multiphase interface representation and enhancing the adaptability of the generated three-dimensional training three-phase structure to the actual phase distribution of the material; corresponding two-dimensional discriminators are set for different spatial directions, and independent discrimination constraints are applied to each two-dimensional discriminator to improve the generative adversarial network's ability to maintain the differences in organization in different directions.

[0210] 3. A multi-dimensional loss function is constructed, including a first adversarial loss function, a second adversarial loss function, a classification loss function, a Dice loss function, a three-phase constraint loss function, and an inter-layer constraint loss function. This function can jointly constrain the accuracy of category discrimination, boundary fidelity, rationality of three-phase proportions, and inter-layer topological continuity during the generation of three-dimensional training three-phase structures. Compared with generation methods that rely solely on adversarial losses, this invention is more suitable for generating microstructures of resin-based fiber rigid ceramic thermal insulation tiles with complex multiphase boundaries, significant differences in pore scale, and high requirements for inter-layer continuity. This is beneficial for improving the physical rationality and structural integrity of the generated final three-dimensional three-phase structure.

[0211] 4. Based on the three-phase structure, a trained performance prediction model is obtained by enhancing the structure-performance dataset for predicting the performance of rigid thermal insulation tiles, forming an application from three-dimensional structure generation to structure-performance mapping. The three-dimensional microstructural information of the rigid thermal insulation tile is directly converted into structural parameter data (e.g., thermal conductivity) for performance prediction, realizing a quantitative correlation between the microstructure and performance parameters of the rigid thermal insulation tile, thereby improving the practicality of this invention in the structural characterization and thermal performance prediction of thermal insulation materials.

[0212] 5. Using thickness-direction thermal conductivity as the performance prediction target can better reflect the key heat transfer characteristics of rigid thermal insulation tiles under the influence of layup structure and interface debonding. Compared with averaging thermal conductivity in three directions, this embodiment is more consistent with the anisotropic heat transfer characteristics of this type of material, and also helps to highlight the important significance of thickness-direction heat transfer behavior for thermal insulation performance evaluation. Based on generative adversarial networks, the generation (i.e., three-phase structure) and application (performance parameter prediction) of the microstructure of rigid thermal insulation tiles can provide methodological support for the digital characterization of the microstructure, thermal performance analysis and subsequent optimization design of this type of composite thermal insulation material, and has good engineering application value.

[0213] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0214] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for generating the three-phase microstructure of a rigid thermal insulation tile, characterized in that, include: Obtain a real slice sample set in different spatial directions; wherein, the real slice sample set includes several three-phase labeled slices; The generative adversarial network is trained using the real slice sample set in all spatial directions and a multidimensional loss function to obtain the trained generative adversarial network; wherein, the generative adversarial network includes a three-dimensional generator and multiple two-dimensional discriminators; The final three-phase structure is obtained using the trained 3D generator.

2. The method according to claim 1, characterized in that, The generative adversarial network (GAN) is trained using the real slice sample set across all spatial directions and a multidimensional loss function to obtain the trained GAN, including: The three-dimensional generator is used to generate a training three-phase probability volume, and several three-phase generated slices in different spatial directions are obtained. Each of the three-phase generated slices, each of the three-phase labeled slices, and the multidimensional loss function are used to train each of the two-dimensional discriminators; The three-dimensional generator is trained using the training three-phase probability body, each of the three-phase generation slices, each of the three-phase label slices, and the multidimensional loss function; Once the training stopping condition is met, the trained generative adversarial network is obtained.

3. The method according to claim 2, characterized in that, The multidimensional loss function includes a first adversarial loss function; Training each of the two-dimensional discriminators using the three-phase generated slices, the three-phase labeled slices, and the multidimensional loss function includes: Each three-phase generated slice and each three-phase labeled slice in each spatial direction are input into the corresponding two-dimensional discriminator to obtain the corresponding discrimination result; wherein, each spatial direction corresponds to one two-dimensional discriminator; Based on the discrimination results, the corresponding first adversarial loss value is calculated using the first adversarial loss function; The corresponding two-dimensional discriminator is trained based on each of the first adversarial loss values.

4. The method according to claim 3, characterized in that, The first adversarial loss function is expressed as: In the formula, Indicates the first The two-dimensional discriminator corresponding to each spatial direction The first adversarial loss value, Indicates the first The real slice sample set in each spatial direction, Indicates the first The three-phase generation slices in each spatial direction This refers to the two-dimensional discriminator. The three-phase generation slice The aforementioned discrimination result, express Includes each of the three-phase generated slices Corresponding discrimination results Expectations Indicates the first Each of the three-phase tag slices in each spatial direction The set, This refers to the two-dimensional discriminator. For the three-phase label slice The aforementioned discrimination result, express Includes each of the aforementioned three-phase tag slices The corresponding discrimination result Expectations This refers to the two-dimensional discriminator. Three-phase interpolation slices The aforementioned discrimination result, This represents the three-phase interpolation slice. The corresponding partial derivative gradient The 2-norm, Represents all the aforementioned three-phase interpolation slices corresponding Expectations This represents the gradient penalty coefficient.

5. The method according to claim 2, characterized in that, The multidimensional loss function also includes a second adversarial loss function, a classification loss function, a Dice loss function, a three-phase constraint loss function, and an inter-layer constraint loss function; The 3D generator is trained using the training three-phase probability body, each of the three-phase generated slices, each of the three-phase label slices, and the multidimensional loss function, including: Based on each of the three-phase generated slices and each of the three-phase labeled slices in all spatial directions, the corresponding second adversarial loss value, classification loss value, and Dice loss value are calculated using the second adversarial loss function, the classification loss function, and the Dice loss function. Based on the training three-phase probability body and each of the three-phase label slices, the corresponding three-phase constraint loss value and inter-layer constraint loss value are calculated using the three-phase constraint loss function and the inter-layer constraint loss function. The generator's total loss value is calculated based on the second adversarial loss value, the classification loss value, the Dice loss value, the three-phase constraint loss value, and the inter-layer constraint loss value. The 3D generator is trained based on the total loss value of the generator.

6. The method according to claim 5, characterized in that, The inter-layer constraint loss function is expressed as follows: In the formula, This represents the interlayer constraint loss value. Indicates the number of floors. Indicates the first Layer, First line, number The predicted probability array of the column. Indicates the first Layer, First line, number The predicted probability array of the column, express The 2-norm.

7. A method for predicting the performance of rigid thermal insulation tiles, characterized in that, include: For each three-phase structure, parameter values ​​corresponding to multiple structural parameters are extracted, and the parameter values ​​corresponding to the performance parameters are calculated; wherein, the three-phase structure includes the final three-phase structure obtained by any one of claims 1-6; the performance parameters include thermal conductivity; Based on the correlation between the structural parameters and the performance parameters, key structural parameters are selected to construct an enhanced structure-performance dataset. The enhanced structure-performance dataset is used to train several performance prediction models under constraints, resulting in several trained performance prediction models. Based on the prediction results of several performance prediction models that have been trained, a performance analysis result is generated.

8. The method according to claim 7, characterized in that, Based on the correlation between the structural parameters and the performance parameters, key structural parameters are selected to construct an enhanced structure-performance dataset, including: Based on the parameter values ​​of the structural parameters and performance parameters corresponding to each of the three-phase structures, the correlation coefficient between each structural parameter and the performance parameter is calculated, and key structural parameters are selected according to the correlation coefficients. Based on the key structural parameters and the parameter values ​​corresponding to the performance parameters, a basic structure-performance dataset is constructed. Based on the infrastructure-performance dataset, a Gaussian mixture model is used to perform sample augmentation, generating multiple augmented samples, which are then added to the infrastructure-performance dataset to obtain the augmented infrastructure-performance dataset.

9. The method according to claim 7, characterized in that, The performance prediction model includes a multilayer perceptron model; The training objective function corresponding to the training is expressed as follows: In the formula, , , The training objective loss, data fitting loss, and physical constraint loss corresponding to the multilayer perceptron model are represented in that order, respectively. Indicates the weight of physical constraints; in, , In the formula, This indicates the number of training samples corresponding to the constrained training. Indicates the first training samples The corresponding prediction performance value, Indicates the first The training samples The parameter values ​​corresponding to the performance parameters, No. The training samples The Porosity perturbation sample The corresponding predicted performance value, No. The training samples The fiber volume fraction perturbation sample The corresponding predicted performance value.

10. A three-phase microstructure generation system for rigid thermal insulation tiles, characterized in that, include: The sample set management module is used to acquire real slice sample sets in different spatial directions; wherein, the real slice sample set includes several three-phase labeled slices; The network training module is used to train the generative adversarial network using the real slice sample set in all spatial directions and a multidimensional loss function to obtain the trained generative adversarial network; wherein, the generative adversarial network includes a three-dimensional generator and multiple two-dimensional discriminators; The structure generation module is used to obtain the final three-phase structure using the trained 3D generator.

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