A method for probabilistic representation of mechanical property parameters of ceramic matrix composite components
By establishing a target finite element model and a neural network model for ceramic matrix composites, and combining them with Bayesian parameter inference methods, the problem that traditional measurement techniques are difficult to characterize the micromechanical properties of CMCs was solved, and accurate probability distribution modeling and performance analysis were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-02-06
- Publication Date
- 2026-05-29
Smart Images
Figure CN121683389B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of computer-aided processing technology, and more specifically to a probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials. Background Technology
[0002] Ceramic matrix composites (CMCs) are materials composed of fiber bundles and a matrix, exhibiting complex multi-scale structures and mechanical properties. They hold great promise for applications in extreme environments, such as hot-end components and thermal protection systems in aerospace equipment. However, the complex manufacturing processes and inherent multi-scale heterogeneous structures of CMCs lead to significant dispersion and uncertainty in their mechanical properties, severely limiting their widespread engineering applications in high-reliability systems.
[0003] Traditional measurement techniques struggle to efficiently and comprehensively measure the anisotropic micromechanical properties of composite materials (CMCs). They can only obtain limited macroscopic performance parameters through experiments such as tension, compression, and shear, and these methods are costly, further hindering research on the performance dispersion of CMCs. Therefore, some researchers have employed parametric inversion methods for indirect identification and characterization. However, existing inversion methods have several limitations, such as difficulty in assessing uncertainties in composite materials within a deterministic framework, and limited accuracy in parameter identification. Furthermore, due to the extremely high numerical computation costs resulting from the complex multi-scale structure of CMCs, there are currently few publicly available methods capable of accurately probabilistically characterizing the anisotropic performance parameters of CMC microstructures.
[0004] Therefore, a probabilistic characterization method for the mechanical property parameters of ceramic matrix composite components is needed to solve the above problems. Summary of the Invention
[0005] This invention provides a probabilistic characterization method for the mechanical property parameters of ceramic matrix composite components to solve the problems of the prior art.
[0006] The probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials of the present invention adopts the following technical solution, including:
[0007] Establish a target finite element model of ceramic matrix composite specimens under a combination of macroscopic and mesoscopic scales;
[0008] 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, and a dataset is constructed based on the combination of mechanical property parameters, the calculated values of 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] The experimental measurements of the surface strain field and stress-strain curve of the ceramic matrix composite material are obtained. 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.
[0011] Based on the error function, a likelihood function is constructed in the Bayesian parameter inference method. Based on the likelihood function and the preset prior distribution, the posterior distribution of the mechanical property parameters of the ceramic matrix composite components is obtained. The posterior distribution of the mechanical property parameters of the ceramic matrix composite components is probabilistically modeled to obtain a probability distribution model.
[0012] 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:
[0013] 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.
[0014] A macroscopically homogeneous finite element model was constructed based on the macroscopic dimensions of ceramic matrix composite specimens.
[0015] 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.
[0016] A further technical solution of the present invention is to sample the mechanical property parameters of the ceramic matrix composite material components from a preset range of mechanical property parameters to obtain multiple combinations of mechanical property parameters.
[0017] A further technical solution of the present invention is to input the combination of mechanical performance parameters into a finite element model for simulation analysis and calculation, and obtain the calculated values of the surface strain field and stress-strain curve of the ceramic matrix composite material under each combination of mechanical performance parameters.
[0018] A further technical solution of the present invention is that the neural network model is a multi-task convolutional neural network, the main path of the multi-task convolutional neural network is used to predict the surface strain field, and the branch paths of the multi-task convolutional neural network predict the stress-strain curve.
[0019] A further technical solution of the present invention is to conduct a uniaxial tensile mechanical test on a ceramic matrix composite specimen to obtain experimentally measured values of the surface strain field and stress-strain curve of the ceramic matrix composite.
[0020] A further technical solution of the present invention is that the expression of the error function is:
[0021]
[0022] 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.
[0023] A further technical solution of the present invention is that the expression of the likelihood function is:
[0024]
[0025] 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.
[0026] 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 the ceramic matrix composite material components is as follows: based on the likelihood function and a 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.
[0027] A further technical solution of the present invention is that the step of probabilistically modeling the posterior distribution of the mechanical property parameters of the ceramic matrix composite material components to obtain a probability distribution model is as follows:
[0028] By using normal distribution, log-normal distribution or Weibull distribution to probabilistically model the posterior distribution of each mechanical property parameter of ceramic matrix composite components, the initial probability distribution model corresponding to the normal distribution, log-normal distribution or Weibull distribution under each mechanical property parameter is obtained;
[0029] The KS test method was used to obtain the fitting accuracy of the initial probability distribution model corresponding to the normal distribution, log-normal distribution, or Weibull distribution, respectively.
[0030] The initial probability distribution model corresponding to the maximum fitting accuracy is used as the probability distribution model corresponding to the mechanical performance parameter.
[0031] The beneficial effects of this invention are:
[0032] A target finite element model of ceramic matrix composite specimens was established at both macroscopic and mesoscopic scales. A dataset was constructed and a neural network model was trained. The trained target neural network model was used to predict the surface strain field and stress-strain curve of the ceramic matrix composite under each combination of mechanical property parameters. Based on the predicted surface strain field, experimentally measured values, and predicted and experimentally measured stress-strain curves, an error function was constructed to evaluate the difference between the predicted and experimental values. The purpose of constructing the target finite element model is to obtain the strain field required in the error function using the mesoscopic part of the target finite element model, while the macroscopic model has a relatively coarse mesh and fewer meshes to balance the overall mesh count of the model and avoid excessive mesh count, thereby reducing computational costs. The error function establishes a mapping relationship between the predicted strain field, stress-strain curve, and experimentally measured strain field and stress-strain curve, facilitating the inverse inference of mechanical property parameters based on the experimental measurement data of the ceramic matrix composite. Therefore, a likelihood function for the Bayesian inference method is constructed based on the error function. Based on this likelihood function and using the MCMC method within the Bayesian inference method for sampling, the posterior distribution of the mechanical property parameters can be obtained. Finally, a probability distribution model can be derived based on the posterior distribution. In summary, this invention infers the posterior probability distribution of the mechanical property parameters of the micro-scale components (fiber bundles and matrix) of ceramic matrix composites based on experimental measurement data of ceramic matrix composite specimens. Through the analysis and probabilistic modeling of the posterior distribution, an accurate parameter basis can be provided for the quantification of uncertainty, performance dispersion analysis, and performance prediction of ceramic matrix composites. Attached Figure Description
[0033] 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.
[0034] Figure 1 This is a flowchart illustrating a probabilistic characterization method for the mechanical property parameters of ceramic matrix composite components according to the present invention.
[0035] Figure 2 This is a schematic diagram of the target finite element model obtained in an embodiment of the present invention;
[0036] Figure 3 This is a network structure diagram of the neural network model in an embodiment of the present invention;
[0037] Figure 4 This is a schematic diagram of the strain field predicted by the multi-task convolutional network in verification example 1 of this invention;
[0038] Figure 5 This is a schematic diagram of the strain field calculated by the finite element model in verification example 1 of this invention;
[0039] Figure 6 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.
[0040] Figure 7 This is a schematic diagram of the strain field predicted by the multi-task convolutional network in verification example 2 of this invention;
[0041] Figure 8 This is a schematic diagram of the strain field calculated by the finite element model in verification example 2 of this invention;
[0042] Figure 9 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.
[0043] Figure 10 This is a schematic diagram of the strain field predicted by the multi-task convolutional network in verification example 3 of this invention;
[0044] Figure 11 This is a schematic diagram of the strain field calculated by the finite element model in verification example 3 of this invention;
[0045] Figure 12 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.
[0046] Figure 13 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.
[0047] Figure 14 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.
[0048] Figure 15This 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.
[0049] Figure 16 This is a schematic diagram of the surface strain field measured experimentally in an embodiment of the present invention;
[0050] Figure 17 This is a schematic diagram of the stress-strain curves measured experimentally in an embodiment of the present invention;
[0051] Figure 18 This is a schematic diagram illustrating the evaluation of the posterior distribution of three different probability distribution models in the axial modulus of the fiber bundle and the information of each probability distribution model in an embodiment of the present invention.
[0052] Figure 19 This is a schematic diagram illustrating the evaluation of the posterior distribution of three different probability distribution models in the transverse modulus of the fiber bundle and the information of each probability distribution model in an embodiment of the present invention.
[0053] Figure 20 In this embodiment of the invention, three different probability distribution models are evaluated in fiber bundles. xy A schematic diagram of the posterior distribution of Poisson's ratio in the plane and information on various probability distribution models;
[0054] Figure 21 In this embodiment of the invention, three different probability distribution models are evaluated in fiber bundles. yz A schematic diagram of the posterior distribution of Poisson's ratio in the plane and information on various probability distribution models;
[0055] Figure 22 In this embodiment of the invention, three different probability distribution models are evaluated in fiber bundles. xy A schematic diagram of the posterior distribution of the in-plane shear modulus and the information of each probability distribution model;
[0056] Figure 23 In this embodiment of the invention, three different probability distribution models are evaluated in fiber bundles. yz A schematic diagram of the posterior distribution of the in-plane shear modulus and the information of each probability distribution model;
[0057] Figure 24 This is a schematic diagram illustrating the evaluation of the posterior distribution of three different probability distribution models in the matrix modulus and the information of each probability distribution model in an embodiment of the present invention.
[0058] Figure 25 This is a schematic diagram illustrating the evaluation of the posterior distribution of three different probability distribution models in the matrix Poisson's ratio and the information of each probability distribution model in an embodiment of the present invention.
[0059] Figure 26This is a graph showing the result of predicting the probability distribution of stress-strain curves based on the probabilistic characterization results of the mechanical property parameters of ceramic matrix composite materials in an embodiment of the present invention. Detailed Implementation
[0060] 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.
[0061] An embodiment of the probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials according to the present invention, wherein two-dimensional braided SiC is used in this embodiment. 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 vector formed by the elastic parameters 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:
[0062] S1. Establish the target finite element model;
[0063] Specifically, a target finite element model of ceramic matrix composite specimens is established under a combination of macroscopic and mesoscopic scales.
[0064] For example, such as Figure 2 As shown, in a specific embodiment, 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: establishing a matching mesoscopic woven structure finite element model based on the weaving method, fiber bundle size, and porosity parameters of the ceramic matrix composite specimen; constructing a macroscopically homogeneous finite element model based on the macroscopic dimensions of the ceramic matrix composite specimen; and splicing the mesoscopic woven structure finite element model with the macroscopically homogeneous finite element model to form a target finite element model combining macroscopic and mesoscopic scales.
[0065] 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 through CT scan images.
[0066] 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.
[0067] S2. Construct the dataset;
[0068] Specifically, based on the combination of mechanical property parameters of ceramic matrix composite components and the target finite element model, the calculated values of the surface strain field and stress-strain curve of ceramic matrix composites under each combination of mechanical property parameters are obtained, and a dataset is constructed based on the combination of mechanical property parameters, the surface strain field and the calculated values of stress-strain curve.
[0069] 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.
[0070] Table 1
[0071]
[0072] 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.
[0073] 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.
[0074] S3. Construct a neural network model and train it;
[0075] 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.
[0076] For example, such as Figure 3 As shown, in one specific embodiment, the neural network model is a 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 3 The 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 structure is designed to inherit the training results of the main path to the branch paths, thereby improving the prediction accuracy of the branch paths under the condition of a small number of stress-strain curve samples 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. In this embodiment... Figure 3 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. 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.
[0077] 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 4-6 As shown in Example 2, the prediction accuracy of the multi-task convolutional neural network after training is verified. Figures 7-9 As shown in Example 3, the prediction accuracy of the multi-task convolutional neural network after training is verified as follows: Figures 10-12 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. 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 3 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.
[0078] The reason for transforming the one-dimensional stress-strain data prediction task into an image prediction branch of the ResUNet network is that SiC f / 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 13 to 15 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.
[0079] 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.
[0080] S4. Construct the error function;
[0081] Specifically, a target neural network model is used to predict the surface strain field and stress-strain curve of ceramic matrix composites under each combination of mechanical property parameters; experimental measurements of the surface strain field and stress-strain curve of ceramic matrix composites are obtained; and an error function is constructed to evaluate the difference between the predicted and experimental measurements based on the predicted surface strain field, the predicted stress-strain curve, and the experimental measurements.
[0082] For example, in one specific embodiment, the step of obtaining the experimentally measured values corresponding to the surface strain field and stress-strain curve of the ceramic matrix composite material is as follows: using a universal electronic testing machine to test the SiC... f / SiC m - Composite material specimens were subjected to uniaxial tensile testing, and non-contact measurement techniques were used to obtain results such as... Figure 16 The SiC shown f / SiC m - Surface strain field of composite materials and Figure 17 The SiC shown f / SiC m - Stress-strain curves of composite materials.
[0083] For example, in one specific embodiment, the expression for the error function used to evaluate the difference between the predicted value and the experimental measurement value is:
[0084]
[0085] 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.
[0086] In this embodiment, the stress-strain error term The expression is:
[0087]
[0088] 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 And 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.
[0089] S5. Construct the likelihood function and obtain the probability distribution model;
[0090] Specifically, 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 property parameters of the ceramic matrix composite components is obtained. The posterior distribution of the mechanical property parameters of the ceramic matrix composite components is probabilistically modeled to obtain a probability distribution model.
[0091] For example, in one specific embodiment, the expression for the likelihood function is:
[0092]
[0093] 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.
[0094] For example, in one specific embodiment, the step of obtaining the posterior distribution of the mechanical property parameters of the ceramic matrix composite material components based on the likelihood function and a preset prior distribution is as follows:
[0095] Markov Monte Carlo (MCMC) sampling is performed in the Bayesian parameter inference method. In this embodiment, 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.
[0096] Table 2
[0097]
[0098] 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.
[0099] Table 3
[0100]
[0101] For example, in one specific embodiment, the step of probabilistically modeling the posterior distribution of the mechanical property parameters of the ceramic matrix composite component to obtain a probability distribution model is as follows: using a normal distribution, log-normal distribution, or Weibull distribution to probabilistically model the posterior distribution of each mechanical property parameter of the ceramic matrix composite component to obtain an initial probability distribution model corresponding to the normal distribution, log-normal distribution, or Weibull distribution for each mechanical property parameter; using the KS test method to obtain the fitting accuracy of the initial probability distribution model corresponding to the normal distribution, log-normal distribution, or Weibull distribution respectively; and taking the initial probability distribution model corresponding to the maximum fitting accuracy as the probability distribution model corresponding to the mechanical property parameter.
[0102] Specifically, in this embodiment, 500 samples are randomly sampled from the posterior distributions of each mechanical performance parameter in Table 3. The Kolmogorov-Smirnov test is used to evaluate the fitting accuracy of three commonly used probability models—normal distribution, log-normal distribution, and Weibull distribution—on the posterior distributions of the mechanical performance parameters. The final posterior distributions of each mechanical performance parameter and the information of each probability distribution model are as follows: Figures 18-25 As shown. From Figures 18-25 As can be seen, after the Bayesian parameter inference method in this embodiment is updated, the posterior distribution range of each mechanical property parameter is significantly more concentrated than the prior uniform distribution in Table 2, and exhibits a clear unimodal distribution shape, indicating the effectiveness of the parameter inference process in this embodiment. Among them, the fiber bundle axial modulus ( Figure 18 ), fiber bundle transverse modulus ( Figure 19 ) and matrix modulus ( Figure 24 The distribution of ) exhibits regular normal distribution characteristics. Figures 20-23 as well as Figure 24 The posterior distributions of the corresponding parameters exhibit a certain degree of skewness. The Karl von Sorcery (KS) test was used to compare the fitting accuracy of three commonly used probability models, and the best-fitting probability model was used to fit each model. This achieved accurate probabilistic modeling of the posterior distributions of the mechanical performance parameters.
[0103] like Figure 26As shown, this embodiment predicts the corresponding SiC based on the probability distribution model of each mechanical property parameter. f / SiC m - The probability distribution range of the stress-strain curves of ceramic matrix composites, from Figure 26 The predicted SiC can be seen in the image. f / SiC m The stress-strain curve of the ceramic matrix composite material completely encompasses the actual experimental curve, demonstrating that the SiC obtained by the technical solution of this invention... f / SiC m - The accuracy of the posterior distribution of mechanical property parameters of ceramic matrix composite components.
[0104] 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 probabilistic characterization method for the mechanical property parameters of components in a ceramic matrix composite material, characterized in that, include: Establish a target finite element model 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, the calculated values of surface strain field and stress-strain curve of ceramic matrix composite under each combination of mechanical property parameters are obtained, and a dataset is constructed based on the combination of mechanical property parameters, the calculated values of 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. The experimental measurements of the surface strain field and stress-strain curve of the ceramic matrix composite material are obtained. 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 and experimental values. The expression of the error function is as follows: 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; the 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. 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; Based on the error function, a likelihood function is constructed in the Bayesian parameter inference method. Based on the likelihood function and a pre-defined prior distribution, the posterior distribution of the mechanical property parameters of the ceramic matrix composite components is obtained. A probability distribution model is then obtained by probabilistically modeling the posterior distribution of the mechanical property parameters of the ceramic matrix composite components. 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; This represents the error function.
2. The probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials 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: A finite element model of a matching micro-woven structure was 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.
3. The probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials according to claim 1, characterized in that, The mechanical properties of the ceramic matrix composite components are sampled from a preset range of mechanical property parameters to obtain multiple combinations of mechanical property parameters.
4. The probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials according to claim 1, characterized in that, The mechanical property parameters are input into the finite element model for simulation analysis and calculation, and 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 obtained.
5. The probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials according to claim 1, characterized in that, The neural network model is a 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 curve.
6. The probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials according to claim 1, characterized in that, Uniaxial tensile mechanical tests were conducted on ceramic matrix composite specimens to obtain experimental measurements of the surface strain field and stress-strain curves of the ceramic matrix composites.
7. The probabilistic characterization method for the mechanical property parameters 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 ceramic matrix composite components based on the likelihood function and the preset prior distribution are as follows: Based on the likelihood function and the preset prior distribution, the posterior distribution of the mechanical property parameters of ceramic matrix composite components is extracted using the Markov Monte Carlo sampling method.
8. The probabilistic characterization method for the mechanical property parameters of ceramic matrix composite materials according to claim 1, characterized in that, The steps for probabilistically modeling the posterior distribution of the mechanical property parameters of ceramic matrix composite components to obtain the probability distribution model are as follows: By using normal distribution, log-normal distribution or Weibull distribution to probabilistically model the posterior distribution of each mechanical property parameter of ceramic matrix composite components, the initial probability distribution model corresponding to the normal distribution, log-normal distribution or Weibull distribution under each mechanical property parameter is obtained; The KS test method was used to obtain the fitting accuracy of the initial probability distribution model corresponding to the normal distribution, log-normal distribution, or Weibull distribution, respectively. The initial probability distribution model corresponding to the maximum fitting accuracy is used as the probability distribution model corresponding to the mechanical performance parameter.