A method and system for predicting the resistivity performance of multiphase carbon ceramics based on entropy descriptors

Abstract

This application belongs to the field of functional ceramic material performance optimization technology, specifically disclosing a method and system for predicting the performance of multiphase carbon ceramic resistors based on entropy descriptors. The method includes: determining the multi-source microstructure characteristic parameters of the carbon ceramic resistor to be tested; inputting the multi-source microstructure characteristic parameters of the carbon ceramic resistor to be tested into a carbon ceramic resistor performance prediction model to obtain the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor to be tested output by the carbon ceramic resistor performance prediction model, thereby determining the energy tolerance performance of the carbon ceramic resistor to be tested; the carbon ceramic resistor performance prediction model is trained based on the multi-source microstructure characteristic parameter samples of the carbon ceramic resistor sample and the label information of their corresponding comprehensive performance entropy descriptors; the comprehensive performance entropy descriptor is used to characterize the degree of energy dissipation order of the carbon ceramic resistor material. Through this application, accurate and efficient prediction of the performance of carbon ceramic resistor materials can be achieved.

Description

Technical Field

[0001] This application belongs to the field of functional ceramic material performance optimization technology, specifically to the field of machine learning technology, and more specifically, to a method and system for predicting the resistivity performance of multiphase carbon ceramics based on entropy descriptors. Background Technology

[0002] Carbon ceramic resistors, as key components in high-power energy dissipation, are widely used in important nodes of new power systems such as high-voltage circuit breakers, converter stations, energy storage cabinets, and grid-connected devices, playing a crucial role in ensuring the safe and stable operation of power equipment. With the increasing demands for transient energy regulation and absorption due to the "high-voltage and high-power" characteristics of new power systems, extremely high requirements are placed on the transient energy tolerance and operating temperature of key energy-absorbing components like carbon ceramic resistors. Carbon ceramic resistors are made by high-temperature sintering of carbon black, clay, and ceramic aggregates, and their macroscopic electrothermal properties are closely related to their internal multiphase microstructure. Under the electro-thermal-mechanical multi-physics field coupling effect caused by transient energy injection, multiphase carbon ceramic resistors exhibit complex microstructure evolution and failure mechanisms. Therefore, the key to improving the energy tolerance performance of multiphase carbon ceramic resistors lies in optimizing their microstructure characteristics to obtain the optimal electro-thermal-mechanical integrated response.

[0003] However, while current finite element simulation methods can reveal the physical processes underlying the resistance energy tolerance of multiphase carbon ceramics, the features extracted by these data-driven methods, which directly predict performance using raw microscopic image data, are disconnected from the material's physical mechanisms. This results in a lack of physical interpretability and low prediction accuracy.

[0004] Therefore, how to better predict the resistivity of multiphase carbon ceramics has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this application is to better predict the resistivity of multiphase carbon ceramics, and to solve the problem of low prediction accuracy of existing prediction methods.

[0006] To achieve the above objectives, in a first aspect, this application provides a method for predicting the resistivity performance of multiphase carbon ceramics based on entropy descriptors, comprising: Determine the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test; The multi-source microstructure characteristic parameters of the carbon ceramic resistor under test are input into the carbon ceramic resistor performance prediction model to obtain the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor under test output by the carbon ceramic resistor performance prediction model, so as to determine the energy tolerance performance of the carbon ceramic resistor under test. The carbon ceramic resistor performance prediction model is obtained by training based on the multi-source microstructure feature parameter samples of carbon ceramic resistor samples and the label information of their corresponding comprehensive performance entropy descriptors. The comprehensive performance entropy descriptor is determined by the performance parameters extracted from the multi-physics transient coupling simulation of the numerical calculation model constructed using the carbon-aluminum element concentration distribution matrix of the carbon ceramic resistor material. It is used to characterize the degree of energy dissipation order of the carbon ceramic resistor material.

[0007] Optionally, determining the multi-source microstructure characteristic parameters of the carbon ceramic resistor to be tested includes: Obtain the X-ray intensity distribution map of the carbon and aluminum element characteristics of the carbon ceramic resistor under test; Based on the X-ray intensity distribution map, normalization calculations and binarization processing are performed to obtain carbon element concentration distribution map, aluminum element concentration distribution map and pore structure binary distribution map; Based on the carbon element concentration distribution map, the carbon chain conductive network quality parameters are determined, and based on the carbon element concentration distribution map, the carbon phase distribution uniformity index parameters are determined. Based on the binary distribution map of the pore structure, the composite parameters of the pore structure characteristics are determined; Based on the aluminum element concentration distribution map, the structural integrity index parameters of the ceramic matrix are determined; The multi-source microstructure characteristic parameters include the carbon chain conductive network quality parameter, the carbon phase distribution uniformity index parameter, the pore structure characteristic composite parameter, and the ceramic matrix structural integrity index parameter. The carbon chain conductive network quality parameter is used to quantify the physical connectivity of the conductive carbon network and the effectiveness of the conductive path. The carbon phase distribution uniformity index parameter is used to characterize the spatial distribution fluctuation of carbon elements. The pore structure characteristic composite parameter is used to comprehensively quantify the pore structure characteristics. The ceramic matrix structural integrity index parameter is used to characterize the structural integrity of the ceramic matrix and its relationship with the volume and spatial structural stability of its ceramic phase.

[0008] Optionally, determining the carbon chain conductive network quality parameters based on the carbon element concentration distribution map includes: The carbon element concentration distribution map is binarized to obtain a carbon phase binary map, and the carbon phase skeleton of the carbon phase binary map is extracted to obtain a carbon phase skeleton map. Determine the connectivity density of the carbon phase framework diagram; A morphological closing operation is performed on the carbon phase skeleton diagram to obtain the processed carbon phase skeleton diagram, and the linearity of the conductive path is determined based on the processed carbon phase skeleton diagram. The quality parameters of the carbon chain conductive network are determined based on the connectivity density and the linearity of the conductive path.

[0009] Optionally, determining the carbon phase distribution uniformity index parameter based on the carbon element concentration distribution map includes: A sliding window analysis is performed on the carbon element concentration distribution map to determine multiple analysis windows and the local uniformity information of the pixel region corresponding to each analysis window; The carbon phase distribution uniformity index parameter is determined by performing an arithmetic average calculation based on the local uniformity information of the pixel region corresponding to each analysis window.

[0010] Optionally, determining the composite parameters of the pore structure features based on the binary distribution map of the pore structure includes: Connectivity analysis and measurement are performed on the binary distribution map of the pore structure to determine the number of pore regions and the pixel area occupied by each pore region. Based on the number of pore regions, the pixel area occupied by each pore region, and the total number of pixels in the distribution map, the average size of the pores and the pore surface density are determined. Based on the average pore size and the pore areal density, the composite parameters of the pore structure characteristics are determined.

[0011] Optionally, determining the ceramic matrix structural integrity index parameter based on the aluminum element concentration distribution map includes: The aluminum element concentration distribution map is binarized to obtain a binary map of the aluminum phase; Based on the aforementioned aluminum phase binary map, the volume fraction of the ceramic phase region is determined. Perform Euclidean distance transformation on the aluminum phase binary image to determine the Euclidean distance transformation value corresponding to each pixel in the ceramic phase region and the average value of the Euclidean distance transformation values ​​corresponding to all pixels; The structural integrity index parameter of the ceramic matrix is ​​determined based on the average value of the volume fraction and the Euclidean distance transformation value.

[0012] Optionally, the step of determining the comprehensive performance entropy descriptor specifically includes: The physical parameters of the geometric model were calibrated using the carbon element concentration distribution map, aluminum element concentration distribution map and the binary distribution map of the pore structure of the carbon ceramic resistor material, and the conductivity model of the carbon ceramic resistor material was determined. Numerical simulation calculations were performed on the conductivity model to determine the current density distribution uniformity index parameter, heat distribution uniformity index parameter, and thermal stress safety index parameter of the carbon ceramic resistor material. The current density distribution uniformity index parameter, the heat distribution uniformity index parameter, and the thermal stress safety index parameter are respectively converted into performance defect degree parameters to obtain the current density distribution defect degree parameter corresponding to the current density distribution uniformity index parameter, the heat distribution defect degree parameter corresponding to the heat distribution uniformity index parameter, and the stress concentration defect degree parameter corresponding to the thermal stress safety index parameter. The comprehensive performance entropy descriptor is determined based on the current density distribution defect degree parameter, the heat distribution defect degree parameter, and the stress concentration defect degree parameter.

[0013] Secondly, this application provides a multiphase carbon ceramic resistivity performance prediction system based on entropy descriptors, including: The processing module is used to determine the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test; The prediction module is used to input the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test into the carbon ceramic resistor performance prediction model, and obtain the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor under test output by the carbon ceramic resistor performance prediction model, so as to determine the energy tolerance performance of the carbon ceramic resistor under test. The carbon ceramic resistor performance prediction model is obtained by training based on the multi-source microstructure feature parameter samples of the carbon ceramic resistor sample and the label information of its corresponding comprehensive performance entropy descriptor. The comprehensive performance entropy descriptor is determined by the performance parameters extracted by multi-physics transient coupling simulation using a numerical calculation model constructed using the carbon-aluminum element concentration distribution matrix of the carbon ceramic resistor material. It is used to characterize the degree of energy dissipation order of the carbon ceramic resistor material.

[0014] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0015] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0016] Fifthly, this application provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0017] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0018] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: This application provides a method and system for predicting the performance of multiphase carbon ceramic resistors based on entropy descriptors. By adopting a strategy of "digital characterization of microstructure - construction of comprehensive performance entropy descriptor - neural network prediction", the key microstructure feature parameters of carbon ceramic resistors are extracted using digital characterization. A comprehensive performance entropy descriptor is constructed based on multiphysics simulation to characterize the degree of order of material energy dissipation of carbon ceramic resistor samples. Finally, a fast mapping model from the microscopic features of carbon ceramic resistors to macroscopic performance is established by training a neural network. This enables accurate and efficient prediction of the performance of carbon ceramic resistor materials, greatly improving the accuracy and efficiency of multiphase carbon ceramic resistor performance prediction. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the method for predicting the resistivity of multiphase carbon ceramics based on entropy descriptors provided in the embodiments of this application. Figure 2 (a) is a schematic diagram of the sample dataset distribution of the carbon chain conductive network quality parameters provided in the embodiments of this application; (b) is a schematic diagram of the sample dataset distribution of the carbon phase distribution uniformity index parameters; (c) is a schematic diagram of the sample dataset distribution of the composite parameters of the pore structure characteristics; (d) is a schematic diagram of the sample dataset distribution of the ceramic matrix structure integrity index parameters; and (e) is a schematic diagram of the sample dataset distribution of the comprehensive performance entropy descriptor. Figure 3 This is a schematic diagram of the loss function curves of the training set and validation set of the carbon ceramic resistance performance prediction model provided in the embodiments of this application; Figure 4 This is a schematic diagram comparing the predicted values ​​of the carbon ceramic resistance performance prediction model provided in the embodiments of this application with the actual values; Figure 5 In the above, (a) is a histogram of the residual distribution of the test set of the carbon ceramic resistance performance prediction model provided in the embodiments of this application, and (b) is a cumulative distribution of the absolute residuals of the test set of the carbon ceramic resistance performance prediction model. Figure 6 This is a schematic diagram of the current density distribution under multiphysics transient coupling simulation provided in the embodiments of this application; Figure 7 This is a schematic diagram of the structure of the multiphase carbon ceramic resistance performance prediction device based on entropy descriptors provided in the embodiments of this application; Figure 8 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0021] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0022] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0023] The embodiments of this application are described below with reference to the accompanying drawings.

[0024] Figure 1 This is a flowchart illustrating the method for predicting the resistivity of multiphase carbon ceramics based on entropy descriptors provided in this application. Figure 1 As shown, it includes: Step S1: Determine the multi-source microstructure characteristic parameters of the carbon ceramic resistor to be tested; Step S2: Input the multi-source microstructure characteristic parameters of the carbon ceramic resistor to be tested into the carbon ceramic resistor performance prediction model to obtain the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor to be tested output by the carbon ceramic resistor performance prediction model, so as to determine the energy tolerance performance of the carbon ceramic resistor to be tested. The carbon ceramic resistor performance prediction model is obtained by training based on the multi-source microstructure feature parameter samples of carbon ceramic resistor samples and the label information of their corresponding comprehensive performance entropy descriptors. The comprehensive performance entropy descriptor is determined by the performance parameters extracted from the multiphysics transient coupling simulation of the numerical calculation model constructed using the carbon and aluminum element concentration distribution matrix of the carbon ceramic resistor samples. It is used to characterize the degree of energy dissipation order of the carbon ceramic resistor material.

[0025] Specifically, the multi-source microstructure characteristic parameters described in the embodiments of this application refer to multiple characteristic parameters associated with the microstructure of multiphase carbon ceramic resistor materials, used to achieve quantitative and digital characterization of multiphase microstructures. Specifically, these parameters can be obtained by using an X-ray energy dispersive spectroscopy (EDS) instrument to scan the carbon ceramic resistor surface to obtain X-ray intensity distribution maps of carbon and aluminum elemental characteristics in representative micro-regions, and then extracting core microstructure characteristic parameters from this pixelated concentration matrix data.

[0026] The carbon and aluminum element concentration distribution matrix described in this application embodiment is used to characterize the spatial distribution information of carbon and aluminum element components in carbon ceramic resistor samples. It can be obtained by global normalization of pixel intensity values ​​using X-ray intensity distribution maps of carbon and aluminum element characteristics of carbon ceramic resistor samples.

[0027] Here, the microstructure of multiphase carbon ceramic resistor materials mainly includes three key components: carbon chain network, ceramic matrix, and pore structure. Among them, the distribution of carbon chain network paths determines the conductivity of the material; the structure of the ceramic matrix mainly affects its mechanical strength and heat dissipation performance; and the arrangement of the pore structure is related to the heat dissipation and mechanical behavior of the device.

[0028] The comprehensive performance entropy descriptor described in the embodiments of this application can be determined by the performance parameters extracted from the multiphysics transient coupling simulation of the numerical calculation model constructed using the carbon and aluminum element concentration distribution matrix of the carbon ceramic resistor sample. It is used to characterize the degree of material energy dissipation order of the carbon ceramic resistor sample and reflect the energy tolerance performance of the carbon ceramic resistor.

[0029] Here, multiphysics transient coupling simulation specifically refers to multiphysics transient coupling simulation involving electro-thermal-mechanical fields. Therefore, the performance parameters extracted during the process can specifically include three key performance indices: current density distribution uniformity index, heat distribution uniformity index, and thermal stress safety index.

[0030] It is understood that the label of the comprehensive performance entropy descriptor described in the embodiments of this application refers to the comprehensive performance entropy descriptor information that is assigned a label attribute during the training of the neural network model; the comprehensive performance entropy descriptor prediction information refers to the data information about the comprehensive performance entropy descriptor obtained by predicting the carbon ceramic resistance performance prediction model.

[0031] The carbon ceramic resistor performance prediction model described in this application embodiment can be obtained by training a preset deep neural network using the multi-source microstructure feature parameter samples of carbon ceramic resistor samples and the label information of their corresponding comprehensive performance entropy descriptors. This model is used to learn the intrinsic correlation between the multi-source microstructure feature parameters of carbon ceramic resistors and their comprehensive performance entropy descriptor information.

[0032] Here, the deep neural network can be a multi-layer feedforward neural network architecture, such as a BP neural network or a convolutional neural network architecture, and this application does not make any specific restrictions on it.

[0033] In the embodiments of this application, the model training samples consist of multiple sets of multi-source microstructure feature parameter samples carrying comprehensive performance entropy descriptor label information. It can be understood that the comprehensive performance entropy descriptor label information is predetermined based on the multi-source microstructure feature parameter samples and corresponds one-to-one with each sample. That is, each multi-source microstructure feature parameter sample in the training samples is pre-set to carry a corresponding comprehensive performance entropy descriptor label information.

[0034] In the embodiments of this application, step S1 involves determining the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test. Specifically, this can be achieved by obtaining the characteristic X-ray intensity distribution maps of carbon and aluminum elements in representative micro-regions of the carbon ceramic resistor under test through EDS surface scanning. After digital filtering for noise reduction and pixelation, the intensity values ​​of each pixel are globally normalized to obtain a standardized concentration matrix. Based on scientific thresholds, the pore distribution is determined, and finally, a set of spatially aligned digital matrices of carbon and aluminum concentrations and pores is output, resulting in carbon element concentration distribution maps, aluminum element concentration distribution maps, and binary distribution maps of pore structure, laying the data foundation for subsequent analysis.

[0035] Furthermore, core microstructure feature parameters can be extracted from the pixelated concentration data represented by the above distribution map and used as the input layer of the carbon ceramic resistance performance prediction model. These multi-source microstructure feature parameters can include carbon chain conductive network quality parameters, carbon phase distribution uniformity index parameters, pore structure feature composite parameters, and ceramic matrix structural integrity index parameters. Specifically, the carbon chain conductive network quality can be calculated by threshold segmentation and skeleton extraction of the carbon element concentration distribution map; the carbon phase distribution uniformity index can be calculated by analyzing the spatial fluctuations of carbon element concentration using the sliding window method; pore connectivity domain analysis can be performed on the binary distribution map of the pore structure to construct the pore structure feature composite parameters; and the ceramic matrix structural integrity index can be calculated using the aluminum element concentration distribution map, combined with the aluminum phase volume filling rate and regional stability measure. These four microstructure feature parameters constitute a concise yet comprehensive set of feature parameters.

[0036] In the embodiments of this application, before performing step S2, it is necessary to pre-train the carbon ceramic resistance performance prediction model to obtain a trained carbon ceramic resistance performance prediction model. Specifically, a set of standard carbon ceramic resistance samples are prepared using a uniform formula and sintering process. Using a field emission scanning electron microscope equipped with EDS, at least three statistically representative micro-regions are selected as the analysis field of view on the polished surface of each sample. Then, each carbon ceramic resistance sample is processed according to the method in step S1 to obtain multiple corresponding digital concentration matrices and multiple sets of multi-source microstructure characteristic parameter samples. It can be understood that the multiple sets of multi-source microstructure characteristic parameter samples may include carbon chain conductive network quality parameter samples, carbon phase distribution uniformity index parameter samples, pore structure characteristic composite parameter samples, and ceramic matrix structure integrity index parameter samples.

[0037] Simultaneously, the aforementioned digital concentration matrix can be mapped to a numerical calculation model, such as a finite element calculation model. Based on the component concentration corresponding to each unit in the model, gradient material properties (electrical conductivity, thermal conductivity, elastic modulus, coefficient of thermal expansion, etc.) can be dynamically assigned through the mixing rule. Then, transient voltage excitation can be applied to perform multi-physics coupling simulation. The current density distribution uniformity index parameter, heat distribution uniformity index parameter, and thermal stress safety index parameter can be quantitatively extracted from the full field results, providing direct input data for constructing a comprehensive performance entropy descriptor.

[0038] Furthermore, the aforementioned uniformity indices of current, heat, and stress distribution can be converted into corresponding defect degree parameters. Then, based on the physical coupling relationship between the electric, thermal, and mechanical fields, a chain correction is performed on the basic defect degree to quantify the transmission and amplification effects of defects. Subsequently, a weighted geometric average method is used to synthesize the corrected multiple defect degrees into a comprehensive defect degree. Finally, an exponential function maps the comprehensive defect degree to a comprehensive performance entropy descriptor with values ​​in (0,1). E The descriptor E A higher value indicates a more ordered energy dissipation and better tolerance performance in the material. This descriptor has a clear physical meaning, condensing complex multiphysics responses into a scalar target value that can be directly used for performance grading, comparison, and machine learning model training, thus achieving the normalization and quantitative rating of complex performance. Therefore, the comprehensive performance entropy descriptor label information corresponding to each group of multi-source microstructure feature parameter samples can be determined.

[0039] Furthermore, using the four microstructure parameters extracted in step 1 as the input layer, the calculated comprehensive performance entropy descriptor... EFor the output layer, a fully connected neural network with several hidden layers is constructed. The multi-source microstructure feature parameter samples and their corresponding comprehensive performance entropy descriptor labels obtained earlier are used as model training samples. Data augmentation techniques can be employed to expand the sample dataset, and training, validation, and test sets are created. The Adam optimizer is used, with mean squared error as the loss function for training, and dynamic adjustment of the learning rate and early stopping strategies are introduced to prevent overfitting. The training objective is to enable the model to accurately capture the complex nonlinear mapping relationship between microstructure parameters and macroscopic performance. Thus, model training is completed, and a trained carbon ceramic resistor performance prediction model is obtained.

[0040] In one specific embodiment of this application, the carbon ceramic resistor performance prediction model can adopt a multi-layer feedforward network architecture, specifically including an input layer, three hidden layers, and an output layer. The input layer contains four neurons, corresponding to the four key microstructural parameters of the carbon ceramic resistor mentioned above. The first hidden layer contains 64 neurons, employing a modified linear unit activation function (MTU), and a random deactivation layer is set after the output of this layer to prevent overfitting. The second hidden layer contains 32 neurons, also employing a MTU and a random deactivation layer. The third hidden layer contains 16 neurons, employing a MTU and a random deactivation layer. The fifth layer is the output layer, containing a single neuron, which directly outputs the predicted value of the carbon ceramic resistor's comprehensive performance entropy descriptor.

[0041] Furthermore, the model sample dataset was organized, and the model was trained until the loss function reached the convergence condition, achieving good training results. Specifically, the four microstructure parameters calculated based on the elemental concentration distribution map were used as input parameters of the model's neural network, and the comprehensive performance entropy descriptor constructed based on the performance parameters was used as the prediction parameters of the neural network. After obtaining the multi-source microstructure feature parameter samples of carbon ceramic resistors and the corresponding comprehensive performance entropy descriptor label information, the original samples were augmented.

[0042] Specifically, based on the statistical distribution characteristics of actual samples, a synthetic minority class oversampling technique (SMOTE) combined with Gaussian noise injection is used to generate new samples. Specifically, the four microstructural feature parameters of each real sample are linearly interpolated in its multidimensional feature space to generate synthetic samples located on the lines connecting adjacent samples in the feature space. Simultaneously, random perturbations conforming to a multidimensional normal distribution are introduced, with the perturbation amplitude controlled within 5% to 15% of the original feature standard deviation to simulate natural fluctuations under actual conditions. During the expansion process, pre-defined physical constraints are systematically applied to correct the synthetic samples. The correlation coefficient between the carbon chain conductive network quality and the carbon phase distribution uniformity index is forcibly adjusted to ensure it is not lower than the lower limit of 0.6 obtained from the statistical analysis of the measured samples. The composite parameters of the pore structure features are mapped to intervals to ensure their values ​​fall within the statistical intervals of the measured samples, ensuring physical consistency between microstructural features and macroscopic performance indicators. Under the premise of adhering to the laws of materials science, the small batch of original data is effectively expanded to the data scale required for training machine learning models. The resulting dataset possesses both statistical diversity and physical authenticity.

[0043] In this embodiment, the parameter distribution of the processed dataset is as follows: Figure 2 As shown, Figure 2 (a) is a schematic diagram of the sample dataset distribution of the carbon chain conductive network quality parameters provided in the embodiments of this application; (b) is a schematic diagram of the sample dataset distribution of the carbon phase distribution uniformity index parameter; (c) is a schematic diagram of the sample dataset distribution of the composite parameters of pore structure characteristics; (d) is a schematic diagram of the sample dataset distribution of the ceramic matrix structure integrity index parameter; and (e) is a schematic diagram of the sample dataset distribution of the comprehensive performance entropy descriptor. In each subplot, the horizontal axis represents the normalized value of the parameter, and the vertical axis represents the sample frequency within the corresponding interval. The histogram bars are colored using a color-gradient mapping, with the lowest frequency bar appearing dark purple, gradually transitioning to yellow as the frequency increases, thus visually demonstrating the concentration of samples in each numerical interval. The distribution of the four microstructure characteristic parameters and the comprehensive performance entropy descriptor can be generated through non-normal distribution mixing and nonlinear transformation. For example, Figure 2 The ceramic matrix structure integrity index shown in (d) exhibits an asymmetrical distribution pattern, with fewer samples in the high integrity region. This reflects the process characteristics in actual production, where the matrix is ​​difficult to achieve ideal integrity due to the limitations of raw material particle size distribution and sintering temperature tolerance. The data distribution is authentic and diverse.

[0044] The complete dataset was randomly divided into three sets: 80% training, 10% validation, and 10% test. During network training, the Adam algorithm was used as the optimizer, with the loss function calculated using mean squared error. The initial learning rate was set to 0.001, and an L2 regularization term with a weight decay coefficient of 0.0001 was introduced. A dynamic learning rate scheduling mechanism was configured during training: if the validation set loss did not decrease for 10 consecutive training epochs, the learning rate decayed by 0.5, with a minimum learning rate limit of 0.000001. An early stopping mechanism was also employed: if the validation set loss did not show significant improvement for 15 consecutive training epochs, training was automatically terminated, and the model parameters were restored to the state with the minimum validation loss, effectively avoiding overfitting. This neural network model, through the aforementioned hierarchical structure and nonlinear transformations, can accurately establish the complex mapping relationship between the microstructure parameters of carbon ceramic resistors and the comprehensive performance entropy descriptor, providing a reliable predictive tool for the performance optimization of carbon ceramic resistors.

[0045] Furthermore, in the embodiments of this application, the comprehensive performance entropy descriptor of the carbon ceramic resistor sample is predicted using the trained carbon ceramic resistor performance prediction model, and compared with the true value constructed from the performance parameters obtained by electrothermal coupling simulation, thereby verifying the accuracy of the prediction system.

[0046] The convergence characteristics of the model training process are monitored and presented through the loss function curve. For example... Figure 3 As shown, the curves depicting the changes in training and validation losses over training cycles indicate that the loss function decreases rapidly and steadily during the first 20 training cycles, suggesting that the model parameters are quickly learning the basic mapping relationships in the data. In the subsequent 20 to 40 training cycles, the rate of decrease in the loss function value slows significantly and tends to stabilize, entering the fine-tuning and convergence phase. When training has progressed to approximately 50 cycles, the early stopping mechanism is triggered because the validation set loss has not shown a significant decrease exceeding a preset minimum threshold for 15 consecutive cycles, automatically terminating the training. This process effectively prevents the model from overfitting on the training set, ensuring the model's generalization ability.

[0047] After training, the model enters the testing phase. Using the trained neural network model, the comprehensive performance entropy descriptor of independent test set samples is predicted. The predicted results are then compared with the performance parameters obtained from electrothermal coupling simulation to verify the accuracy of the entire prediction system. The coefficient of determination (R²) between the predicted and actual values ​​is calculated. 2 The determination coefficient R0 is used to measure the explanatory power and goodness of fit of the model. The test results show that the determination coefficient R0 is... 2The result of 0.9480 indicates that the carbon ceramic resistance performance prediction model provided in this application can explain 94.80% of the variance in the test set data, and the predicted values ​​are in high agreement with the actual values, verifying that the model has excellent prediction accuracy and generalization ability. The prediction effect of the model is intuitively displayed through visualization comparison, as shown in the scatter plot comparing the actual values ​​and predicted values ​​on the test set. Figure 4 As shown in the figure, the data points are closely distributed along the ideal reference line ( y = x The high coefficient of determination on both sides further confirms the aforementioned high coefficient of determination, intuitively demonstrating the consistency between the model's predictions and the actual values.

[0048] In the embodiments of this application, the model prediction residuals were also evaluated in depth using error analysis plots. Figure 5 The residual distribution histogram shown in (a) shows that the prediction residuals (predicted value - actual value) of the vast majority of samples are concentrated in the narrow interval [-0.02, 0.02]. Figure 5 The cumulative distribution curve of the absolute residuals shown in (b) indicates that the absolute residuals are less than 0.03 when the cumulative probability reaches 0.9. Both analyses together demonstrate that the carbon ceramic resistance performance prediction model provided in this application has low prediction error and high prediction accuracy for most samples.

[0049] Furthermore, in the embodiments of this application, in step S2, the multi-source microstructure feature parameters of the carbon ceramic resistor to be tested obtained in step S1 are input into the trained carbon ceramic resistor performance prediction model. The carbon ceramic resistor performance prediction model accurately captures the mapping relationship between the microstructure parameters of the carbon ceramic resistor material and its macroscopic performance, and finally outputs the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor to be tested. Then, the comprehensive performance entropy descriptor is used to predict the performance. E The predicted information determines the energy tolerance performance of the carbon ceramic resistor under test.

[0050] In the embodiments of this application, the comprehensive performance entropy descriptor E The calculation results can be directly used for performance grading evaluation. Based on experimental verification, it can typically be set as follows: when... E Excellent performance at ≥0.8, 0.6≤ E Performance is good when <0.8, and good when 0.4≤ E Performance is acceptable when <0.6. E Performance is unacceptable when the value is less than 0.4. Therefore, this provides a quantitative basis for the rapid determination of the performance of the carbon ceramic resistive material under test.

[0051] The method described in this application is not only applicable to predicting the resistivity of carbon ceramics, but can also provide a theoretical framework and implementation approach for functional ceramics and even the broader field of composite materials to condense multi-physics properties into interpretable descriptors and achieve rapid performance prediction.

[0052] The method in this application not only enables the evaluation of the energy tolerance performance of materials, but also transforms the performance improvement target into a quantitative improvement requirement for key microstructure parameters through reverse derivation, providing a clear and executable optimization direction for the preparation process. This forms a complete technical closed loop from microscopic characterization to performance prediction to process optimization, providing a new and interpretable technical approach for improving the transient energy tolerance performance of carbon ceramic resistors.

[0053] The multiphase carbon ceramic resistor performance prediction method based on entropy descriptors in this application adopts a strategy of "digital characterization of microstructure - construction of comprehensive performance entropy descriptor - neural network prediction". It uses digital characterization to extract key microstructure feature parameters of carbon ceramic resistors, and constructs a comprehensive performance entropy descriptor based on multiphysics simulation to characterize the degree of order of material energy dissipation of carbon ceramic resistor samples. Finally, it establishes a fast mapping model from microscopic features of carbon ceramic resistors to macroscopic performance by training a neural network. This method can achieve accurate and efficient prediction of the performance of carbon ceramic resistor materials, greatly improving the accuracy and efficiency of multiphase carbon ceramic resistor performance prediction.

[0054] Based on the above embodiments, as an optional embodiment, step S1, determining the multi-source microstructure characteristic parameters of the carbon ceramic resistor to be tested, includes: Obtain the X-ray intensity distribution map of carbon and aluminum element characteristics of the carbon ceramic resistor under test; Based on the X-ray intensity distribution map, normalization calculations and binarization processing were performed to obtain carbon element concentration distribution map, aluminum element concentration distribution map and pore structure binary distribution map. Based on the carbon element concentration distribution map, the quality parameters of the carbon chain conductive network are determined, and the carbon phase distribution uniformity index parameter is determined based on the carbon element concentration distribution map. Based on the binary distribution map of pore structure, the composite parameters of pore structure characteristics are determined. Based on the aluminum element concentration distribution map, the parameters of the ceramic matrix structural integrity index were determined; Multi-source microstructure characteristic parameters include carbon chain conductive network quality parameters, carbon phase distribution uniformity index parameters, pore structure characteristic composite parameters, and ceramic matrix structural integrity index parameters. The carbon chain conductive network quality parameters are used to quantify the physical connectivity of the conductive carbon network and the effectiveness of the conductive path. The carbon phase distribution uniformity index parameters are used to characterize the spatial distribution fluctuation of carbon elements. The pore structure characteristic composite parameters are used to comprehensively quantify the pore structure characteristics. The ceramic matrix structural integrity index parameters are used to characterize the structural integrity of the ceramic matrix and its relationship with the volume and spatial structural stability of its ceramic phase.

[0055] Specifically, in the embodiments of this application, the microstructure of the carbon ceramic resistor under test is characterized by EDS surface scanning. Image processing yields digital matrices of carbon, aluminum, and pore concentration distributions, namely, carbon concentration distribution maps, aluminum concentration distribution maps, and binary pore structure distribution maps. Specifically, a field emission scanning electron microscope equipped with an energy dispersive spectroscopy (EDS) instrument is used to select at least three statistically representative micro-regions on the polished surface of the carbon ceramic resistor under test as analytical fields of view. Under preset accelerating voltage and beam current conditions, EDS surface scanning is performed on the selected fields of view, simultaneously acquiring characteristic X-ray intensity distribution maps of carbon and aluminum elements that strictly correspond to the spatial positions of the selected fields of view. These are used to characterize the spatial distribution of the conductive carbon chain network and the ceramic matrix, respectively. After acquisition, the original X-ray intensity distribution maps are digitally filtered to suppress background noise, obtaining initial image data for subsequent quantitative analysis.

[0056] Furthermore, the filtered and noise-removed X-ray intensity distribution data is subjected to pixel-level digitization to generate a pixelated image with a resolution of 128×128 pixels. For each pixel location, global normalization calculation is performed on the characteristic X-ray intensity values ​​of carbon and aluminum elements according to formula (1) to obtain the carbon element concentration distribution map, i.e.: (1); in, This represents the normalized carbon concentration of the current pixel. This represents the characteristic X-ray intensity value of the original carbon element. This represents the global maximum value of the characteristic X-ray intensity of carbon elements in the entire image.

[0057] Similarly, the method for representing aluminum concentration is the same, resulting in an aluminum concentration distribution map. This normalization method ensures that all element concentration values ​​are within the standardized range of [0,1].

[0058] Furthermore, based on statistical analysis of experimental data from standard samples, a criterion for distinguishing between the material matrix and pore structure was established, and image binarization processing was performed accordingly. Specifically, an empirical threshold for total concentration was set.T K =0.12. This threshold was established considering the background noise level of the instrument measurements and the intrinsic properties of the material, ensuring the accuracy and reliability of the pore identification results. When the sum of the normalized carbon and aluminum concentrations of a detected pixel is less than this set threshold... T K If the value is 1, the region can be determined to be a pore structure, and the pixel value of the pixel is set to 1; otherwise, it is set to 0, thereby realizing the binarization of the pore structure distribution and obtaining a binary distribution map of the pore structure.

[0059] Furthermore, in the embodiments of this application, after obtaining the carbon element concentration distribution map of the carbon ceramic resistor to be tested, the carbon chain conductive network quality parameters can be determined by threshold segmentation and skeleton extraction of the carbon element concentration distribution map.

[0060] Based on the above embodiments, as an optional embodiment, the quality parameters of the carbon chain conductive network are determined based on the carbon element concentration distribution map, including: The carbon element concentration distribution map is binarized to obtain a carbon phase binary map, and the carbon phase skeleton is extracted from the carbon phase binary map to obtain a carbon phase skeleton map. Determine the connectivity density of the carbon phase framework diagram; A morphological closing operation is performed on the carbon phase framework diagram to obtain the processed carbon phase framework diagram, and the linearity of the conductive path is determined based on the processed carbon phase framework diagram. The quality parameters of the carbon chain conductive network are determined based on the connectivity density and the linearity of the conductive path.

[0061] Specifically, in the embodiments of this application, the carbon element concentration distribution map is binarized into carbon phase regions: an empirical threshold is set. T C =0.3, which is used to distinguish between "effectively conductive carbon phase" and "low-concentration carbon". Pixels with values ​​greater than this threshold are set to 1, and others are set to 0, thus constructing a binary image of the carbon phase. Furthermore, the Zhang-Suen algorithm can be used to process the binary image of the carbon phase. Extract the carbon phase skeleton by iteratively deleting boundary pixels until the region width becomes one pixel while maintaining the connectivity of the region. The final output is a carbon phase skeleton map. .

[0062] Here, the boundary pixel is specifically defined as at least one pixel with a value of 0 (belonging to low-concentration carbon in the background and not constituting an effective conductive carbon phase) among the 8 neighboring pixels of a pixel with a value of 1 (belonging to the effective conductive carbon phase in the foreground). This pixel can be classified as the boundary connecting effective and ineffective conductive carbon. The region width represents the width of the foreground pixel of the effective conductive carbon phase measured at any local location in the effective conductive carbon phase region along a direction perpendicular to the carbon phase skeleton.

[0063] Furthermore, in the embodiments of this application, a carbon phase framework diagram is determined. The connectivity density. Specifically, calculate the above carbon phase framework diagram. Total number of pixels with a median value of 1 , Let be the total number of pixels in the region, then the connectivity density of the carbon phase skeleton map is: It can be used to assess the physical connectivity of networks and avoid isolated carbon islands.

[0064] Furthermore, in the embodiments of this application, the carbon phase framework diagram is... S kel ( x , y Perform a morphological closing operation, slightly connect very close breakpoints and smooth out minor protrusions to obtain the processed carbon phase framework diagram. The effective conductive path length is calculated based on the total number of overlapping pixels before and after optimization. The ratio of this effective conductive path length to the actual conductive path length yields the conductive path linearity. L The calculation formula is as follows: (2); Finally, based on connectivity density and linearity of conductive path Synthesis parameters That is, the quality parameters of the carbon chain conductive network are obtained. .

[0065] The method in this application embodiment, by employing image binarization, skeleton extraction, and morphological analysis, comprehensively and quantitatively evaluates the physical connectivity, continuity, and effectiveness of current transmission paths of the conductive network in carbon ceramic resistor materials. This is beneficial for improving the physical interpretability of the prediction model driven by data and increasing the accuracy of carbon ceramic resistor performance prediction.

[0066] Furthermore, in the embodiments of this application, after obtaining the carbon element concentration distribution map of the carbon ceramic resistor to be tested, a sliding window statistical analysis technique can be used on the carbon element concentration distribution map to analyze the spatial fluctuation of carbon concentration and determine the carbon phase distribution uniformity index parameter.

[0067] Based on the above embodiments, as an optional embodiment, the carbon phase distribution uniformity index parameter is determined based on the carbon element concentration distribution map, including: A sliding window analysis was performed on the carbon element concentration distribution map to determine multiple analysis windows and the local uniformity information of the pixel region corresponding to each analysis window; The arithmetic mean of the local uniformity information of the pixel region corresponding to each analysis window is used to determine the carbon phase distribution uniformity index parameter.

[0068] Specifically, in the embodiments of this application, after obtaining the carbon element concentration distribution map of the carbon ceramic resistor under test, a sliding window analysis can be performed based on the 128×128 pixel normalized carbon concentration distribution matrix to calculate the carbon phase distribution spatial uniformity index. More specifically, the side length of the square analysis window can be predefined as 16 pixels, the sliding step size as 8 pixels, and a very small constant can be introduced. To ensure numerical stability, based on the above parameters, a total of [number] values ​​can be generated within the effective analysis region. M =225 partially overlapping analysis windows.

[0069] For the first one k Each analysis window is used to calculate the local uniformity information of the pixel region corresponding to that window. Specifically, this can be achieved by calculating the arithmetic mean of the carbon concentration values ​​of all pixels within that analysis window. and standard deviation Furthermore, the local uniformity unit value This refers to information on local homogeneity, which can be obtained by calculating the ratio of the average carbon concentration to the standard deviation within the analysis window. The corresponding calculation formula is shown below: (3); Ultimately, the spatial uniformity index of carbon phase distribution The arithmetic mean can be calculated based on the local uniformity information of the pixel region corresponding to each analysis window. This process can be represented as: (4); The method in this application employs a sliding window statistical analysis technique to divide the entire carbon concentration matrix into multiple overlapping local sub-regions. The ratio of the average carbon concentration to the standard deviation in each sub-region is calculated to measure the uniformity of the local region. Finally, the local uniformity values ​​of all sub-regions are arithmetically averaged to obtain a global spatial uniformity evaluation index, which is directly related to the uniformity of current distribution and the risk of local Joule heat concentration. This is beneficial to further improve the physical interpretability of the prediction model data-driven approach and enhance the accuracy of performance prediction.

[0070] Furthermore, in the embodiments of this application, after obtaining the binary distribution map of the pore structure, the average equivalent diameter and areal density of all pores can be calculated by performing connected component analysis on the binary distribution map of the pores, and the two can be multiplied to comprehensively reflect the size and distribution density characteristics of the material pores, thereby determining the composite parameters of the pore structure characteristics.

[0071] Based on the above embodiments, as an optional embodiment, the composite parameters of pore structure features are determined based on the binary distribution map of the pore structure, including: Connectivity analysis and measurement are performed on the binary distribution map of pore structure to determine the number of pore regions and the pixel area occupied by each pore region. The average size and surface density of pores are determined based on the number of pore regions, the pixel area occupied by each pore region, and the total number of pixels in the distribution map. Based on the average pore size and pore areal density, composite parameters of pore structure characteristics are determined.

[0072] Specifically, in the embodiments of this application, after obtaining the binary distribution map of the pores of the carbon ceramic resistor to be tested, connected component analysis and measurement can be performed on the binary distribution map characterizing the pore structure of the material. Specifically, an eight-connected region labeling algorithm can be executed to identify and label each independent pore region, and the total number of labeled connected regions is counted. This involves obtaining the number of stomata; and measuring each stomata region individually. j The pixel area occupied .

[0073] Furthermore, the pixel area occupied by each pore region is converted into an equivalent geometric dimension, and its equivalent circle diameter is calculated. Calculate the arithmetic mean of the equivalent diameters of all pore regions to obtain the average pore size. Simultaneously, the number of pores per unit area is calculated, thus obtaining the porosity. Ultimately, the composite parameters of the pore structure characteristics... It can be formed by the product of the average pore size and the pore areal density, that is: (5); The method in this application constructs a composite parameter for pore structure characteristics by multiplying and coupling the average equivalent diameter of pores with the areal density. This solves the technical problem that traditional separate parameters cannot effectively characterize the synergistic effect of pore size and its spatial distribution on the integrity of the microstructure. Furthermore, this solution is based on the analysis of the failure mechanism of carbon ceramic resistors under electro-thermal-mechanical multi-field coupling. The final performance degradation of the material is often dominated by pores exceeding the characteristic size range, or by the spatial distribution of pores exhibiting high areal density aggregation in local areas. The synergistic effect of such defects is difficult to quantify using a single morphological parameter. The multiplicative form used mathematically directly constructs a correlation function between size and distribution factors, making the composite parameter value highly sensitive to the aforementioned high-risk microstructural characteristics. This allows for a more accurate assessment of the potential failure risk of carbon ceramic resistor materials.

[0074] Furthermore, in the embodiments of this application, after obtaining the aluminum element concentration distribution map, the ceramic matrix structure integrity index parameter can be determined by calculating the ceramic phase volume filling rate and measuring the regional stability of the aluminum element concentration distribution map.

[0075] The method in this application extracts four key microstructure feature parameters from the carbon ceramic resistivity element concentration distribution matrix. These parameters are physically related and can dominate and explain macroscopic performance changes. They are then used as input features for subsequent machine learning models. This method combines characterization ability and dimensionality reduction effect, which can further improve the model's prediction accuracy and efficiency.

[0076] Based on the above embodiments, as an optional embodiment, the structural integrity index parameter of the ceramic matrix is ​​determined based on the aluminum element concentration distribution map, including: The aluminum element concentration distribution map is binarized to obtain a binary map of the aluminum phase. Based on the binary map of the aluminum phase, the volume fraction of the ceramic phase region is determined; Perform Euclidean distance transformation on the binary image of the aluminum phase to determine the Euclidean distance transformation value corresponding to each pixel in the ceramic phase region and the average value of the Euclidean distance transformation values ​​corresponding to all pixels. The parameters of the ceramic matrix structural integrity index are determined based on the average value of the volume fraction and the Euclidean distance transformation value.

[0077] It should be noted that in the carbon ceramic resistive material system, aluminum is a characteristic constituent element of the ceramic phase (Al2O3). The characteristic X-ray intensity distribution map of aluminum obtained by EDS surface scanning can directly reflect the spatial density of aluminum atoms, and thus reflect the spatial distribution and enrichment degree of the ceramic phase in the material.

[0078] Specifically, in the embodiments of this application, after obtaining the aluminum element concentration distribution map of the carbon ceramic resistor to be tested, an empirical threshold can be set. T Al =0.3, perform binarization processing on the aluminum element concentration distribution map, that is, set the pixel value of the aluminum element concentration value is greater than the threshold to 1, and the other is set to 0, so as to obtain the aluminum phase binary map. This is used to characterize the ceramic phase region and to count the total number of pixels with a pixel value of 1 in the binarized region. Calculate the volume fill rate This is used to characterize the volume fraction of the ceramic phase.

[0079] Furthermore, the binary diagram of the aluminum phase... Perform a Euclidean distance transformation. Specifically, for Calculate the Euclidean distance transformation graph For each pixel within the ceramic phase region, the Euclidean distance transformation value is... The value of is equal to the Euclidean distance from that pixel to the nearest region boundary, and thus the average value of the Euclidean distance transformation corresponding to all ceramic phase pixels can be calculated. The calculation formula is shown in Equation (6). The larger the value, the more "thick" the ceramic phase region is as a whole, the farther the average distance between the point and the potential crack boundary, and the more stable the structure.

[0080] (6); In the embodiments of this application, the structural integrity index of the ceramic matrix is ​​determined according to formula (7) based on the average value of the volume fraction and the Euclidean distance transformation value. This indicates that the structural integrity of the ceramic matrix is ​​positively correlated with both its content and the stability of its own structure.

[0081] (7); The method in this application calculates the ceramic phase volume filling rate from the aluminum element concentration distribution map and obtains the "thickness" and stability of the ceramic phase region through distance transformation. It comprehensively evaluates the load-bearing capacity as a mechanical skeleton and constructs the ceramic matrix structure integrity index parameter. This is beneficial to further improve the physical interpretability of the prediction model data-driven approach and improve the accuracy of performance prediction.

[0082] Based on the above embodiments, as an optional embodiment, the step of determining the comprehensive performance entropy descriptor specifically includes: The physical parameters of the geometric model were calibrated using the carbon element concentration distribution map, aluminum element concentration distribution map and the binary distribution map of the pore structure of the carbon ceramic resistor material, and the conductivity model of the carbon ceramic resistor material was determined. Numerical simulation calculations were performed on the conductivity model to determine the current density distribution uniformity index parameter, heat distribution uniformity index parameter, and thermal stress safety index parameter of the carbon ceramic resistor material. The performance defect degree parameters of the current density distribution uniformity index parameter, the heat distribution uniformity index parameter, and the thermal stress safety index parameter are converted into performance defect degree parameters respectively to obtain the current density distribution defect degree parameters corresponding to the current density distribution uniformity index parameter, the heat distribution defect degree parameters corresponding to the heat distribution uniformity index parameter, and the stress concentration defect degree parameters corresponding to the thermal stress safety index parameter. Based on the current density distribution defect parameter, thermal distribution defect parameter, and stress concentration defect parameter, the comprehensive performance entropy descriptor is determined.

[0083] Specifically, in the embodiments of this application, based on the content of the above embodiments, carbon element concentration distribution map, aluminum element concentration distribution map and pore structure binary distribution map of carbon ceramic resistor material can be obtained. Numerical simulation calculations can be performed using these element concentration distribution maps to construct a finite element model and assign gradient physical properties. Then, electrothermal coupling simulation can be performed on the finite element model to extract the performance parameters of carbon ceramic resistor material.

[0084] More specifically, based on the aforementioned carbon and aluminum concentration distribution maps, the physical parameters of the geometric model are calibrated, and each pixel unit is assigned a corresponding physical attribute value. Taking electrical conductivity (σ) as an example, the assignment process is as follows: for each pixel unit, a predetermined electrical conductivity grading interval is set for the carbon concentration in the original digital matrix, the concentration value is converted into a specific electrical conductivity value, and assigned to the pixel unit. This method can map the spatial distribution information of the components contained in the element concentration matrix into a physical parameter field with continuous gradient changes in the finite element model. If the sum of the normalized concentrations of carbon and aluminum in the pixel unit is less than the threshold determined in step 1, the pixel unit is set as a porous phase material; otherwise, the pixel unit is set as a carbon-ceramic composite phase material, and its electrical conductivity is calculated using the linear interpolation model shown in the following formula (8). This represents the normalized carbon concentration of the current pixel. and These are the material electrical conductivities set when the current pixel is determined to be either a carbon chain or ceramic. The thermal conductivity is calculated using the same linear model principle.

[0085] (8); In the embodiments of this application, a transient voltage excitation is applied to the finite element model, and the target optimized performance parameters are obtained through simulation calculation. Specifically, these parameters include the current density distribution uniformity index parameter, the heat distribution uniformity index parameter, and the thermal stress safety index parameter of the carbon ceramic resistive material.

[0086] The current density distribution uniformity index parameter is used to quantify the uniformity of current distribution across the material cross-section. Non-uniform current distribution leads to excessively high local current densities, causing Joule heat concentration, which is a major cause of localized overheating, ablation, and even failure of the material. By calculating the relative fluctuation of the current density distribution, the effectiveness of the material's conductive path and its current equalization capability can be assessed.

[0087] In the embodiments of this application, such as Figure 6 As shown, current density distribution data can be extracted by applying transient voltage excitation to the finite element model, and the scalar value of current density for each pixel unit can be derived. J (i,j) are then used to construct the current density distribution matrix. Further, the arithmetic mean of all elements in the entire current density distribution matrix is ​​first calculated. and standard deviation Then, the uniformity index of current density distribution is calculated according to the following formula (9). The introduction of "1" in the denominator of the formula avoids issues related to standard deviation. When the value is extremely small, the exponent tends to infinity, ensuring the stability and boundedness of the calculation results.

[0088] (9); In the embodiments of this application, the heat distribution uniformity index parameter is used to characterize the uniformity of the temperature field of the material during electrothermal processes. Due to the significant difference in thermal conductivity between the carbon phase and the ceramic phase, heat tends to accumulate in areas of lower thermal conductivity, forming localized hot spots. Localized overheating accelerates material oxidation, reduces mechanical strength, and may induce thermal stress cracks. Therefore, the uniformity of temperature distribution is a core indicator for evaluating the thermal stability and long-term reliability of materials.

[0089] Extract the temperature value of each pixel unit under steady-state conditions (i.e., the temperature field no longer changes with time) from the electrothermal coupling simulation results. T ( i , j This forms a steady-state temperature distribution matrix. Calculate the arithmetic mean and standard deviation of all elements in this matrix. Standard deviation Compared with reference temperature Substituting the ratio into the following formula (10), the thermal distribution uniformity index parameter can be obtained. T u .

[0090] (10); In the embodiments of this application, the thermal stress safety index is used to assess the degree of thermal stress concentration caused by the mismatch of the thermal expansion coefficients of the material components and temperature gradients. During pulsed energy loading, rapid temperature changes generate significant thermal stress. Excessive thermal stress, especially stress concentration at defects such as pores and microcracks, can lead to the formation of new microcracks within the material or the propagation of existing cracks, ultimately causing structural cracking or delamination failure.

[0091] Temperature field distribution obtained from simulation T Given (i,j) and the pre-assigned elastic modulus, Poisson's ratio, and coefficient of thermal expansion for each pixel unit, the thermal stress tensor of each pixel unit caused by the temperature field is calculated through thermo-mechanical coupling analysis; this stress tensor is then converted into von Mises equivalent stress. σ VM (i,j) is used to obtain the equivalent stress distribution matrix, and the maximum value is found in it. Calculate the average value of all units. The ratio of the two directly reflects the degree of stress concentration, and its reciprocal is the thermal stress safety index parameter. ,Right now: (11); When the maximum stress equals the mean stress S a =1 indicates no stress concentration.

[0092] Furthermore, in the embodiments of this application, a comprehensive performance entropy descriptor is constructed based on the three performance parameters obtained above. This descriptor is used to reflect the energy tolerance performance of the carbon ceramic resistor and serves as a prediction parameter for the neural network. This constructs a "microstructure parameter-comprehensive performance entropy" prediction model, namely, a carbon ceramic resistor performance prediction model.

[0093] Specifically, based on the aforementioned obtained current density distribution uniformity index parameters Heat distribution uniformity index parameter and thermal stress safety index parameters To construct a single scalar index for comprehensively evaluating the energy withstand performance of carbon ceramic resistors, namely the comprehensive performance entropy descriptor. E This is then used as the output of subsequent neural network models. The specific construction method is as follows: Furthermore, the current density distribution uniformity index parameter, heat distribution uniformity index parameter, and thermal stress safety index parameter are respectively converted into performance defect degree parameters. That is, the three indices characterizing the performance are converted into corresponding performance defect degree parameters. The conversion relationship is as follows: (12); (13); (14); in, , , These are the current density distribution defect parameter, the heat distribution defect parameter, and the stress concentration defect parameter, respectively. All three are dimensionless parameters with values ​​ranging from [0,1].

[0094] Based on the causal transmission relationship between defects in multiphysics, the basic defect degree is amplified and corrected by chain coupling, and the thermal distribution defect degree parameter after coupling correction is calculated. With stress concentration defect degree parameter This process can be represented as: (15); (16); In the formula, This is the coupling amplification factor of the current distribution defect to the thermal distribution defect, which can be taken as 0.35; This is the coupling amplification factor of thermal distribution defects on stress concentration defects, which can be taken as 0.20; This is the direct coupling amplification factor of the current distribution defect to the stress concentration defect, which can be 0.10.

[0095] Furthermore, the weighted geometric mean method is used to calculate the comprehensive defect degree parameter. ,Right now: (17); in, , , The weighting index of each defect parameter in the overall evaluation satisfies... > Typical values ​​can be taken. =3.0, =2.0, =1.0. Finally, the comprehensive defect parameter is calculated using an exponential decay function. Mapped to a comprehensive performance entropy descriptor E ,Right now: (18); In the formula, This is the performance degradation factor, and a typical value of 2.5 can be taken. E is the final comprehensive performance entropy descriptor, a dimensionless scalar with a value range of (0,1], and a larger value indicates better energy tolerance performance.

[0096] The method in this application's embodiment maps the digital concentration matrix of the carbon ceramic resistor material to a finite element calculation model. Based on the component concentration corresponding to each pixel unit, gradient material properties (electrical conductivity, thermal conductivity, elastic modulus, coefficient of thermal expansion, etc.) are dynamically assigned according to the mixing rule. Multiphysics coupling simulation is performed by applying transient voltage excitation. The current density distribution uniformity index, heat distribution uniformity index, and thermal stress safety index are quantitatively extracted from the full-field results to construct a multiphysics uniformity entropy descriptor, which is used as the prediction target. This condenses the complex multiphysics simulation results into a single-valued scalar output with clear physical meaning, which simplifies the structure of the subsequently constructed neural network model, makes model training more efficient and stable, and helps to significantly improve the accuracy and efficiency of carbon ceramic resistor performance prediction.

[0097] The following describes the multiphase carbon ceramic resistance performance prediction system based on entropy descriptors provided in this application. The multiphase carbon ceramic resistance performance prediction system based on entropy descriptors described below can be referred to in correspondence with the multiphase carbon ceramic resistance performance prediction method based on entropy descriptors described above.

[0098] Figure 7 This is a schematic diagram of the structure of the multiphase carbon ceramic resistivity performance prediction system based on entropy descriptors provided in the embodiments of this application, as shown below. Figure 7 As shown, it includes: Processing module 10 is used to determine the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test; Prediction module 20 is used to input the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test into the carbon ceramic resistor performance prediction model, and obtain the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor under test output by the carbon ceramic resistor performance prediction model, so as to determine the energy tolerance performance of the carbon ceramic resistor under test. The carbon ceramic resistor performance prediction model is obtained by training based on the multi-source microstructure feature parameter samples of carbon ceramic resistor samples and the label information of their corresponding comprehensive performance entropy descriptors. The comprehensive performance entropy descriptor is determined by the performance parameters extracted from the multiphysics transient coupling simulation of the numerical calculation model constructed using the carbon-aluminum element concentration distribution matrix of the carbon ceramic resistor material. It is used to characterize the degree of energy dissipation order of the carbon ceramic resistor material.

[0099] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.

[0100] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0101] The entropy descriptor-based multiphase carbon ceramic resistor performance prediction system of this application adopts a strategy of "digital characterization of microstructure - construction of comprehensive performance entropy descriptor - neural network prediction". It uses digital characterization to extract key microstructure feature parameters of carbon ceramic resistors, and constructs a comprehensive performance entropy descriptor based on multiphysics simulation to characterize the degree of order of material energy dissipation of carbon ceramic resistor samples. Finally, it establishes a fast mapping model from microscopic features of carbon ceramic resistors to macroscopic performance by training a neural network. This system can achieve accurate and efficient prediction of the performance of carbon ceramic resistor materials, greatly improving the accuracy and efficiency of multiphase carbon ceramic resistor performance prediction.

[0102] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 8 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other via the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.

[0103] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0104] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0105] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0106] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0107] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0108] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0109] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0110] It should be understood that expressions such as “comprising” and “may include” used in this application indicate the existence of the disclosed functions, operations, or constituent elements, and do not limit one or more additional functions, operations, and constituent elements. In this application, terms such as “comprising” and / or “having” are to be interpreted as indicating a particular characteristic, number, operation, constituent element, component, or combination thereof, but not to exclude the existence or possibility of adding one or more other characteristics, numbers, operations, constituent elements, components, or combinations thereof.

[0111] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting the resistivity of multiphase carbon ceramics based on entropy descriptors, characterized in that, include: Determine the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test; The multi-source microstructure characteristic parameters of the carbon ceramic resistor under test are input into the carbon ceramic resistor performance prediction model to obtain the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor under test output by the carbon ceramic resistor performance prediction model, so as to determine the energy tolerance performance of the carbon ceramic resistor under test. The carbon ceramic resistor performance prediction model is trained based on the label information of the multi-source microstructure feature parameter samples of the carbon ceramic resistor sample and their corresponding comprehensive performance entropy descriptor. The comprehensive performance entropy descriptor is determined by the performance parameters extracted from the multiphysics transient coupling simulation of the numerical calculation model constructed using the carbon-aluminum element concentration distribution matrix of the carbon ceramic resistor material. It is used to characterize the degree of energy dissipation order of the carbon ceramic resistor material. Specifically, the step of determining the comprehensive performance entropy descriptor includes: The physical parameters of the geometric model were calibrated using the carbon element concentration distribution map, aluminum element concentration distribution map and the binary distribution map of the pore structure of the carbon ceramic resistor material, and the conductivity model of the carbon ceramic resistor material was determined. Numerical simulation calculations were performed on the conductivity model to determine the current density distribution uniformity index parameter, heat distribution uniformity index parameter, and thermal stress safety index parameter of the carbon ceramic resistor material. The current density distribution uniformity index parameter, the heat distribution uniformity index parameter, and the thermal stress safety index parameter are respectively converted into performance defect degree parameters to obtain the current density distribution defect degree parameter corresponding to the current density distribution uniformity index parameter, the heat distribution defect degree parameter corresponding to the heat distribution uniformity index parameter, and the stress concentration defect degree parameter corresponding to the thermal stress safety index parameter. The comprehensive performance entropy descriptor is determined based on the current density distribution defect degree parameter, the heat distribution defect degree parameter, and the stress concentration defect degree parameter.

2. The method for predicting the resistivity of multiphase carbon ceramics according to claim 1, characterized in that, The determination of the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test includes: Obtain the X-ray intensity distribution map of the carbon and aluminum element characteristics of the carbon ceramic resistor under test; Based on the X-ray intensity distribution map, normalization calculations and binarization processing are performed to obtain carbon element concentration distribution map, aluminum element concentration distribution map and pore structure binary distribution map. Based on the carbon element concentration distribution map, the carbon chain conductive network quality parameters are determined, and based on the carbon element concentration distribution map, the carbon phase distribution uniformity index parameters are determined. Based on the binary distribution map of the pore structure, the composite parameters of the pore structure characteristics are determined; Based on the aluminum element concentration distribution map, the structural integrity index parameters of the ceramic matrix are determined; The multi-source microstructure characteristic parameters include the carbon chain conductive network quality parameter, the carbon phase distribution uniformity index parameter, the pore structure characteristic composite parameter, and the ceramic matrix structural integrity index parameter. The carbon chain conductive network quality parameter is used to quantify the physical connectivity of the conductive carbon network and the effectiveness of the conductive path. The carbon phase distribution uniformity index parameter is used to characterize the spatial distribution fluctuation of carbon elements. The pore structure characteristic composite parameter is used to comprehensively quantify the pore structure characteristics. The ceramic matrix structural integrity index parameter is used to characterize the structural integrity of the ceramic matrix and its relationship with the volume and spatial structural stability of its ceramic phase.

3. The method for predicting the resistivity of multiphase carbon ceramics according to claim 2, characterized in that, The determination of carbon chain conductive network quality parameters based on the carbon element concentration distribution map includes: The carbon element concentration distribution map is binarized to obtain a carbon phase binary map, and the carbon phase skeleton of the carbon phase binary map is extracted to obtain a carbon phase skeleton map. Determine the connectivity density of the carbon phase framework diagram; A morphological closing operation is performed on the carbon phase skeleton diagram to obtain the processed carbon phase skeleton diagram, and the linearity of the conductive path is determined based on the processed carbon phase skeleton diagram. The quality parameters of the carbon chain conductive network are determined based on the connectivity density and the linearity of the conductive path.

4. The method for predicting the resistivity of multiphase carbon ceramics according to claim 2, characterized in that, The determination of the carbon phase distribution uniformity index parameter based on the carbon element concentration distribution map includes: A sliding window analysis is performed on the carbon element concentration distribution map to determine multiple analysis windows and the local uniformity information of the pixel region corresponding to each analysis window; The carbon phase distribution uniformity index parameter is determined by performing an arithmetic average calculation based on the local uniformity information of the pixel region corresponding to each analysis window.

5. The method for predicting the resistivity of multiphase carbon ceramics according to claim 2, characterized in that, The determination of composite parameters of pore structure features based on the binary distribution map of the pore structure includes: Connectivity analysis and measurement are performed on the binary distribution map of the pore structure to determine the number of pore regions and the pixel area occupied by each pore region. Based on the number of pore regions, the pixel area occupied by each pore region, and the total number of pixels in the distribution map, the average size of the pores and the pore surface density are determined. Based on the average pore size and the pore areal density, the composite parameters of the pore structure characteristics are determined.

6. The method for predicting the resistivity of multiphase carbon ceramics according to claim 2, characterized in that, The determination of the ceramic matrix structural integrity index parameters based on the aluminum element concentration distribution map includes: The aluminum element concentration distribution map is binarized to obtain a binary map of the aluminum phase; Based on the aforementioned aluminum phase binary map, the volume fraction of the ceramic phase region is determined. Perform Euclidean distance transformation on the aluminum phase binary image to determine the Euclidean distance transformation value corresponding to each pixel in the ceramic phase region and the average value of the Euclidean distance transformation values ​​corresponding to all pixels; The structural integrity index parameter of the ceramic matrix is ​​determined based on the average value of the volume fraction and the Euclidean distance transformation value.

7. A system for predicting the resistivity of multiphase carbon ceramics based on entropy descriptors, characterized in that, include: The processing module is used to determine the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test; The prediction module is used to input the multi-source microstructure characteristic parameters of the carbon ceramic resistor under test into the carbon ceramic resistor performance prediction model, and obtain the comprehensive performance entropy descriptor prediction information of the carbon ceramic resistor under test output by the carbon ceramic resistor performance prediction model, so as to determine the energy tolerance performance of the carbon ceramic resistor under test. The carbon ceramic resistor performance prediction model is trained based on the label information of the multi-source microstructure feature parameter samples of the carbon ceramic resistor sample and their corresponding comprehensive performance entropy descriptor. The comprehensive performance entropy descriptor is determined by the performance parameters extracted from the multiphysics transient coupling simulation of the numerical calculation model constructed using the carbon-aluminum element concentration distribution matrix of the carbon ceramic resistor material. It is used to characterize the degree of energy dissipation order of the carbon ceramic resistor material. Specifically, the step of determining the comprehensive performance entropy descriptor includes: The physical parameters of the geometric model were calibrated using the carbon element concentration distribution map, aluminum element concentration distribution map and the binary distribution map of the pore structure of the carbon ceramic resistor material, and the conductivity model of the carbon ceramic resistor material was determined. Numerical simulation calculations were performed on the conductivity model to determine the current density distribution uniformity index parameter, heat distribution uniformity index parameter, and thermal stress safety index parameter of the carbon ceramic resistor material. The current density distribution uniformity index parameter, the heat distribution uniformity index parameter, and the thermal stress safety index parameter are respectively converted into performance defect degree parameters to obtain the current density distribution defect degree parameter corresponding to the current density distribution uniformity index parameter, the heat distribution defect degree parameter corresponding to the heat distribution uniformity index parameter, and the stress concentration defect degree parameter corresponding to the thermal stress safety index parameter. The comprehensive performance entropy descriptor is determined based on the current density distribution defect degree parameter, the heat distribution defect degree parameter, and the stress concentration defect degree parameter.

8. An electronic device, characterized in that, Includes memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-6.

9. A computer-readable storage medium comprising instructions, characterized in that: When the instructions are executed on an electronic device, the electronic device causes the electronic device to perform the method as described in any one of claims 1-6.

Images