Quantitative analysis method for dispersion of mechanical properties of ceramic matrix composite component

Abstract

The present application relates to the technical field of data processing, and particularly relates to a kind of ceramic matrix composite component mechanical property dispersity quantitative analysis method, comprising: obtaining the experimental measurement corresponding to surface strain field and stress-strain curve;Data set is constructed;Neural network model is constructed, and the prediction value corresponding to surface strain field and stress-strain curve is obtained;The posterior distribution of the mechanical property parameter of each test piece is obtained;Hierarchical Bayesian inference model is constructed, and the posterior distribution of hierarchical Bayesian inference model hyperparameter is obtained;The quantitative analysis result of the mechanical property dispersity of ceramic matrix composite component is obtained.The present application realizes the system quantification and consistency evaluation of material performance dispersity, and provides effective data support for the quality control, reliability design and engineering application of ceramic matrix composite.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and specifically to a method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components. Background Technology

[0002] Ceramic matrix composites (CMCs) are composed of fiber bundles and a matrix, exhibiting complex multi-scale structures and excellent high-temperature mechanical properties, showing significant application potential in high-temperature, high-load extreme environments such as hot-end components of aero-engines and thermal protection systems. However, due to the randomness of the microstructure, such as fiber arrangement, interface characteristics, and pore distribution within the material, its component mechanical properties exhibit dispersion characteristics. This characteristic severely limits its widespread engineering application in high-reliability systems.

[0003] Traditional measurement techniques struggle to directly and effectively measure the mechanical properties of microscopic components such as fiber bundles and matrices. Attempts to systematically characterize the dispersion characteristics of materials through numerous experiments face the challenges of drastically increasing sample sizes and prohibitively high testing costs, making them impractical in engineering applications. Furthermore, existing characterization methods cannot effectively distinguish between measurement errors and the inherent dispersion of materials, leading to biased assessments of true dispersion.

[0004] Therefore, there is a need to provide a quantitative analysis method for the dispersion of mechanical properties of ceramic matrix composite components to solve the above problems. Summary of the Invention

[0005] To address the technical problems of existing characterization methods being unable to accurately quantify the dispersion characteristics of material properties and having difficulty distinguishing between measurement errors and inherent variability, this invention provides a quantitative analysis method for the dispersion of mechanical properties of ceramic matrix composite components. This method ensures accurate quantification of the dispersion of mechanical property parameters of ceramic matrix composite components within a reasonable cost range, providing a scientific basis for the reliability design and engineering application of ceramic matrix composites in high-end equipment.

[0006] The present invention provides a method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components, which adopts the following technical solution:

[0007] Multiple specimens of ceramic matrix composites were obtained, and the experimental measurements corresponding to the surface strain field and stress-strain curves of the ceramic matrix composites of the specimens were obtained.

[0008] Establish target finite element models of ceramic matrix composite specimens under a combination of macroscopic and mesoscopic scales; based on the combination of mechanical property parameters of ceramic matrix composite components and the target finite element model, obtain the calculated values ​​of surface strain field and stress-strain curve of ceramic matrix composite under each combination of mechanical property parameters, and construct a dataset based on the combination of mechanical property parameters, surface strain field and stress-strain curve.

[0009] A neural network model is established, and the model is trained based on a dataset to obtain a trained target neural network model. The target neural network model is then used to predict the surface strain field and stress-strain curve of the ceramic matrix composite material under each combination of mechanical property parameters.

[0010] Based on the predicted values ​​of the surface strain field, experimental measurements, predicted values ​​of the stress-strain curve, and experimental measurements, an error function is constructed to evaluate the difference between the predicted values ​​and the experimental measurements. Based on the error function, a likelihood function in the Bayesian parameter inference method is constructed. Based on the likelihood function and the preset prior distribution, the posterior distribution of the mechanical property parameters of each specimen is obtained.

[0011] Based on the posterior distribution of the mechanical property parameters of each specimen, a hierarchical Bayesian inference model is constructed for the quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components.

[0012] The hyperparameters of the hierarchical Bayesian inference model are sampled to obtain the posterior distribution of the hyperparameters. Based on the posterior distribution of the hyperparameters, the quantitative analysis results of the mechanical property dispersion of the ceramic matrix composite components are obtained. The quantitative analysis results are: population posterior mean, variance, and the highest posterior density interval of 95%.

[0013] A further technical solution of the present invention is that the steps for obtaining multiple specimens of ceramic matrix composite material are as follows:

[0014] Multiple initial specimens were obtained by sampling at different locations along the raw ceramic matrix composite material;

[0015] Multiple initial specimens were machined according to a unified standard to obtain multiple specimens.

[0016] A further technical solution of the present invention is that the step of obtaining experimental measurement values ​​of the specimen surface is as follows:

[0017] Uniaxial tensile tests were performed on the specimens, and the experimental measurements were recorded using a DIC device during the loading process.

[0018] A further technical solution of the present invention is that the steps for establishing a target finite element model of a ceramic matrix composite specimen under a combination of macroscopic and mesoscopic scales are as follows:

[0019] Finite element models of matching micro-woven structures were established based on the weaving method, fiber bundle size, and porosity parameters of ceramic matrix composite specimens.

[0020] A macroscopically homogeneous finite element model was constructed based on the macroscopic dimensions of ceramic matrix composite specimens.

[0021] The finite element model of the micro-woven structure is spliced ​​with the macro-homogeneous finite element model to form a target finite element model combining macro- and micro-scales.

[0022] A further technical solution of the present invention is that the expression of the error function is:

[0023]

[0024] In the formula, Represents the error function; This represents the surface strain field error term, which consists of the predicted and experimentally measured values ​​of the surface strain field. A vector representing the mechanical property parameters of the components in a ceramic matrix composite material; Represents a vector based on mechanical performance parameters The obtained surface strain field of the first Predicted values ​​for each data point; Represents the first in the surface strain field Experimental measurements of each data point; This represents the amplification factor for the surface strain field error term; This represents the stress-strain error term, which consists of the predicted values ​​and experimental measurements of the stress-strain curve. This represents the total number of data points in the surface strain field.

[0025] A further technical solution of the present invention is that the expression of the likelihood function is:

[0026]

[0027] In the formula, Represents the likelihood function; express The variance of a normal Gaussian distribution when its value follows such a distribution; This represents the error function.

[0028] A further technical solution of the present invention is that, based on the likelihood function and a preset prior distribution, the step of obtaining the posterior distribution of the mechanical property parameters of each component of the specimen is as follows:

[0029] Based on the likelihood function and a pre-defined prior distribution, the posterior distribution of the mechanical property parameters of ceramic matrix composite components is extracted using the Markov Monte Carlo sampling method.

[0030] A further technical solution of the present invention is that the expression of the hierarchical Bayesian inference model is:

[0031]

[0032] In the formula, Hyperparameters The posterior distribution of; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... The mean of the experimental measurement parameters; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... The standard deviation of each experimental measurement parameter; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... Experimental measurements of each parameter; This represents the variance of the noise measured in the experiment; express The prior distribution; express The prior distribution of .

[0033] A further technical solution of the present invention is to use the Markov Monte Carlo sampling method to sample the hyperparameters of the hierarchical Bayesian inference model and obtain the posterior distribution of the hyperparameters.

[0034] A further technical solution of the present invention is that the steps for obtaining the quantitative analysis results of the mechanical property dispersion of ceramic matrix composite components based on the posterior distribution of hyperparameters are as follows:

[0035] Based on the posterior distribution of hyperparameters, a population probability distribution model is constructed using the kernel density estimation method;

[0036] The population probability distribution model is used to obtain the population posterior mean, variance, and 95% highest posterior density interval for each mechanical performance parameter.

[0037] The beneficial effects of this invention are:

[0038] This invention systematically samples multiple specimens and conducts standardized experiments, integrating experimental mechanical measurements with neural network model predictions to construct a multi-dimensional error function. Based on this error function, a likelihood function in Bayesian inference is built. A hierarchical Bayesian inference model based on multi-source data is established using the likelihood function and a pre-defined prior distribution. Markov chain Monte Carlo (MCMC) sampling technology is employed to achieve accurate probabilistic characterization and quantitative analysis of the dispersion of mechanical property parameters of ceramic matrix composite components. In summary, based on the technical solution of this invention, the statistical distribution characteristics of mechanical property parameters of ceramic matrix composite components (fiber bundles and matrix) can be obtained based on multi-specimen experimental data, enabling systematic quantification and consistency assessment of material property dispersion. This provides effective data support for the quality control, reliability design, and engineering applications of ceramic matrix composites. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating a method for quantitatively analyzing the dispersion of mechanical properties of ceramic matrix composite components according to the present invention.

[0041] Figure 2 This is a schematic diagram of the target finite element model obtained in an embodiment of the present invention;

[0042] Figure 3 This is a schematic diagram of the surface strain field measured experimentally in an embodiment of the present invention;

[0043] Figure 4 This is a schematic diagram of the stress-strain curves measured experimentally in an embodiment of the present invention;

[0044] Figure 5 This is a network structure diagram of the neural network model in an embodiment of the present invention;

[0045] Figure 6 This is a schematic diagram of the strain field predicted by the multi-task convolutional network in verification example 1 of this invention;

[0046] Figure 7 This is a schematic diagram of the strain field calculated by the finite element model in verification example 1 of this invention;

[0047] Figure 8 This is a schematic diagram illustrating the error between the strain field predicted by the multi-task convolutional network and the strain field calculated by the finite element model in Example 1 of this invention.

[0048] Figure 9 This is a schematic diagram of the strain field predicted by the multi-task convolutional network in verification example 2 of this invention;

[0049] Figure 10 This is a schematic diagram of the strain field calculated by the finite element model in verification example 2 of this invention;

[0050] Figure 11 This is a schematic diagram illustrating the error between the strain field predicted by the multi-task convolutional network and the strain field calculated by the finite element model in Example 2 of this invention.

[0051] Figure 12 This is a schematic diagram of the strain field predicted by the multi-task convolutional network in verification example 3 of this invention;

[0052] Figure 13 This is a schematic diagram of the strain field calculated by the finite element model in verification example 3 of this invention;

[0053] Figure 14 This is a schematic diagram illustrating the error between the strain field predicted by the multi-task convolutional network and the strain field calculated by the finite element model in Example 3 of this invention.

[0054] Figure 15 This is a schematic diagram showing the stress-strain curve of the branch path prediction of the multi-task convolutional network in Example 1 of the present invention and its comparison with the prediction results of other network models.

[0055] Figure 16 This is a schematic diagram showing the stress-strain curve of the branch path prediction of the multi-task convolutional network in Example 2 of the present invention and its comparison with the prediction results of other network models.

[0056] Figure 17 This is a schematic diagram showing the stress-strain curve of the branch path prediction of the multi-task convolutional network in Example 3 of the present invention and its comparison with the prediction results of other network models.

[0057] Figure 18 This is a schematic diagram of the posterior distribution and probability distribution model information of the inherent dispersion of the axial modulus of the fiber bundle in an embodiment of the present invention;

[0058] Figure 19 This is a schematic diagram of the posterior distribution and probability distribution model information of the inherent dispersion of the transverse modulus of the fiber bundle in an embodiment of the present invention;

[0059] Figure 20 In the embodiments of the present invention, the fiber bundle is in xy A schematic diagram of the inherent dispersion posterior distribution and probability distribution model information of Poisson's ratio in the plane;

[0060] Figure 21 In the embodiments of the present invention, the fiber bundle is in yz A schematic diagram of the inherent dispersion posterior distribution and probability distribution model information of Poisson's ratio in the plane;

[0061] Figure 22 In the embodiments of the present invention, the fiber bundle is in xy A schematic diagram of the intrinsic dispersion posterior distribution and probability distribution model information of the in-plane shear modulus;

[0062] Figure 23 In the embodiments of the present invention, the fiber bundle is in yz A schematic diagram of the intrinsic dispersion posterior distribution and probability distribution model information of the in-plane shear modulus;

[0063] Figure 24 This is a schematic diagram of the posterior distribution and probability distribution model information of the inherent dispersion of the matrix modulus in an embodiment of the present invention;

[0064] Figure 25 This is a schematic diagram of the posterior distribution and probability distribution model information of the inherent dispersion of the matrix Poisson's ratio in an embodiment of the present invention.

[0065] Figure 26 This is the 95% confidence interval of the stress-strain curve predicted by posterior distribution sampling based on the inherent dispersion of the mechanical property parameters of ceramic matrix composite components in this embodiment of the invention, and its comparison with the data of the verification specimen.

[0066] Figure 27 This invention presents the 95% confidence intervals of failure strain and tensile strength predicted by posterior distribution sampling based on the inherent dispersion of mechanical property parameters of ceramic matrix composite components in this embodiment of the invention, and their comparison with the data of the verification specimen.

[0067] Figure 28 This invention presents the distribution of tensile modulus predicted by posterior distribution sampling based on the inherent dispersion of mechanical property parameters of ceramic matrix composite components in this embodiment of the invention, and its comparison with the data of the verification specimen.

[0068] Figure 29 This is a schematic diagram illustrating the dispersion quantification parameters of the mechanical properties of ceramic matrix composite components inferred by the layered Bayesian inference model in an embodiment of the present invention. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] An embodiment of the present invention provides a method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components. In this embodiment, two-dimensional braided SiC is used. f / SiC m - Taking ceramic matrix composites (silicon carbide fiber-reinforced silicon carbide ceramic matrix composites) as the object, two-dimensional braided SiC f / SiC m The mechanical property parameters of ceramic matrix composite components include the anisotropic elastic parameters of the fiber bundles and the matrix, i.e., the mechanical property parameter vector is... ,in, The axial modulus of the fiber bundle is denoted as . The transverse modulus of the fiber bundle. For fiber bundles in xy Poisson's ratio in the plane For fiber bundles in yz Poisson's ratio in the plane For fiber bundles in xy In-plane shear modulus For fiber bundles in yz In-plane shear modulus For matrix modulus, The matrix Poisson's ratio is given by the subscript 1, indicating that the ratio in space is... x Axial direction; subscript 2 indicates space y The axis direction, with the subscript 3 indicating the direction in space. z In the axial direction, in this embodiment x The axial direction is the fiber bundle axis. y The axial direction is the radial direction of the fiber bundle; superscript The term "fiber bundles" refers to bundles of fibers. The matrix means the base material, such as... Figure 1 As shown, the method includes:

[0071] S1. Obtain the experimental measurements corresponding to the surface strain field and stress-strain curve;

[0072] Specifically, multiple specimens of ceramic matrix composites were obtained, and the experimental measurements corresponding to the surface strain field and stress-strain curves of the ceramic matrix composites of the specimens were obtained.

[0073] For example, in one specific embodiment, the steps for obtaining multiple specimens of ceramic matrix composite material are as follows: sampling is performed at different locations along the raw material of ceramic matrix composite material to obtain multiple initial specimens; the multiple initial specimens are machined according to a uniform standard to obtain multiple specimens.

[0074] For example, in one specific embodiment, the step of obtaining experimental measurement values ​​on the surface of the specimen is as follows: a uniaxial tensile test is performed on the specimen, and the experimental measurement values ​​during the loading process are recorded using a DIC device. In this embodiment, the uniaxial tensile test process is as follows: under room temperature conditions, a uniaxial tensile test is conducted on the ceramic matrix composite specimen using a materials mechanics testing machine. The testing machine is set to displacement loading mode, a loading displacement is given and maintained, and loading continues until the specimen fractures; non-contact measurement technology is used to obtain the following values: Figure 3 The SiC shown f / SiC m - Surface strain field of composite materials and Figure 4 The SiC shown f / SiC m - Stress-strain curves of composite materials.

[0075] S2. Construct the dataset;

[0076] Specifically, a target finite element model of ceramic matrix composite specimens is established under a combination of macroscopic and mesoscopic scales. Based on the combination of mechanical property parameters of ceramic matrix composite components and the target finite element model, the calculated values ​​of surface strain field and stress-strain curve of ceramic matrix composite under each combination of mechanical property parameters are obtained. A dataset is constructed based on the calculated values ​​of mechanical property parameter combination, surface strain field and stress-strain curve.

[0077] For example, in one specific embodiment, the steps for establishing a target finite element model of a ceramic matrix composite specimen at a combination of macroscopic and mesoscopic scales are as follows: Figure 2 As shown, a finite element model of a matching mesoscopic woven structure is established based on the weaving method, fiber bundle size, and porosity parameters of the ceramic matrix composite specimen; a macroscopically homogeneous finite element model is constructed based on the macroscopic dimensions of the ceramic matrix composite specimen; the finite element model of the mesoscopic woven structure and the macroscopically homogeneous finite element model are then combined to form a target finite element model combining macroscopic and mesoscopic scales. In this embodiment, the weaving method, fiber bundle size, and porosity parameters of the ceramic matrix composite specimen are provided by the material manufacturer or obtained from CT scan images.

[0078] It should be noted that, in this embodiment, the finite element model of the micro-woven structure is used to accurately calculate the strain field and stress-strain curve of the material surface, while the macro-homogeneous finite element model is used to reduce the overall mesh number of the model and balance the calculation accuracy and calculation cost.

[0079] For example, in one specific embodiment, the step of obtaining the mechanical property parameter combination of the ceramic matrix composite component is as follows: sampling the mechanical property parameters of the ceramic matrix composite component from a preset mechanical property parameter range to obtain multiple mechanical property parameter combinations, wherein the preset mechanical property parameter range is shown in Table 1.

[0080] Table 1

[0081]

[0082] For example, in one specific embodiment, the steps for obtaining the calculated values ​​of the surface strain field and stress-strain curve of the ceramic matrix composite material under each combination of mechanical property parameters are as follows: inputting the combination of mechanical property parameters into the finite element model for simulation analysis and calculation, and obtaining the calculated values ​​of the surface strain field and stress-strain curve of the ceramic matrix composite material under each combination of mechanical property parameters.

[0083] At this point, a dataset can be constructed based on the combination of mechanical performance parameters, the surface strain field, and the calculated values ​​corresponding to the stress-strain curve. Since the calculation cost of the surface strain field is lower than that of the nonlinear stress-strain curve, in this embodiment, the number of training samples for the surface strain field is 2000, and the number of training samples for the stress-strain curve is 220.

[0084] S3. Construct a neural network model and obtain the predicted values ​​corresponding to the surface strain field and stress-strain curve;

[0085] Specifically, a neural network model is constructed, and the neural network model is trained based on the dataset to obtain a trained target neural network model. The target neural network model is then used to predict the surface strain field and stress-strain curve of the ceramic matrix composite material under each combination of mechanical property parameters.

[0086] For example, such as Figure 5 As shown, in one specific embodiment, the neural network model is a ResUNet network (multi-task convolutional neural network). The main path of the multi-task convolutional neural network is used to predict the surface strain field; the branch paths of the multi-task convolutional neural network predict the stress-strain curves. It should be noted that... Figure 5The network structure involves max pooling, convolution with different kernel sizes, deconvolution, and upsampling. Residual and skip connections are used to improve prediction accuracy. The network design aims to inherit the training results of the main path to the branch paths, thereby improving the prediction accuracy of the branch paths under the limited stress-strain curve sample conditions in step S2. Supervised learning is used to train the neural network model, enabling it to accurately map component mechanical parameters to macroscopic mechanical responses, providing an efficient surrogate model for subsequent inversion analysis. Figure 5 The network input is a 64×64 feature map with 64 channels output by the parametric encoder, which is composed of mechanical performance parameter vectors. The data is obtained through linear transformation and deconvolution. After four downsampling operations including residual connections, the number of data channels gradually increases to 1024, and the feature map size gradually compresses to 4×4. Subsequent upsampling operations are divided into two paths. The strain field prediction path, through deconvolution and four upsampling operations including residual connections, gradually restores the feature map size to 64×64. The final output is a 3-channel 64×64 matrix, corresponding to SiC. f / SiC m - The strain field in three directions on the surface of the ceramic matrix composite sample, i.e. strain field in the direction , in-plane shear strain field , strain field in the direction The stress-strain curve prediction path gradually expands the feature map size to 256×256 through six upsampling operations, ultimately outputting a stress-strain curve image with a resolution of 256×256 in the same coordinate system. Stress-strain data points are then extracted from this image using image processing algorithms. The main function of residual links in the network is to add the input of a certain layer to the output after nonlinear transformation, preventing the gradient from rapidly decaying or exploding during backpropagation due to increasing layer depth. This improves the network's performance under fixed sample size conditions. Besides residual links, multi-task convolutional neural networks also contain skip links that concatenate feature maps from different stages of the encoder (downsampling process) with the corresponding feature maps of the decoder (upsampling stage). These skip links directly inject features from different encoder levels into the corresponding decoder layers, achieving feature fusion at different abstraction levels. This ensures that the detailed distribution features in the strain field image are not lost during deep encoding, guaranteeing the network's prediction accuracy for the strain field image. Regarding network training, SiC... f / SiC m- The surface strain field of ceramic matrix composite specimens has relatively lower computational cost, enabling the provision of more samples for network training. In this embodiment, the parametric encoder-downsampling process-strain field prediction upsampling process is considered the main path of the multi-task convolutional neural network, using the Latin hypercube sampling (LHS) method to sample 2000 vectors from the upper and lower limits of the component elastic parameters. θ The strain field images obtained from the input macro-micro combined finite element model are used to form the training sample set for the main path. The Smooth L1 function is used as the loss function during training, and early stopping and dynamic learning rate adjustment mechanisms are added. The AdamW optimizer is used to achieve fast and stable training of the main path of the multi-task convolutional neural network.

[0087] In this embodiment, three different mechanical performance parameter vectors are used as validation example 1, validation example 2, and validation example 3 to verify the prediction accuracy of the multi-task convolutional network. Specifically, validation example 1 is used to verify the prediction accuracy of the multi-task convolutional neural network after training. Figures 6-8 As shown in Example 2, the prediction accuracy of the multi-task convolutional neural network after training is verified. Figures 9-11 As shown in Example 3, the prediction accuracy of the multi-task convolutional neural network after training is verified as follows: Figures 12-14 As shown, to verify the results in example 3. Taking strain fields as an example, the network can accurately predict strain field images under different distribution patterns, with minimal error between the prediction results and numerical strain field images. The upsampling prediction process of the stress-strain curve image is a branch path of the ResUNet network, using 220 sampled vectors. θ The system was trained using stress-strain data calculated by a progressive damage model. Each sample was an image with a resolution of 256×256, with the horizontal axis uniformly set to 0-0.015 mm / mm and the vertical axis to 0-400 MPa. Figure 5 The stress-strain curve in the stress-strain plot on the right is 10 pixels wide and black, with a white background. The loss function consists of the BCELoss and DiceLoss functions from the PyTorch library, with a weight ratio of 7:3. The main function of BCELoss is pixel-level binary classification, that is, determining whether each pixel in the predicted image belongs to the curve region. The main function of DiceLoss is to evaluate the degree of overlap between the curve regions in the predicted image and the real image, penalizing the deviation of the prediction result. The training process uses the AdamW optimizer and early stopping and learning rate adjustment mechanisms. During training, the parameters of the encoder and downsampling process in the main path are frozen, and only the parameters of the upsampling process in the branch paths are updated.

[0088] The reason for transforming the one-dimensional stress-strain data prediction task into an image prediction branch of the ResUNet network is that SiCf / SiC m The computational cost of calculating the progressive damage of ceramic matrix composite specimens is very high, requiring only 220 samples for network training, which is severely imbalanced with the number of strain field samples in the main path. The parameter encoder and downsampling process in the main path, supported by a large sample set, can learn a more accurate mapping relationship between component elastic parameters and deep features. These large-sample training results are transferred to the branch paths with scarce samples, giving the stress-strain curve prediction a high-quality feature foundation. Figures 15 to 17 This paper presents a comparative diagram of the stress-strain curve prediction results of the ResUNet curve prediction branch, the independent CNN network, and the independent DNN network under three validation examples. The parameter counts of the independent convolutional network, the fully connected network, and the total parameter count of the downsampling process plus the curve prediction branch in the ResUNet network are approximately the same. It can be seen that the prediction results of the ResUNet curve prediction branch are very close to the numerical curves, while the independent CNN network has a larger error at the end of the curve, and the independent DNN network has a larger error at the beginning of the curve, with the predicted curve exhibiting a non-smooth, broken-line distribution. The main reason for this difference is that after converting the prediction of stress-strain curve data points into image prediction, the image samples naturally satisfy the key features of a smooth curve and an origin-starting point. This allows the ResUNet curve prediction branch to accurately predict complete, smooth stress-strain curves based on the large-sample training results of the main transfer learning path. In contrast, the DNN network requires complex loss functions or physical constraints to achieve the same feature capture effect, and the independent CNN network lacks sufficient accuracy in predicting the end of the curve due to a smaller sample size.

[0089] Thus, based on the trained neural network model, the predicted values ​​of the surface strain field and stress-strain curve of ceramic matrix composites under each combination of mechanical property parameters can be accurately predicted.

[0090] S4. Obtain the posterior distribution of the mechanical property parameters of each specimen;

[0091] Specifically, based on the predicted values ​​of the surface strain field, the experimental measurements, the predicted values ​​of the stress-strain curves, and the experimental measurements, an error function is constructed to evaluate the difference between the predicted values ​​and the experimental measurements. Based on the error function, a likelihood function in the Bayesian parameter inference method is constructed. Based on the likelihood function and the preset prior distribution, the posterior distribution of the mechanical property parameters of each specimen is obtained.

[0092] For example, in one specific embodiment, the expression for the error function is:

[0093] (1)

[0094] In the formula, Represents the error function; This represents the surface strain field error term, which consists of the predicted and experimentally measured values ​​of the surface strain field. A vector representing the mechanical property parameters of the components in a ceramic matrix composite material, i.e. ; Represents a vector based on mechanical performance parameters The obtained surface strain field of the first Predicted values ​​for each data point; Represents the first in the surface strain field Experimental measurements of each data point; This represents the amplification factor for the surface strain field error term; This represents the stress-strain error term, which consists of the predicted values ​​and experimental measurements of the stress-strain curve. This represents the total number of data points in the surface strain field; in this embodiment... The value is 1×10 6 This value can amplify the order of magnitude of the surface strain field error term, avoiding algorithm accuracy problems caused by excessively small numerical values.

[0095] In this embodiment, the stress-strain error term The expression is:

[0096]

[0097] In the formula, The purpose of this study is to measure the dtw distance between the predicted normalized stress-strain curve calculated using the Dynamic Time Warping (dtw) algorithm and the experimentally measured normalized stress-strain curve. This distance aims to characterize the overall difference between the predicted and experimentally measured stress-strain curves. The experimentally measured value of the normalized stress; The normalized experimental strain measurement. The normalized stress-strain curve For vector-based The normalized stress-strain curves predicted by the target neural network model are used. The difference in slope between the predicted and experimentally measured stress-strain curves corresponding to the elastic segments is represented by a dimensionless term. This term aims to characterize the difference in macroscopic tensile modulus of the ceramic matrix composite material corresponding to the predicted and experimentally measured values ​​of the stress-strain curves. The macroscopic tensile modulus of the ceramic matrix composite material is calculated from the predicted values ​​of the stress-strain curve. For vector-based And the stress prediction value is used in the stress-strain curve predicted by the target neural network model; For vector-based And the strain prediction value is used from the stress-strain curve predicted by the target neural network model. To calculate the macroscopic tensile modulus of ceramic matrix composites from experimentally measured values ​​of stress-strain curves, The stress is the experimentally measured value of the stress within the elastic segment of the stress-strain curve. The experimentally measured value of the strain within the elastic segment of the stress-strain curve; The difference between the predicted stress-strain curve and the experimentally measured stress-strain curve in terms of failure strain and tensile strength parameters is represented by a dimensionless term, where... This refers to the strain value corresponding to the end of the experimental stress-strain curve, i.e., the failure strain of the material specimen. This represents the stress value corresponding to the end of the experimental stress-strain curve, i.e., the tensile strength of the material specimen. Similarly, The failure strain is the stress-strain curve predicted by the target neural network model. The tensile strength is the stress-strain curve predicted by the target neural network model. These are the weighting coefficients for the dtw distance; The weighting coefficient for the slope difference value. The weighting coefficient for the difference between the predicted stress-strain curve and the experimentally measured stress-strain curve in terms of failure strain and tensile strength parameters is taken in this embodiment. , , This combination of values ​​can unify the order of magnitude of each error term and the order of magnitude of the strain field error term, making the contribution of each error term to the error function value approximately the same.

[0098] For example, in one specific embodiment, the expression for the likelihood function is:

[0099] (3)

[0100] In the formula, Represents the likelihood function; express The variance of a normal Gaussian distribution when its value follows such a distribution; This represents the error function.

[0101] For example, in one specific embodiment, the step of obtaining the posterior distribution of the mechanical property parameters of each specimen is as follows: based on the likelihood function and the preset prior distribution, the posterior distribution of the mechanical property parameters of the ceramic matrix composite material components is extracted using the Markov Monte Carlo sampling method.

[0102] In this embodiment, Markov Monte Carlo (MCMC) sampling is performed in the Bayesian parameter inference method. The relevant sampling program is written in Python. Based on empirical knowledge, this embodiment assumes that the prior distribution of mechanical performance parameters is uniform. The specific range of the prior distribution is shown in Table 2.

[0103] Table 2

[0104]

[0105] Therefore, based on the prior distribution range and likelihood function in Table 1, SiC can be extracted. f / SiC m - The posterior distribution of the mechanical property parameters of the composite material components is shown in Table 3. It can be seen that, after the update of the Bayesian parameter inference method in this embodiment, the posterior distribution range of each mechanical property parameter is significantly more concentrated than the broad uniform distribution in Table 2, indicating the effectiveness of the parameter inference method in this embodiment.

[0106] Table 3

[0107]

[0108] S5. Construct a hierarchical Bayesian inference model and obtain the posterior distribution of the hyperparameters of the hierarchical Bayesian inference model;

[0109] Specifically, in this embodiment, a hierarchical Bayesian inference model for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components is constructed based on the posterior distribution of the mechanical property parameters of the six specimens; the hyperparameters of the hierarchical Bayesian inference model are sampled to obtain the posterior distribution of the hyperparameters.

[0110] For example, such as Figure 29 As shown, in one specific embodiment, the steps for constructing a hierarchical Bayesian inference model for the quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components are as follows:

[0111] With SiC f / Machining property parameter vector of SiC material composition θ A certain mechanical property parameter For example, suppose there are a total of M One test piece, k =1,2,…, M Follows a mean The variance is Normal distribution:

[0112] (4)

[0113] In the formula, Representing mechanical performance parameters The average value, The variance represents the normal distribution and reflects the inherent dispersion of the component's elastic parameters.

[0114] Among them, the mechanical performance parameters obtained by inversion based on Bayesian inference method The recognition result value It is the coupling between the true value and the measurement noise uncertainty, as expressed in the following expression:

[0115] (5)

[0116] In the formula, Indicates parameters The estimated uncertainty variance; The mean is variance is It follows a normal distribution.

[0117] Because of variance and uncertainty variance Since they are independent, combining equations (4) and (5) yields... The distribution is as follows:

[0118] (6)

[0119] Equation (6) shows that the variance of the mechanical property parameters estimated by the Bayesian parameter inference method is the variance of the material's inherent dispersion. and uncertainty variance sum; The mean is variance is It follows a normal distribution.

[0120] Hyperparameters characterizing the true dispersion of component mechanical properties were obtained using Bayesian inference methods. and That is, it can achieve SiC f / SiC m Quantitative analysis of the dispersion of material mechanical properties requires, in Bayesian inference methods, the hyperparameter. and Specify the prior distribution:

[0121] (7)

[0122] (8)

[0123] In the formula, This is called hyperparameter The mean of the specified prior distribution; This is called hyperparameter The variance of the specified prior distribution; For hyperparameters The standard deviation of the specified prior distribution; This indicates that the mean is 0 and the standard deviation is 0. The semi-normal distribution; , and From various SiC f / SiC m The parameters of mechanical properties of the specimen components were obtained by processing the Bayesian inference results.

[0124] The overall joint probability distribution of the hierarchical Bayesian inference model (including the recognition result value) Potential real mechanical performance parameters and hyperparameters )for:

[0125] (9)

[0126] In the formula, These are experimentally measured values ​​of mechanical performance parameters. The likelihood; These are the mechanical property parameters of the actual components. The likelihood, Hyperparameters The prior distribution; Hyperparameters The prior distribution of .

[0127] The inference objective of the hierarchical Bayesian inference model in this invention is the hyperparameter. and The focus is on Given observation data and known measurement uncertainty The following is the posterior distribution:

[0128] (10)

[0129] In the formula, It is the marginal likelihood function, obtained by considering mechanical performance parameters. The integral yields:

[0130] (11)

[0131] Will and Substituting into equation (11), we get:

[0132] (12)

[0133] Substituting equation (11) into equation (10), we obtain the hyperparameters. The posterior distribution is:

[0134] (13)

[0135] In the formula, Hyperparameters The posterior distribution of; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... Experimental measurements of each mechanical property parameter The mean; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... Experimental measurements of each mechanical property parameter Standard deviation; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... Mechanical performance parameters The experimental measurements; This represents the variance of the noise measured in the experiment; express The prior distribution; express The prior distribution of .

[0136] S6. Obtain the quantitative analysis results of the mechanical property dispersion of ceramic matrix composite components;

[0137] Based on the posterior distribution of hyperparameters, the quantitative analysis results of the mechanical property dispersion of ceramic matrix composite components are obtained. The quantitative analysis results are: population posterior mean, variance, and the highest posterior density interval of 95%.

[0138] For example, in this embodiment, the posterior distribution results obtained by constructing a hierarchical Bayesian model based on 6 specimens are shown in Table 4, including the mean. mean 95% highest posterior density interval, standard deviation Standard deviation Based on the posterior distribution results of the hyperparameters, the 95% highest posterior density interval, the coefficient of variation (CV), and the 95% highest posterior density interval of the CV, the quantitative analysis results of the mechanical property dispersion of the ceramic matrix composite components can be obtained. The quantitative analysis results are as follows: Figures 18-28 As shown.

[0139] Table 4

[0140]

[0141] In this embodiment, the distribution accuracy is verified based on the remaining specimens: using data from four specimens not involved in the construction of the hierarchical Bayesian inference model, the predictive performance of the population probability distribution is verified. 3000 samples are sampled from the inherently dispersed posterior distribution, and 3000 corresponding stress-strain curves are predicted using the curve prediction branch path of a multi-task convolutional neural network. The corresponding tensile modulus (i.e., the slope of the elastic segment of the curve), failure strain, and tensile strength (i.e., the coordinates of the curve's endpoint) are calculated from the predicted curves and compared with the data from the four verification specimens not involved in the construction of the hierarchical Bayesian model. The results are as follows: Figures 26-28 ,from Figures 26-28 It can be seen that the 95% confidence interval of the predicted stress-strain curves completely encompasses the four verification curves. The 95% confidence intervals of the predicted failure strain and tensile strength also completely encompass the verification data. Furthermore, the tensile modulus data of the four verification specimens are distributed near the central peak of the predicted results. This demonstrates that the dispersion quantification analysis method provided in this embodiment can accurately perform dispersion probability analysis on the component mechanical property parameters of ceramic matrix composites and provide an accurate basis for predicting the mechanical characteristics of other materials.

[0142] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for quantitative analysis of the dispersion of mechanical properties of components in ceramic matrix composites, characterized in that, include: Multiple specimens of ceramic matrix composites were obtained, and the experimental measurements corresponding to the surface strain field and stress-strain curves of the ceramic matrix composites of the specimens were obtained. Establish target finite element models of ceramic matrix composite specimens under a combination of macroscopic and mesoscopic scales; based on the combination of mechanical property parameters of ceramic matrix composite components and the target finite element model, obtain the calculated values ​​of surface strain field and stress-strain curve of ceramic matrix composite under each combination of mechanical property parameters, and construct a dataset based on the combination of mechanical property parameters, surface strain field and stress-strain curve. A neural network model is established, and the model is trained based on a dataset to obtain a trained target neural network model. The target neural network model is then used to predict the surface strain field and stress-strain curve of the ceramic matrix composite material under each combination of mechanical property parameters. Based on the predicted values ​​of the surface strain field, the experimental measurements, the predicted values ​​of the stress-strain curve, and the experimental measurements, an error function is constructed to evaluate the difference between the predicted values ​​and the experimental measurements. The likelihood function in the Bayesian parameter inference method is constructed based on the error function. Based on the likelihood function and the preset prior distribution, the posterior distribution of the mechanical performance parameters of each specimen is obtained. The expression for the error function is: In the formula, Represents the error function; This represents the surface strain field error term, which consists of the predicted and experimentally measured values ​​of the surface strain field. A vector representing the mechanical property parameters of the components in a ceramic matrix composite material; Represents a vector based on mechanical performance parameters The obtained surface strain field of the first Predicted values ​​for each data point; Represents the first in the surface strain field Experimental measurements of each data point; This represents the amplification factor for the surface strain field error term; This represents the stress-strain error term, which consists of the predicted values ​​and experimental measurements of the stress-strain curve. This represents the total number of data points in the surface strain field; Stress-strain error term The expression is: In the formula, The purpose of calculating the dtw distance between the predicted normalized stress-strain curve obtained using the dynamic time warping algorithm and the experimentally measured normalized stress-strain curve is to characterize the overall difference between the predicted and experimentally measured stress-strain curves. The experimentally measured value of the normalized stress; The normalized experimental strain measurement. The normalized stress-strain curve For vector-based The normalized stress-strain curves predicted by the target neural network model are used. The difference in slope between the predicted and experimentally measured stress-strain curves corresponding to the elastic segments is represented by a dimensionless term. This term aims to characterize the difference in macroscopic tensile modulus of the ceramic matrix composite material corresponding to the predicted and experimentally measured values ​​of the stress-strain curves. The macroscopic tensile modulus of the ceramic matrix composite material is calculated from the predicted values ​​of the stress-strain curve. For vector-based And the stress prediction value is used in the stress-strain curve predicted by the target neural network model; For vector-based And the strain prediction value is used from the stress-strain curve predicted by the target neural network model. To calculate the macroscopic tensile modulus of ceramic matrix composites from experimentally measured values ​​of stress-strain curves, The stress is the experimentally measured value of the stress within the elastic segment of the stress-strain curve. The experimentally measured value of the strain within the elastic segment of the stress-strain curve; The difference between the predicted stress-strain curve and the experimentally measured stress-strain curve in terms of failure strain and tensile strength parameters is represented by a dimensionless term, where... This refers to the strain value corresponding to the end of the experimental stress-strain curve, i.e., the failure strain of the material specimen. This represents the stress value corresponding to the end of the experimental stress-strain curve, i.e., the tensile strength of the material specimen. Similarly, The failure strain is the stress-strain curve predicted by the target neural network model. The tensile strength is the stress-strain curve predicted by the target neural network model. These are the weighting coefficients for the dtw distance; The weighting coefficient for the slope difference value. The weighting coefficients for the differences between the predicted stress-strain curve and the experimentally measured stress-strain curve in terms of failure strain and tensile strength parameters; The expression for the likelihood function is: In the formula, Represents the likelihood function; express The variance of a normal Gaussian distribution when its value follows such a distribution; Represents the error function; Based on the posterior distribution of the mechanical property parameters of each specimen, a hierarchical Bayesian inference model is constructed for the quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components. The hyperparameters of the hierarchical Bayesian inference model are sampled to obtain the posterior distribution of the hyperparameters. Based on the posterior distribution of the hyperparameters, the quantitative analysis results of the mechanical property dispersion of the ceramic matrix composite components are obtained. The quantitative analysis results are: population posterior mean, variance, and the highest posterior density interval of 95%.

2. The method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components according to claim 1, characterized in that, The steps for obtaining multiple specimens of ceramic matrix composites are as follows: Multiple initial specimens were obtained by sampling at different locations along the raw ceramic matrix composite material; Multiple initial specimens were machined according to a unified standard to obtain multiple specimens.

3. The method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components according to claim 1, characterized in that, The steps for obtaining experimental measurements of the specimen surface are as follows: Uniaxial tensile tests were performed on the specimens, and the experimental measurements were recorded using a DIC device during the loading process.

4. The method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components according to claim 1, characterized in that, The steps for establishing a target finite element model of a ceramic matrix composite specimen at a combination of macroscopic and mesoscopic scales are as follows: Finite element models of matching micro-woven structures were established based on the weaving method, fiber bundle size, and porosity parameters of ceramic matrix composite specimens. A macroscopically homogeneous finite element model was constructed based on the macroscopic dimensions of ceramic matrix composite specimens. The finite element model of the micro-woven structure is spliced ​​with the macro-homogeneous finite element model to form a target finite element model combining macro- and micro-scales.

5. The method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components according to claim 1, characterized in that, The steps for obtaining the posterior distribution of the mechanical property parameters of each component of the specimen based on the likelihood function and the preset prior distribution are as follows: Based on the likelihood function and a pre-defined prior distribution, the posterior distribution of the mechanical property parameters of ceramic matrix composite components is extracted using the Markov Monte Carlo sampling method.

6. The method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components according to claim 1, characterized in that, The expression for the hierarchical Bayesian inference model is: In the formula, Hyperparameters The posterior distribution of; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... The mean of the experimentally measured parameters; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... The standard deviation of each experimental measurement parameter; The first parameter in the vector representing the mechanical property parameters of ceramic matrix composite components is... Experimental measurement parameters of each parameter; This represents the variance of the noise measured in the experiment; express The prior distribution; express The prior distribution of .

7. The method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components according to claim 1, characterized in that, The Markov Monte Carlo sampling method is used to sample the hyperparameters of the hierarchical Bayesian inference model to obtain the posterior distribution of the hyperparameters.

8. The method for quantitative analysis of the dispersion of mechanical properties of ceramic matrix composite components according to claim 1, characterized in that, The steps for obtaining the quantitative analysis results of the mechanical property dispersion of ceramic matrix composite components based on the posterior distribution of hyperparameters are as follows: Based on the posterior distribution of hyperparameters, a population probability distribution model is constructed using the kernel density estimation method; The population probability distribution model is used to obtain the population posterior mean, variance, and 95% highest posterior density interval for each mechanical performance parameter.

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